spectral characterisation of infrared optical materials and filters

The University of ReadingDepartment of Cybernetics

Spectral Characterisation of InfraredOptical Materials and Filters

A thesis submitted for the degree ofDoctor of Philosophy

by

Gary J. HawkinsCPhys, MInstP, MOSA, MEOS

December 1998

To Angela and Amy,for their support and understanding.

“... We have to remember that what we observe is not nature,but nature exposed to our method of questioning.”

Werner Karl HeisenbergPhysics and Philosophy (1955)

Spectral Characterisation of Infrared Optical Materials and FiltersDr. Gary J. Hawkins PhD Thesis (#R7935) - The University of Reading, UK December 1998________________________________________________________________________________________

ii

ABSTRACT

The optical and semiconductor properties of the materials used in the design and manufacture ofinfrared interference filters play a vital role in defining the spectral performance achievable from a multilayerfilter design. This thesis examines the theoretical basis of the behaviour of absorptive and dispersive mechanismsin optical materials and derives methods of determining values for their complex optical constants.

By applying these properties to the multilayer filter design, a predictive model for the filter performancehas been constructed to determine if a chosen design can achieve the specified spectral performancerequirements, prior to manufacture. Examples are given demonstrating the convergence of prediction withpractice.

This predictive model approach has then been expanded to develop a method for determining thespectral design requirements for the individual filters and coatings integrated into an atmospheric radiometerinstrument. This process uses an integrated systems approach, by which the characteristics of all the contributingelements provide a predicted spectral model of the instrument. By then applying reverse synthesis to this model,the particular spectral requirements of the individual filters can be determined. Examples are given of particularspectral design requirements for filters derived using this method.

The effects of the space environment on the spectral and physical properties of infrared filters andmaterials is also presented. This includes a description of the radiation environments to which filters aresubjected in low Earth orbit. A quantitative analysis of the effects of this environment on the spectralcharacteristics of exposed filters and materials is made, together with an assessment of the physical degradationmechanisms that affect filter performance.

ACKNOWLEDGEMENTS

The work described in this thesis was carried out while I was employed as a Research Fellow in theUniversity of Reading Infrared Multilayer Laboratory. It is the result of combining my part-time researchactivities together with the design and manufacturing requirements of infrared filters and coatings for use invarious spaceflight radiometer projects.

I would especially like to thank Roger Hunneman for his constant encouragement and support in thedevelopment of this research, particularly for the many stimulating and instructive discussions we had on thepractice of thin film design and manufacture. I am also extremely grateful to Dr. John Seeley for his guidanceand inspiration during the formative stages of this research, and to my supervisor Dr. John Bowen.

I also wish to thank all my colleagues, both past and present, from the Infrared Multilayer Laboratory inthe Department of Cybernetics for their assistance during the progression of this research, and to colleagues atOxford University and Rutherford Appleton Laboratory for the development of the project work for which manyof the filters were destined. Finally, I would like to acknowledge the partial funding of my post during thedevelopment of this research by the UK Natural Environment Research Council.

G.J. HawkinsDecember 1998


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CONTENTS Page

Abstract iiAcknowledgements iiTable of Contents iiiPreface vIntroduction v

1. INFRARED MATERIALS ABSORPTION THEORY1.1 General description of absorption 11.2 Electronic absorption 31.3 Lattice absorption 51.4 Phonons 5

1.4.1 Phonon absorption theory 61.4.2 Phonon dispersion theory 6

1.5 Single phonon absorption 71.6 Multi-phonon absorption 81.7 Dielectric dispersion 101.8 Temperature-dependent effects 12

1.8.1 Thermal vibrations 151.8.2 Thermal expansion coefficients 16

1.9 Infrared material properties 171.9.1 Germanium 18

1.9.1.1 Germanium absorption 191.9.1.2 Germanium dispersion 201.9.1.3 Germanium resistivity 21

1.9.2 Silicon 221.9.2.1 Silicon absorption 231.9.2.2 Silicon dispersion 23

1.9.3 Zinc Selenide 251.9.3.1 Zinc Selenide absorption 261.9.3.2 Zinc Selenide dispersion 27

1.9.4 Zinc Sulphide 281.9.4.1 Zinc Sulphide absorption 291.9.4.2 Zinc Sulphide dispersion 30

1.9.5 Cadmium Telluride 301.9.5.1 Cadmium Telluride dispersion 31

1.10 Conclusion 32

2 INFRARED SUBSTRATE CHARACTERISATION2.0 Introduction 332.1 Absorption (α) and extinction coefficient (k) theory 332.2 Loss-free incoherent internal reflection 342.3 Incoherent multiple internal reflection including absorption 392.4 Predictive substrate thickness calculations 46

2.4.1 Thickness model validation 522.5 Reduced substrate-temperature effects 53

2.5.1 Temperature model verification 582.6 Angle of incidence effects 59

2.6.1 Total internal reflection 672.7 Coherence of multiple internal reflections 682.8 Conclusion 70


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3 INFRARED THIN FILM CHARACTERISATION AND DEPOSITION TECHNIQUE3.1 Lead telluride (PbTe) dispersion 713.2 Lead telluride (PbTe) absorption 73

3.2.1 Modified lead telluride photo-absorption spectra 753.3 Zinc selenide (ZnSe) dispersion 763.4 Thin film deposition technique 78

3.4.1 Fractional thickness reflection monitoring 803.5 Nucleation, growth and structure of infrared thin films 843.6 Conclusion 88

4 MULTILAYER CALCULATION THEORY AND APPLICATIONS4.1 Loss-free multilayer matrix calculation 904.2 Multilayer calculations including layer absorption 944.3 Predictive design modelling of a ultra-wide (5-30µm) passband filter 97

4.3.1 Infrared materials selection 974.3.2 5-30µm passband filter design method 984.3.3 Performance prediction and comparison with measurement 98

4.4 Systems design of far-infrared filters 1004.5 Conclusion 102

5 AN INTEGRATED SYSTEMS PERFORMANCE APPROACHTO INFRARED SPECTRAL INSTRUMENT DESIGN

5.0 Introduction 1035.1 Advantages of an integrated spectral systems approach 1045.2 HIRDLS Optical system layout 1045.3 Filter design requirements 106

5.3.1 Bandpass filter design 1085.3.2 Blocking filter design 1115.3.3 Antireflection coatings 112

5.3.3.1 Germanium lens thickness distribution 1135.4 Instrument performance requirements 114

5.4.1 Margin Ratio 1145.4.2 Ghost-image suppression 1195.4.3 Corrective spectral passband placement requirements 1205.4.4 Thermal background suppression 121

5.5 Instrument performance verification 1215.5.1 Instrument channel passband profile 1225.5.2 Instrument channel blocking performance 123

5.6 Conclusion 126

6 EFFECTS OF THE SPACE ENVIRONMEN ON INFRARED FILTERS AND MATERIALS6.1 LDEF Experiment background 1286.2 Thermal cycling effects 129

6.2.1 Solar flux 1296.3 Ionizing radiation 1316.4 Atomic Oxygen 1326.5 Filter experiment construction 1346.6 Pre-launch / post-recovery filter analysis 138

6.6.1 Uncoated crystal materials 1386.6.2 Soft substrate / coating materials 1396.6.3 Hard substrate / coating materials 1406.6.4 Results summary 141

6.7 LDEF Orbital meteoroid and debris impacts 1436.7.1 Micrometeorite impact characteristics 144

6.8 Experiment conclusions 146


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7. SUMMARY AND CONCLUSIONS 147

8. FUTURE RESEARCH 147

9. REFERENCES 148

10. APPENDICES 152Appendix A Temperature-dependent complex refractive indices Appendix B Thickness-dependent polynomial coefficientsAppendix C Absorption program algorithmAppendix D Multilayer matrix calculation with absorptionAppendix E Publications listAppendix F Refractive Index Data Sources

PREFACE

In the development of the research for this thesis I am indebted to many co-workers and colleagues whohave helped in the formation of the concepts that have been described. In particular I would like to acknowledgethe discussions with John Barnett and John Whitney from the University of Oxford which resulted in theintegrated system approach to the spectral design of the HIRDLS instrument. Where other work is directlyattributable to other workers, principally in the area of refractive index data, these sources have been listed inAppendix F, in addition to being cited by the references.

My main contributions to this subject and the responsibilities I have had for the work described in thisthesis include; the development of methods for the determination of precise values of complex refractive indexof infrared materials using data from existing sources and new spectral measurements which are presented here;the spectral design, manufacture and verification of filters and coatings for use in the HIRDLS instrument, andthe analysis of the spectral design of the instrument. Further, I was also directly responsible for carrying out thepost-flight spectral and physical analysis of the infrared samples flown by the University of Reading on the LongDuration Exposure Facility.

This PhD thesis was submitted to The University of Reading in December 1998 and will not be used orsubmitted to any other University for future examination.

INTRODUCTION

This thesis describes the results of an investigation into the spectral characteristics of infrared substrateand thin film materials, and their implementation in the design and manufacture of interference filters for space-flight radiometer instruments. It is a necessary requirement in infrared spectrometry and radiometry to haveeffective and precise filtering for the elimination of unwanted radiation, whilst maximising the performance ofthe isolated spectral passband. In these types of application, the integrated rejection of radiation on either side ofthe passband is just as important as the precise spectral definition given to the filter. Detailed knowledge of thespectral characteristics of the materials, and how to best utilise them, is therefore a crucial element inunderstanding the limitations to the design and fabrication of high performance filters. Substrate and coatingmaterials are required to be highly transparent across the spectral passband region of interest, and mechanicallyrobust enough to withstand the range of environmental conditions to which they are frequently subjected. Yet,where filters are required to operate in regions remote from the optimum characteristics of the availablematerials, knowledge of the ultimate performance by predictive design analysis is essential to determine if theperformance of the realised filter has been achieved.

Research into the properties of infrared optical materials has significantly increased over the past fewyears. This has been facilitated by the technological growth of computing facilities combined with the dataacquisition and advanced software capabilities now available. These developments have permitted spectralanalysis of infrared materials to be performed to a higher data point resolution and accuracy. Advances inFourier Transform Infrared (FTIR) spectrophotometer design and cryopumping technology have also permittedspectral measurements to be made across a wider wavelength and temperature range than previously available.


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Many differing methods for the determination of the complex refractive index variables n and k havebeen developed by workers in the optics community. Many of these have now published accurate models whichdescribe these characteristics across various differing wavelength and temperature ranges. As part of this thesis Ihave brought together many of the differing refractive index models described in the reference literature whichdefine the real part of the refractive index to formulate algorithms which can now be used to describe both theirwavelength and temperature-dependent characteristics. The determination of values for k to complete thischaracterisation has been performed by combining the values calculated from the algorithms for the real part ofthe refractive index (n) to the spectral measurements of bulk materials. These calculations use incoherentreflection from two or more surfaces and include multiple internal reflections to determine the absorptioncoefficient (α) and hence extinction coefficient (k). By combining the absorption calculations with the real partof the refractive index, a complete database model of the complex refractive index has been derived and verifiedfor a selection of differing infrared materials.

As a result of combining the theoretical models with measurements available from FTIR spectroscopy,the extrapolation and interpolation of measured data to predict the spectral characteristics of alternative substratethicknesses and operating temperatures is now reliably accurate and valid as a method of predictive performance.Additionally, the advantages of using a predictive performance model based on measured characteristics includethe ability to account for spectral anomalies which cannot be predicted by generic absorption models.

The growth in high speed computing has also created the capability to predict the performance ofcomplete instrument designs. This requires the spectral combination of multiple components, to derive theinstrument throughput response prior to manufacture, assembly and calibration testing. These advances havesubsequently demanded higher levels of material performance and characterisation.

Large scale spectral performance calculations through the use of multi-page relational spreadsheetshave also improved coating design and manufacturing efficiency. As a result of distributing the multilayerblocking over a number of elements, the continuous spectral blocking previously required on single componentfilters has been removed. This approach has allowed an optimal instrument design to be created in which eachelement is only required to perform its own specialised function.

This thesis characterises the spectral performance of a variety of different infrared materials over awider frequency, temperature and thickness range than currently available from traditional literature sources.From this, predictive performance models are now possible for applications where direct measurements areunobtainable or unavailable. Additionally, a fully integrated spectral systems design model is presented, in whichthe performance requirements specified at the instrument level are fed back through the instrument to define thespecific characteristics required by the filters.

The first two chapters of this thesis describe the development of the research. An initial survey of thegeneral theories of materials, including electronic absorption, lattice absorption and dispersion are presented inChapter 1. This is followed in Chapter 2 by a detailed study of the characteristics of the most frequently usedinfrared filter substrate materials and the implementation of predictive modelling algorithms to derive thespectral characteristics of materials of differing thickness and/or operating temperatures.

Chapter 3 contains details of the spectral characteristics of the thin-film deposition materials used in thedesign and manufacture of infrared multilayers. The thin film deposition technique, and structural characteristicsof deposited multilayers is also described.

Multilayer calculation theory and applications are discussed in Chapter 4. These computationalmethods, which include substrate and thin-film layer absorption are described there. In order to assess thepracticality of predictive performance modelling, examples of analyses for manufactured filters and infraredsystems design are included in this chapter.

Chapter 5 presents the integrated systems performance approach to infrared spectral instrument design.Using the EOS HIRDLS instrument as an example with a specified instrument level channel response, theprocess of determining the spectral requirements for the two bandpass filters and antireflection coatings isdescribed. This process takes into account the spectral characteristics of the optical materials in the transmissiveoptics, the relative spectral response of the detector, the expected atmospheric signal, and thermal emission fromthe instrument. This design approach allows an improved design for the filters, by minimising the number oflayers, maximising the transmission and aiding filter manufacture. The use of the design model also allows the


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instrument spectral performance to be verified using the spectral profiles of manufactured components. Thespectral calculations for example channels are discussed together with the spreadsheet calculation method.

In order to assess the durability and stability of manufactured infrared filters and materials, a selectionof components manufactured by the University of Reading Infrared Multilayer Laboratory were exposed to thespace environment in low Earth orbit on the NASA Long Duration Exposure Facility (LDEF) for a period of 69months. Chapter 6 summarises the most recent results from the effects of that environment on the physical andoptical properties of the filters and material flown, and compares this with the environmental conditions requiredfor survival of filters and coatings in current spaceflight instruments.

Spectral Characterisation of Infrared Optical Materials and Filters Dr. Gary J. Hawkins PhD Thesis (#R7935) - University of Reading, UK December 1998 _________________________________________________________________________________________

1

CHAPTER 1 INFRARED MATERIALS ABSORPTION THEORY

The design of any infrared filtering system requires the selection of materials based upon knowledge of the optical, mechanical and thermal properties available. Frequently, the selection of suitable materials results from compromises between these various properties as no single material will possess the ideal characteristics required to suit the wide variety of applications. A study of the infrared material characteristics, particularly the absorption and dispersion processes is therefore essential for the selection of suitable materials for use both as substrates and evaporated layer materials. 1.1 General description of absorption This chapter highlights the absorption processes that occur in five of the most frequently used filter substrate materials, namely; Group IV materials Silicon (Si) and Germanium (Ge), and Group II-VI materials Zinc Selenide (ZnSe), Zinc Sulphide (ZnS) and Cadmium Telluride (CdTe). These substrate materials have been selected from the wide range of infrared materials available as they represent filter substrates onto which evaporated layer materials are frequently and successfully deposited, having selective regions of high transparency and good thermal conductivity. All of the observed intrinsic absorption characteristics present in the spectrum of an infrared optical material can be classified by three fundamental processes involving interaction between the material and the incident electromagnetic radiation, namely; electronic absorption, lattice or phonon absorption and free-carrier absorption. The electronic absorption characteristics observed towards the higher frequency end of the infrared spectrum are the result of interaction between the incident radiation and the motions of electrons or holes within the material. Only electromagnetic radiation with sufficient energy to cause an electron to transfer between the valence band and conduction band (hf) will be absorbed by this mechanism. The various transitions of these electrons define the position of the short wavelength absorption edge. The resulting spectrum provides information on the width of the energy band-gap of the material, and through spectral anomalies, can indicate the presence of impurities.

The lattice absorption characteristics observed at the lower frequency regions, in the middle to far-infrared wavelength range, define the long wavelength transparency limit of the material, and are the result of the interactive coupling between the motions of thermally induced vibrations of the constituent atoms of the substrate crystal lattice and the incident radiation. Hence, all materials are bounded by limiting regions of absorption caused by atomic vibrations in the far-infrared (>10µm), and motions of electrons and/or holes in the short-wave visible regions. In the interband region, the frequency of the incident radiation has insufficient energy (E=hf) to transfer electrons to the conduction band and cause absorption; here the material is essentially loss-free. In addition to the fundamental electronic and lattice absorption process, free-carrier absorption in semiconductors can be present. This involves electronic transitions between initial and final states within the same energy band. The absorption or emission of the resulting photons is accompanied by scattering by optical or acoustic-mode phonon vibrations or by charged impurities. This type of absorption is evident where the spectral profile of the material is highly absorbing, producing considerably lower transmission than otherwise expected. These intrinsic absorption properties of semiconductors and insulators define the transparency of the material. To be transmitted in the region between the electronic and lattice absorptions, the incident radiation must have a lower frequency than the band-gap (Eg) of the material. This is defined by the short wavelength semiconductor edge at λ = hc/eEg, preventing electrons transferring to the conduction band. The generalised profile of the electronic absorption edge is known as the Urbach tail[1] where the exponentially increasing absorption coefficient follows the general relationship:


2

( ) kThf1)(ln

=∂∂ α

(1-1)

The illustrations in Figures 1-1 and 1-2 show the effects of these various absorption and dispersion mechanisms present in a typical crystalline material across the uv-visible to far-infrared wavelength regions.

Figure 1-1 Optical dispersion properties of a typical crystalline material

Figure 1-2 Optical absorption properties of a typical crystalline material


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1.2 Electronic Absorption In conductors, absorption due to the presence of a cloud of free electrons or holes is continuous, with a magnitude that increases approximately as the square of the incident wavelength. Overlapping valence and conduction bands provide high reflectivity but prohibit transparency throughout the entire infrared. As the electron energy bands become separated in semiconductors however, the extent to which free electron carriers cause absorption becomes dependent upon the size of the energy gap at any given temperature, and the absence of impurities. The electronic absorption processes at the higher frequency end of the infrared spectrum caused by band-to-band or band-to-exciton (electron in an electrostatically attracted combination with a hole) transitions can be divided into four main categories for semiconductor materials; i) Intrinsic absorption, where in a pure semiconductor transitions between full valence bands and empty conduction bands are free to occur. ii) Extrinsic absorption, where transitions occur between the valence or conduction band and donor or acceptor sites in the band gap. iii) Free carrier absorption in which transitions occur within any one energy band, and iv) Localised energy states caused by defects or impurities, where electrons or holes may be excited into a higher energy state. At frequencies close to the electronic absorption edge, a change in the bandgap (Eg) of the crystal by a fraction of an electron volt can change the absorption coefficient (α) by nearly four orders of magnitude. By measurement of the spectral position and profile of the absorption edge, values for the energy band-gap (Eg) can be determined, together with other general information about the energy states either side of the forbidden band responsible for electrical conduction[2]. However, the estimation of the energy gap from the absorption edge is not a straightforward process (and is outside the scope of this thesis) for the following reason; As the momentum of a photon (h/λ) is very small compared to the crystal momentum (h/a), where a is the lattice constant, the photon-absorption process should conserve the momentum of the electron. However, the absorption coefficient (α) for a given photon energy hf is proportional to the probability (Pi,f) for the transition from the initial state (ni) to the final state (nf) , the density of electrons in the initial state, and also to the density of available final states. These processes must be summed for all the possible transitions between states that are

separated by an energy difference equal to hf, ( )α hf i f i fi

f

P n n= ∑ , . Therefore both the exact positioning and

shape of the electronic absorption edge cannot easily be predicted or modelled through solid state theory without detailed knowledge of all the allowed & forbidden, direct & indirect transitions available, together with knowledge of the density of electrons as given by the product of the density of states and the Fermi-Dirac function, with the probability of an electron level possessing an electron given by:

f EE E

kTf

( )exp

=+

−⎛⎝⎜

⎞⎠⎟

1

1 (1-2)

where, E is the energy level, Ef is the Fermi-energy level, k is Boltzmann’s constant and T is the absolute temperature. Figure 1-3 illustrates the various electronic absorption energy band transitions available in a typical semiconductor material.


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Energy

(C)

Band-gap (Eg)

ValenceBand

Direct Energy

ConductionBand

(D)

(A)

(E)

Indirect energyband-gap(B)

Figure 1-3 Electronic absorption energy band transitions

(A) Direct valence to conduction band transitions (constant k vector) (B) Indirect valence to conduction band transitions aided by photon/phonon coupling interactions (C) Inter-valence band transitions (D) Valence band free-carrier transitions aided by impurities or photon/phonon interactions (E) Conduction band free-carrier transitions aided by impurities or photon/phonon interactions Optical materials that are opaque in the visible, because of comparatively small bandgaps (≤ 1.25eV), are arbitrarily classified as infrared semiconductors whilst materials of larger bandgap, and whose lattice absorption is present in the far-infrared are insulators. Figure 1-4 illustrates the generalised distinction between semiconductor and insulator materials, where the energy band gap (Eg) is plotted against molecular / atomic weight. Infrared semiconductors comprising Group IV elements and certain Group III-V compounds are positioned below the horizontal line, whilst infrared II-VI and lighter III-V insulator materials are above.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 50 100 150 200 250 300 350Molecular Weight

Ener

gy B

and

Gap

(Eg)

GeSi

SnInAs

GaAs

GaP

SiC

ZnS

ZnSe

CdSe

ZnTe

CdTe

PbTe

(IV)

(III-V) (II-VI)

InSb

Figure 1-4 Energy band-gap of infrared semiconductors and insulators at 300K vs molecular weight


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1.3 Lattice Absorption The conductive properties of many materials that are suitable for use as optical substrates can provide a good indication of the expected spectral performance, as the systematic tendencies in the electrical properties tend to parallel the optical behaviour. Insulator materials show some regions of transparency, either in the near or far-infrared, whilst good electrical and thermal conductors exhibit a continuous background of electronic absorption over the whole infrared region All of the resonant absorption processes involved in an infrared material can be explained by the same common principal. At particular frequencies the incident radiation is allowed to propagate through the crystal lattice producing the observed transparency, other frequencies however, are forbidden when the incident radiation is at resonance with any of the properties of the lattice material, and as such are transferred as thermal energy, exciting the atoms or electrons. The resonant vibrational absorption characteristics created by the lattice are highly complex, consisting of several types of fundamental vibrations. In order that a mode of vibration can absorb, a mechanism for coupling the vibrational motion to the electromagnetic radiation must exist. Transfer of electromagnetic radiation from the incident medium to the material is in the form of a couple, where the lattice vibration produces an oscillating dipole moment which can be driven by the oscillating electric field (E) of the radiation. In order for the total transfer of energy to be complete, the following three conditions must be satisfied; i) the conservation of energy is maintained, ii) the conservation of momentum is maintained, and iii) a coupling mechanism between the material and the incident medium is present. The conservation of momentum is governed by the relationship between de Broglie’s particle/wave duality, from the photon and phonon momenta, where the photon momentum is P = h/λ. The phonon momentum in the crystal is given by P = h/a, where a is the lattice constant for the unit cell. When λ=a, the conservation of momentum is preserved between the incident photon and thermal phonon, resulting in complete absorption of the incident radiation by the lattice. However, the photon has a low momentum when compared to the momentum of a phonon, therefore two or more photons are required to satisfy the conservation of momentum and produce total absorption. The coupling mechanism between the incident photon and the lattice phonon is produced by a change of state in the electric dipole moment (M) of the crystal. A dipole moment arises when two equal and opposite charges are situated a very short distance apart, and is the product of either of the charges with the distance between them. Thus energy absorbed from the radiation will be converted into vibrational motion of the atoms. In simple gas molecules this gives rise to a characteristic spectral absorption band, as the many molecules form a large number of coupled dipole moments. In more complex lattice structures, in order for a mode of vibration to absorb any incident radiation, the basic mechanism for coupling must be present. Three different coupled absorption mechanisms exist [3] ; i) Reststrahl absorption, this only occurs in ionic crystals and is caused by the creation of single phonons in the lattice. ii) Multi-phonon absorption which occurs when two or more phonons simultaneously interact and produce an electric moment with which the incident radiation may couple. iii) Defect induced one phonon absorption, which in a pure crystal is where the creation of a single phonon is not accompanied by a transitional change of state in dipole moment that can act as a couple, but is induced by the existence of a crystal defect or impurity to aid the coupling mechanism. 1.4 Phonons Although vibrations generated in the crystal lattice may be considered as a sequence of hypothetical oscillators and their associated coupling mechanisms. The crystal lattice can also be considered as a single large vibrating system, which is able to pulsate at various frequencies generating its own oscillations. As the superposition of all the displacements at the various points within the system must be the same as the atomic displacements at those points, then the various modes of vibration can be considered as applying to the whole crystal lattice assembly. In this composite system, the energy associated with the modes of vibration can still only change in discrete steps, only now these quanta of vibrational energy involve displacements of all the atoms rather than by a single coupled atom. Where the temperature is raised in a crystal lattice, the amplitude of


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the atomic vibrations increases, which in turn produces an increase in the number of phonons in the system. 1.4.1 Phonon absorption theory Whereas a static lattice model deals with the average positions of atoms in a crystal, the idea of lattice dynamics extends the concept of the crystal lattice to an array of atoms with finite masses that are capable of motion. This motion is not random but a superposition of discrete standing and/or travelling waves that interact with the atomic vibrations to produce phonons. The phonons produced are continually scattered by various barriers or interactions that limit the mean free path of the vibration. The scattering processes are caused by combinations of either interactions between phonons, point defects caused by impurities, or grain boundaries and dislocations. For each of these mechanisms there will be a thermal resistance which will increase the amount of absorption. This absorption will also depend upon the incident wavelength, as a change in temperature will alter the nature of the phonon spectrum. At low temperatures only the longest wavelength phonons are excited and cause absorption; at high temperatures absorption will tend to become dominant at shorter wavelengths. Both harmonic (linear propagation) and anharmonic (non-linear propagation) waves can be superimposed on the lattice vibrations. At low temperatures where the amplitude of the vibrations is small the higher order anharmonic terms may be neglected, whereas at higher temperatures where atomic displacements are greater, anharmonic wave interactions become appreciable, causing energy from a wave to become converted into a wave with a different frequency and creating an additional phonon. This will subsequently change the absorption profile of the material. The possible combinations of phonons is a complex problem, and beyond the scope of this thesis, however, in general the mechanisms of combining phonons is defined by the Umklapp process[4]. The idea of which is that if two incident phonons have large wave vectors, the resultant wave vector may be sufficiently large that its corresponding wavelength may be shorter than twice the interatomic spacing. This would cause the phonon velocity to become reversed meaning that the phonon travelling in the opposite direction will reduce any heat transfer through the substrate but will produce its own thermal resistance. This occurs as a result of the material having discrete and periodic modes of vibration. 1.4.2 Phonon dispersion theory The longitudinal and transverse modes of vibration in a crystal lattice are most suitably described by phonon dispersion. Phonon dispersion is the relationship between the frequency of vibration of the phonon (ω) as a function of the wave vector (k), where k = 2π/λ. For acoustic phonons, where there exists only one atom per unit cell, longitudinal deformations create atomic displacements parallel to the propagation of the wave with forces between adjacent atoms that obey Hooke’s law of elasticity. The illustration in Figure 1-5 represents the acoustic dispersion in the first Brillouin zone.

Figure 1-5 Acoustic phonon dispersion for a monatomic lattice

An important feature of this dispersion curve is the periodicity of the function. For a unit cell of length a, the repeat period is 2π/a, which is equal to the unit cell length of the reciprocal lattice. Therefore, the useful profile information is contained in the waves with wave vectors lying between the limits -π/a < k < π/a. This range of vectors is called the first Brillouin zone. At the Brillouin zone boundaries the nearest atoms of the


7

chain vibrate in the opposite directions and the wave becomes a standing wave. As k approaches zero at longer wavelengths, the phase velocity (ν0) is equivalent to the velocity of sound in the crystal. For optical phonons, where there are different kinds of atoms per unit cell such as in compound semiconductors and insulators, the lattice modes of vibration require two solutions for vibrations of the two contributing atoms in the structure. In this case both an acoustic and optical branch are present, as illustrated in Figure 1-6, where M and m are the masses of the constituent atoms and β is a force constant for the material.

Figure 1-6 Acoustic and Optical phonon dispersion for a diatomic lattice representative of a compound semiconductor.

The allowed frequencies of propagation of the wave are split into an upper optical branch and a lower

acoustic branch. Between these branches there is a band of frequencies in which waves cannot propagate. The width of this forbidden band depends on the difference of the atomic masses. If the atomic masses are identical, the two branches join at the boundaries of the first Brillouin zone at π/2a. It should be noted in this case the first Brillouin zone goes from k = -π/2a to k = +π/2a compared to π/a in the monatomic lattice. The profile of the acoustic branch is similar to that of the monatomic lattice, but the optical branch represents a completely different form of wave motion. The difference between acoustical and optical branches can be found at long wavelength, where contrary to the optical phonons, the two atoms in the unit cell move opposite to each other; the one with the lighter mass possessing a greater amplitude. At the same long wavelength part of the spectrum for acoustical phonons the displacement of both atoms has the same amplitude, direction and phase. 1.5 Single phonon absorption Single phonon Reststrahl absorption can occur in any material possessing an ionic character with an alternating pattern of positive and negative ions. This fundamental one-phonon absorption process is associated with the electrostatic motions of opposite charges which produce an oscillating electric field with which the incident radiation can couple. The wave vectors associated with this absorption only follow the longitudinal and transverse optical branches of the phonon dispersion curves as there exists two or more atoms per unit cell. In diatomic ionic crystals, when the interaction between the photon and phonon conserve the wave vector momentum, such that k = 2π/λ ≅ 0, the theory predicts the strongest absorption will be present, such that the crystal becomes totally reflecting, between the transverse and longitudinal optical vibration frequencies at a resonant frequency that corresponds to Equation 1-3,

ωmax

/

= +⎛⎝⎜

⎞⎠⎟

⎧⎨⎩

⎫⎬⎭

21 1 1 2

Fm M

(1-3)

where m and M are the masses of the two ions. If one ion is much heavier than the other, the smaller of the two masses will determine the value of the bond strength (F). Therefore to achieve transparency to the longest wavelength, requires both ions to be as heavy as possible.


8

The behaviour of this type of absorption is most suitably described as a damped Lorentz classical oscillator. This is based on the assumption that the material contains charged particles which are bound to equilibrium positions by Hooke’s law forces (i.e. for a certain range of atomic stresses (vibrations), the strain produced is proportional to the stress applied). If the magnitude of the force is assumed to be inversely proportional to the square of the distance between the atoms (Coulombic), the resonant frequencies for materials with different atomic masses can be predicted from empirical estimations of F. This general rule has been found to be correct to within about 20% of the measured spectral position for a number of diatomic infrared crystals[5]. In general, ionic crystals exhibit good transmission with constant refractive index and low absorption coefficient up to the lattice absorption band (typically beyond 6µm) at which point the single phonon produces a heavily absorbing mode of vibration and subsequent strong reflection coefficient. The refractive index undergoes a rapid change forcing the Fresnel reflection coefficient to become quiet high. The extinction coefficient also rises rapidly. At wavelengths longer than the resonant Reststrahl frequency, the absorption coefficient decreases, and the refractive index falls to a level slightly higher than on the short wavelength side of the absorption band. The difference in refractive index is characteristic of this absorption mechanism in ionic crystals. The long wavelength limit of transparency is therefore set by the Reststrahl frequency with the absorption falling rapidly at higher frequencies. For most ionic materials more than one absorption peak is present. Figure 1-7 shows the measured Reststrahl absorption peaks for a selection of ionic crystals. As the temperature of the material is reduced, the Reststrahl frequency moves slightly towards shorter wavelengths and the peak reflection increases. The refractive index however is unaffected, other than by the characteristic change defined by the temperature-dependent dispersion coefficients.

1400.0 1300 1200 1100 1000 900 800 700 600 500 400 300 220.0Wavenumber (cm-1)

Ref

lect

ion

Fused Silica

Sapphire

Magnesium Fluoride

Calcium Fluoride

Barium Fluoride

Figure 1-7 Measured reststrahl absorption peaks for various ionic crystals. In homopolar crystals (Ge, Si) where there is an absence of polar electric field interactions, the atomic motions are determined only by the local elastic restoring forces, and as such there is no single phonon interactive coupling and the longitudinal vibration then equals the transverse vibration mode. Hence only weak multi-phonon absorption harmonics are present. 1.6 Multi-phonon absorption Multi-phonon absorption occurs when two or more phonons simultaneously interact to produce electric dipole moments with which the incident radiation may couple. These dipoles can absorb energy from the incident radiation, reaching a maximum coupling with the radiation when the frequency is equal to the vibrational mode of the dipole in the far-infrared. The different vibration modes are complex, comprising several different types of vibrations. There are two modes of vibrations of atoms in crystals, longitudinal and


9

transverse. In the longitudinal mode the displacement of atoms from their positions of equilibrium coincides with the propagation direction of the wave, for transverse modes, atoms move perpendicular to the propagation of the wave. Where there is only one atom per unit cell, the phonon dispersion curves are represented only by acoustic branches. If there is more than one atom per unit cell both acoustic and optical branches appear. The difference between acoustic and optical branches being the greater number of vibration modes available. In a diatomic cell the acoustic branch is formed when both atoms move together in-phase, the optical branch being formed by out-of-phase vibrations. Generally, for N atoms per unit cell there will be 3 acoustic branches (1 longitudinal and 2 transverse) and 3N-3 optical branches (N-1 longitudinal and 2N-2 transverse). Compound semiconductors have two transverse optical modes (TO), two transverse acoustic modes (TA), one longitudinal optical mode (LO), and a longitudinal acoustic mode (LA). The two transverse modes can exhibit similar dispersion characteristics on the energy / wave vector diagrams. As phonon emission is quantized, selectivity forbids certain combinations of phonon absorption modes, however the varied combination of all the modes available produces a highly complex absorption structure. In single compound (homopolar) covalently bonded semiconductors such as Silicon and Germanium where there is no bonding dipole, the incident radiation induces a dipole moment with a stronger couple, producing more phonons (usually <4) as illustrated for a measured Silicon substrate in Figure 1-8 and Table 1-1.

0

1

2

3

4

5

6

7

8

9

10

02004006008001000120014001600Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/c

m)

LO+TA

TO+TA

LO+LA

TO+LA

TO+LO2TO+LO

3TO

2TO

2TO+LA

Data Source : FTIR Measurement

Figure 1-8 Measured far-infrared multi-phonon absorption profile of Silicon @ 293K

Table 1-1 Multi-phonon assignments in Silicon [6]

Wavenumber (cm-1) Peak Energy (eV) Phonon Assignment

1448 0.1795 3TO 1378 0.1708 2TO+LO 1121 0.1614 2TO+LA 964 0.1195 2TO 896 0.1111 TO+LO 819 0.1015 TO+LA 740 0.0917 LO+LA 689 0.0756 TO+TA 610 0.0702 LO+TA

Where; TO = 0.0598eV, LO = 0.0513eV, LA = 0.0414eV, TA = 0.0158eV Multi-phonon absorption also occurs in ionic crystals in a form similar to that in homopolar crystals. Its strength is usually greater than in the homopolar case but is substantially weaker than one-phonon reststrahl absorption.


10

1.7 Dielectric Dispersion The real part (n) of the complex refractive index (N=n-ik) of an infrared dielectric or semiconductor material is not independent of the extinction coefficient (k) but was proved by Kronig[7] in 1926 to be related through the Kramers-Kronig relationship to take the form;

( )( ) ( )

n Pnk

d22 2

0

1 2 2ω

πω

ω ωωω− =

−−

∞

∫ ''

'' (1-4)

where P denotes the principal value integral and ω the angular frequency (2π/λ). The absorptive term 2nk is integrated over all frequencies (ω′) for which there is no absorption. Therefore in a material containing absorption, any change in the value of n is controlled by the size of the absorption. At both short and long infrared wavelengths the deviations from this relationship are associated mainly with k rather than n, therefore the transmission tends to be affected more than the reflectivity. This relationship is characterised by the generalised shape of the dispersion profiles for the various different infrared materials as illustrated in Fig. 1-9.

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0Wavelength (µm )

Ref

ract

ive

Inde

x (n

)

Ge (F-1)

Si (F-2)

CdTe (F-3)

ZnSe (F-4)ZnS (F-5)

Al2O3 (F-6)

BaF2 (F-7)CaF2 (F-8)

Data sources referenced in Appendix F

Figure 1-9 Refractive index dispersion of several common infrared substrate materials at 300K

There are many different numerical methods for characterising the optical properties of infrared materials in this interband region[8]. Each of which generally falls into one of four categories : (i) empirical formula, (ii) harmonic-oscillator models, (iii) quantum-mechanical treatments and (iv) point-by-point analysis of the Brillouin zone. Each of these methods possess certain advantages for particular materials but are often constrained by limited wavelength ranges in their application. (i) Optical properties determined from empirical formulas, such as the Sellmeier and Herzberger equations for the refractive index and Urbach’s rule for the absorption coefficient, are not directly related through the Kramers-Kronig dispersion relationship between n and k. But as formulations derived through curve fitting algorithms, they usually provide a good approximation of the dispersive material profiles but are generally only valid across a narrow wavelength range. (ii) The harmonic-oscillator models do not incorporate any optical energy band-gap (Eg) function. Therefore, the optical energy band gap cannot be determined from this approach and would then require the additional use of many different curve fitting functions to describe n and k in this region.


11

(iii) Quantum-mechanical treatments involve either a quantized electromagnetic photon interaction, where an infinite lifetime for the excited electron state is assumed, or a non-quantized electromagnetic interaction where finite lifetime assumptions are used. This type of approach provides optical constants that are highly accurate but only over extremely small energy or wavelength ranges. (iv) The point-by-point analysis of the Brillouin zone does not provide equations for the optical constants in any algebraic form, but is derived from critical point analysis of observed peaks in the optical spectra. Agreement with experimental results is often poor. A similar behaviour pattern is found in the spectra of all dielectric and semiconductor materials, namely a continuum of absorption at short wavelengths preceding an electronic absorption edge and succeeded by the interband transparent region and subsequent lattice absorption. The transparent region is subject to increasing absorption from charge carriers, if present, and is then itself interrupted by lattice resonances and harmonics, each contributing to a significant change in the refractive index dispersion profile. The effect of temperature change on the dielectric and semiconductor dispersion profiles generally exhibits a linear displacement in the shape of the dispersion profile with decreasing refractive index as the temperature is reduced. The refractive index declines towards long wavelengths due to the influence of lattice absorption. When the material cools the amount of lattice absorption reduces, and the dispersion profiles at the differing temperatures converge at long wavelength, where the high frequency lattice dielectric constant (ε∞) is a fixed valve for the material. All materials exhibit this decline in refractive index with increasing wavelength in the loss free interband region. The shape of the dispersion curve has been defined by the classical oscillator to which Sellmeier, Herzberger and Lorentzian mathematical functions have been applied. Modified temperature-dependent Sellmeier equations and polynomial regression coefficients have proved the most suitable curve fitting algorithms for calculations of refractive index data for the group IV and II-VI materials as defined by Equation 1-5. These have therefore been used to produce many of the dispersion models implemented in this thesis.

( ) ( )n A BC

DE

= +−

+−

+λ

λλ

λ

2

2

2

21 (1-5)

where the coefficients A-E are temperature-dependent. In semiconductor and semi-insulator materials free electrons can also contribute to the dispersion profile setting up an intense absorption edge at short wavelength, as the absorption increases with wavelength due to free carriers. When carrier dispersion is superimposed on intrinsic material there is significant additional decline of refractive index towards long wavelength dependent upon the carrier concentration[9]. Generally, in dielectric materials, the low conductivity indicates that practically all the electronic charges are bound to their parent atoms, and are therefore not free to migrate under the action of an applied field[10]. The action of an applied radiation field (E) to the bound charges in the dielectric displaces them relative to each other, the positive charges being displaced in the direction of the field, the negative charges in the opposite direction. Each atom thus acquires an electric dipole moment parallel to, and in the same direction as the applied field. This effect is the dielectric polarization with an electric polarization vector (P), and is defined as the electric dipole moment per unit volume. P is generally proportional to E and related by equation;

P = χ′ εo E (1-6) where εo is the permittivity of free space and χ′ is the real electric susceptibility constant for a given material at a given frequency and temperature, and is independent of E. To describe the combined effects of the applied field E and the electric polarization vector P the electric displacement is then added;

D = εo E + P (1-7) where for a vacuum: χ′ = 0, P = 0, giving the electric displacement as D = εoE and for a real dielectric material D = ε′ E, where ε′ is the real dielectric constant given by (1+ χ′ )εo. The dielectric constant (ε′) is therefore determined entirely by localised electrons bound to the lattice, the size of which is a function of the electron polarizability.


12

To summarise, dielectrics show strong periodic resonances that define the profile of the dispersion curve, as represented in Figure 1-10 for characteristic dielectric dispersion, whereas semiconductors show only weak multi-phonon harmonics. Semiconductors are dominated by the electronic absorption edge with carrier absorption thereafter, whereas dielectrics have a considerably wider interband region and have no contribution from these effects, and in semiconductors, dispersion due to free carriers can be considerable and additive to the dispersion intrinsically present.

Figure 1-10 Dielectric dispersion at an absorption peak

1.8 Temperature-dependent effects Obtaining detailed knowledge of the effects of temperature on the optical properties of infrared substrate materials is an essential prerequisite for achieving an optimum filter design performance. The range of material transparency, refractive index and amount of absorption can be highly temperature-dependent and often used to considerable advantage if the effects are quantified. The advantages to infrared systems of using cooled detectors are well known, with the signal-to-noise ratio being increased, photon detector sensitivity being improved and the possible elimination of stray radiation from an instrument itself. Additionally if a source being viewed through a radiometer is itself cold, progressively cooling the radiometer optics can also reduce spurious signals. By modelling the effects of the temperature dependence on the dispersive spectrum of a material, the filter performance on cooling can be simulated and compared. Of the three physical processes that affect the intrinsic optical properties of an infrared material, namely; electronic transitions, lattice vibrations and free-carrier absorption, the dominating absorption effect depends on the material. However at all temperatures, all materials possess contributions to the complex refractive index from electronic transitions. Additionally, semiconductors are influenced by free carrier effects with the size of contribution being dependent on the carrier concentration. Dielectric insulators and semiconductors additionally require characterisation of the lattice vibrations at reduced temperatures to define the effect. In the transparent region of an infrared material, more subtle processes such as impurities, defects and scattering are also important irrespective of temperature. Intrinsic Rayleigh scattering by the crystalline structure is generally a weak effect, but extrinsic scattering by defects or grain boundaries can be of more significant concern depending on the spectral region of interest. Neither of these scattering effects are discussed in detail here, though they are of fundamental interest to the properties of the materials themselves, they are dependent on the manufacturing process and are considered constant with temperature. The temperature-dependent effects of the materials characterised in this thesis have been defined in Section 1.9 for both the refractive index and long wavelength lattice absorption. The following Figures 1-11 to


13

1-16 characterise the changes in refractive index (dn/dT) with temperature and illustrate calculated extinction coefficients measured at reduced temperature for the five materials selected.

1.0E-06

5.1E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

3.5E-04

4.0E-04

4.5E-04

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0

Wavelength (µm)

Tem

pera

ture

Coe

ffic

ient

(dn/

dT)

Ge (F-1)

Si (F-9)

ZnSe (F-9)

ZnS (F-10)

CdTe (F-11)

Data sources referenced in Appendix F

Figure 1-11 Temperature-index coefficient (dn/dT) for various infrared substrate materials

1E-05

1E-04

1E-03

1E-02

2503003504004505005506006507007508008509009501000Wavenumber (1/cm)

Extin

ctio

n C

oeff

icie

nt (

k)

50K

300K


Figure 1-12 Calculated extinction coefficient (k) profile from measured multi-phonon absorption spectra of

Germanium (Ge) at 300 and 50K


14

1E-06

1E-05

1E-04

1E-03

1E-02

250350450550650750850950105011501250135014501550Wavenumber (1/cm)

Extin

ctio

n C

oeff

icie

nt (

k)

50K

300K


Figure 1-13 Calculated extinction coefficient (k) profile from measured multi-phonon absorption spectra of Cz

Silicon (Si) at 300 and 50K

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

250300350400450500550600650700Wavenumber (1/cm)

Extin

ctio

n C

oeff

icie

nt (

k)

50K

300K



Zinc Selenide (ZnSe) at 300 and 50K


15

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

5005506006507007508008509009501000Wavenumber (1/cm)

Extin

ctio

n C

oeff

icie

nt (

k)

50K

300K



Zinc Sulphide (ZnS) at 300 and 50K

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

250300350400450500Wavenumber (1/cm)

Extin

ctio

n C

oeff

icie

nt (k

)

50K

300K


Figure 1-16 Calculated extinction coefficient (k) profile from measured multi-phonon absorption

spectra of Cadmium Telluride (CdTe) at 300 and 50K

1.8.1 Thermal vibrations The concepts of temperature and thermal equilibrium associated with crystal solids are based on individual atoms in the system possessing vibrational motion. The classical theory of thermal energy by atomic vibrations, though providing suitable explanations at elevated temperatures, has proved unsatisfactory at reduced or cryogenic temperatures. Quantum mechanics has subsequently provided theories based upon statistical probability that have provided possible mechanisms to explain some of the observed phenomena. A system of vibrating atoms in a crystal is highly complicated, and beyond the realm of any realisable theoretical method of analysis or calculations to verify spectral measurements from the total thermal energy of a crystalline


16

substrate. However, there are general rules for atomic lattice structures in thermal equilibrium which give a relative probability of particles in the crystal having different energies. For a system of distinguishable particles, the probability statistics of the energy of the system are described by the Maxwell-Boltzmann general equation fMB = A exp(-E/kT). If particles are indistinguishable they are divided into two types; (i) electrons, which are subject to the Pauli exclusion principal and obey Fermi-Dirac statistics fFD = [exp(E-EF)/kT+1]-1, where EF is the Fermi-energy. (ii) photons and phonons which are defined by Bose-Einstein statistics fBE = [exp(E-α)/kT-1]-1, where α is a normalising constant, adjusted so the total probability is equal to unity when each function is summed over all the energy states available. When a particle is bound to a crystal, the energy can only have discrete values as defined by the energy band structure. The quantum-mechanics of a one-dimensional simple harmonic oscillator gives permitted energies of (n+½)hω where ω is the angular frequency and n is the permitted energy integer. At a position of minimum energy (0K) the energy can never be zero, but has energy of hω (zero-point energy) and as such will still provide crystal vibration. As an atom can vibrate independently in three dimensions it is equivalent to three separate oscillators. The total thermal energy for N atoms will then be 3NkT, ignoring the hω term, the specific heat required to change the temperature by one degree will then be 3Nk where the specific heat of a solid for a given number of atoms is independent of temperature if N is the Avagadro number (6.02x1023). A detailed calculation of this form would require a knowledge of the number of atoms vibrating with frequencies ω1 ...ωn, which would depend on the density of states, and integration over the whole range of atomic vibrational frequencies would be required. The thermal vibrations in a solid produce atomic displacements, which in a three dimensional lattice can be resolved into different states of polarization such that vibrations parallel to the wave vector are longitudinal waves and the two directions at right angles to the wave vector are transverse waves. As the rules of quantum mechanics apply to all the different atomic vibrations in the crystal, the lattice pulsates as a complete assembly in discrete energy steps of hω (phonons). The phonon is related to both the frequency of vibration and the temperature. If the temperature is raised, the amplitude of atomic vibration increases, and in quantum terms this is considered as an increase in the number of phonons in the system. The concept of the phonon is therefore considered as the quantum of lattice vibrational energy onto which is superimposed a complex pattern of standing and/or travelling waves that represent changes in temperature. If the crystal is at a uniform temperature the standing wave concept is adequate as the phonon vibrations are uniformly distributed. 1.8.2 Thermal expansion During the temperature change between the elevated thermal conditions during filter deposition and the practical application of a filter operating at cryogenic temperatures, the infrared substrate is subjected to a wide range of thermal and mechanical stresses. The linear thermal expansion coefficient is therefore an important parameter in the selection of the most suitable substrate material for a particular application as it will determine the amount of stress in a coating caused by dimensional changes and heat flow during the thermal cycling process. When a substrate is cooled, the reduction in thermal energy causes a decrease in the vibrational amplitudes of the individual atoms. The average separation between atoms therefore decreases and the substrate contracts. This process is described by the coefficient of linear expansion (α), defined in the case of a circular substrate as the ratio of change in diameter (∆θ) per degree to the diameter of the substrate (θ). The temperature-dependence on this value is obviously crucial where wide temperature range excursions are anticipated. Browder et al [11] investigated the coefficients of linear thermal expansion by interferometric measurement for Chemical Vapour Deposition (CVD) infrared materials ZnS & ZnSe, together with both single crystal and polycrystalline Ge across a temperature range of 300-80K. Interpolated data from these results, as


17

illustrated in Figure 1-17, show germanium to possess a low thermal expansion, with characteristics similar to ZnS. These results showed no appreciable difference between single and polycrystalline germanium.

0

1

2

3

4

5

6

7

8

50 75 100 125 150 175 200 225 250 275 300Temperature (K)

Ther

mal

Exp

ansi

on C

oeff

icie

nt (1

0-6/

K)

ZnSe

ZnS

Ge

Data Source : Appendix F-12

Figure 1-17 Temperature-dependent thermal expansion coefficients of Ge, ZnS and ZnSe

1.9 Infrared material properties There are many high quality crystalline substrate materials that now exist for optical filtering that possess good transparent properties over a wide range of infrared wavelengths. From the numerous materials available, the five materials selected as suitable candidates of typical filter substrates have been employed in various infrared radiometer instruments for which the optical properties are described in this section. Figures 1-18 and 1-19 show the measured spectral profiles for each of these materials from which the relative transparency bandwidths and long wavelength absorption characteristics can be seen.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

050001000015000200002500030000

Wavenumber (1/cm)

Tran

smitt

ance

ZnS ZnSe CdTe Si Ge

Figure 1-18 Measured transmission profiles of Ge, Si, ZnS, ZnSe & CdTe bulk substrate materials

showing comparative transparency widths.


18

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0200400600800100012001400160018002000

ZnS ZnSe CdTe

Si

Ge

Figure 1-19 Measured long wavelength lattice absorption profiles of Ge, Si, ZnS, ZnSe & CdTe

bulk substrate materials (5-300µm) The bulk properties of a given substrate material can vary considerably depending on the impurity levels, precise composition, state of internal strain, and variations in the manufacturing process, affecting homogeneity. The following materials characterisation in sections 1.9.1 to 1.9.5 provides a indication of the predicted performance to be expected from generic properties of these materials for the various thicknesses and operating temperatures most frequently used in filtering applications. 1.9.1 Germanium Germanium has proved to be the most useful semiconductor substrate for applications as a window or lens material in the 1.6 - 18µm region. Having the highest refractive index (n ≈ 4.0) of any of the infrared bulk transmitting substrate materials and low dispersion properties across a wide range of temperatures avoids chromatic aberration in many applications. This combination of high refractive index and low dispersion also means imaging by a single Ge lens with low f-number is easily achievable. Its surface hardness and robust mechanical strength also aid applications where ruggedness is a requirement. It is also non-hydroscopic, non-toxic and possesses good thermal conductivity. The principal region of transparency extends from ≈1.8-18µm at 300K extending to ≈1.5-18µm at 50K. The short wavelength cut-off corresponds to an energy gap between 0.68eV at 300K to 0.83eV at 50K and a transmission level of approximately 47% from a refractive index of ≅ 4.0. The long wavelength multi-phonon absorption profiles for a predicted low resistivity (4-20Ωcm) substrate, calculated from a 1.3mm reference measurement, are shown in Figure 1-20 for calculated substrate thicknesses 1.0-3.5mm at 293K.


19

0.00

0.10

0.20

0.30

0.40

0.50

0500100015002000250030003500400045005000550060006500

Wavenumber (1/cm)

Tran

smitt

ance

1.00

1.50

2.00

2.50

3.00

3.50

Data Source: FTIR Measurement

Figure 1-20 Calculated transmission profiles of Germanium (Ge) at 293K for substrate thicknesses

between 1.0-3.5 mm 1.9.1.1 Germanium absorption Both germanium and silicon have a diamond type structure, where each atom is surrounded by four adjacent atoms occupying the corner points of a tetrahedron, to which it is bound by covalently bonded electron paired bonds. The diamond structure is considered as two interpenetrating face-centred-cubic lattices, in which one lattice is displaced from the other by one quarter of the main body diagonal. The vibration modes experienced from this arrangement consist of the displacement of one sub-lattice with respect to the other, giving rise to displacements and therefore polarizations that are exactly opposite and 180° out of phase producing no resultant polarization and hence no coupling mechanism to the incident radiation. This is the principal reason no Reststrahl type absorption occurs in the Group IV elements, particularly as there is no dipole moment (homopolar) to couple with the incident radiation. However, since there are two atoms per unit cell, there are still optical and acoustic branches of the phonon dispersion curves to generate the multi-phonon absorption. The multi-phonon absorption profile in germanium is complex, consisting of several types of phonon vibrations, primarily due to the transfer of energy from low energy photons to free carriers, this is accompanied by the transfer of momentum between free carriers and phonons in the crystalline lattice. For the absorption to occur, these processes must coincide jointly to retain the conservation of energy and momentum. The mechanism for the two phonon absorption is that one of the vibrational modes induces a charge on the atoms and a second mode simultaneously causes a vibration of the induced charge producing a second order electric moment and coupling to the incident radiation. This electric moment will occur at a sum or difference in frequency of the two phonons, giving discrete absorption bands at these frequencies. Detailed phonon vibration modes of germanium are scarcely reported in any of the reference literature sources available. S.D. Smith et al [12] investigated phonon absorption by neutron irradiating material from which electrons showed no induced vibrational absorption, with radiation of 5x1018 , 2 MeV electrons, whilst another sample showed such a high background absorption that no adequate measurements could be made. Figure 1-21 shows the predicted multi-phonon absorption profiles calculated for 0.5mm thick germanium across the 300-50K temperature range (10-40µm).


20

0.00

0.10

0.20

0.30

0.40

0.50

2503003504004505005506006507007508008509009501000

Wavenumber (1/cm)

Tran

smitt

ance

50

100

150

200

250

300


Figure 1-21 Calculated multiphonon absorption profiles of 0.5 mm thick Germanium (Ge) for 300-50K

temperature range 1.9.1.2 Germanium dispersion Accurate dispersive refractive index data has been extensively investigated over a number of years. In 1976, Icenogle et al [13] reported refractive index values for a discrete series of four temperatures between 297K and 94K and wavelengths between 2.5 and 13µm. Barnes and Piltch[14] utilised this data to derive a fitted temperature-dependent modified Sellmeier equation (1-8) and published the following values for the coefficients in 1979

( ) ( )n A BC

DE

22

2

2

2= +

−+

−λ

λλ

λ (1-8)

where; A = -6.040 x 10-3 T + 11.05128, B = 9.295 x 10-3 T + 4.00536, C = -5.392 x 10-4 T + 0.599034 D = 4.151 x 10-4 T + 0.09145 and E = 1.51408 T + 3426.5 Calculations from this equation has been evaluated[15] from which accurate values for high-grade optical quality germanium are within 0.025% or better, over the 2.5-14µm range, and are considered sufficiently accurate to extrapolate to 40µm, as illustrated in Figure 1-22 and tabulated in Appendix A. Interpolation of this equation has been extensively used in the calculation spreadsheet models to predict the performance of filter profiles as described in Chapter 2. From this model, the refractive index varies over the temperature range of 250K by approximately 45ppm/K from a mean temperature coefficient (dn/dT) of +4.1x10-4 K-1 between 2-20µm.


21

3.85

3.90

3.95

4.00

4.05

4.10

4.15

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Wavelength (µm)

Ref

ract

ive

Inde

x (n

)30025020015010050

300K

50K


Figure 1-22 Temperature-dependent refractive index dispersion profiles for Germanium (Ge) between 300-50K 1.9.1.3 Germanium resistivity Absorption of n-type single crystal material was originally found by Capron and Brill[16] , in 1973, to be superior to that of p-type germanium from ninety two samples investigated with resistivities ranging from 0.9Ωcm to 57Ωcm. They also found that the absorption increased with increasing temperature. The maximum transmittance derived from this experiment, at 300K and 10.6µm, was for samples doped with antimony to a resistivity of 5-10Ωcm with n-type conductivity producing an absorption coefficient of 0.02cm-1 . This agreed well with similar measurements by Horrigan et al [17] for n-type single crystal Ge with impurity concentrations less than 1013 cm-3 using a CO2 laser. Further studies by Osmer et al [18] in 1989 found antimony doping can improve the high temperature transmission of Ge, between 70-120°C at the expense of degraded room temperature performance across the 8-12µm region. Thornton[19] conducted experiments on low resistivity (0.85-3.8Ωcm) germanium between 7-20µm across the 70-150°C range of temperatures from which the interpolated data in Figure 1-23 averaged over the 8-11µm waveband were derived.

0.5

2.0

3.5

3070

90105

130150

0

5

10

15

20

25

30

35

40

45

50

Tran

smis

sion

(%)

ResistivityTemperature (C)

45-5040-4535-4030-3525-3020-2515-2010-155-100-5

Figure 1-23 Temperature profile of single crystal n-type Germanium vs transmission and resistivity


22

Free carrier (electron and hole) absorption can occur throughout the transparent region of the infrared spectrum in addition to the intrinsic absorption processes created by doping to produce n-type or p-type material. Holes in germanium absorb more energy than electrons, creating greater absorption. For intrinsically neutral Ge, the number of holes times the number of electrons is a constant. Reducing the number of holes to produce lower resitivity material is performed by increasing the number of electrons by the addition of group V donor atoms. However, excessive addition leads to higher electron concentration and subsequent increased absorption. Therefore, achieving high quality optical germanium is a compromise between dopant levels and intrinsic hole concentration. Germanium is not usually used at high temperatures because of the excessive absorption caused by the increased number of thermally generated holes. However, doping to lower n-type resistivities can make it useful at temperatures as high as 80°C. 1.9.2 Silicon During the past few decades, silicon has been developed to be the world’s most widely produced semiconductor material, and as such is the most readily available for use in infrared systems, producing consistently high purity and sufficiently large quantities and dimensions to suit most applications. Investigations on the general optical properties of the material have been extensively reported over many years. Its refractive index and low dispersion properties are nearly as favourable as germanium. However, unlike germanium, no correlation between resistivity and transmissivity appears to exist, limiting the user to define “optical grade” material as the only procurement specification requirement available. Silicon is a robust, high melting point (1420°C) material that can be finished by ordinary glass working processes. On crystallisation it forms a diamond lattice structure that exists in either single or polycrystalline form. Two different methods of ingot production are used to obtain a high quality monocrystalline Si substrate material: the Czochralski (Cz) crystal pulling technique, where a seeded crystal is pulled from the melt in a silica crucible and permitted to grow in a mechanically unconstrained environment, permitting precise control of the crystal orientation and shape (standard grade), and the Float Zone (Fz) refining technique (premium hyperpure grade), where a seeded molten zone is supported by surface tension between two vertical cylindrical rods of the material and passed through a heated crucible, re-orientating and refining the crystal through its travel. The most noticeable optical difference between the two grades is the presence of a significantly more pronounced absorption band at approximately 9µm (1110 cm-1) in Cz material, and a reduced absorption profile in premium hyperpure grade (Fz) material beyond 20µm, following the multi-phonon absorption region, where the material exhibits a nearly complete transparency recovery. The transmittance of premium hyperpure grade (Fz) material is shown in Figure 1-24 The transmittance spectrum is free from major absorption from the electronic edge at 1.2µm up to about 6.5µm where the multi-phonon absorption commences.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

010002000300040005000600070008000900010000

Wavenumber (1/cm)

Tran

smitt

ance

1.001.502.002.503.003.50


Figure 1-24 Calculated transmission profiles of hyperpure Silicon (Si) at 293K for substrate thicknesses

between 1.0-3.5 mm


23

1.9.2.1 Silicon absorption. The intrinsic multi-phonon absorption properties of silicon, shown in Figure 1-25, show the predicted effects of temperature between 300K and 50K for two different thickness of substrate (0.5 & 3mm). Various interrelated factors determine the highly complex spectral structure of both silicon and germanium, comparative even to partially ionic II-VI semiconductors such as ZnS, ZnSe and CdTe where multi-phonon absorption is also present. The multi-phonon absorption profile exhibits a number of well-separated highly resonant absorption peaks in contrast to the fewer broader peaks exhibited by the II-VI materials. Additionally, because of the small anharmonic (non-linear propagation) broadening of the different vibration modes, many of the individual phonon absorption features in the spectrum remain distinct. More than twenty five different two and three phonon modes of vibration have been measured and reported[20] in silicon for this wavelength range involving all combinations of the two TO modes, two TA modes, LO mode and LA mode.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

250350450550650750850950105011501250135014501550

Wavenumber (1/cm)

Tran

smitt

ance

0.5mm-50K0.5mm-100K0.5mm-150K0.5mm-200K0.5mm-250K0.5mm-300K4mm-50K4mm-100K4mm-150K4mm-200K4mm-250K4mm-300K

0.5mm

4.0mm


Figure 1-25 Calculated multiphonon absorption profiles of standard optical Cz grade Si for thicknesses of

0.5 and 4.0 mm between 300-50K 1.9.2.2 Silicon dispersion The refractive index of the transparent region of silicon has been reported by a number of investigators

[21-24] using a variety of techniques. Each of these reports has found variations in accuracy such that no coherent set of temperature dependent dispersion profiles have emerged even though high purity optical quality single crystal material was used. This can be seen for various temperatures for material from differing sources in Figure 1-26. Consequently, the refractive index data derived for a temperature-dependent predictive dispersion model is the result of selective data across different wavelength regions.


24

3.38

3.40

3.42

3.44

3.46

3.48

3.50

3.52

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0

Wavelength (µm)

Ref

ract

ive

Inde

x (n

)

343K

104K

293K

Data Sources : Appendix F-2, F-9, F-10, F-13, F-14, F-15

Figure 1-26 Incomplete refractive index data of Silicon between 343 and 104K

The dispersion equation (1-9) producing the best fit to this disparate data set for ambient room temperature (293K) was derived by Edwards et al [23] (thick line) with the following modified Sellmeier expression.

( )n A B22

12

212

= + +−

ελ

λλ λ

(1-9)

where λ1 = 1.1071µm, ε = 1.16858x101, A = 9.39816 x 10-1 and B = 8.10461 x 10-3. From refractive index measurements at cryogenic temperatures published by Wolfe et al [25] , the temperature variation of the dispersion profiles were highly non-linear, providing spurious analysis results. However, the effects of temperature on the refractive index profile of silicon had been further investigated across a narrower temperature range (243-343K) by Barron[26] using a Buchdahl refractive index polynomial. Using this narrow wavelength range data, I was able to determine a temperature-dependant polynomial regression from which the refractive index profile illustrated in Figure 1-27 could be interpolated and extrapolated to provide the refractive index data required for the predicted model between 0.2-12µm. Beyond this wavelength, where there is a high degree of absorption, a constant value from the appropriate temperature profile was used, as shown in Figure 1-27.

n = A + Bλ + Cλ2 + Dλ3 + Eλ4 (1-10) where A = 1.600x10-4 T + 3.431, B = - 2.643x10-2, C = 4.324x10-3, D = - 3.194x10-4, & E = 8.835x10-6


25

3.36

3.38

3.40

3.42

3.44

3.46

3.48

0.0 2.0 4.0 6.0 8.0 10.0 12.0Wavelength (µm)

Ref

ract

ive

Inde

x (n

)50100150200250300300K

50KData Source : Appendix F-9

Figure 1-27 Temperature-dependent refractive index dispersion profile for Silicon (Si)

1.9.3 Zinc Selenide Zinc selenide is a clear yellow polycrystalline material with a grain size of approximately 70µm, transmitting in the range 0.5-15µm. It is essentially free of extrinsic impurity absorptions, providing extremely low bulk losses from scatter. The main identifiable extrinsic bulk absorption is zinc hydride, whose free diatomic molecule has a vibrational mode at 1608cm-1. Having a very low absorption of energy makes it useful for optical components in high power laser window and multispectral applications, providing good imaging characteristics. ZnSe is also useful in high resolution thermal imaging systems, where it is used to correct for colour distortion which is often inherent in other lenses used in the system. The predicted substrate transmittance spectra of II-VI CVD ZnSe shown in Figure 1-28, for substrate thicknesses between 2.0-4.5mm, has an observed electronic absorption edge at approximately 0.476µm (≈ 2.6eV) at 300K and far infrared multi-phonon absorption edge commencing at approximately 22.2µm

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

02500500075001000012500150001750020000

Wavenumber (1/cm)

Tran

smitt

ance

2.002.503.003.504.004.50


Figure 1-28 Calculated transmission profiles of Zinc Selenide (ZnSe) at 293K for thicknesses

between 2.0 and 4.5 mm


26

1.9.3.1 ZnSe absorption The multi-phonon lattice absorption of ZnSe has been extensively investigated since the first transmission and reflection measurements were made by Aven et al [27] on cubic ZnSe in 1961. Since neutron-scattering and Raman-scattering have become available in the early 1970’s, as has the increased availability of CVD ZnSe, investigations of ZnSe has demonstrated that in the three and four-phonon regions, ZnSe exhibits a characteristic structure consistent with predicted calculations by Bendow et al [28]. Figure 1-29, shows a predicted far-infrared transmission profile calculated for a thin specimen of CVD ZnSe (t = 0.5mm) material at temperatures ranging from 50-250K in the two-phonon region. Eight features have been identified to correspond with lattice absorption from published Raman spectroscopy characteristics [29-31] defined in Table 2.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

300320340360380400420440460480500

Wavenumber (1/cm)

50100150200250

12345678


Figure 1-29 Transmittance of calculated 0.5 mm thick CVD ZnSe in the 2-phonon absorption region for a

temperature range 50-250K

Table 2 2-Phonon absorption assignments for CVD ZnSe Feature Absorption Assignment Position (cm-1)

1 2A 300 2 O+A 329 3 2LA 362 4 2LA 380 5 TO+LA 401 6 2TO 412 7 LO+TO 430 8 2LO 448

Where features 1 and 2 are attributed to acoustic and optical+acoustic assignments due to unknown transverse or longitudinal modes. Characterisation involving three phonon absorption has required the use of thick specimens to provide adequate absorption profiles. Figure 1-30 shows a predicted far-infrared transmission profile calculated for a thick specimen of CVD ZnSe, (t = 3mm) material at temperatures ranging from 50-250K in the three-phonon region. Twelve features have been identified in this region to correspond with lattice absorption from the published Raman spectroscopy characteristics [29-31] as defined in Table 3.


27

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

450470490510530550570590610630650670

Wavenumber (1/cm)

50100150200250

91011121314151617181920


Figure 1-30 Transmittance of calculated 3 mm thick CVD ZnSe in 3-phonon absorption region for a

temperature range 50-250K

Table 3 3-Phonon absorption assignments for CVD ZnSe Feature Absorption Assignment Position (cm-1)

9 TO+2LA 466 10 2TO+TA 473 11 LO+2LA 484 12 LO+TO+TA 491 13 2LO+TA 509 14 2TO+LA 539 15 LO+TO+LA 557 16 2LO+LA 575 17 3TO 612 18 LO+2TO 630 19 2LO+TO 648 20 3LO 666

Detailed characteristics of the temperature dependence of multi-phonon absorption in ZnSe has further been investigated by Miles[32] where the bulk and surface absorption coefficients were measured by 10.6µm laser calorimetry between 20-300°C. Temperature variations of certain transverse and optical mode vibration frequencies were derived across this range to be approximately 10cm-1/°C. This effect can be observed from the long wavelength shifts illustrated in Figure 1-29 between the 50-250K predicted calculations. 1.9.3.2 Zinc Selenide dispersion At wavelengths between the visible and infrared regions, ZnSe behaves as a dielectric material, with a refractive index decreasing with increasing wavelength. The mean value of n being approximately 2.4 at 300K. Over this same region, the extinction coefficient k is very small (<10-5), providing uniformly high transmission. As a result of these characteristics, ZnSe has been used extensively for optical components and windows. Marple[33] derived the following Sellmeier type dispersion equation (1-11) at 300K with a claimed experimental error of ± 0.002 ;

n = +−

4 0 1900113

2

2. ..λ

λ (1-11 )

The effects of temperature on this refractive index profile was investigated across a narrow temperature range (243-343K) by Barron[34] using a Buchdahl refractive index polynomial. From this limited


28

data set, I could derive a temperature-dependant polynomial regression, in Equation 1-12, from which the refractive index profile illustrated in Figure 1-31 was interpolated and extrapolated to provide the refractive index data required for the predicted model for this material.

n = A + Bλ + Cλ2 + Dλ3 (1-12 ) where; A = 1.509x10-4 T + 2.407, B = -1.801x10-5 T - 2.564x10-4 C = 1.300x10-6 T - 1.308x10-5 , D = -3.878x10-8 T - 1.480x10-5

2.30

2.32

2.34

2.36

2.38

2.40

2.42

2.44

2.46

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0Wavelength (µm)

Ref

ract

ive

Inde

x (n

)

50100150200250300

300K

50K


Figure 1-31 Temperature-dependent refractive index dispersion profile for CVD Zinc Selenide (ZnSe)

1.9.4 Zinc Sulphide Zinc Sulphide (ZnS) exists both in a natural and synthetic crystalline form possessing cubic (Zinc blende) or hexagonal (Wurtzite) lattice structures. Substantial amounts of impurity, principally iron, are usually found in the composition of natural ZnS minerals that affect the physical and optical properties, preventing reproducible characterisation. A variety of techniques have been developed to obtain synthetic ZnS in large, high purity crystals, including evaporation, sublimation, high pressure growth from molten ZnS, and sintered hot-pressed polycrystalline ZnS (IRTRAN 2). For the purposes of this study, optical characterisation was performed on CVD ZnS (Cleartran®) material. This is chemically formed under low pressure, high temperature conditions through a reaction furnace to produce traditional ZnS which is then post deposition treated to improve scatter and homogeneity properties, by removal of zinc hydrides from the material. The transmittance of ZnS is shown in Figure 1-32, between 0.33 and 250µm at 293K for substrate thicknesses between 2-4.5mm. The electronic absorption edge at approximately 0.33µm corresponds to an energy band gap of 3.7eV, and a transparency region until approximately 10µm where multi-phonon absorption dominates. The short wavelength roll off is attributed to the combination of intrinsic Rayleigh scattering of microcrystals in its structure, and a significant contribution of extrinsic scattering caused by Zn-H (zinc hydride) impurity absorption and sulphur vacancies incorporated during the vapour growth process, as proposed by Lewis et al [35].


29

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

050001000015000200002500030000

Wavenumber (1/cm)

Tran

smitt

ance

2.002.503.003.504.004.50


Figure 1-32 Calculated Transmission profiles of ZnS at 293K for thicknesses between 2.0-4.5 mm

1.9.4.1 Zinc Sulphide absorption A number of investigations have been performed on the multi-phonon lattice absorption spectra of ZnS. However, it was not until 1980 when consistent thick samples of CVD polycrystalline ZnS became commercially available that definitive measurements of the two and three phonon regions could be made[36]. Klein and Donadio performed critical point analysis of two-phonon absorption modes from which the following features were identified. These are illustrated in Figure 1-33 for a predicted 1mm thick ZnS substrate in the temperature range 300-50K.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

500550600650700750800

Wavenumber (1/cm)

50100150200250300

11234567891011


Figure 1-33 Calculated transmittance of 1.0 mm thick ZnS in 2-phonon absorption region for a

temperature range of 50-300K

Table 3 2-Phonon absorption assignments for CVD ZnS Feature Phonon Assignment Position (cm-1)

1 LO+LA 526 2 TO+LA 530 3 LO+LA 544 4 2TO 596 5 2O 602


30

6 2O 612 7 2TO 636 8 LO+TO 650 9 2O 662

10 2LO 668 11 2LO 704

Features 5, 6 and 9 are attributed to optical assignments due to unknown transverse or longitudinal modes. 1.9.4.2 Zinc Sulphide Dispersion Feldman[37] measured the refractive index of ZnS at 293K from which the following polynomial regression coefficients could be fitted across the wavelength range from 1-18µm :

n = 2.29819 - 1.798x10-2 λ + 2.19x10-3 λ2 -1.614x10-4 λ3 + 2.538x10-6 λ4 (1-13)

The effects of temperature across the range 243-343K had been reported by Barron[38] across the 3-5µm and 7-12µm bands, from which I could determine the following temperature-dependent polynomial regression as illustrated in Figure 1-34.

n = A + Bλ + Cλ2 + Dλ3 + Eλ4 (1- 14) where ; A = 5.608x10-5 T + 2.282, B = -8.671x10-6 T - 1.563x10-2 C = 5.549x10-7 T + 2.067x10-3 , D = 2.597x10-8 T - 1.714x10-4 E = -9.798x10-10 T + 2.884x10-6

1.90

1.95

2.00

2.05

2.10

2.15

2.20

2.25

2.30

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Wavelength (µm)

Ref

ract

ive

Inde

x (n

)

50100150200250300

50K

300K


Figure 1-34 Temperature-dependent refractive index dispersion profile of Zinc Sulphide (300-50K)

This dispersion model was compared to measured values obtained by Wolfe et al [39] at 295.9 and 84.9K from which a mean variation in refractive index over the 2-14µm range averaged 0.02% representing only a 5x10-4 difference in refractive index. This is in good agreement with the experimental data and is subsequently used for the ZnS material predictive performance model. 1.9.5 Cadmium Telluride Of the long wavelength (>18µm) transparent II-IV materials available, cadmium telluride has proven to provide good optical performance across a wide range of temperatures and has provided adequate mechanical robustness to be used as a substrate material[40]. Compared to the limited selection of alternative materials capable of transmitting in these long wavelengths (viz. KRS-5, KRS-6, CsI, CsBr, Diamond) CdTe has a high resistance to moisture sensitivity, is available at a reasonable price and can operate at elevated filter deposition temperatures without disassociating. It is however also the softest of the II-VI materials and is most easily scratched or prone to cleaving. Its external transmittance spectrum is shown in Figure 1-35. The external


31

transmittance spectrum has an electronic absorption edge at approximately 0.83µm which corresponds to an energy band gap of 1.49eV at 293K, and a far-infrared multi-phonon absorption edge commencing at approximately 27µm. The multi-phonon absorption spectrum for CVD CdTe (20-40µm) is shown in Figure 1-36 for a predicted 3mm thick substrate for the temperature range 300K - 50K.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

020004000600080001000012000Wavenumber (1/cm)

Tran

smitt

ance

2.002.503.003.504.004.50


Figure 1-35 Calculated transmission profiles of Cadmium Telluride (CdTe) at 293K for thicknesses

between 2.0-4.5 mm

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

250300350400450500Wavenumber (1/cm)

Tran

smitt

ance

50100150200250300


Figure 1-36 Calculated transmittance of multi-phonon absorption profiles for 3.0 mm thick CdTe (300-50K)

1.9.5.1 Cadmium Telluride dispersion Marple et al [41] originally measured the refractive index at 300K from a prism of melt-grown material with polished surfaces in 1962 from which the following modified Sellmeier equation (1-15) was derived;

n A BC

= +−λ

λ

2

2 2 (1-15)

where A = 5.68, B= 1.53, and C2 = 0.366 For CVD material, in 1966 Ladd[42] was able to fit a modified Sellmeier equation of the following form and established a temperature coefficient of 1.0x10-4 /K


32

n2-1 = A1λ2/(λ2-λ21) + A2λ2/(λ2-λ2

2) (1-16)

with A1 = 6.1977889, A2 = 3.2243821, λ21 = 0.1005326µm2, and λ2

2 = 5279.518µm2. Subsequent measurements of CVD CdTe by Harvey and Wolfe[43] across a range of reduced temperatures (80-300K) provided adequate data for Barnes et al [44] to fit a temperature-dependant Sellmeier dispersion equation (1-17) of the form ;

( ) ( )n A BC

DE

= +−

+−

λλ

λλ

2

2

2

2 (1-17)

where ; A = -2.973x10-4 T + 3.8466, B = 8.057x10-4 T + 3.2215 C = -1.10x10-4 T + 0.1866, D = -2.160x10-2 T + 12.718 E = -3.160x101 T + 18753 The temperature-dependence of this model were derived in both linear form and using a quadratic polynomial. The temperature deviation from a straight line fit to the quadratic however resulted in a greater deviation in the quadratic than the experimental evidence suggested. This temperature dependant model as illustrated in Figure 1-37 has now been used to provide the dispersive index characteristics for the predicted performance calculations for this material.

2.60

2.62

2.64

2.66

2.68

2.70

2.72

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0Wavelength (µm)

Ref

ract

ive

Inde

x (n

)

30025020015010050

50K

300K


Figure 1-37 Temperature-dependent refractive index dispersion profile of Cadmium Telluride (300-50K)

1.10 Conclusion As a result of the research for this chapter, I have been able to bring together a wide range of disparate information sources to define the real part of the complex refractive index for the infrared materials selected. This has produced a concise set of temperature-dependent dispersive index models which can now be applied to the spectral measurements obtained from real substrate materials to determine their absorption properties and thus quantify their complex refractive index. This process has required extensive interpolation of the refractive index models to achieve the data point resolution and accuracy required to correspond with the measurements. This was performed using polynomial curve fitting algorithms in Microcal ORIGIN® software through which interpolations were calculated for both wavelength and temperature.

Spectral Characterisation of Infrared Optical Materials and FiltersDr. Gary J. Hawkins PhD Thesis (#R7935) - University of Reading, UK December 1998_________________________________________________________________________________________

33

CHAPTER 2PREDICTIVE BULK SUBSTRATE CHARACTERISATION

2.0 Introduction

The bulk optical properties of a crystalline substrate material are represented by the complex refractiveindex as a function of wavelength and temperature. Materials for the visible spectrum change comparatively littlewith temperature or wavelength. However, in the infrared every material is strongly influenced by the effects oflattice absorption and dispersion, with additional effects caused by pronounced changes with temperature. Theuse of predictive modelling of these properties can therefore be of considerable benefit in understanding thelimitations, or advantages, in the filter performance, which can be achieved from knowledge of the materialsprior to the multilayer design.

Modelling of these properties firstly requires the construction of a database for refractive index andextinction coefficient spectra, followed by computations to demonstrate the performance changes withtemperature and substrate thickness. By combining the temperature-dependent dispersion algorithms derived inChapter 1 with spectral measurements obtained for differing temperatures and substrate thicknesses, a databaseof calculated n and k substrate values can be implemented into the multilayer thin-film design process.

2.1 Absorption (αααα) and extinction coefficient (k) theory

The velocity of propagation of a electromagnetic wave through a solid is given by the frequency-dependent complex refractive index N n ik= − where the real part, n is related to the velocity, and k , theextinction coefficient is related to the decay, or damping of the oscillation amplitude of the incident electricfield. The optical properties of the solid are therefore governed by the interaction between the solid and theelectric field of the electromagnetic wave.

If a plane wave of frequency (f) propagates through a solid with velocity (ν) in a direction defined by(x), the electric field (E) is described by the following progressive wave equation:

[ ] E E i= 0 2exp π νf t - (x / (2-1)

Where, (E0) is the incident electric field vector and [ ] i2π νf t - (x / is the displacement at time t after a

disturbance, created by the electric field at a point situated at x along the line of propagation.

From Maxwell’s equations on electromagnetic theory, the speed of light in a vacuum c is related to thepermittivity of free space ε0, (the degree to which a medium can resist the flow of charge, defined by the ratio ofthe electric displacement to the intensity of the electric field that produces it), and the permeability of free spaceµ0 (the ratio of the magnetic flux density in a solid to the external magnetic field strength inducing it, µ = B/H.)by the equation c=1/(µ0ε0)

1.

The velocity of propagation through the solid of complex refractive index N n ik= − is related to thespeed of light in a vacuum, c, by ν = c N/ , then:

1

ν= −n

c

ik

c(2-2)

Therefore, substituting 1/ν into equation (2-1) above produces:

( )E = E exp ft expxn

expfkx

0 ii

c c2

2 2π

π π−

−

(2-3)

where the last term ( )− 2π x / cfk is a measure of the damping factor, or extinction coefficient (k).

As the power (P) or intensity of an incident wave through a solid is the conductivity (σ) of the solidmultiplied by the square of the electric field vector (P=σE2), then using the damping factor term, the fraction ofthe incident power that has propagated from position (o) to a distance (x) through the material with conductivity(σ) is given by:


34

( )( )

( )( )

P x

P 0

E x

E

fkx2

2= =−

σσ

π0

4exp

c(2-4)

from which the absorption coefficient (α) can be expressed in terms of the extinction coefficient (k) as:

απ

=4 fk

c(2-5)

As the velocity of light in a vacuum, c = fλ, then α = 4πk/λ, and the power or intensity is P = Poexp-αx.This equation is known as Bouguer’s law or Lambert’s law of absorption, by which radiation is absorbed to anextent that depends on the wavelength of the radiation and the thickness and nature of the medium. Theabsorption coefficient is therefore described as the reciprocal of the depth of penetration of radiation into a bulksolid, i.e., it is equal to the depth at which the energy of the radiation has decreased by the factor of e-αx, oralternatively, the intensity of the incident radiation is attenuated by the solid to 1/e of its initial value at adistance from the surface boundary defined by λ/4πk.

When electromagnetic radiation passes from one medium into another the values of the relativepermittivity εr and relative permeability µr must alter according to the characteristics of the materials. In additionto this, boundary conditions are required to be defined to ensure waves in the two media match at the interface.This requires the tangential components of E (electric field vector) and H (magnetic field vector) to becontinuous across the boundary, and the normal components of D (electric displacement vector) and B (magneticflux density vector) to also be continuous across the boundary.Hence, ε0ε1E1 = ε0ε2E2 and µ0µ1H1 = µ0µ2H2.

The optical impedance of a material is another useful parameter in considering reflection andtransmission of electromagnetic waves across an interface, Z=Ex/Hy=Ey/Hx=(µ0µr/ε0εr)

1. By substituting valuesfor ε0 (8.854x10-12 Fm-1) and µ0 (1.257x10-6 Hm-1), the impedance of free space Z0 = (µ0/ε0)

1 = 377Ω. Theoptical admittance of free space, Y, is given by Y = 1/Z0 = (ε0/µ0)

1 = 2.654x10-3Ω-1. In a dielectric with arelative permittivity given by εr and a relative permeability given by µr which is at unity, the admittance is givenby y = (ε0εr/µ0)

1 = Y εr1 = Y N = Y (n-ik)

The effects of thin-film interfaces can be calculated in terms of E and H, parallel to the boundary,however this notation can become cumbersome, particularly where exact values of εr and µr are not wellquantified, therefore a modified optical admittance η is introduced to connect H and E (η = H/E). At normalincidence, η = y = Y N, while at oblique incidence where the incident wave becomes polarisedηp = y/cosθ = Y N/cosθ and ηs = ycosθ = NY cosθ.

In the case of an absorbing material, the behaviour of a beam of radiation incident in a medium ofrefractive index n1 on an absorbing medium of complex refractive index n2 = n2-ik2, with an angle of incidenceθ1, using Snell’s law in complex form is then defined by:

n1sinθ1 = n2sinθ2 = (n2 - ik2)sinθ2 (2-6)

2.2 Loss-free incoherent internal reflection

When radiation originating in air (n=1) is incident on the surface of an optically transparent material,some of the radiation is reflected from the surface and some is transmitted into the material. The fraction ofradiation reflected for the electric and magnetic fields is given by:

( )( )

Rn

nE =

− −

+ −

cos sin

cos sin

θ θ

θ θ

2 22

2 22 (2-7)

Rn

nn

nn

nH =

− −

+ −

cos sin

cos sin

θ θ

θ θ

1

1

2 22

2 22 (2-8)


35

where, RE and RH are the fraction reflected of the electric and magnetic field vectors when the electric field isperpendicular to the incidence plane, and magnetic field is parallel to the incidence plane. θ is the angle ofincidence (measured from the normal to the surface) and n is the refractive index of the material. For natural(unpolarized) radiation at normal incidence (θ=0), the fraction of radiation reflected is the mean of these twoequations. This will determine the reflection from the front surface only. Before the radiation can exit from theopposite side, it undergoes a second reflection from the inside of the second surface boundary. This secondsurface reflection is further reflected back from the front surface again, producing multiple internal reflections. Ifthese reflections are all added up, the total theoretical external transmittance (Tab) of a polished, uncoated, planeparallel substrate, in a transparent region remote from the materials absorption edges, and with no scatteringwithin the material can be predicted from the real part of the refractive index (n) of the substrate.

Tn

nab =+

2

12(2-9)

The refractive index has also been characterised by an empirical relationship between the index ofrefraction and the energy gap of a semiconductor, known as the Moss rule[45],

nEg

=

Constant1

4

(2-10)

where Eg = semiconductor bandgap energy derived from the cut-on position of the short wavelength absorptionedge.

If no absorption losses are present in the substrate (k=0), and taking into account multiple internalreflections from both surfaces, the reflection coefficient is:

Rn

nab = −

+1

2

12(2-11)

In the range of frequencies in which the absorption is weak or absent(i.e. k2 << (n-1)2), and where there exists no second surface for internal reflections, the value of the reflectioncoefficient from the incident surface reduces to:

( )( )

Rn

na =

−+

1

1

2

2 (2-12)

Where losses occur during the propagation of a wave through the substrate, the imaginary part of thecomplex refractive index is added to the reflection coefficient as a frequency-independent measure of uniformlyattenuated radiation.

( )( )

Rn k

n ka =

− ++ +

1

1

2 2

2 2(2-13)

The extinction coefficient, k will only be zero when the conductivity (σ) of the material is zero, i.e. thematerial is essentially loss-free. If the conductivity is not zero, and the material is not perfectly transparent orreflective then the radiation experiences a loss. When the conductivity is high, both n and k become large andnearly equal, in this case the material becomes perfectly reflective.

The following illustration in Figure 2-1 summarises the effects of the reflections from the surfaces of aloss-free uncoated substrate.


36

Figure 2-1 Simplified energy flow through an uncoated substrate

Io = Radiation intensity on the incident surface of the substrate at an angle normal to the optical surfaceRa

- = Energy reflected from the incident surfaceTa

+ = Transmitted energy through the incident surfaceTb

- = Attenuated energy impinging on the second surfaceRb

- = Reflected energy from the second surface boundaryTb

+= Energy transmitted through the second surfaceTab = External transmittance observed through the substrateRab = Reflection coefficient of the substrate (1-Tab)

Where there are no absorption losses and using an incoherent source, the total reflectivity is thesummation of the multiple internal reflection intensities from the front and rear surfaces[46] :

Rab = Ra+ + Ta

+Rb+Ta

- [1 + Ra-Rb

+ + (Ra-Rb

+)2 + ... ] (2-14)this is equivalent to :

Rab = Ra+ + Ta

+Rb+Ta

- /(1 - Ra- Rb

+ ) (2-15)

As the values of T+ and T- are identical and where there are no absorption losses, such that Ra = Ra+ =

Ra- , Ta = Ta

+ = Ta- and Ra + Ta = 1, then:

R = R + R - 2 R R

1 - R Rab

a b a b

a b (2-16)

The total transmitted energy, by the same summation is given by:

Tab = Ta+ + Tb

+ [1 + Ra-Rb

+ + (Ra-Rb

+)2 + ... ] (2-17)

T = T T

1 - R Rab

a b

a b- +

(2-18)

Where there is no absorption, this can be re-arranged such that as Ra = 1-Ta andRb = 1-Tb then the total throughput transmittance is given by:

T

T T

ab

a b

=+ −

11 1

1 (2-19)

Figure 2-2 illustrates this relationship between the transmittance and reflectance of the front and rear surfacesand the total transmittance or reflectance of the substrate.

(a) (b)

Ra- Rb

-

Ta+ Tb

- Tb+

Rab

Tab

SecondSurface

Substrate

IncidentSurface t

Air Air

Incident

Radiation Io

n


37

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Ra=Rb, Ta=Tb

Rab

, Tab Rab

Tab

Figure 2-2 Calculated total transmittance (Tab) and reflectance (Rab) values for a loss free uncoated substrate.

Calculations of transmittance from the loss-free dispersive refractive index models used in this thesisfor predictive performance calculations are compared in Figures 2-3 to 2-7 with spectral measurements at 293Kacross the full interband region for each material using various substrate thicknesses. For the Group IV materialsin Figures 2-3 and 2-4, Ge and Si, the coincidence is in good agreement between the calculation andmeasurement (within 1%), validating the refractive index model, and illustrating the high transparency of thesematerials in the loss free interband regions. The Group II-VI materials in Figures 2-5 to 2-7 however show theextent of scattering caused by lattice vacancies and/or interstitial excess ions and impurity absorption present inthe crystalline structure of the material. The coincidence progressively improves towards long wavelength in allthese materials, where the effects of scattering are less pronounced and the material closely exhibits loss-freecharacteristics prior to the multi-phonon lattice absorption edge.

0.00

0.10

0.20

0.30

0.40

0.50

50010001500200025003000350040004500500055006000Wavenumber (1/cm)

Tra

nsm

ittan

ce

Calculation

Measurement

Figure 2-3 Overlay of predicted loss-free dispersive refractive index model of Germanium at 293K compared toa spectral measurement for a 1.3mm thick uncoated substrate (1.6-20µm)


38

0.00

0.10

0.20

0.30

0.40

0.50

0.60

10002000300040005000600070008000900010000

Wavenumber (1/cm)

Tra

nsm

ittan

ceCalculation

Measurement

Figure 2-4 Overlay of predicted loss free dispersive refractive index model of Fz Silicon at 293K compared to aspectral measurement for a 1.9mm thick uncoated substrate (1-10µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0200040006000800010000120001400016000180002000022000

Wavenumber (1/cm)

Tra

nsm

ittan

ce

Calculation

Measurement

Figure 2-5 Overlay of predicted loss free dispersive refractive index model of Zinc Selenide at 293K comparedto a spectral measurement for a 4.8mm thick uncoated substrate (0.45-40µm)


39

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

050001000015000200002500030000

Wavenumber (1/cm)

Tra

nsm

ittan

ce

Calculation

Measurement

Figure 2-6 Overlay of predicted loss free dispersive refractive index model of Zinc Sulphide at 293K comparedto a spectral measurement for a 2.5mm thick uncoated substrate (0.3-40µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0100020003000400050006000700080009000100001100012000

Wavenumber (1/cm)

Tra

nsm

ittan

ce Measurement

Calculation

Figure 2-7 Overlay of predicted loss free dispersive refractive index model of Cadmium Telluride at 293Kcompared to a spectral measurement for a 2.0mm thick uncoated substrate (0.85-40µm)

2.3 Incoherent multiple internal reflection including absorption

Figure 2-8 illustrates the effects of incoherent multiple internal reflections on the energy flow through afinite thickness substrate. For a given optical substrate of finite thickness (t), absorption coefficient (α), andreflectivity from front and rear surfaces of (Ra

-) and (Rb+), the amount of transmitted radiation traversing the first

interface Ta+ will be (1-Ra

+)Io, where Io is the intensity of the incident wave. After travelling through a distance(t) of the substrate the incident radiation is attenuated by e-αt. The radiation therefore reaching the secondinterface (Ta

-) is (1-Ra+)Ioe

-αt. Due to reflection (Rb-) at the interface of the second surface, only the fraction given

by (1-Ra+)(1-Rb

-)Ioe-αt will emerge. The amount internally reflected as Rb

-(1-Rb-)Ioe

-αt will become progressivelymore attenuated as a result of the multiple internal reflections becoming absorbed within the material oremerging as a negligible contribution compared to the first order reflectivity.


40

(1-R)Io e

R(1-R)Io e

R (1-R)Io e3

R (1-R)Io e

R (1-R)Io e

Negligible

--

R(1-R) Io e2

RIo

Io

2

R (1-R)Io e

R (1-R)Io e

R (1-R)Io e4

3

2

4

- ααααt4

- tαααα4

-2ααααt

R(1-R)Io e

2ααααt

(1-R)Io

a

-2 tαααα

t

2(n-1)R (1-R) Io e2 -2n-1

αααα

ααααt

R (1-R) Io e

R (1-R) Io e

- ααααt5

- tαααα3

- ααααt3

4-5

5

-2

23

(1-R) Io e

-ααααt

- ααααt

b

2 tαααα-

αααα

2α2α2α2α

t

2(1-R) e-

1-R e2 -

t

tIo

Figure 2-8 Analysis of the energy flow through a substrate of finitethickness inclusive of multiple internal reflections.

The results of these multiple internal reflections produce an overall external transmittance (Tab) given by:

( )( )T

R R

R Rab

a bt

a bt

=− −

−

+ − −

+ − −

1 1

1 2

exp

exp

α

α (2-20)

Where the 2nd order internal reflection term becomes negligible if the thickness becomes very large,reducing the external transmission coefficient (Tab) to:

( )( )T R Rab a bt= − −+ − −1 1 exp α (2-21)

If a homogeneous substrate is used, where Ra+ = Rb

- = R, Ta = Tb = 1 - R, and I0 = incident intensity,then the transmitted intensity (I) becomes:

( )I

I 0 =

−−

−

−

1

1

2

2 2

R

R

t

t

exp

exp

α

α (2-22)

All higher order internal reflections are negligible compared to the 2nd order term and as such areignored in the derivation.

Prediction of an uncoated substrate transmission can therefore be calculated across a range ofthicknesses from the determination of the absorption coefficient (α) using a reference measurement providingthe dispersive bulk refractive index is known.

For high substrate thickness values, particularly in spectral wavelength regions where there is highabsorption, the 2nd order denominator term can be neglected when compared to the size of the numerator,therefore:

( )I I 0 = − −12

R texp α (2-23)

or by re-arranging :

( )αt = ln I - ln I + 2 ln 1- R0 (2-24)

from which the absorption coefficient (α) can be derived :


41

( )

α =

+

±ln

T T T T R R T

T

a b a b a b ab

ab

224

2

t (2-25)

The effects of these equations on the overall transmittance through an uncoated substrate are illustratedin Figures 2-9 and 2-10. Figure 2-9 shows the variation in external transmittance vs absorption coefficient (α)for different refractive indices calculated for a 1mm substrate, where in regions containing high absorption theeffect on the transmittance caused by inaccurate refractive index data is progressively less pronounced than inregions of low absorption. Therefore in the electronic and lattice absorption regions of the spectrum reasonablyaccurate predictive models are still achievable and valid, though exact values of n maybe unobtainable.

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50Absorption Coefficient (1/cm)

Tra

nsm

issi

on (

%)

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

n=1

n=6

Figure 2-9 Variation in transmission (Tab) vs absorption coefficient (α) for different refractive indicesbetween 1.0-6.0 for a 1mm substrate.

In comparison to this, Figure 2-10 shows the effect of the absorption coefficient on differingthicknesses of substrate for a fixed refractive index (n=4), where in regions of high absorption, the transmittancefalls rapidly with increasing substrate thickness, and in regions of low absorption the effect of thickness is lesspronounced. Hence there is a desire to use differing substrate thicknesses for the accurate determination of thecomplete material absorption profile.


42

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45 50Absorption Coefficient (1/cm)

Tra

nsm

issi

on (

%)

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

0.5mm

3mm

Figure 2-10 Variation in transmission (Tab) vs absorption coefficient for different thicknesses of Germaniumin the range (0.5 - 3.0mm) at 10µm.

Additionally, if the dispersive refractive index or surface reflectivities of the substrate are unknown,then by measuring two samples of different thicknesses (t1 and t2), a value of α can be obtained from Equation 2-26, as illustrated in Figure 2-11, where the absorption coefficient is compared between a single thicknesscalculation of known dispersive index and subtractive calculations from two substrates of known thickness.

( )T

T

ab

ab

t t1

2

2 1= − −exp α(2-26)

This method can also be used for determination of the extinction coefficient using Lambert’s law ofabsorption, which relates the transmittance (T), thickness (t) and values of k through the equation

λπ /4 kteT −= (2-27)For two known thicknesses values of k are then obtained from:

( )[ ]12

2

1

4

ln

tt

TT

k−

=π

λ(2-28)

where the wavelength λ is in the same units as t

0

5

10

15

20

25

30

35

250300350400450500550600650700

Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-11 Comparison of absorption coefficient calculations for Germanium between single thickness (solid)and subtractive calculations from two differing substrate thicknesses (dashed).


43

The absorption coefficient (α) profiles in Figures 2-12 to 2-21 illustrate the implementation of theabsorption Equation 2-25 to calculate the far-infrared multi-phonon and electronic absorption databases fromwhich predictive uncoated substrate performances are calculated.

0

5

10

15

20

25

30

050100150200250300350400450500550600650700750800

Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-12 Far-infrared multi-phonon absorption profile of measured Germanium at 293K (12.5-250µm)

0

20

40

60

80

100

120

140

45004700490051005300550057005900610063006500

Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-13 Electronic absorption profile of Germanium at 293K (1.54-2.2µm)


44

0

2

4

6

8

10

02004006008001000120014001600Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-14 Far-infrared multi-phonon absorption profile of measured Fz hyperpure Siliconat 293K (6.25-250µm)

0

5

10

15

20

25

30

35

40

45

800082008400860088009000920094009600980010000Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-15 Electronic absorption profile of Fz Silicon at 293K (1-1.25µm)

0

5

10

15

20

0100200300400500600700800Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-16 Far-infrared multi-phonon absorption profile of measured ZnSeat 293K (12.5-250µm)


45

0

5

10

15

20

15000160001700018000190002000021000

Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-17 Electronic absorption profile of ZnSe at 293K (0.47-0.67µm)

0

5

10

15

20

25

30

35

40

020040060080010001200

Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-18 Far infrared multi-phonon absorption profile of measured ZnSat 293K (8.3-250µm)

0

5

10

15

20

25

30

35

2000021000220002300024000250002600027000280002900030000

Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-19 Electronic absorption profile of ZnS at 293K (0.33-0.5µm)


46

0

5

10

15

20

25

30

35

250300350400450500550600Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-20 Far-infrared multi-phonon absorption profile of measured CdTeat 293K (16.6-40µm)

0

5

10

15

20

25

30

35

40

45

100001025010500107501100011250115001175012000Wavenumber (1/cm)

Abs

orpt

ion

Coe

ffic

ient

(1/

cm)

Figure 2-21 Electronic absorption profile of CdTe at 293K (0.83-1µm)

2.4 Predictive substrate thickness calculations

In order to predict the characteristic absorption profiles of the uncoated substrate material, a referencespectral database was first created containing the transmission profile together with details of the appropriaterefractive index profile corresponding to the measurement temperature for the sequential series of wavenumberpoints and substrate thickness. Obtaining a highly accurate transmission measurement from this referencesubstrate was essential to achieve a good accuracy for the predicted model, as all subsequent calculations will beperformed on the information contained within this initial spectral database. Using this reference data and theinternal reflectance algorithms defined in Section 2.3, the absorption coefficient (α) and extinction coefficient(k) were calculated. From this reference absorption profile in combination with the real part of the predicteddispersion profile derived in Chapter 1, the spectral profiles of alternative substrate thicknesses were determined.

To obtain an accurate reference database, the use of differing thicknesses of reference substrate materialwas preferred. This ensured the transmission profile of the differing strong and weak absorption regions wereexhibited to best effect. By definition, the absorption coefficient represents the amount of absorption per unitthickness. Therefore, the accuracy of the calculation should be as valid for thin specimens as for thickerspecimens, provided in thin specimens coherent multiple internal reflection effects are not present. However, asthe number of multiple internal reflection passes are less in a thick specimen, the exponential attenuation is morepronounced, and the accuracy of the calculated absorption coefficients is therefore greater. However, in


47

materials that possess regions of high absorption, the attenuation through a thin specimen is less pronounced, andcan exhibit a spectral structure which is otherwise saturated in thicker specimens. Thin specimens were thereforepreferably used in these high absorption regions for deriving the absorption coefficient profile, as the thickerspecimens became limited by the radiometric measurement accuracy of the spectrometer, producing absorptionprofiles with considerable noise and unsuitable for use in the reference database.

The choice of reference substrate thickness was therefore governed by two constraints, depending onthe absorption characteristics in the regions of interest. Where a material exhibits a low absorption spectrum, athicker substrate was used to enhance the characteristics of the material. Where strong absorption bands arepresent thinner specimens were used in those regions to resolve the individual characteristics of the absorptionbands within the material. The topographic illustrations in Figures 2-22 to 2-26 show the effect of the farinfrared absorption characteristics verses thickness for the different materials selected.

Figures 2-27 to 2-34 shows the results of predicted performance calculations in the electronic andmulti-phonon absorption regions for each of the infrared materials selected across a range of thicknesses. It canbe seen as the thickness is increased the electronic absorption edge shifts to longer wavelengths resulting in areduced transparency bandwidth of the substrate. The size of this shift (dλ/dT) for Ge, Si, ZnSe, ZnS & CdTe is0.0274, 0.0147, 0.0062, 0.0052 & 0.0046 µm/mm respectively. From these spectra an estimation of theexpected loss in transmission as a function of thickness can be derived.

1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100

1

2

3

4

5

6

0.4-0.6

0.2-0.4

0-0.2

Figure 2-22 Germanium absorption topography - plan view (thickness 1-6mm at 293K)

1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100

1

2

3

4

5

6

0.4-0.6

0.2-0.4

0-0.2

Figure 2-23 Fz Silicon absorption topography - plan view (thickness 1-6mm at 293K)

1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100

1

2

3

4

5

6

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

Figure 2-24 Zinc Sulphide absorption topography - plan view (thickness 1-6mm at 293K)


48

1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100

1

2

3

4

5

6

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

Figure 2-25 Zinc Selenide absorption topography - plan view (thickness 1-6mm at 293K)

1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100

1

2

3

4

5

6

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

Figure 2-26 Cadmium Telluride absorption topography - plan view (thickness 1-6mm at 293K)

0.00

0.10

0.20

0.30

0.40

0.50

050100150200250300350400450500550600650700750800

Wavenumber (1/cm)

Tra

nsm

ittan

ce

1.00

1.50

2.00

2.50

3.00

3.50

Figure 2-27 Predicted far-infrared multi-phonon absorption of uncoated Gefor substrate thicknesses of 1.0-3.5mm at 293K (12.5-250µm)


49

0.00

0.10

0.20

0.30

0.40

0.50

470048004900500051005200530054005500560057005800590060006100

Wavenumber (1/cm)

Tra

nsm

ittan

ce

1.00

1.50

2.00

2.50

3.00

3.50

Figure 2-28 Predicted electronic absorption edge of uncoated Ge for substrate thicknesses of 1.0-3.5mm at 293K (1.64-2.13µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

02004006008001000120014001600

Wavenumber (1/cm)

Tra

nsm

ittan

ce

1.00

1.50

2.00

2.50

3.00

3.50

Figure 2-29 Predicted far-infrared multiphonon absorption of uncoated Fz Sifor substrate thicknesses of 1.0-3.5mm at 293K (6.26-250µ)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

800082008400860088009000920094009600980010000

Wavenumber (1/cm)

Tra

nsm

ittan

ce

1.00

1.50

2.00

2.50

3.00

3.50

Figure 2-30 Predicted electronic absorption edge of uncoated Fz Sifor substrate thicknesses of 1.0-3.5mm at 293K (1-1.25µm)


50

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0100200300400500600700800

Wavenumber (1/cm)

Tra

nsm

ittan

ce2.00

2.50

3.00

3.50

4.00

4.50

Figure 2-31 Predicted far-infrared multi-phonon absorption of uncoated ZnSe for substrate thicknesses of 2.0-4.5mm at 293K (12.5-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

1500016000170001800019000200002100022000

Wavenumber (1/cm)

Tra

nsm

ittan

ce

2.00

2.50

3.00

3.50

4.00

4.50

Figure 2-32 Predicted electronic absorption edge of uncoated ZnSefor substrate thicknesses of 2.0-4.5mm at 293K (0.45-0.67µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0100200300400500600700800900100011001200Wavenumber (1/cm)

Tra

nsm

ittan

ce

2.00

2.50

3.00

3.50

4.00

4.50

Figure 2-33 Predicted far-infrared multi-phonon absorption of uncoated ZnSfor substrate thicknesses of 2.0-4.5mm at 293K (8.3-250µm)


51

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

1000012000140001600018000200002200024000260002800030000Wavenumber (1/cm)

Tra

nsm

ittan

ce2.00

2.50

3.00

3.50

4.00

4.50

Figure 2-34 Predicted electronic absorption edge of uncoated ZnSfor substrate thicknesses of 2.0-4.5mm at 293K (0.33-1.0µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

250275300325350375400425450475500525550575600Wavenumber (1/cm)

Tra

nsm

ittan

ce

2.00

2.50

3.00

3.50

4.00

4.50

Figure 2-35 Predicted far-infrared multi-phonon absorption of uncoated CdTefor substrate thickneses of 2.5-4.5mm at 293K (16.7-40µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

80008500900095001000010500110001150012000Wavenumber (1/cm)

Tra

nsm

ittan

ce

2.00

2.50

3.00

3.50

4.00

4.50

Figure 2-36 Predicted electronic absorption edge of uncoated CdTefor substrate thicknesses of 2.0-4.5mm at 293K (0.83-1.25µm)


52

2.4.1 Thickness model validation

In order to validate the integrity of the n and k dispersion models derived by this method of analysis,spectral performance calculations of alternative thicknesses of substrate have been carried out. These revealtransmission profiles to be accurate to within approximately 1% of the measurement result. Figures 2-37 and 2-38 show the performance variation between the calculated and measured results of alternative substratethicknesses in both the far-infrared multi-phonon, and near-infrared electronic absorption regions of Germanium.Figure 2-39 is an overlay of the transmission variations exhibited for the far-infrared region, illustrating the sizeof the error envelope using this method.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

2503003504004505005506006507007508008509009501000Wavenumber (1/cm)

Tra

nsm

itta

nce

5.00C5.00M

2.85C2.85M1.30C

1.30M1.09C

1.09M0.84C0.84M

0.41C0.41M

5.0mm

0.41mm

2.85mm

1.3mm

C :- CalculatedM :- Measured

1.09mm

0.84mm

Figure 2-37 Overlay of predicted and measured spectral profiles of Germanium for various substrate thicknessesat 293K (8-40µm)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

450047505000525055005750600062506500Wavenumber (1/cm)

Tra

nsm

itta

nce

5.00C

5.00M

1.30C

1.30M

0.84C

0.84M

0.41C

0.41M

C :- CalculatedM :- Measured

Figure 2-38 Overlay of calculated and measured spectral profiles of the Germanium electronic absorption edgefor various substrate thicknesses at 293K (1.54-2.2µm)


53

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

2503003504004505005506006507007508008509009501000Wavenumber (1/cm)

Tra

nsm

itta

nce

Var

iati

on5.00

2.85

1.30

1.09

0.84

0.41

Figure 2-39 Variation between calculated and measured spectral profiles of Germanium multi-phononabsorption for various substrate thicknesses at 293K (10-40µm)

2.5 Reduced substrate-temperature effects

The transmittance of all optical substrate materials used in the far-infrared are strongly temperaturedependent. When these materials are used at reduced cryogenic temperatures, the ambient room temperature dataon the optical properties is frequently inadequate for obtaining an accurate predictive performance model.

In semiconductor materials, the most dominant absorption mechanism is caused by two-phononabsorption. As the temperature reduces, the two-phonon absorption bands become significantly weaker andnarrower, increasing the transparency bandwidth of the material. The absorption in this region results from thecombined effect of two inter-related mechanisms, (i) the electric moment (M) associated with the distributedcharge density of the atomic bonding, to which the incident radiation couples, and (ii) anharmonic interactionsdistributed between the atomic charge density states of the crystal. As the phonon vibration modes are excited byinteraction with the electric moment (M), they may also further dissipate energy through anharmonic interactionswithin the crystal, creating additional harmonics to that caused by the primary coupling absorption mechanism.As the temperature is reduced the lattice contracts and oscillations of the atoms about their equilibrium pointsreduces. This in turn reduces the size of the phonon vibration amplitudes and subsequently reduces the intensityof the absorption profile. The detailed effects of temperature on the thermal vibrations of a crystal lattice is ahighly complex branch of semiconductor theory, and is outside the realm of this thesis.

The availability of information on the optical properties of infrared materials at reduced temperatures islimited, even non-existent, from most reference literature sources. Stierwalt[47] measured the transmittancespectra of BaF2, Sapphire, KRS-5, Irtran 2 (ZnS) and Quartz materials at 77 and 4K in the early 1980’s using aBeckman IR-3 spectrophotometer. To make these low temperature measurements, a sample dewar wasconstructed to fit into the gas compartment of the spectrophotometer comprising a central liquid helium chamberto which the sample was attached. Surrounding this was a copper radiation shield cooled with liquid nitrogen andfitted with KBr windows. Results from this experiment showed a significant reduction in absorption coefficient,falling to nearly half its room temperature value at 4K. Most other literature references detail the temperaturedependence of specific isolated absorption features and predict deviations through multi-phonon theory. Aninvestigation into the effects of temperature is therefore opportune to characterise the performance of substratematerials operating at reduced temperature.

In this thesis, changes of profile in the multi-phonon absorption region have been used to predict theperformance of the materials at reduced temperatures. Low temperature measurements of the materials reportedhere was performed using a Perkin Elmer Spectrum 2000 optica FTIR spectrophotometer, to which a AirProducts Displex DE202 cryogeneic cooler, fitted with KRS-5 windows, was attached. Samples were clampedto the cold finger of the cooler in a fixture using screws and indium shims to ensure intimate thermal contact.


54

Stabilised temperature control was achieved using an in-built controlled heater regulated by a temperaturemeasurement from a reverse biased diode. Experimentally no evidence of temperature changes due to either thepresence or absence of illumination from the spectrophotometer infrared source were observed.

Figures 2-40 to 2-44 show the calculated extinction coefficient (k) profiles derived for the selectedsubstrate materials between 300-50K which were obtained from analysis of these spectral measurements. Bycombining the appropriate temperature-dependent dispersive refractive index data to the extinction coefficientprofiles produced a predicted complex refractive index model which was subsequently interpolated to determinethe spectral profile of materials of alternative thickness and temperatures. Predicted far-infrared transmittanceprofiles for a 2mm thick substrate are illustrated for each material between 300 and 50K in Figures 2-45 to 2-49.Appendix B lists the temperature-dependent polynomial regression analysis derived from the measurements foreach of the materials, from which the transmittance profile of alternative temperatures can be derived.

1E-05

1E-04

1E-03

1E-02

2503003504004505005506006507007508008509009501000

Wavenumber (1/cm)

Ext

inct

ion

Coe

ffici

ent

(k)

300K

250K

200K

150K

100K

50K

50K

300K

Figure 2-40 Calculated extinction coefficient (k) profiles from measured Germaniumat temperatures between 300-50K (10-40µm)

1E-05

1E-04

1E-03

300400500600700800900100011001200130014001500Wavenumber (1/cm)

Ext

inct

ion

Coe

ffici

ent (

k)

300K

250K

200K

150K

100K

50K

300K

Figure 2-41 Calculated extinction coefficient (k) profiles from measured Cz Siliconat temperatures between 300-50K (6.7-33.3µm)


55

1E-05

1E-04

1E-03

1E-02

300350400450500550600650700Wavenumber (1/cm)

Ext

inct

ion

Coe

ffici

ent

(k)

300K

250K

200K

150K

100K

50K

300K

50K

Figure 2-42 Calculated extinction coefficient (k) profiles from measured ZnSeat temperatures between 300-50K (14.3-33.3µm)

1E-06

1E-05

1E-04

1E-03

1E-02

50060070080090010001100

Wavenumber (1/cm)

Ext

inct

ion

Coe

ffici

ent

(k)

300K

250K

200K

150K

100K

50K

300K

50K

Figure 2-43 Calculated extinction coefficient (k) profiles from measured Zinc Sulphideat temperatures between 300-50K (10-20µm)

1E-06

1E-05

1E-04

1E-03

1E-02

250300350400450500550Wavenumber (1/cm)

Ext

inct

ion

Coe

ffici

ent

(k)

300K

250K

200K

150K

100K

50K

50K

300K

Figure 2-44 Calculated extinction coefficient (k) profiles from measured CdTe at temperatures between 300-50K (20-40µm)


56

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10 15 20 25 30 35 40

Wavelength (um )

Tra

nsm

itta

nce

300

250

200

150

100

50

Figure 2-45 Calculated transmission profile of 2.0mm thick uncoated Germaniumat temperatures between 300-50K (10-40µm)

0

0.1

0.2

0.3

0.4

0.5

0.6

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Wavelength (um )

Tra

nsm

itta

nce 300

250

200

150

100

50

Figure 2-46 Calculated transmission profile of 2.0mm thick uncoated Cz Siliconat temperatures between 300-50K (6-20µm)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Wavelength (um )

Tra

nsm

itta

nce

300

250

200

150

100

50

Figure 2-47 Calculated transmission profile of 2.0mm thick uncoated ZnSeat temperatures between 300-50K (10-30µm)


57

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 11 12 13 14 15 16 17 18 19 20

Wavelength (um )

Tra

nsm

itta

nce 300

250

200

150

100

50

Figure 2-48 Calculated transmission profile of 2.0mm thick uncoated ZnSat temperatures between 300-50K (10-20µm)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

15 20 25 30 35 40Wavelength (um )

Tra

nsm

itta

nce

300

250

200

150

100

50

Figure 2-49 Calculated transmission profile of 2.0mm thick uncoated CdTeat temperatures between 300-50K (15-40µm)

For the electronic absorption edge, the effects of reduced temperature on the forbidden energy gapreduces the size of the gap proportionately to the square of the temperature, shifting the edge position to shorterwavelengths. This shift has been fitted for various materials by the following empirical relationship[48] :

E T ET

Tg g( ) ( )= −+

02αβ

(2-29)

where Eg(0) is the value of the energy gap at zero Kelvin and α and β are constants. The effect of this shortwavelength shift is shown in Figure 2-50 for Germanium and Silicon, where the shift in absorption edge position(dλ/dT) is approximately 0.7nm/K for Germanium and 0.15nm/K for Silicon.


58

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

0 50 100 150 200 250 300

Temperature (K)

Wav

elen

gth

(um

)

Ge

Si

Figure 2-50 Variation in semiconductor edge position with temperature for Germanium and Silicon.

2.5.1 Temperature model verification

In order to verify the accuracy of the calculated absorption profiles, derived using the dispersive n and kdatabase. Examples of the calculated deviations between the predicted and measured values are shown in Figures2-51 and 2-52 for germanium and silicon. These results show a reasonable agreement between the calculatedmodel and the measured spectral performance, to within a mean experimental accuracy of approximately 1% forgermanium and 2% for silicon. The difference in deviation between the calculations of the germanium andsilicon reinforces the need for a highly accurate set of reference measurements from which the extinctioncoefficient (k) database is derived. This is an area of research which would benefit re-visiting in the future, withincreased temperature control and stability, a greater accuracy is achievable.

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

250300350400450500550600650700750800Wavenumber (1/cm)

Tra

nsm

issi

on (

%)

Dev

iati

on

300

250

200

150

100

50

Figure 2-51 Overlay of transmittance deviation between calculated transmittanceand measured profiles for Ge at 300, 250, 200, 150 and 50K


59

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

250350450550650750850950105011501250135014501550Wavenumber (1/cm)

Tra

nsm

issi

on (

%)

Dev

iati

on

300

250

200

150

100

50

Figure 2-52 Overlay of transmittance deviation between calculated transmittanceand measured profiles for Cz Si at 300, 250, 200, 150 and 50K

2.6 Angle of incidence effects

The reflection and refraction of plane waves at a boundary between two media of differing propertiesare well known[49], following Snell’s law and the Fresnel formulas. A plane wave incident on a dielectricdiscontinuity is split into two waves; the transmitted wave proceeding into the second medium and the reflectedwave propagating back into the incident medium from which the following relation is derived.

n1 sin θi = n1 sin θr = n2 sin θt (2-30)

where θi, θr, and θt are the incident , reflected and transmitted angles, and n1 & n2 are the refractive indices of theincident and transmitted mediums. As (θr = θi) then the transmitted angle θt into the second medium is definedas:

sinsinθ θ

tin

n= 1

2

(2-31)

Although this is true for all forms of electromagnetic wave propagation, the dynamic properties ofreflected and transmitted waves, such as intensity, phase changes, polarization effects depend entirely upon thespecific nature of the wave propagation and the interface conditions. At an uncoated substrate boundary with aplane wave incident at an oblique angle, the electric and magnetic field vectors are split into two polarizationcomponents that are parallel (p) and perpendicular (s) to the incident plane. Both the transmitted and reflectedpolarization components can be calculated for each orientation separately and then combined to produce aresultant mean polarization effect.

The p-wave is also known as a TM wave, (as the magnetic field vector H is transverse to the plane ofincidence), and the s-wave is alternatively known as a TE wave, (as the electric field vector E is transverse to theplane of incidence). The conventions for defining the reflection and refraction of s and p polarized waves areillustrated in Figure 2-53.


60

(a) (b)

Figure 2-53 Reflection and refraction of p(a) and s (b) polarization waves

The Fresnel reflection and transmission coefficient formulas for these s and p polarizations are :s-polarization

rn n

n ns = −+

1 1 2 2

1 1 2 2

cos cos

cos cos

θ θθ θ

(2-32), tn

n ns =+

2 1 1

1 1 2 2

cos

cos cos

θθ θ

(2-33)

p-polarization

rn n

n np = −+

1 2 2 1

1 2 2 1

cos cos

cos cos

θ θθ θ

(2-34), tn

n np =+

2 1 1

1 2 2 1

cos

cos cos

θθ θ

(2-35)

These formulae give the ratio of the amplitude of the reflected and transmitted waves relative to theamplitude of the incident wave. The total energy reflected from the boundary and transmitted into the substrate isthe square of the Fresnel coefficients. Figures 2-54 to 2-56 illustrate the variation of loss-free transmitted andreflected energy with angle of incidence for refractive index values of 1.25 to 4.0 (in 0.25 increments) for the s,p and mean polarizations.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 10 20 30 40 50 60 70 80 90Angle (Deg)

Ref

lect

ance

/ T

rans

mitt

ance

Figure 2-54 R and T vs Angle of incidence for n = 1.25-4.0 P-Polarization

H

E

H

E

H

E

i

rp

tp

no n1

θ1

θ2

iH

E H

E

H

E

rs

ts

θ2

θ1

no n1


61

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 10 20 30 40 50 60 70 80 90Angle (Deg)

Ref

lect

ance

/ T

rans

mitt

ance

Figure 2-55 R and T vs Angle of incidence for n = 1.25-4.0 S-Polarization

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 10 20 30 40 50 60 70 80 90Angle (Deg)

Ref

lect

ance

/ T

rans

mitt

ance

Figure 2-56 R and T vs Angle of incidence for n = 1.25-4.0 Mean - Polarization

For normal incidence there is no difference between the s and p polarizations and the Fresnelreflectance and transmittance energies become Equations 2-36 and 2-37.

R Rn n

n ns p= = −+

1 2

1 2

2

(2-36),

( )T T

n n

n ns p= =

+4 1 2

1 2

2 (2-37)

The Fresnel coefficients rs , rp , ts , tp change differently as a function of the angle of incidence, with thereflectance of the s wave always being greater than the p wave. In Figure 2-54 it can be seen the reflectance ofthe p-polarization falls to zero at a definite angle (Brewster’s angle). At this particular angle, the result of theFresnel reflectance (rp) and refracted transmission (tp) waves are at an angle of 90° to each other which producesa reflected beam which is plane polarized in the plane of incidence with oscillations parallel to the surface, andelectric vector perpendicular to the plane of polarization. The angle at which this occurs is given by θB = tan-1 n2

/ n1 , which for Ge, Si, CdTe, ZnSe and ZnS are at angles of 76.0°, 73.6°, 69.5°, 67.4°, and 65.6° respectively.


62

This effect is most noticeably observed in the predicted p-polarization spectra illustrated in Figures 2-57, 60, 63,66, and 69, where there is a reduced transmission at angles greater than the Brewster angle, reducing theresultant mean-polarization throughput.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0100020003000400050006000Wavenumber (1/cm)

Tra

nsm

itta

nce

89

50403020

100

70

60

80

Figure 2-57 Calculated Ge P-Polarization (0-89°) at 293K (1.67-250µm)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0100020003000400050006000Wavenumber (1/cm)

Tra

nsm

itta

nce

010

203040

5060

708089

Figure 2-58 Calculated Ge S-Polarization (0-89°) at 293K (1.67-250µm)


63

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0100020003000400050006000Wavenumber (1/cm)

Tra

nsm

itta

nce

89

80706050

4030

20100

Figure 2-59 Calculated Ge Mean-Polarization (0-89°) at 293K (1.67-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

010002000300040005000600070008000900010000Wavenumber (1/cm)

Tra

nsm

itta

nce

7080

605040

3020

100

89

Figure 2-60 Calculated Fz Si P-Polarization (0-89°) at 293K (1-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

010002000300040005000600070008000900010000Wavenumber (1/cm)

Tra

nsm

itta

nce

01020

30

405060

7080

89

Figure 2-61 Calculated Fz Si S-Polarization (0-89°) at 293K (1-250µm)


64

0.00

0.10

0.20

0.30

0.40

0.50

0.60

010002000300040005000600070008000900010000Wavenumber (1/cm)

Tra

nsm

itta

nce

7060

50403020

100

80

89

Figure 2-62 Calculated Fz Si Mean-Polarization (0-89°) at 293K (1-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

05000100001500020000Wavenumber (1/cm)

Tra

nsm

itta

nce

706050

40302010

0 80

89

Figure 2-63 Calculated ZnSe P-Polarization (0-89°) at 293K (0.45-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

05000100001500020000Wavenumber (1/cm)

Tra

nsm

itta

nce

01020

304050

6070

8089

Figure 2-64 Calculated ZnSe S-Polarization (0-89°) at 293K (0.45-250µm)


65

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

05000100001500020000Wavenumber (1/cm)

Tra

nsm

itta

nce

01020304050

60708089

Figure 2-65 Calculated ZnSe Mean-Polarization (0-89°) at 293K (0.45-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

050001000015000200002500030000Wavenumber (1/cm)

Tra

nsm

itta

nce

70605040

3020

100

80

89

Figure 2-66 Calculated ZnS P-Polarization (0-89°) at 293K (0.33-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

050001000015000200002500030000Wavenumber (1/cm)

Tra

nsm

itta

nce

01020

304050

60

70

80

89

Figure 2-67 Calculated ZnS S-Polarization (0-89°) at 293K (0.33-250µm)


66

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

050001000015000200002500030000Wavenumber (1/cm)

Tra

nsm

itta

nce

0-50

60

70

80

89

Figure 2-68 Calculated ZnS Mean-Polarization (0-89°) at 293K (0.33-250µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

020004000600080001000012000Wavenumber (1/cm)

Tra

nsm

itta

nce

7060

504030

20100

80

89

Figure 2-69 Calculated CdTe P-Polarization (0-89°) at 293K (0.83-40µm)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

020004000600080001000012000Wavenumber (1/cm)

Tra

nsm

itta

nce

01020

3040

50

60

70

80

89

Figure 2-70 Calculated CdTe S-Polarization (0-89°) at 293K (0.83-40µm)


67

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

020004000600080001000012000Wavenumber (1/cm)

Tra

nsm

itta

nce

0-60

70

80

89

Figure 2-71 Calculated CdTe Mean-Polarization (0-89°) at 293K (0.83-40µm)

2.6.1 Total internal reflection

Under circumstances where the incident medium has a refractive index which is larger than the secondmedium, as is the case for the rear surface boundary of an uncoated substrate, and if the incident angle (θ) islarge, then Snell’s law, as defined in equation 2-33 gives values that become meaningless as sinθt has valuesgreater than 1. The refracted wave under these circumstances then propagates parallel to the rear surface. Thecritical angle of incidence defining this condition being given by θc = sin-1(n2/n1), where n2<n1. For Ge, Si,CdTe, ZnSe and ZnS the values of this critical angle are 14.5°, 17.1°, 22.0°, 24.6° and 27.0°. At incident anglesgreater than these values there can be no energy flow across the boundary and the wave becomes totallyinternally reflected. The amplitude of the reflected wave differs from the incident amplitude by a change ofphase to the s and p polarizations given by:

s-pol φ θ θθs

c= −−

−2

11

21

2

21

1 2

tansin sin

sin

/

(2-38)

p-pol φ π θ θθp

c n

n= − + −

−

−21

12

12

21

1 2

1

2

2

tansin sin

sin

/

(2-39)

The effects of this phase change on the various substrate materials are shown inFigure 2-72. The s and p polarizations undergo different phase changes upon total internal reflection, wherelinearly polarized radiation becomes elliptically polarized upon reflection. The degree of polarization beingdefined by the size of phase difference between the two polarizations. The relative phase difference between thes and p polarizations (∆ ≡ φp - φs) derived from Equations 2-38 and 2-39 is given in Equation 2-40:

∆ = − = − +−−φ φ π

θ θ θθp s

c2 1 1

21

2

21

tancos sin sin

sin(2-40)


68

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 10 20 30 40 50 60 70 80 90Angle (Degrees)

Pha

se (

Rad

ians

)

P-Pol (+ pi)

Ge / Si / CdTe / ZnSe / ZnS

Ge / Si / CdTe / ZnSe / ZnS

S-Pol

Figure 2-72 Totally internally reflected phase of s and p-polarizations vs angle of incidence forGe, Si, CdTe, ZnSe and ZnS materials.

2.7 Coherence of multiple internal reflections

When a finite thickness substrate is viewed with wide-band uncollimated radiation, the multiple-beaminterference created by reflectance deviations between the front and rear surfaces cancel, and the energy of thereflected beams can be summed, as described in Section 2.3. However, when a highly flat and parallel substrateis illuminated by quasi-monochromatic radiation, with a narrow frequency bandwidth from a scanningspectrometer, then the interference effects between the front and rear surfaces can be observed as a pattern ofFabry-Perot fringes, known as a channel spectrum. This channel spectrum is superimposed on the spectral profileof the substrate, modulating its transmission as illustrated in Figure 2-73, under which circumstances theamplitude reflectances are required to be summed, taking into account the phase differences of the reflectedbeams. On a wavenumber scale, this channel spectrum will have a constant periodicity, with a fixed frequencyinterval, whilst on a wavelength scale the ripple frequency will decrease with increasing wavelength.

Figure 2-73 Overlaid spectra of substrate fringes in 0.41mm Germanium and 0.575mm Silicon


69

Liddel and Macleod derived the following coherent mathematical expression for determination of thetotal fringe amplitude which could be applied to highly collimated narrow bandwidth radiation with highlyparallel thin substrates.

TT T

R R R Rab

a b

a b a b=

+ −−1 2 21 2 1 22

/ / cos( )δ ψ (2-41)

where δ is the thickness and ψ reflection phase changes.

However, the practical implementation of this algorithm was considered by Liddel and Macleod[50] tobe a particularly complex problem to solve, as in order to estimate the total effect of this equation it must beintegrated over the complete range of possible thickness variations within the substrate, over the range ofwavelengths and angles of incidence defined by the bandwidth of the incident radiation and with theappropriately distributed weight proportion for each angle.

The combination of the reflected waves from the two surfaces can be considered similar to the principalof superposition which applies to all electromagnetic fields. This is defined as the total electric field created bydifferent sources as being the summation of fields due to each source. The sources of two plane waves aremutually coherent between the two surfaces if the phase difference (φ2 - φ1) is constant. If the phase differencevaries with time in a random manner , the sources of the two waves are mutually incoherent. The degree ofmutual coherence is derived from time-averaged intensity distributions of the interference pattern formed by thetwo waves. If the two waves are mutually coherent (i.e. φ2 = φ1) the interference pattern is stationary with aspatial period given by;

Λ = λθ2 2sin( / )

(2-44)

where θ is the angle between the two wave vectors.

If the two waves are not coherent, the phase difference varies over a time interval (τ). Being able toobserve this will depend on the speed of the detection process, as the intensity is averaged over the time intervalof the phase difference. The degree of mutual coherence is defined by Equation 2-43 :

γτ

φ φτ

= −∫1 2 1

0

e dtj ( ) (2-43)

When γ = 1, there is complete mutual coherence (i.e. perfect temporal coherence), ifγ = 0-1, there is partial mutual coherence and if γ = 0 there is complete mutual incoherence.

In the case of the parallel sided substrate where the phase difference produces a value of γ between 0-1,and the path difference between the two beams does not exceed the coherence length of the wave lc = cτc , whereτc is the coherence time, then interference fringes will appear. As the frequency f = 1/τ , the coherence time canalso be defined by ∆f =1/τc where ∆f is caused by the sum of randomly emitted wave trains from a sourceproducing a spectrum of finite bandwidth. The coherence length is then defined by the distance the radiationtravels within the coherence time τc given by lc = cτc = c/∆f. This approximates to lc = λ2/∆λ where ∆λ is thebandwidth or resolution of the incident radiation. The condition of spectral fringes from a parallel sided substrateis therefore when the thickness of the substrate is less than the coherence length of the incident radiation.

By example, for the above illustration with a scanning resolution of 2cm-1 the coherence length variesfrom 5.6mm at 16.6µm to 5.1mm at 33µm, causing the substrate to act as an interference layer. Elimination ofthe channel spectrum for this thickness of substrate will therefore only occur if radiation is used with a scanningresolution of approximately 20cm-1.


70

2.8 Conclusion

The implementation of the analysis methods derived in this chapter have provided a concise set ofdispersive n and k values for the selected infrared materials, across a wide range of temperatures, wavelengthsand thicknesses. These dispersive models can now be incorporated as an integral part of future filter designcalculations.


71

CHAPTER 3INFRARED THIN FILM CHARACTERISATION

AND DEPOSITION TECHNIQUE

In order for an infrared material to be useful in a multilayer interference coating, it must be able to fulfilcertain requirements. Amongst these are high transparency, particular refractive index values, homogeneity, highpacking density, good adhesion, low stress, hardness and be able to survive the widest range of possibleenvironmental conditions. The choice of layer materials that are available for use in the infrared which meetthese criterion is limited when the combination of high transparency over the widest possible range ofwavelengths and selection of appropriate refractive index values are the main requirements. In this chapter Ishall be reporting on the optical characterisation of two of the most frequently deposited layer materials used inthe infrared, together with the deposition technique and details of the nucleation, growth and microstructure ofsome representative multilayers.

Lead Telluride (PbTe) and II-VI materials tend to dominate the multilayer materials selection for thedesign of filters operating in the mid to long-infrared wavelengths both at room and reduced temperatures. Thehigh value of refractive index contrast between the two materials (nH/nL) is the most desirable parameter in thedesign of a multilayer, particularly as this keeps the number of layers and the physical thicknesses to a minimumfor performing a particular spectral function. The combination of the PbTe/II-VI high refractive index contrast,together with the advantages of the PbTe negative optical expansion coefficient and position of the PbTesemiconductor absorption edge all assist to produce efficient multilayer designs. Zinc Selenide (ZnSe) is a goodcomplementary II-VI multilayer material to PbTe, providing a high index contrast and transparency out to the20µm region in bulk form, beyond which multi-phonon absorption then dominates. As ZnSe is a hard-coatingmaterial, it also provides good environmental resistance to the multilayer.

3.1 Lead Telluride (PbTe) Dispersion

The use of PbTe as a high index (H-layer) material has significant advantages in a multilayer, bysatisfying both the spectral filtering requirement with the minimum number of layers in order to maximiseoptical throughput, and providing continuous short wavelength blocking, due to the long wavelength position ofits semiconductor absorption edge. Its high refractive index also enhances the stop-band width, and provides ahigh effective index (n*), reducing the size of any spectral shifts caused by inclined illumination. Thesemiconductor absorption edge at 3.5µm at 300K removes the need for a large number of subsidiary blockingstacks that would normally be required to provide continuous short wavelength blocking to link up with thesubstrate electronic absorption edge (at ≅ 1.5µm for Ge). The long wavelength shift of this edge position toaround 5.5µm at 65K, then further improves this advantage beyond that achievable with multilayers containinggermanium as the principal H-layer material. A further advantage of PbTe as a layer material is long wavelengthReststrahl wavelength (≅ 110µm) making it particularly attractive for use in filters beyond 15µm, wherealternative high index materials are becoming absorbing. The refractive index of PbTe is one of the highestknown of the usable infrared layer materials, with a value of n ≅ 5.5 at 300K rising to ≅ 5.7 at 200K and ≅ 5.85at 80K.

The optical dispersion properties of PbTe material are primarily defined by the carrier concentration,substrate (deposition) temperature, pressure conditions, deposition rate and departure from stoichiometry. Non-stoichiometries in PbTe have been found to induce additional concentrations of free carriers in the material fromwhich an accelerated reduction in refractive index and increased absorption is exhibited with increasingwavelength. Evans et al [51] determined that an excess of only one part in 106 of either Pb or Te was adequate tosignificantly degrade the performance of a narrow band filter at 15µm. These excesses of either element areconsidered to exist in the deposited layer as interstitial atoms, which to a limited extent, can diffuse out atdislocations or grain boundaries by annealing[52]. However, the practice of annealing is not ideal when therequirements for precise and reproducible spectral positioning and shape of a required filter profile are tightlyspecified. Therefore, in stoichiometric PbTe material, as depletion of any one of the vaporisation products cansignificantly affect the optical performance, the layer must be deposited under optimum deposition conditions toproduce highly transparent and reproducible films direct from the deposition chamber.

The introduction of oxygen into the evaporation chamber during a PbTe layer deposition has beenfound to compensate for a tolerable range of non-stoichiometry in the evaporation vapour. This is done with apartial pressure of 5x10-5 Torr, from which complete transparency of the material can be restored. The


72

transparency of the material is then sensitive to the combination of the partial pressure, deposition temperatureand deposition rate. The best deposition temperature for the PbTe/II-VI materials has been found to be around185°C with a rate of approximately 5Ås-1.

An alternative approach to restoring departures from stoichiometry has been the use of non-stoichiometric source material. As free-carrier absorption becomes noticeable under conditions of depletedoxygen supply, an investigation in our laboratory into depositions using tellurium-enriched source material wasinitiated for a series of long wavelength (>15µm) filters. This revealed that using a source material containing1% excess of tellurium was adequate to restore complete transparency of the material at these wavelengths, withno addition of partial pressure of oxygen being required. However, though adequate for long wavelength filtersoperating in ambient room temperature conditions, upon cooling, this material was subsequently found todegrade with greater amounts of absorption than that exhibited by stoichiometric material when deposited underideal conditions. Analysis of the optical and semiconductor properties of a single film of excess-Te PbTe,deposited on germanium and silicon substrates, was investigated by Zhang[53] from which further analysisrequired for constructing the refractive index database for this research has produced a temperature-dependantdispersive index model using the following algorithm in Equation 3-1 and illustrated in Figure 3-1 for predictedtemperatures of 25, 50, 100, 150, 200, 250 & 300K.

n A B C D E= + + + +λ λ λ λ 2 3 4 (3-1)where :

A = -2.885x10-3 T + 7.542, B = 3.280x10-6 T - 3.250, C = 4.068x10-5 T + 2.286x10-2,D = - 3.186x10-6 T - 6.903x10-4, & E = 6.646x10-8 T + 6.855x10-6

5.20

5.40

5.60

5.80

6.00

6.20

6.40

6.60

6.80

3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0

Wavelength (µm)

Ref

ract

ive

Inde

x (n

)

25

50

100

150

200

250

300

300K

25K

Figure 3-1 Temperature-dependent refractive index profiles of PbTe containing 1% excess Te

As a result of variations in the deposition parameters, which affect the exact optical properties of thedeposited PbTe films, reproducible characterisation of the dispersion and absorption properties forstoichiometric PbTe material has proved to be notoriously difficult. The sensitivity to the amount of shortwavelength scatter which varies with the exact deposition conditions, combined with the relatively longwavelength semiconductor edge, has meant that the amount of data available for analysis in the transparentregion of the substrate, prior to the lattice absorption, is limited. Approximations using bulk material propertiesfrom semiconductor theory have therefore to be used to characterise this material for an n and k database[54]. Thisis not such a problem with tellurium-enriched material as the short wavelength scatter is considerably less due tothe absence of oxygen, making the deposited film denser and more glassy, and providing better reference datafor analysis.

For intrinsic PbTe material, the predicted index dispersion profile generally follows the simple classicaloscillator of resonant wavelength (λ0) from which the dielectric constant (ε=n2) varies with wavelengthaccording to Equation 3-2. Onto this can then be superimposed the effects of varying carrier concentrations.


73

εε

λλ

∞ −−

= −

1

11

0

2 0 for λ > λphoto (3-2)

In this equation, the value of ε∞ is an asymptotic value of the dielectric constant (ε0) at longwavelengths and λphoto is the threshold wavelength for intrinsic photoconductivity. Walton and Moss[55] measuredthe index of single crystals of PbTe in the range 4.5µm to 8.0µm. These samples had an intrinsic carrierconcentration of 1018 carriers per cm3, the effect of which was considered negligible to the value of the refractiveindex at these wavelengths. They found values of n∞ = 5.64 ± 0.03 and λ0 = 1.27µm. By combining this datawith values of the high frequency dielectric constants reported by Dalven[56] as given in Table 3-1 fortemperatures of 373, 300 and 77K, an intrinsic dispersion curve can be plotted for the three temperatures, asillustrated in Figure 3-2. In general, the lower the temperature, the higher the refractive index is at any givenwavelength and the shorter the wavelength, the greater is the change of refractive index with temperature.

Table 3-1 Dielectric properties of intrinsic PbTeTemperature 77K 300K 373K

Bandgap (eV) 0.22 0.31 0.33λphoto (µm) 5.71 4.00 3.65

ε∞ 36.9 32.8 32.0N 5x1014 1016 1017

For additional concentrations of carriers, the superposition of carrier dispersion on the intrinsicrefractive index (n) profile can be calculated[57] by addition of Equation 3-2 relating the refractive index andcarrier concentration.

( )n nNe

m c≅ −0

22

02

2

2*ε πλ

(3-3)

where; N is the carrier concentration, e the electronic charge, m* the effective mass (PbTe ≈ 0.1e), ε0 the staticdielectric constant, c the velocity of light and n0 the intrinsic dielectric dispersion.

5

5.2

5.4

5.6

5.8

6

6.2

6.4

6.6

6.8

7

3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5

Wavelength (µm)

Ref

ract

ive

Inde

x (

n)

77K

300K

373K

No

No No x 10

No

No x 10

No x 100

Figure 3-2 Dielectric dispersion for bulk PbTe with added concentrations of carrier dispersion

3.2 Lead Telluride (PbTe) Absorption

A major problem limiting both the performance and possible characterisation of PbTe-based multilayerfilters are the effects of scattering and absorption in the individual layers of a multilayer stack. Scattering losses


74

caused by deflections of the incident radiation by volume or surface defects, or the formation of microcrystalgrain boundaries in the deposited films are difficult to quantify as the amount of scattering is dependant on thesurface preparation, deposition conditions and material characteristics of the film. Absorption however, being aninterdependent function of the complex refractive index has been thoroughly investigated over many years andreported for many infrared materials[58].

The PbTe absorption spectra in Figure 3-3 shows the effects of temperature on both the amount ofabsorption and positioning of the absorption features at temperatures of 300 and 77K. Contrary to the behaviourof most semiconductor materials, the position of the PbTe electronic absorption edge moves to longerwavelengths on cooling. This is considered to be due to the anomalous decrease in size of the forbidden band-gap (≅ 4.2x10-4 eV/K). In order for the PbTe to transmit, the band-gap must be larger than the wavelengths ofinterest, the band-gap defining the position of the short wavelength transmittance limit (λ=hc/eEg). Theabsorption characteristic provides a continuum of intense absorption at short wavelengths which is bounded by asteep absorption edge. In this region, the extinction coefficient (k) is close to an exponential function inmagnitude and extends over several decades. Its onset is caused by the optical excitation of electrons obtainingsufficient energy to achieve either direct or indirect transitions into the conduction band. The type of transitionbeing dependent on the exact structure of the energy bands. In intrinsic PbTe between 450K and 100K the band-gap changes from ≅ 0.4eV to ≅ 0.25eV. The size of the wavelength shift is proportional to the reciprocal of thetemperature, moving from ≈ 3.2 to 5.0µm across this temperature range.

1E-04

1E-03

1E-02

1E-01

1E+00

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Wavelength (µm)

Ext

inct

ion

Coe

ffici

ent (

k)

77K

Photo-absorption

region

Figure 3-3 Semiconductor model of PbTe extinction coefficient (k) at 300 and 77K

In intrinsic material, the amount of photo-absorption at wavelengths shorter than the principalsemiconductor edge is dependent on both the carrier concentration and temperature. The effect of temperaturedisplaces the entire spectrum in proportion to the shift in position of the photo-absorption threshold wavelength.The photo-absorption effect, caused by direct electron transfers from the valence to conduction band, involvesthe electron in an increase of energy equal to the forbidden gap. There is no change in the momentum of theelectron, with the k-vector (2π/λ) remaining constant. In this region the refractive index reduces slowly from thethreshold value. The intrinsic absorption profile of PbTe is considered to exist with two distinct absorptionprocesses, initially the linear photo-absorption region which is followed by the electronic absorption edge.

By extension of the previous dispersion analysis, the following bulk semiconductor model[59] inEquation 3-4 and illustrated in Figure 3-3 represents a model of the extinction coefficient profile for PbTe at 300and 77K. This profile shows both absorption processes and can be used to predict the performance of filters oncooling.

22

2

20

33nk

Ne

m c≅

( ) ( )* ε µ πλ

(3-4)


75

where; N = carrier concentration, e = electronic charge, m* = effective mass (≈ 0.1 me), ε0 = absolute dielectricconstant, c = velocity of light, & µ = carrier mobility (≈ 1800 cm2/V/sec)

3.2.1 Modified lead telluride (PbTe) photo-absorption spectra

Though in regions remote from the absorption edge this model gives a good indication of the shift infilter profile. I have suggested [60] further modifications were required to this model in the region between thephoto-absorption and intrinsic semiconductor edge to simulate experimental effects which have been observedon the spectral profile of long-wave pass edge filters operating in this region. When a filter passband overlapswith the absorption edge, the agreement of the model is poor. The measured performance exhibits a smootherand less steep profile in this region than that supported by the calculation. This indicates that k changes moregradually and smoothly in practice than the simplified model would suggest, and that the absorption edge is morerepresentative of a single stage process, merging the photo-absorption regions and electronic semiconductoredge together. Improvements to the microstructure of the deposited multilayer would be a more desirableoutcome, but is difficult to achieve using conventional thermal evaporation technology.

The modified lead telluride absorption spectra illustrated in Figure 3-4 which I have proposed for thismaterial show a more gradual short wavelength roll-off of the photo-absorption region as opposed to the linearabsorption profile described previously. This modified profile indicates that at short wavelengths there is aninteraction between both the photo-absorption and electronic absorption processes. This involves both direct andindirect electrons making transitions, with certain electrons experiencing a change in momentum due to phononinteraction, others making the transition directly. Previously, the two processes were considered to beindependent, however experimental evidence from the effect of cooling on a long wave pass edge filter in Figure3-5 containing PbTe as the principal H-layer material indicate a merging of the two processes, with only certainproportions of the electrons absorbing incident radiation, and making the transition directly. Other possiblereasons for smoothing the photo-absorption characteristic are;i) Not all of the available atoms are absorbing the incident radiation (or some are re-radiating), creating onlypreferential absorption at certain wavelengths.ii) The interfacial boundaries of each PbTe surface may be exhibiting unexpected amounts of absorption that aredifferent to that found within the bulk material properties of the layer, depending on the microstructure of thefilm, andiii) Free charges which may be liberated at the surface of a layer may remain trapped to localised surface atoms.

The optical characterisation of stoichiometric thin-film PbTe material is an area of ongoing researchwithin our laboratory still requiring further validation.

1E-04

1E-03

1E-02

1E-01

1E+00

0 5 10 15 20 25 30

Wavelength (µm)

Ext

inct

ion

Coe

ffici

ent

(k)

Modifiedphoto-absorption

region

Figure 3-4 Modified semiconductor model of PbTe extinction coefficient (k) spectra at 300 and 77K


76

0

20

40

60

80

100

120

3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25

Wavelength (µm)

Tra

nsm

issi

on (

%)

300K

90K

Figure 3-5 Measured PbTe-based long-wave pass edge filter at 300K and 90K(showing a gradual transition between the photo and electronic absorption regions)

3.3 Zinc selenide (ZnSe) dispersion

The use of ZnSe as a low index II-VI material (n ≅ 2.35) complements PbTe as a hard dielectric withgood transparency out to wavelengths beyond ≅20µm in its thin-film form. Being a dielectric material, therefractive index is defined by the dielectric constant (ε), which is determined entirely by localised electronsbound to the lattice, the magnitude of this dielectric constant being a function of the electron polarizability. Theshape of the dispersion profile, is characterised by a decline to increasing wavelength which follows theSellmeier[61] dielectric dispersion profile caused by the influence of lattice absorption. As the material cools theamount of lattice absorption reduces and the temperature profiles converge at long wavelength, where the highfrequency dielectric constant (ε∞) becomes a fixed value. Determination of a refractive index profile to use forthe n and k database for this material in its thin film form was derived using the Manificacier[62] envelope methodand verified through reverse synthesis.

This method uses only the transmission measurement of a single dielectric film deposited on a knownsubstrate material in the region of high transparency to determine the real and imaginary parts of the complexrefractive index N = n - ik, and thickness t. This film is bounded by two transparent media with refractiveindices, n0 and n1. In normal incident radiation, the amplitude of the transmitted wave is given by;

( )( )A

t t iN t

r r iN t=

−+ −

1 2

1 2

2

1 4

exp

exp

π λπ λ

(3-5)

where, t1, t2, r1, and r2 are the transmittance and reflection coefficients at the front and rear surfaces. Thetransmittance of the layer is given by;

Tn

nA= 1

0

2 (3-6)

( )( )T

n n n k

C C C C nt=

++ +

16

2 40 1

2 2

12

22 2

1 2

αα α π λcos

(3-7)

where in the case of spectral regions containing weak absorption, such that k2<<(n - n0)2 and k2<< (n - n1)

2, thenthe coefficients are;

( )α π λ= −exp 4 k t (3-8)

( )( )C n n n n1 0 1= + + (3-9)

( )( )C n n n n2 0 1= − − (3-10)


77

From the oscillating spectral profile of a single film, the transmittance maxima and minima of Equation 3-7occur where;

4π λ π nt m= (3-11)

where m is the order number. In the case where n > n1 which corresponds to a semiconducting film on atransparent non-absorbing substrate, C2<0, the extreme values of the transmission are given by Equations 3-12and 3-13

( )Tn n n

C Cmax =

+

16 0 12

1 2

2

αα

(3-12)

( )Tn n n

C Cmin =

−

16 0 12

1 2

2

αα

(3-13)

The ratio of these two equations gives;

( )[ ]( )[ ]α =

−

+

C T T

C T T

1

2

1

1

12

12

max min

max min

(3-14)

From equation 3-9, 3-10 and 3-12,

( )[ ]n N N n n= + −202

12

12

12

(3-15)

where

Nn n

n nT T

T T=

++

−02

12

0 122 max min

max min

(3-16)

The refractive index is therefore determined by knowing Tmax, Tmin, n1 and n0 at the same wavelength.The film thickness can then be calculated from two maxima or minima using equation 3-11;

( ) ( )( )t =−

M

2 n n 1 2

1 2 2 1

λ λλ λ λ λ

(3-18)

where, M is the number of oscillations between the two extrema and λ1, n(λ1) and λ2, n(λ2) are the correspondingwavelengths and refractive indices.

By using this method the refractive index profile in Figure 3-6 was determined for a single film of ZnSewith a optical thickness of 24 quarter-wave optical thickness (QWOT) deposited at a fixed monitoringwavelength of 4µm (physical thickness 10µm). From this, the following polynomial regression in Equation 3-19was determined from which the database for this material could be constructed.

n A B C D E= + + + +λ λ λ λ2 3 4 (3-19)where at 300K, A =2.4615, B = -0.0083, C = -0.0007 , D = 0.0003, E = -0.00002 ,


78

2.405

2.410

2.415

2.420

2.425

2.430

2.435

2.440

2.445

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0Wavelength (µm)

Ref

ract

ive

Inde

x

Calculated Index

PolynomialR i

Figure 3-6 Dispersive refractive index profile of ZnSe at 300K

Modelling the effects of temperature on the optical properties of the various infrared materialsmentioned in both bulk and thin film form has provided a good indication of the amount of dispersion that ispresent across the infrared region. Further refinement and research is still however needed in the characterisationof both PbTe and II-VI layer materials to produce a more complete model of their properties, which time has notpermitted on this occasion.

3.4 Thin film deposition technique

In order to achieve an efficient manufacture of precision infrared filters, the optical thickness control ofthe multilayer during deposition is required to be highly accurate and reproducible. There are several methodsfor monitoring layer thickness, of which quartz crystal and optical monitoring systems are the most common. Inthe infrared region, an optical monitoring system is usually the most effective way to control thickness,particularly as the layer thicknesses can be relatively large, which often limits the operational frequency range ofa quartz crystal, induced by excessive mass loading.

Ensuring the combination of high thickness accuracy, reproducibility and being able to utilize theoptimal spectral characteristics of the thin film materials, all aid to producing successful filter deposition yields.This requirement for high accuracy is also becoming progressively more important as filters and coatings beingemployed in space-flight optics are required to be deposited on tightly specified, high cost components, wherethere exists no opportunity for optical re-working. These requirements therefore dictate that close attention mustbe given to the design of the deposition plant, the substrate mounting methods, and the accurate measurement ofthe optical thickness during deposition. These considerations have resulted in our laboratory developing a uniquefabrication process containing bespoke apparatus designed and manufactured in-house[63].

Filter coatings are fabricated using a Balzers 510 bell jar deposition plant fitted with a cryopump andcontaining a geometry of rotating thermal evaporation sources and stationary substrates. The deposition layermaterials are evaporated from resistance heated Molybdenum sources mounted on a rotating slip ring assembly,as illustrated in Figure 3-7. This tooling configuration allows precise thermal control of the coating substratesduring deposition to ensure a good uniformity of the deposited layers. Further essential control of the substratetemperature is achieved in the deposition by clamping the substrates using Pb annular washers, backing piecesand disc springs. This arrangement provides a low impedance thermal path from the substrate to the temperaturecontrolled coating jig, keeping the substrate temperature constant despite the considerable and variable radiatedthermal flux from the evaporation sources. This is particularly important as the “sticking coefficient” of most ofthe infrared materials deposited is strongly temperature dependant[64]. This reproducible and controlled methodof clamping ensures that there is a minimum of variation in the filter substrate and monitor piece environmentduring the deposition. Thermocouples attached to the coating jig plate are used to monitor the temperature,which by using controlled air cooling varies by approximately ±1-2°C during PbTe deposition and by ± 2-3°Cduring a ZnSe layer. For the deposition of PbTe/ZnSe based infrared coatings, a temperature between 185-200°C


79

has been found to provide an optimum combination of good optical and mechanical properties for thermallydeposited films. Whilst for ZnS/Ge based multilayers a substrate temperature of 125°C is best suited, and forBaF2 films a higher deposition temperature of 230°C is more appropriate.

Modified Balzers BA510 bell jarchamber showing

(a) Temperature controlled substratecoating jig mounting

(b) Evaporant control shutters

(c) Evaporation sources

(d) Rotating slip ring assembly

(e) LT brushes

(f) Ring gear / pinion for rotation

(g) Water cooled support ring

(h) Base plate with lead throughs

Figure 3-7 Balzers BA510 deposition plant layout

The deposition plant geometry of stationary substrates and rotating sources allows in-situ opticalreflectance monitoring of each layer during the deposition process, as illustrated in Figure 3-8. The monitorsubstrate, usually of the same dimensions as the filter substrates, is mounted in the centre of the coating jig inprecisely the same way as the filter substrates as described above. In this way the monitor experiences the samethermal environment as the filter pieces. Signal-to-noise ratio is optimised by removing all unwanted signals, firstlyby coarse grinding the rear surface of the monitor substrate and secondly by anti-reflecting the receiving monitorsurface with a single quarter-wave antireflection coating at the monitor wavelength immediately prior to the firstdeposited layer. This effectively makes the monitor refractive index equal to 1.0. All subsequent layers deposited atthat wavelength will initially rise in reflection to a maximum at the quarter wavelength optical thickness and then fallback to the starting level at the half-wave thickness. Thickness is monitored by observing and recording reflectedinterference fringes at as short a wavelength as possible to obtain the best signal-to-noise ratio from the infrareddetector but also to maximise accuracy by counting as many fringes as possible. Each completed layer is madeeffectively absent by continuing deposition until its reflectivity returns to the starting level. The next layer of thealternating materials can then be deposited in the same way and so on. This monitoring procedure can be carried outfor typically around 31 layers before the monitor piece has to be changed as a result of absorption of the layermaterials. This procedure is known as even order monitoring and is well suited to the manufacture of bandpassfilters, the highly reproducible nature of the process allows filters to be placed in wavelength accuracy to a precisionof around ± 0.3% in the infrared region beyond 3.5µm.

A chopped infrared signal from either a Nernst filament, wire wound resistor or quartz halogen bulb isfocused by CaF2 optics onto the monitor substrate, the reflected signal is then re-focused onto the slit of amonochromator which is set to the desired monitoring wavelength. The monochromatic signal is then furtherfocused by an IRTRAN II (ZnS) lens onto a pyroelectric detector which is then signal processed by a phasesensitive detector, the output of which is used to control the process.


80

Figure 3-8 Substrate thermal contact and layer monitoring arrangement

3.4.1 Fractional thickness reflectance monitoring

In order to manufacture edge filters or broadband antireflection coatings with steep edges or highlytransparent spectral responses over a wide spectral region, it is necessary to deposit layers which are of non-quarterwave, or multiple quarterwave, thicknesses at the monitor wavelength. This is achieved by including anadditional shutter below the substrate plane, as illustrated in Figure 3-9. By the operation of this simple shutterarrangement which isolates the filter pieces from the flux of the evaporant being received by the monitor (and by thefilter pieces up to that point in operation), accurate fractional layer thicknesses can be deposited from the reflectancefringes being deposited as the layer grows on the central monitor piece, as illustrated in Figure 3-10. The followingalgorithm is then used which links reflectance level to optical thickness.

Figure 3-9 Plan view of shutter arrangement


81

Figure 3-10 Reflectance signal during deposition

The signal amplification at time a in Figure 3-10 increases the sensitivity at the layer interfaces foraccurately determining the termination thickness of an integral quarterwave.

Prediction of the reflectance amplitude (Is) versus thickness during layer deposition is calculated by thealgorithm:

( )( )( ) ( )I

R R

R R Rs = −

− −

− + −1

1 1

1 2 12

max min

max max min sin π q(3-20)

where Rmax = (n2 - yo )2/(n2 + yo )

2, Rmin the residual reflectance minimum, n the refractive index of thedepositing layer, q the optical thickness in quarterwaves (4nt/λ), and yo the effective refractive index of theantireflected substrate, and subsequent absentee layers deposited upon it. Comparison of this predicted characteristichas been found to be a near perfect approximation to that derived experimentally[65]. However, for the determinationof the specific reflectance levels associated with a particular layer thickness, further modifications[65] are applied tothis algorithm for operation of the shutters.

The normalised reflectance change (S) of the interference fringe is the reflectance at the particularthickness, minus the minimum level, divided by the total reflectance swing, as given by Equation 3-21;

( )( )S

R R

R R

q=

−

−min

max min

(3-21)

This can then be applied to the formula in Equation (3-22), which is applicable to a layer deposited on anyunderlying structure of existing layers:

( ) ( )SC q

=+

1

1 1 22cot π(3-22)

where C is a contrast figure given by (1-Rmin)/(1-Rmax).For low refractive index materials (L-layers), this is calculated depending on the reflection parameters of the layerbeing deposited:

CR

RL

L

L

=−−

1

1min[ ]

max[ ]

(3-23)


82

Determination of the predicted shutter opening level on the reflectance fringe, which then provides asymmetrical terminating reflectance, can be calculated (in radians) by Equation 3-24:

( )R R

R R

N qC

open L

L L

iL

= +−

+−

max[ ]

min[ ] max[ ]

tan12 2

2π(3-24)

where N is the integral number of quarterwaves out of which the fraction is being subtracted.

The opening lost QWOT (i.e. that thickness deposited on the monitor only prior to the openingreflectance) can then be calculated by Equation 3-25:

q

R R

R R

Copen

L L

open L

L

=

−−

−

−21

1

πtan

min[ ] max[ ]

max[ ](3-25)

Determining the terminating reflectance level is then calculated using the fractional thickness required tobe deposited plus the opening lost QWOT (i.e. qopen+i = qopen + qi ) from which the closing lost QWOT (i.e. thatdeposited on the monitor following the terminating reflectance) can be calculated from Equation 3-26:

q

R R

R R

Cclose

L L

close L

L

=

−−

−

−21

1

πtan

min[ ] max[ ]

max[ ](3-26)

The fraction deposited on the required substrates is therefore ( )q N q qi open close= − + . Converting this

into a reflectance level to determine the terminating reflectance point is then calculated using Equation 3-27:

( )( )

R RR R

q q Cclose L

L L

open i L

= +−

+ +

max[ ]

min[ ] max[ ]

tan12

2π(3-27)

When the quarterwave fraction is required to be subtracted from a multiple number of integralquarterwaves, the maximum and minimum reflectance parameters used to calculate the opening level are calculatedfrom the N=1 reflectance fringe. The terminating reflectance level can then be calculated by substituting valuesappropriately from the N-1 reflectance fringe.

Evans et al [66] showed by a prediction of the reflectance curves from Cartesian (Argand) diagrams whichrepresent the deposition of alternating L and PbTe(H) layers, that as a result of growth increments which occur atthe interface between layers, the determination of a predicted H-layer maximum would provide a more accuratevalue for the contrast calculation than the actual Rmax provided by the layer itself. Therefore, using the reflectanceparameters of the preceding L-layer, the predicted H-maximum can be calculated inclusive of the index contrast(nH/nL) of the two layers, in Equation 3-28:

R

R

R

n

n

R

R

n

n

H

L

L

H

L

L

L

H

L

max[ ]

max[ ]

max[ ]

max[ ]

max[ ]

=

−+

−

++

−

11

1

11

1

2

2

2

2

2

(3-28)

from which the H-layer contrast is then calculated by:


83

CR

RH

L

H

=−−

1

1min[ ]

max[ ]

(3-29)

Calculation of the appropriate reflection levels required for the shutter opening and closing positions arethen determined by substituting the actual deposited H-layer reflectance parameters back into Equations 3-24 to 3-27.

The optical deposition thickness (qi) for each layer is given by:

q Zn

nX Yi i

mon

F

D

i

i

= −

θλλ

0(3-30)

where i is the individual layer number (i=1...n), θ is the quarter-wave optical thickness, λ0 is the design wavelength(i.e. the wavelength at which all the layer design thicknesses are correct), λmon is the monitoring wavelength, nF isthe refractive index of the layer at the deposition temperature, nD is the refractive index at the design temperature, Xand Y are additional growth parameters following layer termination, and Z is the fine tuning coefficient used toaccurately locate the profile to the desired spectral position. From this, the physical thickness (tp) of both theindividual layers and the complete multilayer structure at the deposition temperature (nF) can then be calculatedfrom Equation (3-31).

tq

np moni

Fi

n

i

==∑λ

4

1

(3-31)

The implementation of these algorithms has been used extensively in the successful manufacture of filtersin our laboratory over many years. As part of this research I have translated this algorithm into a multipagerelational spreadsheet which is now used on a regular basis for the optical monitoring of filters during thedeposition process. Table 2 shows a typical example of a coating prescription defining some of the coatingcalculation parameters used in the spreadsheet.


84

Table 2 Example coating prescription recordCOATING PRESCRIPTION

Project / Filter Type Description HIRDLS Channel 15 Common Warm / Cold Filter High Pass + Ext HP BlockerProd 1 - Deposited using Electronic PSD monitoring method

Run Number 4211Run Date 05-Oct-98Design Description 19 Layer ZnSe/PbTe Optimised TSB High Pass Edge Filter + QWS

Required to be at 1075cm-1 at RTOperator GJHDeposition Plant B1Calibration Run Number 0Calibration Run Description 0Design Wavenumber (cm-1) 1268.8 Wavelength (um) 7.881Monitoring Wavelength 5.000Monochromator Drum Reading 4.15 Qm=Qd*Monit Wn/Design WnMonochromator Slit Width 4.00 Qf = (Qm-x)*y*zBlocking Filter Identification 3.9umBlocking Filter Cut-On (um) 3.9umIR Source QIMonitor Material GeMonitor Index 4.00Monitor Diameter (mm) 25.4Monitor Thickness (mm) 2.0

Material nd nf x y ID Temp (C) Lot / Batch No.1 ZnSe 2.35 2.35 0.00 1.00 L 185 02 PbTe 5.5 5.35 0.01 0.99 H 185 03 Ge 4.15 4.15 0.00 1.00 M 120 04 ZnS 2.2 2.2 0.00 1.00 Z 120 05 GeSe 3.3 3.3 0.00 1.00 G 185 0

Fine Tuning Coefficient (Z) 1.0000

Run No. 4211 HIRDLS Channel 15 Common Warm / Cold Filter High Pass + Ext HP BlockerPrint Date 15-Nov-98 19 Layer ZnSe/PbTe Optimised TSB High Pass Edge Filter + QWS

Layer FTG Layer Design Taper Layer Deposition Growth Growth Layer Deposition(from Sub) Design Material Index Correction Thickness Index Correction Correction Material Thickness

Import ID (nd) (Deg) (nf) (x) (y) (Qf)1 2.0000 L 2.35 1.000 180.000 2.35 0.00 1.00 ZnSe 3.1532 2.0000 H 5.50 1.000 180.000 5.35 0.01 0.99 PbTe 3.0263 2.0000 L 2.35 1.000 180.000 2.35 0.00 1.00 ZnSe 3.1534 2.0000 H 5.50 1.000 180.000 5.35 0.01 0.99 PbTe 3.0265 2.0000 L 2.35 1.000 180.000 2.35 0.00 1.00 ZnSe 3.1536 2.0000 H 5.50 1.000 180.000 5.35 0.01 0.99 PbTe 3.0267 2.0000 L 2.35 1.000 180.000 2.35 0.00 1.00 ZnSe 3.1538 2.0000 H 5.50 1.000 180.000 5.35 0.01 0.99 PbTe 3.0269 1.8184 L 2.35 1.000 163.652 2.35 0.00 1.00 ZnSe 2.866

10 1.6229 H 5.50 1.000 146.057 5.35 0.01 0.99 PbTe 2.45411 1.5614 L 2.35 1.000 140.527 2.35 0.00 1.00 ZnSe 2.46112 1.5316 H 5.50 1.000 137.843 5.35 0.01 0.99 PbTe 2.31513 1.5068 L 2.35 1.000 135.613 2.35 0.00 1.00 ZnSe 2.37514 1.5006 H 5.50 1.000 135.053 5.35 0.01 0.99 PbTe 2.26815 1.5343 L 2.35 1.000 138.084 2.35 0.00 1.00 ZnSe 2.41816 1.4610 H 5.50 1.000 131.486 5.35 0.01 0.99 PbTe 2.20817 1.6300 L 2.35 1.000 146.696 2.35 0.00 1.00 ZnSe 2.56918 1.3597 H 5.50 1.000 122.376 5.35 0.01 0.99 PbTe 2.05419 0.8298 L 2.35 1.000 74.678 2.35 0.00 1.00 ZnSe 1.308

3.5 Nucleation, growth and structure of infrared thin films

The optical and physical properties of deposited infrared thin-film materials are known to varyconsiderably from that of the bulk material, particularly if the thickness of the film is very small, or if themicrostructure possesses a high concentration of crystal defects. The microstructure of infrared films depositedby thermal evaporation tends to exhibit a highly columnar structure with a large internal surface area, which isthe primary influence affecting the optical and mechanical properties of the films. These structural characteristicsare responsible for many of the difficulties experienced in the fabrication and subsequent performance of opticalcoatings[67] which are inherent to their method of formation in the deposition process. The deposition of themultilayer films included in this thesis have been prepared by thermal evaporation as discussed earlier in thischapter.


85

The process of film formation with this technique is by condensation from the vapour phase of thematerial. The thermodynamic requirement for condensation to occur is that the partial pressure of the filmmaterial in the gas phase is equal or larger than its vapour pressure in the condensed phase at that temperature.However, this is only true if the condensation occurs on a film material already condensed or on a substratemade of the same material. Generally, the substrate is of a chemical composition different to that of the filmmaterial. In this circumstance an additional adsorption phase is to be considered, where the vapour atoms areadsorbed onto the substrate surface, requiring them to combine with other adsorbed atoms. On an atomic scale, aclean substrate surface is composed of a large number of adsorption sites to which an atom becomes bound witha certain amount of adsorption energy. The adsorbed atom does not remain stationary in this state but there is apossibility of either re-evaporation, with an energy equal or greater than the adsorption energy, or of migration toan alternate adsorption site with less energy. This migration mobility is a phenomenon in which the mobility ofthe atoms or molecules find the lowest energy stable configuration. In addition to migration, other processes,such as collisions, occur depending on the arrival rate of the atoms at the substrate. There is a probability thatone migrating atom will collide with another and form a bond of two atoms or more, creating an localised islandcluster, which is the formation of the primary nucleation. The creation of the isolated nucleation centres meansthe film at this stage is not continuous but provides a lower energy site to which subsequent atoms can condense.The specific shape of the cluster results from a compromise between differing surface characteristics. One tendstowards making the cluster spherical, and the other, being adsorption at alternative sites on the substrate, tends tomake the film flat.

These clusters continue to enlarge until they touch neighbouring clusters where they join together toform a single cluster. This process is called the coalescence or agglomeration stage of the film growth, in whicha network of clusters is formed separated by substrate valleys. The valleys are then slowly filled until a singlecontinuous film is formed. If the depositing vapour atoms possess a low mobility, and the impingement rate ofatoms arriving at the surface is high, then cluster growth in three dimensions during the nucleation andcoalescence stages progresses rapidly. The thin film can then contain microvoids or vacancies during the filmgrowth, which act as centres for inducing structural film defects.

The columnar structure of thermally deposited multilayers is best described by the microstructure zonemodel of Movchan and Demchishin[68] shown in Figure 3-11. Zone 1 in this model shows the deposition of theevaporated vapour at low substrate temperatures. This produces insufficient mobility of the impinging atoms toovercome shadowing effects created in the growth of clusters during the nucleation stages of the film formation,causing a less dense columnar growth. Other effects such as oblique incidence of the vapour and high surfaceroughness of the substrate can also contribute to less dense growth in this zone. Voids are noticeably present inthis zone which may continue throughout the growth of the film. The columns in this zone are usually amorphousor generally consist of smaller disordered crystals. As a result the film growth in this zone, films are oftensubjected to compressive stress upon cooling, lifting the deposited film from the surface of the substrate.

Increasing the substrate temperature increases the mobility of the atoms, enhancing surface diffusionand increasing the density of the film. Zone 2 shows this effect by the formation of a more tightly packedcolumnar structure. In the transition zone between 1 and 2, the film has fewer voids than in zone 1, consisting ofsmall vertical fibrous grains. As the substrate temperature rises further still towards zone 3, film hardness andabrasion resistance increase significantly, however the film is then subjected to increasing tensile stress as themismatch between the thermal expansion coefficients of the deposited layer and substrate induce failure uponcooling. This is characterised by a matrix of right-angled cracks in the film or multilayer caused by the differingrates of contraction.


86

Zone 1 Zone 2 Zone 3

Temperature

Figure 3-11 Temperature-dependent microstructural zones of condensed films

Figure 3-12 shows a high resolution electron micrograph of a thermally deposited ZnSe/PbTe basedmultilayer in which both the columnar structure of the films, and the existence of film voids appear to be evident.To obtain this SEM, the sample was prepared on a thin (400µm) germanium substrate which was then snappedacross its diameter to reveal the multilayer cross-section. As a result of this procedure, these particular voidsmay have been caused by either disordered crystal defects within the layers, which upon breaking removedmaterial from those sites or genuine nucleation voids. These voids have only occurred in this single isolatedregion and within this particular multilayer. The subsequent sample preparation of a similar multilayer treated tothe same process revealed a void-free breakage. These characteristics confirm that the film growths ofmultilayers using our existing thermal evaporation technology is within the transition region between zones 1and 2. This microstructural analysis is a new area of research activity on films currently being conductedbetween our laboratory and Prof. Shigetaro Ogura of Kobe Design University, Japan, from which this is the firstpresented picture obtained for these types of multilayer at this resolution.

PbTe

ZnSe

PbTe

ZnSePbTe

ZnSe

PbTe

ZnSe

PbTeZnSe

Ge

Figure 3-12 Columnar microstructure of a ZnSe/PbTe multilayer deposited on Gecontaining structural voids in the PbTe layers.


87

Further optical assessment of cross-sectioned infrared multilayers has been investigated as a result ofthe filter dimensioning and sizing requirements for the focal plane array of the EOS High Resolution DynamicsLimb Sounder (HIRDLS) instrument. This instrument has required the development of sub-millimetre sized(1.39 x 0.63mm) cooled filters for the detector assembly, as discussed in Chapter 5, for which cutting throughthe multilayer was performed by a 40µm metal-diamond blade mounted to a high precision slitting saw. Figures3-13 and 3-14 show an example of the filter cutting and identification marking required for these filters. Theremoved identification material was performed by ablation using a Krypton Fluoride (KrF) excimer laseroperating at 248nm, from which two pulses with a pulse length of 25ns produced the 60µm high characterswhich are about 0.3µm deep.

Figure 3-13 SEM showing cut-filter size Figure 3-14 Identification marking

The cross-sectioned multilayers in Figures 3-15 and 3-16 are the blocking and bandpass coatings for anarrow bandpass filter at 17.4µm. The multilayer is a alternate sequence of ZnSe/PbTe layers, where the lightbands are PbTe material. The blocking stack in Figure 3-15 is a spectrally overlapping combination of twoHerpin quarterwave stacks on to which is then further deposited an optimised Tschebysheff[69] long-wave passedge filter. This design construction can be seen as a graduated sequence of layer thicknesses increasing from thesubstrate outwards. On the rear surface of this filter is deposited a triple half-wave bandpass filter as shown inFigure 3-16. As can be seen, this filter contains a repeating series of integral quarter-wave thickness layers, andthree cavity layers of multiple quarter-wave thickness.

Figure 3-15 17.4µm Blocking filter Figure 3-16 17.4µm Bandpass filter


88

3.6 Conclusion

As a result of this investigation into the optical and physical properties of these thermally depositedfilms, it has clearly become evident that considerable improvements to the microstructure are needed. The resultsof the optical characterisation have provided some initial models for the dispersive optical properties, to whichfurther refinements can now be applied. However, achieving an accurate determination of the temperature-dependent optical constants is limited by the variabilities of the deposition process to reproducibly manufacturefilms to the high-quality needed. The use of ion-beam assisted deposition techniques during the film growth mayhelp to improve this reproducibility, and increase the density of the films. This equipment was not availableduring my research, but would improve the refractive index of the materials and provide values closer to the bulkproperties. Ion-beam assist may also promote a degree of amorphism in the deposited films by altering themicrostructures and porosity caused by the nucleation of crystallites. This will result in greater spectral andenvironmental stability of the multilayer, and increase its resistance to damage.


89

CHAPTER 4MULTILAYER CALCULATION THEORY AND APPLICATIONS

An example of an idealised multilayer stack is shown in Figure 4-1. It consists of a total of m layersdeposited upon a substrate which has a complex optical refractive index given by n n iks s s= − . Each of the

layers has a physical thickness (tm) and optical constants given by n n ikm m m= − , where nm is the dispersive

refractive index and km is the dispersive extinction coefficient. The incident radiation has an angle (φ) from anon-absorbing incident medium of refractive index (n0). If the layers are non-absorbing, the layer boundaries areparallel and the angle of refraction in the mth layer, θm, is determined from Snell’s law. Each layer in the stack istherefore specified by three parameters, tm, nm and km. These quantities, along with n0, ns, and ks, specify theprincipal optical properties of the multilayer. With these quantities and angle of incidence the reflectance R andtransmittance T of the multilayer can be calculated as a function of wavelength.

Figure 4-1 Nomenclature used for designating the thickness, refractive index,and angle of refraction for each layer in a multilayer stack.

The phase of the mth layer is defined as δm = 2πσnmtm , where σ is the wavenumber of the incidentradiation, σ = 1/λ. The wavenumber (cm-1) is proportional to the frequency of the radiation. In computing thespectral transmittance of a multilayer, the advantages in using this wavenumber scale are that many spectraltransmittance profiles tend to have a even symmetry about some point when plotted on a frequency scale,whereas the profiles are quite asymmetrical when plotted versus wavelength. A further advantage of usingfrequency as the calculation variable is that often maxima and minima on a single film transmittance orreflectance curve are spaced at equal intervals on a frequency scale, whereas on a wavelength scale they arespread out to long wavelengths and compressed together in the short wavelength region.

When radiation is incident upon a multilayer at oblique incidence, both R and T must be computedseparately in each plane of polarization. Rp, Tp in the p-plane of polarization, where the electric vector is parallelto the plane of incidence and Rs, Ts in the s-plane, where the electric vector is perpendicular to the plane ofincidence. Generally, when unpolarized radiation is incident upon a multilayer at non-normal incidence, both thereflected and transmitted light becomes partially plane polarized. If the incident radiation is ellipticallypolarized, as illustrated in Figure 4-2, the degree of elliptical polarization of both the reflected and transmittedradiation is altered. This is because not only is the reflectance and transmittance different in the two planes, butalso because the phase shift on reflectance is different for the two planes. If the radiation which is obliquelyincident on a multilayer is initially unpolarized then the polarizing effect of the multilayer can be neglected andthe average reflectance and average transmittance is the mean of the two polarizations (i.e. Rave = (Rp + Rs)/2 ,and Tave = (Tp + Ts)/2).


90

Figure 4-2 Linear (a) and Elliptical (b) polarized radiation

4.1 Loss-free multilayer matrix calculation

The calculation matrix described here, determines the spectral transmittance and reflectance profiles fora loss-free multilayer design on an absorptive substrate. The calculation is for normal incidence radiation, andassumes the films are optically homogeneous. From electromagnetic field theory, the electric field vector (Em-1)and magnetic field vector (Hm-1) at the incident boundary of a film are related to the electric field (Em) andmagnetic field (Hm) vectors at the boundary of the adjacent film by the product of the following matrices perlayer. The matrix is calculated at each boundary throughout the multilayer as the magnitude of the electric andmagnetic field vectors alter with the properties of the layer[70]. Application of the appropriate boundaryconditions between each layer require that the tangential components of the E and H vectors are continuousacross each boundary to the equations of wave propagation. Figure 4-3 illustrates a plane wave incident on a thinfilm.

Figure 4-3 Plane wave incident on a single thin film

The electric and magnetic field vectors of the waves travelling in the direction of incidence are denotedby the symbol “+”, and those waves travelling in the opposite direction by the symbol “-”. At the interface of themth layer, the tangential components of E and H are:

E E Em m m= ++ − (4-1)


91

( )( )H H E E Em m m= −+ −1 1 (4-2)

Neglecting the common phase factors, and where Em and Hm represent the resultants, then:

EH

H EEm

mm

+ = +

1

2 1 1

(4-3)

EH

H EEm

mm

− = − +

1

2 1 1

(4-4)

H HE H

Em mm+ = +

1

21

1

(4-5)

H HE H

Em mm− = −

1

21

1

(4-6)

The fields at the other interface m-1 are similar to Equations (4-3)-(4-6) at the same instant of time andat a position with identical x and y coordinates. These can be determined by multiplying by the phase differencein the z direction given by eiδ or e-iδ where:

δπ θ

λ=

2 1 N1d cos(4-7)

and θ1 may be complex. The values of E and H at this interface are therefore :

E E eH

E em mi m

mi

−+ += = +

1

1

1

2δ δ

η(4-8)

E E eH

E em mi m

mi

−− − − −= = − +

1

1

1

2δ δ

η(4-9)

( )H H e H E em mi

m mi

−+ += = +1 1

1

2δ δη (4-10)

( )H H e H E em mi

m mi

−− − − −= = −1 1

1

2δ δη (4-11)

where η1 is the tilted optical admittance given byη11

1

=H

E.

As the trigonometric identities for eix = cos x + isin x, and e-ix = cos x - isin x, then

( )E E E E H

im m m m m− −

+−

−= + = +1 1 11

cossin

δδ

η(4-12)

( )H H H E

iHm m m m m− −

+−

−= + = +1 1 11

sincos

δη

δ (4-13)

This can then be written in matrix notation as:

( )E

H

i

i

E

Hm

m

m

m

−

−

=

1

1

1

1

cos sin

sin cos

δ δ ηη δ δ

(4-14)

By replacing η with refractive indices of the layer and substrate materials (nm/ns), the initial characteristic matrix( M1 ) per layer (m) can be defined as:

ME

H

in

n

in

n

E

Hm

m

ms

mm

m

sm m

m

m1

1

1

=

=

−

−

cos sin

sin cos

δ δ

δ δ(4-15)

where: δm = 2πnmd cosθm / λ, d is the physical thickness, ns = substrate index, n m = film index, δm = filmthickness (in radians), θ = phase thickness.


92

δm can also be defined by the phase factor of the positive going wave given by:

δθσπλm =

2(4-16)

where σ = wavenumber (cm-1) and λ = design reference wavelength.Let : cosδm = A = D, i m msin /δ η = B, i m mη δsin = C

then:

MA iB

iC D1 =

(4-17)

for successive layers: layer 2 layer 1

MA iB

iC D

A iB

iC D2

2 2

2 2

1 1

1 1

=

(4-18)

MA A iB iC

iC A D iC

A iB iB D

iC iB D D2

2 1 2 1

2 1 2 1

2 1 2 1

2 1 2 1

=++

+

++

(4-19)

as i2 1= − then M2 is:

MA A B C

iC A D jC

A iB iB D

C B D D2

2 1 2 1

2 1 2 1

2 1 2 1

2 1 2 1

=−+

+

+− +

(4-20)

Let: AA A A B C= −2 1 2 1 , BB A iB iB D= +2 1 2 1 , CC iC A D iC= +2 1 2 1 and DD C B D D= − +2 1 2 1 the

matrix ( M1 ) is:

MAA BB

CC DD=

(4-21)

therefore, for a multilayer containing q-layers:

E

HM

E

Hmm

qq

q

0

0 1

=

=∏ (4-22)

The loss-free transmittance and reflectance for the multilayer assembly can be calculated from this productmatrix by:

( ) ( )Tn n

n AA n DD n n BB CCq

s o

o s o s

=+ + +

42 2 (4-23)

( ) ( )( ) ( )Rn AA n DD n n BB CC

n AA n DD n n BB CCq

o s o s

o s o s

=− + −

+ + +

2 2

2 2 (4-24)

Wherever the optical thickness of any layer is an integral number of halfwaves λ/2, λ, 3λ/2, 2λ etc.. the

matrix boundary condition is always M =

1 0

0 1 where, at the given reference design wavelength the value

of the transmittance for that layer will be absentee.

The transmittance profile of the uncoated substrate is given by:

TT T

R Raba b

t

a bt

=−

−

−

exp

exp

α

α1 2(4-25)

where a = incident surface and b = rear surface boundary. By substituting measurements of the spectraltransmittance of the uncoated substrate, combined with the dispersive refractive index model, the absorptioncoefficients (α) is calculated using the algorithm defined in Equation 4-26 across the range of absorbingwavelengths.


93

( )

α =

+

±ln

T T T T R R T

T

a b a b a b ab

ab

224

2

t(4-26)

The transmittance of the multilayer and substrate is then calculated by combining the coefficientsderived from the product matrix with the absorption coefficients determined for the substrate in Equation 4-27:

TT T

R Rab

aq bqt

aq bqt=

−

−

−

exp

exp

α

α1 2 (4-27)

where Taq , Tbq , Raq , Rbq are the transmittance and reflectance coefficients of the multilayer at the mth layeradjacent to the substrate, and αt is the product of the absorption coefficient profile and substrate thickness. Theeffect of applying this calculation to a broadband antireflection coating with and without substrate absorption isillustrated in Figures 4-4 and 4-5, from which the effects of absorption caused by the substrate is demonstratedfor differing thicknesses.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

025050075010001250150017502000Wavenumber (1/cm)

Tra

nsm

ittan

ce

loss free

2mm

2.5mm

3mm

3.5mm

4mm

Loss Free

2.0mm

4.0mm

Figure 4-4 Broadband antireflection coating on ZnSe (5.7-18.2µm)Double side coated loss-free calculation and including substrate absorption

A computer program using this algorithm to determine the effects of substrate absorption in a loss-freemultilayer was written at the commencement of this research using the Apple II basic programming language.The flowdown diagrams of the program are attached in Appendix C, together with details of its operation andimplementation using the database method. With advances in computing technology however, this program wassuperseded by the use of absorption modelling using spreadsheets and advanced thin-film software packages.However, at the time of its development, the program was capable of performing analysis beyond that availableelsewhere.


94

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

025050075010001250150017502000Wavenumber (1/cm)

Tra

nsm

ittan

ce

Loss Free

1mm

1.5mm

2mm

2.5mm

3mm

3.5mm

4mm

Loss Free

4.0mm

Figure 4-5 Broadband antireflection coating on Germanium (5.7-18.2µm)Double side coated, loss-free calculation and including substrate absorption (1-4mm)

4.2 Multilayer calculations including layer absorption

The matrix calculations presented in Section 4.1 are useful for the case of non-absorbing layers, forwhich the Fresnel coefficients are real. This represents the ultimate achievable performance by design, withperfectly transparent materials deposited on an absorbing substrate. The development of the algorithm inclusiveof absorbing layers, for which the refractive indices are replaced by complex dispersive quantities producescomplex Fresnel coefficients, which when combined with the substrate model is then closer to a truerepresentation of the predictive performance of the manufactured filter.

In the absorbing multilayer case, the refractive index in the characteristic matrix is complex (Nm = nm-ikm), comprising the real part of the refractive index nm, and the imaginary part as the extinction coefficient km.The relationship between the electric and magnetic vectors in the medium of incidence to that in the substrate fora single film can be expressed in matrix notation as follows[71] :

( )E

H

i

i

E

Ha

a

b

b

=

cos sin /

sin cos

δ δ ηη δ δ

1

1

(4-28)

where, a is the incident medium boundary and b is the substrate boundary δ = 2πN1 d cosθ1 /λ, η is the opticaladmittance given by ηm =Y (nm – ikm) for the layer material, andY is the admittance of free space given by:

Y = ε

µ0

0

= 0.002654 Ω-1 (4-29)

as the optical admittance ηm = Hm/Em, this matrix can be written as:

( )B

C

i

i

=

cos sin /

sin cos

δ δ ηη δ δ η

1

1 2

1(4-30)

where C/B = Hm1/Em1, B = normalised electric field amplitude and C = normalised magnetic field amplitude.

Extending this assembly to a two layer case as illustrated in Figure 4-6,


95

Figure 4-6 Plane wave incident on a two layer structure

The characteristic matrix is given by:

( )E

Hi

i

E

Hb

b

c

c

=

cos sin /

sin cos

δ δ ηη δ δ

2 2 2

2 2 2

(4-31)

B

C

i

i

i

i m

=

cos sin /

sin cos

cos sin /

sin cos

δ δ ηη δ δ

δ δ ηη δ δ η

1 1 1

1 1 1

2 2 2

2 2 2 3

1(4-32)

This recursive matrix can then be extended to the general case of an assembly ofq-layers, where the characteristic matrix is the product of the individual matrices taken in their sequential order,i.e.,

B

C

i

im m m

m m mm

q

s

=

=∏

cos sin /

sin cos

δ δ ηη δ δ η1

1(4-33)

where the phase factor δm = 2πNmdmcosθm/λ and ηs = Y (ns – iks) for the substrateηm = Y Nmcosθm for s-polarization (TE) (4-34)

ηθm

m

m

N=

Y cos

for p-polarization (TM) (4-35)

and where we have now used the suffix s to define the substrate or exit medium.ηs = Y Ns cosθs for s-polarization (TE) (4-36)

ηθs

s

s

N=

Y cos

for p-polarization (TM) (4-37)

If θ0, the angle of incidence, is given, then the values of θm,s can be found from Snell’s law, i.e.N0sinθ0 = Nmsinθm = Nssinθs (4-38)

As B/C = Ea/Ha , the reflectance, transmittance and absorptance can be calculated as the followingcoefficients, where η0 is the admittance of the incident medium.

RB C

B C

B C

B Cq =−+

−+

∗η

ηηη

0

0

0

0

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( )( )( )

TB C B C

q

s=+ +

∗

4 0

0 0

η η

η η

Re(4-40)

( )( )( )A

BC

B C B Cq

s=−

+ +

∗

∗

4 0

0 0

η η

η η

Re(4-41)

where * = complex conjugate.The reflectance, transmittance and absorptance are then related by R + T + A = 1. A mathematical analysis for asingle film with complex indices using this multilayer calculation procedure is described in Appendix D.

Double-side coated calculations shown in Figures 4-7 and 4-8 are inclusive of the dispersive complexrefractive index models of both the layer and substrate materials as applied to the previous examples ofbroadband antireflection coatings. The predicted design model utilizes the reference complex material databasesfor both the substrate and layer materials for the dispersive calculations, (with the exception of anuncharacterised outer BaF2 layer material responsible for the additional absorption present in the measurement at≈ 750cm-1) . It can be seen that outside of this region which is dominated by the BaF2 that there is goodagreement between the predictive design calculation and the measurement of the manufactured element.

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Figure 4-7 Broadband antireflection coating containing ZnSe/PbTe and BaF2 outer layerdeposited on a 2.0mm ZnSe substrate

(comparison of predicted calculation performance (thin line) and measurement (thick-line) at 300K


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Figure 4-8 Broadband antireflection coating containing ZnSe/PbTe andBaF2 outer layer deposited on a 3.0mm Ge substrate

(comparison of predicted calculation performance (thin line) and measurement (thick-line) at 300K

4.3 Predictive design modelling of a ultra-wide (5-30µµµµm) passband filter

The design and manufacture of an ultra-wide (5-30µm) infrared passband filter for use in FTIR studiespresents an example of the implementation of predictive design modelling. A design model of the filter and thematerials used in its construction has been developed from the data derived in Chapters 1 and 2 capable ofaccurately predicting spectral performance at both 300K and the reduced operating temperature at 200K. Thisdesign model is based on the optical and semiconductor properties of the multilayer filter containing PbTe layermaterial in combination with the dielectric dispersion of ZnSe deposited on a CdTe substrate together with theuse of BaF2 as an antireflection layer. Comparisons between the computed spectral performance of the modeland spectral measurements from manufactured coatings over a wavelength range of 4-30µm and temperaturerange 300-200K are presented.

Fourier Transform Infrared (FTIR) absorption studies of the vibrational modes of the photosyntheticwater-oxidising enzyme Photosystem II has led to the need for the design and manufacture of an ultrawideinfrared passband filter capable of transmitting infrared radiation with wavelengths between 5µm and 30µm[72].(Photosystem II is the enzyme responsible for the oxidation of water to dioxygen in algae and higher plants[73-74]

).The specification requirements demanded for these filters in this study are unique. It is required that the filterprovide high average transmittance across the 5-30µm wavelength band of >75%, with a spectral positioningtolerance at 5µm of ±2%, and edge steepness of <4%. Continuous short wavelength blocking with transmittanceless than 10-4 was needed, and the filters were required to operate at a reduced temperature of 200K.

4.3.1 Infrared materials selection

The choice of substrate and layer materials exhibiting continuous transparency out to the 30µm regionis somewhat limited, particularly where soft and moisture sensitive materials are unacceptable for use, as is thecase in this application. Realistically the choice of possible materials is restricted to the following:- For thesubstrate, CdTe and diamond were the most probable candidates, however, diamond had to be rejected ongrounds of cost and possible availability. The other possibilities of using KRS-5 and CsI were rejected on thegrounds of KRS-5 being too soft and not stable at the filter deposition temperatures, and CsI being highlymoisture sensitive. Cadmium telluride (CdTe) was therefore the most suitable substrate, providing good longwavelength transparency out to 30µm prior to the multi-phonon lattice-absorption region[75], as illustrated inChapter 2. A substrate thickness of 2mm provided adequate mechanical robustness in combination with limitingthe long wavelength transmittance loss.


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For the layer materials, the choice of PbTe for the high index material[76] was straightforward, as theonly other possibility was that of using germanium with greater long wavelength loss. For the lower indexmaterial, zinc selenide was selected because of its relatively low value of refractive index (n = 2.4) comparedwith those of the other possibilities of CdSe (n = 2.54) and CdTe (n = 2.65) all of which possess good longwavelength transparency. Finally, there is a overriding need in the design of filters requiring very wide ranges ofhigh transmittance (5-30µm, a ratio of 6 to 1 in this case) for the use of a very low index material as the outerantireflection layer. For this part of the structure either PbF2 (n =1.75) or BaF2 (n = 1.35) could have been used.The choice was made to use BaF2 as it has a lower refractive index, is less soluble than PbF2 and because PbF2 isknown to sometimes have free Pb in the film causing absorption. yttrium fluoride (YF3) and ytterbium fluoride(YbF3) were also considered as candidate low index fluorides but dismissed due to their shorter reststrahlwavelengths.

It should be realised that BaF2 could have been used throughout the entirety of the filter as the lowerindex material, and not just for the antireflection part of the structure[77]. This would make very little differenceto the final performance, apart from a slight reduction in layer count, as the multilayer part of the design isessentially acting as a dispersive matching layer between the substrate and the antireflection layer. Theoverriding practical reason that BaF2 was not used throughout the design was, that in common with nearly allfluorides, the build up of tensile stress in the BaF2 layers would precipitate mechanical failure of the structure oncooling. Barium fluoride, as with all the fluorides when deposited by thermal evaporation, forms a soft thin-film.To minimise surface roughness and reduce tensile stress, the film was deposited with a higher substratetemperature (≅ 210°C) than the underlying stack (≅185°C), the higher deposition temperature producing adenser, more glassy film. To avoid the influence of moisture, to which all fluorides are susceptible, a ZnSe outerprotection layer was deposited as part of the integral multilayer design. The dispersion profile is described by aLorentzian curve fit[78] as defined in Equation 4-42:

( )n AB

C D= +

− +σ 2 (4-42)

with coefficients A = 8.61x10-1, B = 1.51x109, C = 3.08x104, D = 2.33x109

and σ = wavenumbers (cm-1).

4.3.2 5-30µµµµm passband filter design method

The general design method used to meet the high transmittance requirement over a wide spectralinterval was by the refinement of a Tschebysheff equi-ripple polynominal[79] long-wave pass edge filter. Thistype of filter is characterised by alternate low and high index layers, in this case of ZnSe/PbTe respectively. Inthis design the variable layer thicknesses increase towards the centre of the multilayer, where they become ofequal thickness, followed by a symmetrical thickness decrease towards the outer layers. By using these materials,the equivalent index (n*) of this type of structure approximates to the original substrate refractive index at itsouter surfaces, matching well to the CdTe substrate interface, and providing a good outer interface for theapplication of the BaF2 antireflection and protection multilayer of equivalent index √nSub. The underlyingTschebysheff ZnSe/PbTe edge filter was refined by optimisation to reduce the ripple amplitude, following whicha further refinement with, and including the BaF2 antireflection and ZnSe protection layers was performed. Theresulting structure, deposited on both surfaces of the substrate, is composed of 18 layers, each layer of anoptimized and non-quarterwave fractional thickness. The spectral positioning of the coating on the first surfacewas displaced relative to the coating on the opposite side in order to avoid the coincidence of residual rippleminima still present in the design following its refinement. The combination of materials and design principalsused in this application can be applied to all wideband filters in this wavelength region. The limiting constraintsbeing defined at short wavelengths by the PbTe semiconductor absorption edge and the long wavelength limit bythe CdTe multi-phonon lattice-absorption.

4.3.3 Spectral performance prediction and comparison with measurement

Calculated models of the predicted filter performance at 300K & 200K together with the measurementresults of the manufactured filters are shown in Figures 4-9 & 4-10. Using the dispersion and absorption modelsfor the selection of materials described earlier, good agreement for the observed long wavelength temperatureshift caused by the negative temperature coefficient of the PbTe material has been verified. This amounts to atotal shift of 30cm-1 (1.42%) producing a temperature coefficient for the filter of -0.29cm-1K-1. Predictive


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modelling of the change of edge steepness with temperature has also produced good agreement increasing theedge from 3.26% at 300K to 3.17% at 200K. The transmittance, though not perfectly matched with the predictedcalculation due to random deposition thickness errors is satisfactory for the filter requirements and found bytolerance analysis to be within a 2% envelope of the layer thickness accuracy.

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Figure 4-9 Overlay of the spectral measurement and the predicted calculation performance model at 300K

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Figure 4-10 Overlay of the spectral measurement and the predicted calculation performance model at 200K


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4.4 Systems design of far-infrared filters

In terms of a spectral systems design model, the filters and dichroic beamsplitters used in the longwavelength channels of the Pressure Modulator Infrared Radiometer (PMIRR) shows the degree of complexity anddifficulty in the design and manufacture of a multi-channel system. These coatings consisted of ultra-widebanddichroic beamsplitters and, in the case of Channel 6, a 20µm narrow bandpass filter. The ultra wideband multi-channel dichroic beamsplitters covering the spectral range of 0.3 to 52µm were designed[80] to provide a highlyreflective broad, flat response in the visible and mid-infrared wavelength regions, from 0.3 to 12.2µm, andmaximum transparency across the far-infrared wavelength range from 19.6 to 52.6µm. The detailed opticalarrangement of the dichroics and filter is illustrated in Figure 4-11. The dichroic beamsplitter 202D was required totransmit Channels 6 (510-460cm-1), 7 (340-290cm-1) and 8 (240-190cm-1). Dichroic beamsplitter 302D was requiredto transmit Channel 8 whilst reflecting Channels 6 and 7, and 303D transmits Channel 7 whilst reflecting Channel 6.This group of 3 long wavelength channels at 20.7, 31.9 & 47.2 µm were selected at wavelengths to measure theabundance of atmospheric water vapour, dust and surface temperature.

Figure 4-11 PMIRR optical layout - far infrared channels

The two longest wavelength channels are at wavelengths beyond the limits of conventional multilayerdielectric filter design, requiring dielectric spaced resonant mesh filter designs[81]. The channel 6 filter at 20.7µmhowever, was designed and fabricated as a traditional dielectric multilayer filter on stoichiometric, polished,polycrystalline CdTe substrates, onto which was deposited the following Tellurium-enriched PbTe[82] and ZnSemultilayer bandpass filter design. The use of Te-enriched PbTe provides enhanced long wavelength transmittance at300K, with less absorption than that of stoichiometric material as described in Chapter 3. A triple half-wavebandpass filter with low index material cavity layers and containing an antireflection quarter-wave 3-layersimulation was developed as the band defining filter design. The 3-layer simulation on the outside of the multilayerreplaced an equivalent quarterwave layer with a refractive index of 3.0.

Sub | 0.1L H 2L H L H 2L H L H 2L 0.395L 0.154H 0.395L | Air

The choice of coating and substrate materials for the dichroic beamsplitters required a high transparency atlong wavelengths and a highly absorptive material to achieve a flat response at short wave. Ultra-pure Fz Silicon,which has good transmittance >20µm was used for the substrate material. Various layer material combinations wereassessed resulting in PbTe, Ge and CdTe as offering the most suitable characteristics to satisfy the requirements,though in the far infrared region lattice absorption produces design limitations by restricting the number and totalthickness of the layers that can be used before significant loss in transparency is observed.


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To achieve the spectral profiles required, knowledge of the optical constants of the coating materials inboth the short wavelength electronic absorption regions and long wavelength lattice absorption bands, together withthe effects of dispersion across the wide wavelength range was required. Additionally, experience had shown therewas a need to reduce possible stress induced failures which can be caused by depositing thick layers. This problemof stress in the necessarily thick coatings was encountered when depositing onto the full size (35mm x 35mm)substrates. By re-designing the multilayer to have a much greater number of thinner layers using sub-dividedequivalent 3-layer simulations[83], I was able to reduce this stress, and ensure the spectral performance required atthe critical wavelengths was unimpaired.

Antireflection on the rear surface of these beamsplitters was performed using a low absorbing conformalorganic coating (Parylene N). This provided adequate long wavelength transmittance and was of an index closelymatching the square root of the silicon substrate. This organic coating passed environmental testing requirementsand was temperature cycled between 233 and 313K.

The spectral requirement for this channel was for a fully blocked 10% wide bandpass filter to operate at300K in a fast cone of f/0.81. In addition to the combined system throughput of the three dichroic beamsplitters, inorder to achieve the short wavelength blocking requirements, the rear surface of the bandpass filter comprised 3subsidiary overlapping Herpin multilayers. These blocked the high order transmittance, which in combination withan optimized equi-ripple Tschebysheff low-pass stack[84] defined the cut-on position and provided a broad flatregion of transparency across the passband. A spectral overlay showing the predicted interaction between thedichroic beamsplitters and bandpass filter to achieve the required system response is illustrated bydispersive/absorptive calculations in Figure 4-12. The spectral overlay in Figure 4-13 shows good agreement withthe predicted model for the measured spectra of the manufactured components calculated for the required incidentangles and operating temperatures.

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Figure 4-12 PMIRR Channel 6 (20µm) narrow bandpass filterCalculated spectral throughput using dispersive / absorptive materials


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Figure 4-13 PMIRR Channel 6 (20µm) narrow bandpass filterMeasured spectral throughput for the individual elements and combined system response

4.5 Conclusion

As a result of applying the complex refractive index constants derived for the substrate and thin-filmmaterials to the multilayer calculation algorithms described, predicted spectral performance models for a range ofdiffering filters has been developed. Comparisons of these models with the measured spectral profiles obtained forthe manufactured filters has shown good agreement, and verified the accuracy of both the optical constants and thismethod of analysis. The rationale behind the choice of substrate and coating materials for use in these examplefilters has also been discussed and presented.


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CHAPTER 5AN INTEGRATED SYSTEMS PERFORMANCE APPROACH TO

INFRARED SPECTRAL INSTRUMENT DESIGN

5.0 Introduction

Infrared filters and coatings have been employed on many remote sensing radiometer instruments[85] tomeasure the thermal emission profiles and concentrations of chemical constituents found in planetaryatmospheres. The High Resolution Dynamics Limb Sounder[86] (HIRDLS) is an example of the most recentdevelopments in limb-viewing radiometry by employing a cooled focal plane detector array to providesimultaneous multi-channel monitoring of gas and aerosol emissions.

The High Resolution Dynamics Limb Sounder (HIRDLS) is a limb viewing infrared radiometer forhigh-resolution monitoring of stratospheric and mesospheric temperature, trace chemical species andgeopotential height gradients in the Earth's atmosphere. It is scheduled for launch on the NASA EOS-Chemsatellite in 2003 along with other instruments to make measurements relating to the chemistry of the atmosphere.The HIRDLS instrument will obtain data at higher resolutions than has been measured previously with a verticalresolution of 1km and horizontal scales of 400km or less. These measurements will enable new research inchemical mixing, transport and exchange between the stratospheric and tropospheric layers in the atmosphere tobe performed, and will directly monitor the temperatures and concentrations of the trace elements associatedwith atmospheric changes to world climate.

The HIRDLS instrument is a descendant from earlier infrared limb sounding instruments, namely; theImproved Stratospheric and Mesospheric Sounder[87-89] (ISAMS) on the Upper Atmosphere Research Satellite(UARS), and the Pressure Modulator Infrared Radiometer[90] (PMIRR) on the Mars Observer. Both of theseinstruments use pressure modulation radiometry[91] to measure the emission profiles through an absorption cell inthe optical train. This technique detects radiation from the emission lines of a specific radiatively activeatmospheric constituent gas by modulating the pressure of the same gas in a cell placed in the optical path of theinstrument. Using this arrangement, pressure within the cell is cyclically modulated using an electromagneticallydriven free piston compressor/expander attached to the cell, the resulting absorption fluctuations superimpose anamplitude modulation on the infrared signal passing through the cell. By this method, the target gas is registeredand can be detected against the non-modulated background by the cooled detectors.

These generic types of radiometer have traditionally used discrete detectors and separate optical trainsfor measurements in each spectral channel resulting in a complex optical layout with a large number of coatedcomponents, including sets of spectrally demanding beamsplitters. With advances in focal plane arraytechnology, simultaneous multi-channel measurements can be made using a cooled focal plane detector arraywith integral filters permitting a greater number of spectral channels than would be practical by the pressuremodulation technique.

The radiances to be measured by the HIRDLS instrument are caused by mid-infrared thermal emissionfrom the atmosphere in the vibration/rotational bands of their molecular emitters, and from any aerosol andcloud emissions. The specific passbands selected are chosen to measure emissions from carbon dioxide (CO2),ozone (O3), nitric acid (HNO3), nitrous oxide (N2O), nitrogen dioxide (NO2), dinitrogen pentoxide (N2O5),chlorine nitrate (ClONO2), methane (CH4) water vapour (H2O) and chlorofluorocarbons CFCl3 and CF2Cl2,together with aerosol at several wavelengths.

The instrument contains 21 spectral channels spanning a wavelength range from 6 to 18µm. For each ofthese channels the spectral bandwidth and position are isolated by an interference bandpass filter at 301K placedat an intermediate focal plane of the instrument. A second filter cooled to 65K, positioned at the samewavelength but designed with a wider bandwidth, is placed directly in front of each cooled detector element toreduce stray radiation from internally reflected in-band signals, and to improve the out-of-band blocking.

In this chapter, the process of determining the spectral requirements I have developed for the twobandpass filters and the antireflection coatings used on the lenses and dewar window of the instrument isdescribed. This process uses a system performance approach taking the instrument spectral specification as atarget. It takes into account the spectral characteristics of the transmissive optical materials, the relative spectralresponse of the detectors, thermal emission from the instrument, and the predicted atmospheric signal to


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determine the predicted radiance profile for each channel. Using this design approach a more optimaldesign for the filters has been achieved, minimising the number of layers to improve the in-band transmissionand aid manufacture. The use of this design method has also permitted the instrument spectral performance to beverified using the measured response from manufactured components. The spectral calculations for an examplechannel are discussed, together with the spreadsheet calculation method. All the contributions made by thespectrally active components to the resulting instrument channel throughput are identified.

5.1 Advantages of an integrated spectral systems approach

Traditionally, the design and manufacture of interference filters for use in radiometer instruments hasrequired the development of complex multilayer structures[92-94], often involving the use of a large number oflayers to provide adequate (if not excess) continuous blocking on either side of the passband. This type ofapproach had evolved in part, from the way that the performance of the separate elements of the spectral systemwas specified for procurement purposes, usually being defined in isolation from the rest of the system. This waspartly due to the complexity of carrying out a thorough spectral analysis of the system as a whole, and partly dueto deficiencies in the knowledge of the spectral characteristics of the materials and coatings, with the instrumentdesigner tending to regard the regions of greater than required blocking due to the interaction of the elements inthe design as a bonus. What was probably not realised, was the small but significant loss of in-band performancetogether with the additional risk of mechanical failure induced by the inherent thickness related stress in themultilayer to which this approach leads. With improved knowledge of the spectral characteristics of materials Ihave developed in the previous chapters, and the ability to handle large spreadsheets, an integrated approach tothe spectral design is now more readily achievable.

By adopting an integrated systems approach to the HIRDLS instrument, the spectral performance foreach filter and/or coating can be tailored specifically to perform its own specialised function. This permits adegree of flexibility previously unavailable from spectral radiometer design in the past, as both the individualfilters and the instrument as a whole can be optimised to achieve a more efficient design. This approach has alsoprovided advantages during the evolution of the instrument by including the capability to interactively assessperformance requirement changes as they occur. The ability to assess alternative filter designs and evaluate (andeven possibly compensate for) the effects of a non-compliant performance from a particular component on theoverall system throughput has proved an invaluable tool for the spectral designer.

The instrument spectral throughput is verified on a channel by channel basis using the same model. Themodel now uses the component spectral measurements rather than the predicted component transmissions.Spectral measurements of individual components made at the instrument operating temperatures together withcorrections to the spectral positioning of the filters are used to compensate for the difference in illuminationbetween that existing in the measurements to that experienced in the instrument. Further corrections are thenmade for the effects of coating non-uniformity on the spectral placement, particularly in the case of theantireflection coatings on the curved surfaces of the lenses. Care must be taken to ensure that the accuracy of themeasurements and knowledge of the temperatures at which they are made is adequate to ensure confidence in themodel.

5.2 Optical system layout

The optical system layout for the HIRDLS instrument, as illustrated in Figure 5-1, is that of an off-axisGregorian telescope[95] that focuses infrared radiation from the atmosphere on to the cooled focal plane detectorassembly. The line of sight of the telescope is determined by the horizontal and vertical setting of a 2-axis scanmirror (M0) which reflects the incident beam through a 180mm circular primary diffraction baffle (PDB) and onto the primary parabolic mirror (M1). Radiation reflected from this mirror is focused through the plane of thechopper at the first field stop and on to a secondary ellipsoid mirror (M2), inclined to the paraboloid axis, andpositioned with a focus coincident with that of the primary paraboloid. The secondary ellipsoidal mirror (M2)focuses the reflected ray bundles onto the array of warm band-defining filters (WF1-21) in f/7 illumination whichis thermostatically controlled at 301K. Radiation transmitted through the filters is then directed through theconcave surface of an antireflected germanium lens (L1), from which the divergent ray bundles fall on to a foldmirror (M4). Reflected rays from the fold mirror are then collected by the convex surface of a secondantireflected germanium lens (L2) and focused through the antireflected zinc selenide window (DW) of thedetector package, through the cold filter assembly (CF1-21) in f/1.5 illumination and on to the array of cooleddetectors at 65K


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Primary Diffraction Baffle (PDB)

Warm Filters (WF1-21)

301K

Ge Lens(L1)

Ge Lens (L2)

Paraboloid(M1)

ZnSe Dewar Window (DW)

(M4)

ColdFilters (CF1-21)

65K

Fold MirrorStop

First Field Stop

(M0)MirrorScan

Chopper

(ILS)Lyot Stop Ellipsoid

(M2)

Figure 5-1 HIRDLS Optical system layout

The detector assembly is an array of 21 separate HgCdTe infrared detectors optimised for maximumresponse at the selected measurement wavelength and cooled by a Stirling cycle cooler to a temperature ofapproximately 65K. The whole focal plane assembly, illustrated in Figure 5-2, comprising the secondary ghostimage suppression filters and detectors is contained in a hermetically sealed vacuum dewar.

Figure 5-2 HIRDLS Focal plane array cold filter and detector layout

The filters are deposited onto 16mm diameter low resistivity (5-40Ωcm) monocrystalline germanium. With theneed for the best image quality on the detectors, the thickness of the filter substrates is unique for each spectralchannel to compensate for chromatic and field curvature aberrations (optical path length differences) defocusing


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the telescope subsystem over the wide spectral range of the HIRDLS channels. Additionally the specifiedthickness of the substrate is further adjusted to compensate for the thickness (in “equivalent-germaniumthickness”) of the multilayers themselves, which are of differing thicknesses according to spectral placement andthe physical thickness of the deposited multilayers needed. This desire for best image quality also leads directlyto a tight tolerance on this overall equivalent germanium thickness figure, which in turn necessitates a tightertolerance on the thickness of the manufactured uncoated substrate of ± 5µm with a thickness and parallelismtolerance of ±2µm. The “equivalent germanium thickness” is calculated as the ideal thickness of the filter for itscentral passband wavelength on the assumption that the filter is equivalent to a single thickness of germaniumwith no thin film coatings, as defined in Equation 5-1:

∑

−

−

−=i

ig

gs n

Tn

nTT

11

10 (5-1)

Where :-T0 = Germanium equivalent thickness required,ng = Germanium refractive index at the operating temperatureTi = Total physical thickness of thin-film coating material (i)ni = Refractive index of thin-film coating material (i)Σ = Summation for all the materials in the thin film stack.

5.3 Filter design requirements

The spectral characteristics of each of the 21 radiometric channels in the HIRDLS instrument is definedby a warm band-defining interference filter mounted in the warm filter array at 301K, positioned at theintermediate focal plane of the telescope in f/7 converging illumination. The second filter, mounted in the coldfilter array, is spectrally positioned at the same wavelength as the band-defining filter but having a widerbandwidth, is placed directly in front of each cooled detector element, the detector and filter both operating at65K in f/1.5 converging illumination. The cold filters are designed with a wider bandwidth to ensure that thespectral band is unambiguously defined by the warm filters.

The primary function of the narrower warm band-defining filters is to spectrally isolate the requiredpassband for each channel and provide broadband blocking of unwanted spectral energy by multilayerinterference within the limits of the HIRDLS passband range. The wider, cold bandpass filters of each channelpair is individually tailored to spectrally work in conjunction with its companion by assisting with thesuppression of out-of-field “ghost images”, i.e. spectral cross-talk contamination between channels. This resultsfrom internally reflected out-of-band radiation from a filter in a particular channel returning as in-band signals toanother channel from within the detector package assembly and elsewhere.

There is also a further advantage in this dual filter arrangement as the crucial band-defining filtersoperate in an f/7 cone with minimal degradation of shape due to the illumination, whilst the cold filters operate inf/1.5 illumination at the detector plane, which being of significantly wider bandwidth are less affected than theband-defining filters would have been had they been placed in this illumination. The ratio of in-band to out-of-band signal is also improved when using two filters compared with the performance of a single filter, this avoidsmulti-stack interactions which can lead to unwanted transmission spikes in the stop-band. Additionally, and justas importantly, the filters reduce the amount of thermal background radiation of the instrument from reaching thedetectors and reinforce the out-of-band blocking .

Blocking outside the range of the HIRDLS passband (6-18µm) is provided by the combination of thegermanium and zinc selenide multi-phonon absorption profiles from the two lenses (L1 & L2) and dewarwindow (DW), together with the roll-off of the antireflection coatings. These behave as cut-off filters to short-wave and have a roll-off beyond 18µm as a result of the spectral properties of the bulk and layer materialsdiscussed previously. Account is also taken in the instrument spectral design of the detector wavelengthresponse; this differs according to the various materials used for the different wavelength groupings of channels,and can be used to determine the limits of the interference blocking required from the filters.

Although many of the HIRDLS channels have relatively narrow passbands, down to just 1.0% betweenhalf power points in certain channels, very few of the passbands contain spectral lines from only a singlemolecule. The majority of the channels contain multiple trace constituents and/or contaminants which define the


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spectral structure. Differential spectroscopy is then used to obtain independent measurements of eachquantity by subtracting element concentration profiles across channels. As the radiance emitted by theatmosphere has a structure which varies rapidly with wavelength, the measured emission is highly sensitive tothe passband shape and position (but not to throughput, which is measured by on-board radiometric calibration).This imposes tight requirements for the manufacture of each filter, and even tighter constraints upon theknowledge of the overall instrument spectral response.

The spectral requirements on the filters are :-i) the position of the edges of the passband are required to be typically within ±2cm-1 for the half power points,depending on adjacent spectral features;ii) knowledge of the relative spectral response across the pass-band to within 1% with absolute frequencyaccuracy of 0.2cm-1, andiii) the sensitivity outside the required passband must be sufficiently small that radiance corresponding to thosefrequencies is less than 1% of the wanted in-band radiance or half of the instrument noise whichever is thegreater.

Although these requirements apply to the instrument as a whole, the infrared filters play the primaryrole in determining the spectral response. Additional requirements specifically relating to the filters are;iv) a minimum sensitivity to the effects of non-parallel illumination,v) a minimum temperature coefficient, so as to allow operation within the instrument spectral specification, overas wide a range as possible of temperature in the 65K and 301K regions,vi) highest possible in-band transmission,vii) the spectral bandpass profile should be as square as is practical, consistent with minimising the total numberof layers to maximise transmission. This is specified as the spectral interval between 5% transmission pointswhich is not to exceed 1.6 x FWHH (Full Width Half Height),viii) the filters should be robust enough to survive testing to MIL-F-48616 (this includes humidity and adhesiontesting) as well as dimensioning by diamond sawing under water, and in the case of the cold filters, repeatedtemperature cycling from 300 to 65 Kix) the filters should not show undue degradation in transmission or shift in spectral placement during their 15year life (up to 10 years before launch and a 5 year life in orbit);x) the surface quality of the coatings used in the filters should be such as to minimise scattering. Incidence ofpinholes and spatter from evaporation sources to be reduced to a minimum (there is an opportunity to avoidthese obvious defects by selection after cutting).

Taken together, these requirements make considerable demands on the coating materials and the designand manufacture of the multilayer structures of the filters. Table 5-1 details the end-to-end spectral passbandrequirements for each channel in the HIRDLS instrument. From this, the specific requirements for each of thefilters is derived by taking into account corrections caused by the f-number incident on the two sets of filters inthe instrument, and the wavelength displacement created by the long wavelength characteristics of the materialsand coatings.


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Table 5-1 HIRDLS Instrument spectral requirements

Channel Target SW50% Tol Centre LW50% Tol Bandwidth Min Max FWHM Min MaxNumber Species (cm-1) (cm-1) (cm-1) (cm-1) (cm-1) (cm-1) (cm-1) (cm-1) (%) (%) (%)

1 N20 587.3 1.0 575.4 563.5 2.0 23.8 20.8 26.8 4.14 3.61 4.662 CO2 614.8 1.0 607.7 600.5 2.0 14.3 11.3 17.3 2.35 1.86 2.853 CO2 639.5 2.0 624.8 610.0 3.0 29.5 24.5 34.5 4.72 3.92 5.524 CO2 660.0 3.0 643.0 626.0 3.0 34.0 28.0 40.0 5.29 4.35 6.225 CO2 680.0 3.0 667.5 655.0 3.0 25.0 19.0 31.0 3.75 2.85 4.646 Aerosol 835.0 2.4 828.3 821.5 2.3 13.5 8.8 18.2 1.63 1.06 2.207 CFCl3 852.0 2.4 843.5 835.0 2.4 17.0 12.2 21.8 2.02 1.45 2.588 HNO3 903.5 2.5 882.5 861.5 2.5 42.0 37.0 47.0 4.76 4.19 5.339 CF2Cl2 931.5 2.6 923.8 916.0 2.6 15.5 10.3 20.7 1.68 1.12 2.2410 O3 1009.0 2.8 1000.0 991.0 2.8 18.0 12.4 23.6 1.80 1.24 2.3611 O3 1046.5 2.9 1028.8 1011.0 2.9 35.5 29.7 41.3 3.45 2.89 4.0112 O3 1138.5 3.2 1129.3 1120.0 3.2 18.5 12.1 24.9 1.64 1.07 2.2113 Aerosol 1220.0 3.4 1211.0 1202.0 3.4 18.0 11.2 24.8 1.49 0.92 2.0514 N2O5 1259.8 1.0 1244.7 1229.5 2.0 30.3 27.3 33.3 2.43 2.19 2.6815 N2O 1281.8 1.0 1269.1 1256.3 1.0 25.5 23.5 27.5 2.01 1.85 2.1716 ClONO2 1298.8 1.0 1288.6 1278.3 1.0 20.5 18.5 22.5 1.59 1.44 1.7517 CH4 1367.5 3.8 1346.5 1325.5 3.8 42.0 34.4 49.6 3.12 2.55 3.6818 H2O 1435.0 4.0 1411.0 1387.0 4.0 48.0 40.0 56.0 3.40 2.83 3.9719 Aerosol 1415.8 1.0 1409.1 1402.3 1.0 13.5 11.5 15.5 0.96 0.82 1.1020 H2O 1542.0 4.3 1482.0 1422.0 4.1 120.0 111.6 128.4 8.10 7.53 8.6621 NO2 1630.5 4.6 1608.0 1585.5 4.5 45.0 35.9 54.1 2.80 2.23 3.3622 Alignment 1542.0 4.3 1482.0 1422.0 4.1 120.0 111.6 128.4 8.10 7.53 8.66

MICRONS (as derived from cm-1)

Channel Target SW50% Tol Centre LW50% Tol Bandwidth Min Max FWHM Min MaxNumber Species (um) (+/- nm) (um) (um) (+/- nm) (um) (um) (um) (%) (%) (%)

1 N20 17.03 29.0 17.38 17.75 63.0 0.72 0.63 0.81 4.14 3.61 4.672 CO2 16.27 26.5 16.46 16.65 55.5 0.39 0.31 0.47 2.35 1.86 2.853 CO2 15.64 48.9 16.01 16.39 80.6 0.76 0.63 0.89 4.72 3.92 5.544 CO2 15.15 68.9 15.55 15.97 76.6 0.82 0.68 0.97 5.29 4.36 6.235 CO2 14.71 64.9 14.98 15.27 69.9 0.56 0.43 0.70 3.75 2.85 4.656 Aerosol 11.98 34.4 12.07 12.17 34.1 0.20 0.13 0.27 1.63 1.06 2.207 CFCl3 11.74 33.1 11.86 11.98 34.4 0.24 0.17 0.31 2.02 1.45 2.588 HNO3 11.07 30.6 11.33 11.61 33.7 0.54 0.48 0.60 4.76 4.19 5.339 CF2Cl2 10.74 30.0 10.83 10.92 31.0 0.18 0.12 0.24 1.68 1.12 2.2410 O3 9.91 27.5 10.00 10.09 28.5 0.18 0.12 0.24 1.80 1.24 2.3611 O3 9.56 26.5 9.72 9.89 28.4 0.34 0.28 0.39 3.45 2.89 4.0212 O3 8.78 24.7 8.86 8.93 25.5 0.15 0.09 0.20 1.64 1.07 2.2113 Aerosol 8.20 22.8 8.26 8.32 23.5 0.12 0.08 0.17 1.49 0.92 2.0514 N2O5 7.94 6.3 8.03 8.13 13.2 0.20 0.18 0.22 2.43 2.19 2.6815 N2O 7.80 6.1 7.88 7.96 6.3 0.16 0.15 0.17 2.01 1.85 2.1716 ClONO2 7.70 5.9 7.76 7.82 6.1 0.12 0.11 0.14 1.59 1.44 1.7517 CH4 7.31 20.3 7.43 7.54 21.6 0.23 0.19 0.27 3.12 2.56 3.6818 H2O 6.97 19.4 7.09 7.21 20.8 0.24 0.20 0.28 3.40 2.84 3.9719 Aerosol 7.06 5.0 7.10 7.13 5.1 0.07 0.06 0.08 0.96 0.82 1.1020 H2O 6.49 18.1 6.75 7.03 20.3 0.55 0.51 0.59 8.11 7.54 8.6821 NO2 6.13 17.3 6.22 6.31 17.9 0.17 0.14 0.21 2.80 2.23 3.3722 Alignment 6.49 18.1 6.75 7.03 20.3 0.55 0.51 0.59 8.11 7.54 8.68

5.3.1 Bandpass filter design

To achieve the spectral profile requirements, bandpass filter designs containing multiple half-wavecavities utilising the high refractive index contrasts available from PbTe in combination with the II-VIcompounds ZnSe, ZnS and CdTe are used for both warm and cold filter types. By careful use of these low indexmaterial combinations[96] in the bandpass designs it is possible to fine tune the FWHH of the filter passband. Inother cases group IV element, germanium can be used as a substitute for selected PbTe layers, but with thechange in refractive index being greater, lacks the sensitivity of outcome obtainable using the other materials butis still of occasional use. This approach to narrow band filter design is described by Jacobs[97], it has the greatadvantage that quarter wavelength thickness layers are used throughout the reflector stacks, maintaining thethickness monitoring regime and relative thickness accuracy of the layers. The use of PbTe as a layer material inthe filters has particular advantages both in the design and use of bandpass filters :- i) Its high refractive index value means a minimum number of layers are required to perform a given spectralfunction. The high index also enhances the stop-band width, and provides a high effective refractive index (n*)multilayer, reducing the size of spectral shift caused by inclined illumination. ii) A short wavelength absorptionedge at 3.5µm at room temperature removes the need for subsidiary blocking stacks to link up with thegermanium electronic absorption edge at 1.5µm. The long wavelength movement of this edge to 5.5µm at 65Kthen further improves this advantage beyond that achievable with multilayers using germanium, and iii) It has areststrahl wavelength of 110µm making it particularly attractive for use in filters beyond 15µm where alternativehigh index materials are becoming absorbing.


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All these factors have been considered in manufacturing the HIRDLS filters, with the only filters in the setwhich had to use the equivalent germanium based multilayers being Channel 21 warm and cold filters andChannel 20 cold filter. This was necessary because the bandpass positions of these particular filters was belowthe short-wave electronic absorption edge of the PbTe at their operating temperatures. Figures 5-3 and 5-4illustrate a selection of the PbTe and Ge based L-spaced triple half-wave bandpass filter profiles suitable asprospective candidates to achieve the spectral requirements demanded of each channel filter.

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Figure 5-3 Overlay of candidate triple half-wave (THW) bandpass filters (1-10% FWHM)

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Figure 5-4 Log transmittance plot of candidate triple half-wave (THW) bandpass filters(Note the distinct bands characterise the generic filter design depending on the number of layers, order of the

cavities, and number of intercavity layers)

The squareness of the shape of the passband profile improves as the number of cavities increases havingthe effect of increasing the total number of layers in the structure. In addition to this, the narrower the filter isrequired to be, the larger the number of layers between the cavities is required. The effects of absorption, byreducing the transmission, rises sharply with diminishing bandwidth and the sensitivity of the shape of profile tolayer thickness errors also increases with diminishing bandwidth. All these various factors mitigate against theuse of bandpass filters with greater than three cavities designs for filters narrower than ≈ 2.5% FWHH.


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The cavity type, high or low index, also has to be considered when filters are used with highly convergingillumination. The use of PbTe with ZnSe gives a high effective index (n*) of 2.70 in the low index spacer caseand 3.6 (3.75 cold) in the high index case. Where for high index cavities :

( )n n nH L* = (5-2)

and for low index cavities:

( ) ( )n n

n

n n n nL

L

L H L H

* =− +1

2(5-3)

With the use of an f/1.5 illumination cone at the cold focal plane, it would be preferable to use H-spaced designs, at least for the narrower channels. However, one of the few problems associated with PbTe isthat it possesses a thickness-dependant absorptive loss which becomes apparent in thicknesses typical of thoseused in the spacers of bandpass filters. This loss leads to a 5-10% reduction in peak transmission in the H-spacedas opposed to the L-spaced designs of the same bandwidth. The choice of L or H-spaced, 3 or 4 cavity designbandpass filters is therefore rather difficult. In practice as throughput is important, most of the filters are L-spaced, H-spaced only being used where the effects of conical illumination would be unacceptable. Figure 5-5shows the comparative shift in centre wavenumber with angle of incidence for equivalent L and H-spaced triplehalf-wave bandpass filters.

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tre

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%)

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Figure 5-5 Shift in centre wavenumber with angle of incidence for L and H-spacedtriple half-wave (THW) bandpass designs

The use of L-spaced multiple cavity filters does have one further advantage in that the designsinvariably have a very small temperature coefficient of centre wavelength shift due to the interaction of thenegative temperature coefficient of expansion of the PbTe with the smaller positive temperature coefficient ofthe ZnSe compounded with the layer sensitivities in the filter[98]. In the other case of the H-spaced family thesecoefficients do not tend to cancel out and there is quite large coefficient for the filter. Typical values of thetemperature coefficient for a 2% bandwidth filter with first order spacers over the range 300K to 70 K are; -2.8 x10-5 C-1 for L-spaced designs (a -6 cm-1 shift in centre wavenumber at 10µm over range 300K to 80K), and -10x10-5 C-1 (a -21 cm-1 shift for same example) for the equivalent H-spaced design. With these bandpass design considerations, Figure 5-6 illustrates the predicted transmission throughputprofiles and bandwidths achieved from the various selected L-spaced triple half-wave bandpass designs to meetthe band-defining requirements of each channel in the HIRDLS instrument. The bandpass filters in Figure 5-7are representative of the manufactured bandpass designs from the HIRDLS engineering model corrected for theirrespective operating temperatures and cone angles.


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Figure 5-6 Predicted HIRDLS Warm band-definition bandpass design performance, by channel (5.9-18µm)

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Figure 5-7 Selection of manufactured HIRDLS warm and cold bandpass filters at their required operatingtemperatures and corrected for the appropriate cone angles

5.3.2 Blocking filter design

The filter blocking designs for the HIRDLS instrument are required to satisfy several criterion, theseinclude; (i) the need to suppress ghost-imaging, resulting in an out-of-band blocking requirement oftransmissions <10-4 from the shortest channel passband which commences at 5.75µm to the filter passband shortwavelength edge 10-4 point and transmissions <10-2 from the long wavelength channel 10-2 point of the filterpassband long wavelength edge to the detector cut-off edge at 18.3µm for both warm and cold filters in eachchannel. For the cold filters this requirement is deemed to be satisfied by the product of filter transmission anddetector response. In the case of the warm filters it is met by the product of the filter transmission and the opticalsystem response, not including the detector. (ii) A requirement of the cold blocking coatings is to reduce thethermal background seen by the detectors, in general this requirement is met by the ghost image suppression, andfinally, (iii) The instrument blocking also requires the combination of the blocking from both filters andantireflection coatings to ensure the specified in to out-of-band radiance Margin Ratio is achieved, as describedlater in Section 5.4.1.

The filter blocking is carried out by multilayer interference stacks, placed on the opposite surface of thesubstrate to the bandpass filter. These stacks are constructed from the same layer materials as the bandpass


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filters, taking full advantage of the material features described in Chapters 1 and 2. To satisfy the ghost-suppression requirement, typically there is one, two or three short-wave blocking stacks (except on the shortestwavelength channels (20 & 21) where they are not needed). In all channels, except the longest, where they arenot required, there are one or two long-wave blocking stacks. Overall, in most channels the final blockingcoating has a spectral profile resembling a broadband bandpass filter, being a multilayer combination of the twotypes of short and long wave pass blocking filters. In general, the design methods used to meet the blockingrequirements of the filters use combinations of long and short-wave pass edge filters as illustrated in Figure 5-8.

BLOCKER

BANDPASS

BLOCKER

COLD FILTER

WARM FILTER

BANDPASS

Figure 5-8 Disposition of warm and cold filter coatings

The structure of the multilayer blocking stacks are refinements of extracted Tchebysheff equi-ripplepolynomials[99] and Herpin quarter-wave stacks. The Tschebysheff filter designs are characterised by alternatehigh and low index layers (PbTe/ZnSe) of varying thicknesses which increase towards the centre of themultilayer, where they become of equal non-quarter wave thickness, followed by a symmetrical decrease towardsthe outer layers. Herpin quarter-wave stacks are of symmetrical thickness throughout the multilayer, and inaddition to the Tschebysheff edge filter provides good short wavelength rejection. By using overlappingcombinations of these designs, the equivalent refractive index approximates to the original substrate refractiveindex at its outer surfaces, matching well to the germanium substrate interface and providing a suitableequivalent index at the outer interface for the application of an antireflection multilayer of index √nSub. Theunderlying Tchebysheff and Herpin PbTe/ZnSe blocking filters are refined by optimization to reduce the rippleamplitude and enhance the in-band transmission.

5.3.3 Antireflection Coatings

The broadband antireflection coatings deposited on the ZnSe dewar window and Ge lenses are requiredto have the highest and flattest possible transmission performance over the HIRDLS passband wavelength rangeof 6 to 18µm whilst simultaneously reducing the reflectivity to less than 2.7% per surface (this level being set bythe suppression of ghost images requirement). The minimum acceptable transmission for the coating alone onboth surfaces (ignoring substrate absorption) required an in-band performance for each channel of >92% with aminimum average transmission over all of the HIRDLS bands of 94%.

The antireflection coating developed to satisfy this requirement comprised a single multilayer stackwith 10 layers of alternating high and low refractive index layers of PbTe and ZnSe. The stack is overlaid with athree layer antireflection system comprising layers of ZnSe, BaF2 and outermost mechanical protection layer ofZnSe. The materials were selected for their low absorption in film thickness at wavelengths throughout the 6 to18µm instrument passband range. It is essential to use a low index material at the outside of such a wide bandcoating to obtain the highest and widest transmission zone.

The bulk properties of fluoride materials have been well documented[100], possessing refractive indices valuesless than 2, they suitably provide good index matching across a wide wavelength bandwidth between the


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multilayer stack and incident medium. Barium fluoride (BaF2, n=1.35) was selected after investigating twoother possibly suitable materials (suitable because it was felt that their absorption out to 18µm would be lowenough to be useful). Thorium fluoride (ThF4, n=1.4) was found to have more absorption than BaF2 beyond12µm and in samples tested, suffered with stress induced mechanical failure. It was also unacceptable to useradioactive materials such as ThF4. The other material, Lead Fluoride (PbF2), has a higher refractive index of1.75 which would lead to loss of average transmission and a reduction in passband width, also the depositedlayers can contain free Lead causing excess absorption. The problems with these materials confirmed theoriginal choice of BaF2. The layer thickness of the multilayer stack has been refined to provide an optimal flatspectral response[101]. The spectral response of the two types of antireflection coating deposited on the ZnSe andGe materials are shown in Figure 5-9.

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Figure 5-9 Broadband antireflection coating profiles from the Ge lenses and ZnSe Dewar Window(* - Ge Lens L1 profile is that for Channel 18 footprint)

A few weak absorption bands have been observed in the antireflection coatings, most notably aroundthe 6.4µm region (1570cm-1) between the spectral positions of Channels 20 and 21. These bands are commonlyseen in vacuum deposited fluorides and are probably associated with the loss of fluorine from the coating. Theytend not to be present in measurements of coatings made directly on removal from the deposition plant butgradually get stronger over a few weeks under ambient (uncontrolled) laboratory conditions. Both the ZnSe andGe antireflection coatings have shown this behaviour with the rate of change reducing with time, and appearingto reach equilibrium. The spectral performance of the antireflection coating at the Channels 20 and 21 positionsremains unimpaired.

5.3.3.1 Germanium lens thickness distribution

As a result of depositing the broadband antireflection coating on to the highly curved convex andconcave surfaces required for the germanium lens L1, significant variation in thickness uniformity was exhibitedacross the lens surface. This thickness variation caused the spectral positioning of the antireflection profile tobecome distributed at wavelengths which depended on the thicknesses uniformity of the concentric regionscontoured across the surface, forming an inter-dependent spectral and spatial channel arrangement. In order toquantify the effects of this spectral and spatial distribution on each channel, reduced aperture measurements wereperformed at fixed spatial positions through the lens at positions representative of the mean radial channeldistributions, from which I could derive the contoured thickness gradients relating the spectral and spatial inter-dependence. When these thickness gradients are then super-imposed on the distributed channel footprint of thelens, a predictive spectral design model of the expected antireflection wavelength position can be derived foreach channel.

The resultant effects of this spatial distribution on the spectral profile of the antireflection coatingperformance can be seen in Figure 5-10 in which a significant distribution of the short wavelength edge ispresent. This distribution amounts to a spectral range of 200cm-1 (0.62µm) between the channel at the thickestpart of the coating and closest to the centre (Channel 2) and the channel with the thinnest calculated thickness(Channel 18) on the periphery of the lens. This variation approximates to a thickness distribution of 11% across


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the surface of the lens. It should be noted that for each of the shortest wavelength channels adequateprovision for the spectral and spatial placement was considered in the coating design such that none of thechannels were cut-off as a result of their spatial positioning through the lens. The instrument design had alreadyplaced the longer wavelength channel footprints through the centre of the lens, where the thickness of thecoatings was naturally greater. Had it been otherwise this problem would have been very difficult to resolve, asthe passband is virtually at the limit of spectral width for a coating of this performance. The negligible changeobserved for the long wavelength performance is attributed to the multi-phonon absorption profile of the 3.5mmthick germanium and reststrahl absorption properties in the antireflection layer materials which dominate thechange in antireflection profile caused by variation in thickness across the lens. Evaluation of germanium lens L2has shown negligible effects of thickness distribution as a result of the lesser surface curvatures on the lens.

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Figure 5-10 Calculated effects caused by the spatial channel distributionon the antireflection coating of Ge lens L1

5.4 HIRDLS Instrument performance requirements

The overall (or end-to-end) performance of each channel in the HIRDLS instrument is predictedthrough a multipage relational design spreadsheet configured to derive the requirements for the filter elementsusing an iterative verification method. By this method, each contributing element within the instrument isdefined as a fixed spectral profile on to which various warm and cold filter design solutions can be added andtested to ensure the performance requirements of the instrument are satisfied. The multiple pages within thespreadsheet address each channel specification requirement independently. From these, either tabulated orgraphical analyses are used to assess the proposed filter designs. The spectral analysis of the system verifiescompliance with the following requirements :-

5.4.1 Margin Ratio

Evaluation of the instrument system performance is performed primarily by the determination of a ratiobetween the integrated in-band and out-of-band radiance profiles (Margin Ratio). This Margin Ratio (M)includes the integrated throughput response product of the channel as illustrated for representative Channels 1and 21 in Figures 5-11 to 5-13. This is combined with the Planck function and limb absorption in Figure 5-14 forthe respective target channel heights and temperatures to calculate the wanted in-band radiance (Rw) profile andunwanted out-of-band radiance (Ru) profile. Determination of the acceptance criterion is based upon the ratio bywhich the maximum permitted in-band radiance exceeds the unwanted radiance in Equation 5-4.

u

w

R

nenRMaxM

)5.0*,01.0*(= (5-4)

where nen is the rms radiometic noise (mW/m2/ster).

To satisfy this requirement the total response of the instrument channel must have a value of Mexceeding unity. In order to ensure this requirement is satisfied for the response of actual manufactured


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components integrated into the instrument, a safety margin is included to increase the required value of Mby design to between 3.0 and 5.0. Table 5-2, Section a, illustrates the range of Margin Ratio values achievedfrom the Channel 1 verification analysis example for an nen of 1.2x10-3 Wm-2.ster. It can be seen from the out-of-band requirement column that for other than the 10km height and 300K black body radiation profile of theinternal radiometric calibration target, the response of the instrument is dominated by the need to satisfy theradiometric noise requirement (nen*0.5), rather than by the in-band throughput radiance (Rw*0.01) from theinstrument spectral design. Hence in this case, by achieving a Margin Ratio value greater than unity bymeasurement, the instrument requirement is satisfied.

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Figure 5-11 Predicted blocking design performance of Channel 1 (17.4µm) - Log Transmittance

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Figure 5-12 Predicted blocking design performance for Channel 21 (6.75µm) - Log Transmittance


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Figure 5-13 Predicted design performance of Channel 21 (6.75µm) - Linear Transmittance

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Figure 5-14 Atmospheric limb absorption and Planck function temperatures for target channel heights

The spreadsheet used to calculate the value for the Margin Ratio uses the predicted design performanceof each element on a 2cm-1 wide spectral interval. The in-band and out-of-band filter transmissions are containedin separate columns, with additional columns for the transmissions of the optical train, antireflection coatings,and detector response, and then a set of columns is provided for each atmospheric height of interest (10-70km in10km intervals). Figure 5-15 shows the process of combining the spectra as an example for Channel 19.


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Figure 5-15 Channel 19 example instrument spectral design and throughput

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In addition to satisfying the Margin Ratio requirement for the instrument there is a need to assess thesystem response profile outside of the HIRDLS wavelength range. The relative spectral response of each channelis required to be such that when viewing a 300K black body, the integrated out-of-band radiance across thespectral range between 1.54µm and 40µm is required not to exceed 0.25% of the integrated in-band radiance forthat channel. This ratio has been calculated for the Channel 1 example in Table 5-2, Section b, whichdemonstrates compliance of this ratio to the requirement.

Table 5.2. Channel Blocking Compliance

a. Channel Margin RatioRadiometric Noise (nen) - mw/m2/ster 1.2Height

KmTemperature

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Out-of-BandRequirement

MarginRatio

10 210 109.40 0.2822 1.09 3.8820 220 45.30 0.2080 0.60 2.8830 240 12.05 0.0962 0.60 6.2440 250 4.67 0.0398 0.60 15.0650 230 1.22 0.0117 0.60 51.1560 220 0.28 0.0033 0.60 180.0770 210 0.04 0.0007 0.60 823.36BB 300 547.34 1.5058 5.47 3.63

Channel Specification Margin Ratio Requirement 3.0-5.0

b. Integrated In-Band to Out-of-Band Radiance RatioPlanck Function Temp (K) 300

In/Out of Band Cross Over (%) 0.20Integrated Out-of-Band Radiance 1.41

Integrated In-Band Radiance 547.3Out/In-Band Radiance Ratio (%) 0.25

Channel Specification Requirement Less Than 0.25

c. Cold Filter Thermal Background RejectionPlanck Function Temperature (K) 301

Cold Filter In / Out-of-Band Cross Over (%) 0.2Integrated Out-of-Band Area 10.1

Integrated In-Band Area 5136.0Out-of-Band / In-Band Area Ratio 507.8Channel Specification Requirement Greater than 10.0

5.4.2 Ghost-Image suppression

The effects of cross channel signal contamination is suppressed in the instrument by the array ofsecondary cold (65K) filters housed within the detector assembly. These cooled filters of wider passband widthprevent out-of-band signals internally reflected from either the ZnSe dewar window (DW) or Ge lens (L2) beingrecognised in other channels as in-band signals originating from a different height. Though this effect will beconsiderably reduced by the use of efficient high performance antireflection coatings, this alone is inadequate tosuppress the effects of stray light to an acceptable level.

The selection of suitable cold filter bandwidths required a compromise between satisfying the need forminimum interaction between the cold filter passband and the spectral profile of the warm filter (to ensure theband-definition is unambiguously performed by the warm filter), and minimising the transmission of unwantedstray radiation. To satisfy both criteria the accepted compromise required the 50% points of the cold passband tooverlap between the limits of 1% and 4% points on each edge of the warm filter profile. At wavelengths beyondthese limits the filter would be required to provide continuous blocking to cover all channels within the passbandwavelength range of the instrument. Predicted prototype bandpass profiles, representative of each channel


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wavelength, were analysed by the RAL Optical Science Group. By using a combination of spectral, optical andatmospheric cross-talk matrices they determined that warm and cold filter transmissions of <10-4 to shorterwavelengths of the passband, and <10-2 to longer wavelengths of the passband, would be adequate to reduce theghost image signals to an acceptable level. It should be noted that this requirement is only for instrumentpassband range of 6 to 18µm.

5.4.3 Corrective spectral passband placement requirements

As a result of the combined effects of multi-phonon absorption inherent in the bulk material propertiesof the transmissive optics (particularly Channels 1-9) together with the differing illumination distributions onboth sets of filters generated by the optical design, a displacement of the spectral position and bandwidth of bothwarm and cold filter profiles from the desired instrument requirement will occur. I have therfore madecorrections to the spectral placement and bandwidth of the filter passbands to compensate for thesedisplacements such that when the filters are combined into the system, the end-to-end channel spectral placementis correct.

To quantify the size of this effect for each channel a nominally correct warm and cold bandpass designpair was introduced to the design spreadsheet to calculate the end-to-end channel profile and determine theresultant channel placement and bandwidth. From this analysis a ratio between the warm filter profile andinstrument channel end-to-end profile was calculated, representing the compensation required to the warm filterto negate the effects of absorption. To this ratio the spectral effects of the f/7 warm filter ray count distribution inFigure 5-16, is included to produce a final compensation factor which was then applied to the end-to-end channelpassband placement specification to derive the warm filter spectral position requirement. I have also appliedcompensation ratios to the cold filter passband to ensure correct spectral placement in the f/1.5 cone in Figure 5-17. The Channel 1 spectral profile example in Figure 5-18 illustrates the deviations between the instrument end-to-end specification and the positional corrections required to the warm and cold filter passbands.

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Figure 5-18 Overlay of measured spectral profiles of Channel 1 warm and cold filters corrected for coneangle, bulk material absorption properties, and final corrected channel placement profile

5.4.4 Thermal background suppression

The cold filters additionally serve to reduce the background thermal flux of the instrument reaching thedetectors. Verification of adequate broadband blocking performance of the cold filters is required to showsufficient rejection against radiation from a 301K Planck function. The degree of suppression of thermalbackground radiation from the instrument is derived for each channel from the integrated out-of-band to in-bandarea ratio of the response profile from the combined detector, cold filter and 301K Planck function profiles. Theverification target criterion for this parameter is deemed to be satisfied if the integrated out-of-band rejection isgreater than the integrated in-band throughput by a factor of 10. As it can be seen for the example channel inTable 5-2, Section c previously, this ratio has been comfortably exceeded.

5.5 HIRDLS Instrument performance verification

The spectral measurement and verification procedure used to integrate the response data from theHIRDLS manufactured components is performed through two relational spreadsheets. These are used to verifycompliance with the instrument performance requirements and comprise an instrument verification spreadsheetand an instrument throughput spreadsheet. The instrument verification spreadsheet is used to determine the


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complete spectral response of the instrument on a coarse data interval of 2cm-1. This is used to verify compliance ofthe instrument with the Margin Ratio, thermal background suppression, and total radiance profile for each heightacross the broad spectral range of 1.54µm to 40µm (3125 data points). The instrument throughput spreadsheet isused to provide detailed passband profile analysis of each channel across the channel passband with a fine datainterval of 0.25cm-1 between 5µm and 20µm (6000 data points).

Since each element in the optical path of the instrument is placed some distance apart, and angular beamwalk-off is inevitable as a result of the curved surfaces in the instrument. I have assumed multiple-beaming betweenadjacent components does not occur. Under these circumstances it is appropriate for the spectral profiles from eachelement to be multiplied together within the design and verification spreadsheets together with the Planck functionand limb absorption profiles. This provides considerable improvements to the blocking performance of theinstrument and reduces the sensitivity of the instrument to small spectral leaks caused by either pinholes or minorsurface defects in any of the individual coatings as illustrated in Figure 5-19.

Figure 5-19 High-resolution SEM micrograph showing a coating pinhole

5.5.1 Instrument channel passband profile

The channel placement accuracy of the HIRDLS instrument throughput requires the filter edge positions tobe located typically within ± 2.5cm-1 of the nominal spectral location. For certain channels however, where thereexist unwanted spectral features adjacent to the band of interest, a spectral placement accuracy of ±1.0cm-1 isrequired. The spectral end-to-end spectral throughput of the complete channel requires the shape of the energy graspprofile to meet two specific requirements :- (i) the integrated throughput between the 0.2% and the 50% relativetransmission points is required to contribute no more than 30% of the integrated transmission between the 50%relative transmission points, and (ii) the width of the spectral interval between the 5% relative transmission points isnot to exceed 1.6 times the passband width. By applying these criterion, both the shape and edge steepness of thethroughput profile are defined. Figure 5-20 shows an overlay of the measured spectral performance achieved foreach of the contributing elements in Channel 1, together with the calculated throughput profile. It can be seen fromthe channel passband compliance summary in Table 5-3, that the overall channel throughput has achieved theprofile requirements defined by the specification.


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Table 5-3 Channel Passband Throughput Profile

a. Passband Width Ratio SW Point(cm-1)

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Passband 50% Width 583.6 563.7 19.9Passband 5% Width 585.6 561.1 24.5

50% - 5% Width Ratio 1.23Channel Specification Requirement Less Than 1.60b. Integrated Transmission Ratio

0.2% - 50% Integrated Transmission 29.3450% - 50% Integrated Transmission 159.98

0.2%-50% / 50%-50% Ratio (%) 18.34Channel Specification Requirement Less Than 30%

c. Peak TransmissionMaximum Throughput Transmission 20.3Channel Specification Requirement Greater Than 8.0%

5.5.2 Instrument channel blocking performance

The measured wide-band spectral blocking performance of the components in the Channel 1 and 21examples are illustrated as overlaid spectra in Figures 5-21 to 5-24. Although each individual component onlycontributes a fraction of the total out-of-band blocking, the system as a whole, depending as it does on the productof the individual transmissions, has much lower out-of-band transmissions than required by the specification. Thereare a number of advantages to the use of distributed blocking over a number of components in this way, individualblocking levels at the 10-4 level can actually be verified by measurement together with reduced sensitivity topossible minor coating defects and more margin for minor deviations in blocking. This has also allowed the filters tobenefit such that the required blocking performance is better quantified in terms of the specific wavelength regionsand rejection levels required. Figures 5-25 and 5-26 illustrates an example predicted channel in-band and out-of-band radiance, inclusive of the atmospheric Planck function temperatures and limb absorption features for thevarious target heights to be viewed by the instrument.


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Figure 5-21 Measured Channel 1 (17.4µm) blocking performance and total system throughput

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5.6 Conclusion

In the Channel 1 and 21 cases illustrated here, the measurements have verified that both the warm and coldfilters have achieved the channel blocking requirements defined by the Margin Ratio, integrated in-band to out-of-band radiance ratio and cold filter thermal background rejection as tabulated in Table 5-2. From the systemanalysis, the total throughput model of the instrument has produced a calculated average rejection level of 10-9

within the HIRDLS wavelength range, with additional contributions from the germanium lenses and dewarwindow considerably increasing the channel rejection blocking levels to short-wave. This verification model isof course limited by the low level blocking measurement accuracy on each component at approximately 10-4.Actual rejection levels may be greater as calculated from the design profiles.

It could be argued that I have achieved a non-optimum result, in so far as having achieved a very muchlower level of out-of-band transmission than required, especially at short-wave, and that there may still remainopportunities for further reducing the number of layers. It should be remembered however, that the individualcomponents also have their own out-of-band transmission requirements to meet, as discussed earlier, as well asthere being instrument throughput requirements. Also, in the case of the antireflection coatings, the low levels ofshort-wave out-of-band transmission is a by-product of the coating design, the number of layers and theirthickness being predicated by the need for high and wide in-band transmission. Additionally, at wavelengthsbelow the 5µm region, the electronic absorption edge of the Lead Telluride (PbTe) content of the coatingsdominate and is primarily responsible for reducing the transmission still further. The amount of PbTe used in thecoatings is consistent with the minimum necessary to obtain the best in-band performance together with thenecessary component level blocking, even this amount gives rise to the very low levels of short-wavetransmission observed.

With the results of this work I have developed an integrated system performance approach to thespectral design of HIRDLS instrument which has led to an improved specification for the spectral performancerequirements for the filters. Together with this compliance to the spectral requirements of the instrument havealso been verified by component level spectral measurements integrated into the instrument for the exampleChannels 1 and 21. The predicted spectral performance of the HIRDLS instrument given by the model usingcomponent level measurements are to be compared with the results of the radiometric calibration of theinstrument engineering model and later more comprehensively with that of the flight model.


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CHAPTER 6EFFECTS OF THE SPACE ENVIRONMENTON INFRARED FILTERS AND MATERIALS

With a continuously increasing demand for improvements to spaceflight optical instrumentation, forboth high optical system performance and lengthening operational lifetimes, an investigation into the effects ofthe space environment on the durability and spectral stability of infrared filters and materials on the NASA LongDuration Exposure Facility (LDEF) was opportune. Prior to this experiment, assurance of the survivability offilters had been provided by ground-based testing, in an attempt to simulate those aspects of the spaceenvironment considered the most serious. Such testing, however, cannot prevent occasional anomalousbehaviour or unexplained failures, particularly when filters may have been fabricated at a time considerablyearlier than the proposed operating lifetimes, or delays may have extended the operational lifetime of themission.

To obtain the data necessary for an assessment of the ability of filters to withstand the environmentalrigours of space therefore required that in-situ testing was necessary. The experiment to expose infraredinterference filters and coatings which had been constructed using traditional design and deposition methods wastherefore a necessary requirement for assessing the filter materials suitability and stability when subjected toradiation from the space environment. The optical and physical behaviour of these filters and materials in thespace environment being unconfirmed previously, but is critical to their performance.

The principal objectives of the experiment were to investigate the effects of the space environment onthe spectral and mechanical stability of the multilayers and materials flown. Assess if a lifetime could bedetermined for filters and materials operating in the orbital environment, and determine any degradationmechanisms affecting the optical system performance.

In this chapter I will be presenting results, previously un-published, of the specific environments towhich the individual filters and coatings were exposed, together with summarised details of the pre and postflight spectral measurement correlations. I refer the reader to my published final SERC report entitled “Spaceexposure of infrared filters and materials on the NASA Long Duration Exposure Facility (LDEF)”, Publishedby The University of Reading ISBN 07049 04098 (1991) for a more complete and comprehensive assessment ofthe experiment construction, measurement strategy and performances achieved for each of the individual filtersand materials flown.


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Earth Facing Tray G12

Figure 6-1 Deployment of the LDEF from Challenger Space Shuttle mission 41C.

6.1 LDEF Experiment Background

The NASA Long-Duration Exposure Facility (LDEF) was a free-flying satellite designed to provide aneconomical means of achieving space exposure in the Low Earth Orbit (LEO) of experiments that could benefitfrom post recovery measurements of the retrieved hardware[102]. The LDEF experiment structure was designedand fabricated at NASA Langley in the late 1970’s as a passive reusable satellite for planned repeat missionsusing the two-way transport capability provided by the Space Shuttle. It is a 4.3 meter diameter by 9.1 meterlong aluminium cylindrical structure with the cross section of a 12-sided regular polygon.

Experiments were attached to the exterior of the structure in self contained experiment trays, each traymeasuring 86.4cm x 127cm which could be further sub-divided to accommodate smaller experiments. The9709Kg facility was placed in orbit by the Shuttle Challenger on 7th April 1984 at a 482km circular orbit with a28.4° inclination relative to the equator. The structure was gravity-gradient stabilised and mass loaded so thatone end of the LDEF was always pointed at Earth and one side (leading edge) was always oriented into the orbitpath (sun rising) ram direction. In orbit, the orientation of the structure ended up rotated around its long axissuch that the leading edge was offset from the ram direction by about 8°. This orientation remained constantthroughout the entire operational lifetime of the mission. LDEF also used a viscous damper which was designedto gradually eliminate any destabilising oscillations caused during deployment.

Duration of the exposure was originally anticipated to last for a period of 10-12 months for retrieval inearly 1985. Due to Shuttle re-scheduling and the loss of Challenger, LDEF was not retrieved until the 12thJanuary 1990 after 5 years and 8 months (2106 days) and 32,422 orbits in low Earth orbit, by which time the


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orbit had degraded from 482km to 340km. This extended duration presented a unique opportunity to study thelong term effects of space exposure on the filters and substrate materials flown.

6.2 Thermal cycling effects

A spaceflight vehicle in low Earth orbit will receive radiant thermal energy from three primarysources[103]; the incoming solar radiation (solar constant), reflected solar energy (Earth albedo), and outgoinglongwave radiation emitted by the Earth and atmosphere itself with a blackbody radiation spectrum of 288K.Certain amounts of this energy will be reflected by the vehicle, and the vehicle itself radiates energy into the coldsink of space at 3K. The thermal environment of any spacecraft surfaces will tend towards a temperature whichbalances these energy fluxes with any energy produced internally within the vehicle. A similar thermal balanceprocess applies to the Earth itself. The Earth/atmosphere is in radiative equilibrium with the Sun. However, it isnot in balance everywhere on the globe, as there are variations with respect to geography, and atmosphericconditions. A space vehicle’s motion with respect to the Earth results in its viewing only a continuously changingportion across the full global thermal profile, so it sees these variations as functions of time depending on thethermal time constants of the vehicle. The thermal environment is therefore primarily dependant upon the orbitalparameters.

The LDEF thermal design was completely passive, relying on surface coatings and internal heat pathsfor temperature control and equalisation. To maximise the internal radiation coupling between the spacecraftcomponents, high-emittance coatings were used. All interior surfaces were coated with Chemglaze Z-306 blackpaint. This unexposed coating did not suffer any degradation during the LDEF mission. However, because theLDEF structure was not baked out after being painted, the Chemglaze Z-306 became one the leading sources ofcontamination. Actual internal flight temperatures were recorded at intervals of approximately 112 minutes forthe first 390 days of the LDEF mission. Temperature measurements were taken using five copper-constantanthermocouples, a radiometer and two thermistors for reference measurements. The recorded temperature rangefor all seven locations was from 3.8°C to a maximum of 56.7°C. Figure 6-2 shows the daily averaged cyclictemperature excursions versus time experienced by the closest thermocouple for each of the two trays flown.

The effects of this temperature cycling on a deposited multilayer causes thickness contraction andexpansion of each of the layers, the size of which depend on the thermal expansion coefficient properties of thematerials. As dielectric coatings deposited on optical components are usually brittle, and may be under constanttensile or compressive stress, delamination of the coating can result if the induced thermal mismatch betweenadjacent layers becomes too large. The resultant failure of the coating significantly degrading the spectralperformance of the optical system. In addition to the unwanted thickness variations, which can displace thespectral profile from its desired position, temperature cycling effects can also cause the spectral performance todeteriorate, as the optical dispersion properties of the materials change with temperature, these variations canbecome significant and adversely affect the spectral profile of the filter. The coatings must therefore beconstructed of materials with sufficient adhesion between the interfaces to withstand the thermally inducedexpansions and contractions and possess a low susceptibility to thermally induced dispersion.

6.2.1 Solar flux

All of the exterior surfaces on the LDEF received direct solar illumination for periods of time duringthe mission. The cumulative times for the illumination of individual surfaces on the facility varied from 10-25%of the total mission lifetime. The amount of cumulated illumination time per orbit changed as the angle betweenthe Sun’s illumination vector and the plane of the LDEF orbit varied, as illustrated in Figure 6-3.


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β-angle: angle between the plane of the orbit and the sun illuminationsolar incident: heat due to direct illumination from the sunalbedo: heat due to the portion of the solar incident energy reflected from the planet onto the LDEFplanetary: heat due to energy emitted from the planet

Figure 6-3 Variation of the Sun’s illumination with the plane of the LDEF orbit

The rate of accumulation of solar exposure is calculated in terms of the equivalent number sun hours.This depends upon the solar form factor[104] for direct solar radiation and upon the Earth’s albedo form factorwhich is then combined with an appropriate value of albedo for reflected radiation from the Earth. The solarform factor for a surface on an orbiting spacecraft is a function of its orientation with respect to the Sun’s rays.The Earth albedo form factor for a surface on a spacecraft is a function of the position of the spacecraft relativeto the Earth’s illuminated hemisphere and to the orientation of the surface with respect to the local verticaldirection. Both form factors when averaged over a complete orbit are defined by the angle that the spacecraft’sorbit plane makes with the Sun’s rays and the orientation of the exposed surface with respect to the spacecraft’sheading. The Earth albedo was determined from Nimbus 7 radiometer measurements reported by Smith et al[105]. Figure 6-4 shows the build up of cumulative equivalent sun hours with time for the two exposed trays B08and G12. The solar exposure builds approximately linearly with time except for a visible modulation caused byseasonal variations.

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This accumulated exposure of solar radiation was one of the most important contributors to materialsdegradation on the LDEF. Figures 6-5 and 6-6 shows the effects of this radiation on a As2S3 / KRS-5 coatingdeposited on a KRS-5 substrate from the leading edge tray B08, where gross discoloration and thermal blisteringhad destroyed the sample.

Figure 6-5 Pre-flight B8/19 coatedKRS-5 sample

Figure 6-6 Post-flight B8/19 coatedKRS-5 sample showing thermal fatigue

6.3 Ionizing radiation

LDEF was deployed at an altitude of 482km. At this orbital altitude, three sources of energetic particlesdominate most of the penetrating charge particle radiation encountered[106] - high energy galactic cosmic raysand geomagnetically trapped protons, with energies between ∼100-1000 Mev, and neutrons from theatmosphere. Additionally, where shielding is less than 1g/cm2 geomagnetically trapped electrons make asignificant contribution and dominate the surface absorbed dose. All three sources are strongly shielded by theEarth’s magnetic field. Due to this shielding, the absorbed dose induced by galactic cosmic rays and solarfluences are weak. Thus, trapped proton exposure is primarily responsible for the LDEF absorbed dosemeasurements. This occurs mainly during passes through the South Atlantic Anomaly where the magnetic fieldintensity is at its highest and is produced because the Earth’s magnetic field is not centred on the Earth andgenerates “trapped orbits” for charged particles in the geomagnetic field[107]. Under modest shielding, over 95%of the radiation exposure on the LDEF was from trapped protons encountered in this region. Penetrating chargedparticle radiation presents a significant challenge to the design and operation of a orbiting vehicle as many of theparticles have sufficient energy to penetrate several centimeters of metal and produce significant levels ofionization inside the vehicle. A high level of radiation will significantly affect materials, chemical processes, andliving organisms.

The galactic cosmic rays consist mainly of the nuclei of the elements of hydrogen through to uranium,these have a broad energy spectrum and high average energies of approximately 7 Gev/nucleon. The LDEF dosecontribution from galactic cosmic rays was predicted to be about 6 rad, and decreases slowly with shieldingdepth than the trapped proton dose. The actual LDEF cosmic ray experiments, using about 20 of the actinideelements in the periodic table (i.e. Th, U, etc) with nuclei atomic weights Z>65, showed this contribution to becloser to a value of 10 rad (0.1 Gray). Galactic cosmic ray particles bombard the Earth isotropically with acomposition in the vicinity of Earth being ~98% nuclei and ~2% electrons and positrons. The absorbed dose wastherefore dominated by the heavy nuclei. Rare solar flares that produce energetic particles with energies wellabove 1 Gev also contribute a minor dose component at all shielding depths.

The principal mechanisms that cause damage in dielectric coatings[108] by ionizing radiation areelectronic ionisation and atomic lattice displacements. Charged particles such as protons, deuterons, and heliumions mainly interact with the electrons in the dielectric, whilst neutrons interact only weakly with electrons,principally colliding with nuclei and displacing their position in the lattice. As atoms are considerably larger thantheir nuclei, interactions with the atomic nucleus is much less probable. For charged particles, heavier than the


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electron, little change in direction or energy is suffered by the particle. The electron collision may be knockedout of the atom, producing an ion and free electron. By this process chemical bonds may also be broken andproduce free radicals, new chemical species or induced radioactivity[109].

Electrons and ions produced by these events can be trapped at lattice defects or other low energypositions where a change to the absorption spectra of a material is possible. Darkening or other discoloration canresult, and the coating may degrade as a result of the radiation.

Comparing the proton fluence experienced on the LDEF with that required for the EOS HIRDLSinstrument shows the samples onboard the LDEF were exposed to a greater fluence of trapped protons than thatrequired by the ionizing radiation requirements for EOS spacecraft instruments[110]. Figure 6-7 shows therequired surface incidence fluence of trapped protons and cosmic ray protons for a five year polar orbit at analtitude of 705km with values ranging from approximately 8x109 to 2x105 compared to a range of 5x109 to1.2x107 experienced by the LDEF.

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Figure 6-7 Trapped proton fluence from LDEF compared with the HIRDLS instrument requirements

6.4 Atomic oxygen

The effects of atomic oxygen (monatomic oxygen) bombardment were originally highlighted with theearly shuttle flights, by a visible effect on exposed polymer surfaces such as Kapton, where changes incharacteristics due to atomic oxygen were found to cause undesirable temperature excursions in low Earth orbitand shorten the useful lifetime of many spacecraft components[111]. It has also been proposed that atmosphericatomic oxygen plays a role in the production of a visible shuttle glow upon re-entry into Earth’s atmosphere.Post-flight analysis of painted surfaces on the shuttle were also noted to have been returned with a brightersurface than prior to launch.

Atomic oxygen bombardment contributes significantly to surface degradation, erosion, andcontamination of materials with which it collides due to its high speed of 1.15 km/sec compared to an averagespeed of a spacecraft relative to the atmosphere of 7.24 km/sec, and high collision energies (4-5eV). At thisenergy, atomic oxygen initiates a number of chemical and physical reactions with the materials and penetratesurfaces, substituting oxygen to form oxide compounds, more stable than those originally present. The elementexists in monatomic form in the upper regions of the atmosphere (>400km altitude). The effects of atomicoxygen bombardment on a polymer film produces a heavily etched and eroded surface. Polymer films that havebeen coated with thin metallic layers have suffered atomic oxygen attack through pre-existing pinholes in themetal film, this leads to underlying cavities which eventually produces complete loss of the polymer, leaving afree-standing metal film.

As the orbit of the LDEF was inclined to the equator (28.5°), its 12-sided geometry caused the atomicoxygen fluence to vary from experiment to experiment. The angle of each experiment surface relative to the ramdirection was used to determine the atomic oxygen fluence by the fixed structural geometry of the vehicle and its


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constant flight attitude in orbit[112]. Figures 6-8 and 6-9 shows the atomic oxygen fluxes and fluences for the twoexposed tray surfaces located at the Earth facing location (G12) and the space facing location near to the leadingedge of the vehicle (B8). The extent to which on-board materials were exposed to atomic oxygen, the totalatomic oxygen fluence, is of primary interest. This fluence is the flux (atoms/cm2/sec) times the exposure period(seconds), with the flux defined as the number density of atomic oxygen (atoms/cm3) times the orbital velocity(cm/s). The altitude of the flight, orientation of the surfaces, and the extent of solar activity determine the amountof atomic oxygen exposure.

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Figure 6-8 Atomic oxygen flux vs time for LDEF rows B8 and G12

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Figure 6-9 Atomic oxygen fluence vs time for LDEF rows B8 and G12

Atomic oxygen flux was not constant during the orbital lifetime of the LDEF as decreasing solaractivity caused atomic oxygen flux to decrease during the first three years of the flight. Following this, thecombination of increasing solar activity and decreasing altitude caused the atomic oxygen flux to increaserapidly. The flux during the latter months of the mission was almost two orders of magnitude greater than theflux encountered early in the mission. Figure 6-10 shows the accumulated atomic oxygen fluence expressed as apercentage of the total fluence exposed for the mission. This highlights the combined effect on atomic oxygenfluence caused by the varying solar activity and the loss in altitude. Approximately 75% of the total atomicoxygen exposure accumulated during the last year of the flight with approximately 50% accounted for in the lastsix months.


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Figure 6-10 Cumulative Atomic Oxygen fluence as a percentage of total exposure

Comparing the atomic oxygen fluence experienced on the LDEF with that required for the EOSHIRDLS instrument[113] shows the expected atomic oxygen bombardment to be equivalent to that experienced bythe optical components on the leading edge tray (B8). Figure 6-11 shows the expected atomic oxygen fluenceprofile for a five year polar orbit at an altitude of 705km with values ranging from approximately 8x1020 to1x1020 , this compares to a range of 1x1020 to 5x1021 experienced by the LDEF leading edge tray B8. It shouldbe noted that the optical elements on the LDEF experiment were under direct exposure to the flux of atomicoxygen, whilst in HIRDLS the filters are internal to instrument, providing far greater protection for survival.

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Figure 6-11 Atomic oxygen fluence requirement for the HIRDLS instrument after five years in orbit

6.5 Filter experiment construction

In order to obtain a representative assessment of the effects of exposure to the space environment of theinfrared filters and materials flown on the LDEF, a total of 46 components were distributed between two traylocations, as illustrated in Figure 6-12. One location was positioned to be continuously facing Earth (G12) at anangle of 90.8° off the RAM incidence angle (Figure 6-14), whilst the other location tray was positioned tocontinuously view space on the leading edge of the vehicle (B08) at 38.1° off the RAM incidence angle (Figure6-15). Each tray was designed to maximise the exposure of the full aperture to the complete range of spaceradiation environments and temperature excursions.


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Figure 6-12 Location of exposed filter experiment trays

The filters were each housed in chromic anodized BS.L93 aluminium alloy circular holders andmounted in 6061-T6 chromic anodized aluminium alloy base plates. Thermal contact was ensured by Pb washerslocated either side of the substrate. Induced pressure differentials across the substrates were relieved by a hole ineach backing piece to prevent substrate flexing or deformation. Figure 6-13 shows the substrate holderconstruction.

Figure 6-13 Filter holder assembly


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Figure 6-14 Earth facing tray G12

Earth Facing Exposed Materials (G12)Holder

No.SubstrateMaterial

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5 MgF2 - Uncoated Substrate6 CaF2 - Uncoated Substrate7 KRS-5 - Uncoated Substrate8 KRS-6 - Uncoated Substrate

13 KRS-5 As2S3 /KRS-5 61-Layer Quarter Wave Stack15 CdTe - Uncoated Substrate16 KRS-6 ZnS/KRS-5 - ZnSe/KRS-5 33-Layer Quarter Wave Stack18 KRS-5 CdTe/KRS-5 - As2S3/KRS-5 61-Layer Quarter Wave Stack21 Ge PbTe/ZnS 7.35µm 5% L-Spaced THW BP22 Ge PbTe/ZnS 5.74µm 6% L-Spaced THW BP26 Ge PbTe/ZnS 7.35µm 5% L-Spaced THW BP29 Ge PbTe/ZnS 14.5µm 0.7% L-Spaced FP BP32 Ge PbTe/ZnS 14.5µm 0.7% Split-Spacer FP BP35 Ge PbTe/ZnSe 14.5µm 0.7% Split-Spacer FP BP36 Ge PbTe/ZnS 14.5µm 0.7% L-Spaced FP BP38 Ge PbTe/ZnS 11µm 10% H-Spaced THW BP40 Ge PbTe/ZnS 15µm 10% L-Spaced THW BP41 Ge PbTe/ZnS 15µm 10% L-Spaced THW BP44 ZnSe PbF2/PbF2 10.6µm Single Wavelength AR45 Ge PbTe/ZnS 9.24µm 2% H-Spaced DHW BP


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Figure 6-15 Leading edge tray B08

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Space Facing Exposed Materials (G12)Holder No. Substrate Coating Materials Filter Type

1 MgF2 - Uncoated Substrate2 CaF2 - Uncoated Substrate3 KRS-5 - Uncoated Substrate4 KRS-6 - Uncoated Substrate9 CdTe - Uncoated Substrate

10 Si - Uncoated Substrate11 Y-Quartz - Uncoated Substrate12 Z-Quartz - Uncoated Substrate14 KRS-5 As2S3 / KRS-5 61-Layer Quarter Wave Stack17 KRS-6 ZnSe / KRS-5 - ZnS / KRS-5 33-Layer Quarter Wave Stack19 KRS-5 CdTe / KRS-5 - As2S3 / KRS-5 61-Layer Quarter Wave Stack23 Ge - Uncoated Substrate24 Al2O3 Ge / SiO 4.45µm 3.5% 2L:1H Quarter Wave Stack25 Al2O3 Ge / SiO 4.45µm 3.5% 2L:1H Quarter Wave Stack27 Ge PbTe / ZnS 14.5µm 0.7% L-Spaced Fabry-Perot BP28 Ge PbTe / ZnS 14.5µm 0.7% L-Spaced Fabry-Perot BP30 Ge PbTe / ZnS 14.5µm 0.7% Split-Spacer Fabry-Perot BP31 Ge PbTe / ZnS 14.5µm 0.7% Split-Spacer Fabry-Perot BP33 Ge PbTe / ZnSe 14.5µm 0.7% Split-Spacer Fabry-Perot BP34 Ge PbTe / ZnSe 14.5µm 0.7% Split-Spacer Fabry-Perot BP37 Ge PbTe / ZnS 8-12µm Long-Wave Pass Edge Filter39 Ge PbTe / ZnS 11µm 10% H-Spaced THW BP42 Ge PbTe / ZnS 10.6µm 2.5% H-Spaced DHW BP43 Ge PbTe / ZnS 10.6µm 2.5% H-Spaced DHW BP46 Al2O3 - Uncoated Substrate47 Si SiO 4.4µm Single Wavelength AR


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6.6 Pre-launch / post-recovery filter analysis

The variety of differing samples selected for inclusion on the two experiment locations weresubdivided into three generic material types, viz:- uncoated crystal materials, “soft” multilayer coating /substrates and “hard” multilayer coating / substrates. By subdividing the samples by this criteria directcomparisons of spectral and physical assessments from equivalent exposed and control sample types could bemade. Control specimens fabricated simultaneously with the exposed samples were retained under ambientlaboratory temperature and humidity conditions to assess comparative changes of the two environments.Validating spectral changes which occurred as a direct result of the exposure to the space environment wereonly considered valid if they complied with the following criterion :-i) Representative control samples remain spectrally stable, whilst equivalent exposed samples becomespectrally displaced and/or deformed beyond the tolerance budget.ii) Where no control samples exist, exposed samples have spectrally changed by either displacement and/ordeformation beyond the normal expectations of the coating and/or substrate materials durability.

Spectral variations occurring from the experimental samples were considered to be unchanged, if as aresult of the exposure, the following was found :-i) Situations in which the exposed samples have remained spectrally stable, but where control specimens havebecome displaced and/or deformed are considered to be unaffected by the space environment and indicate spaceto be a more benign environment than component storage under normal laboratory conditions.ii) Both the exposed and control samples have become spectrally displaced and/or deformed by an equivalentamount and in the same direction.iii) Where no control sample exists the exposed sample remains spectrally unaltered from the originalmeasurement and/or the expectation of the substrate/coating material properties.iv) Both the exposed and control samples remain spectrally unaltered from the original measurement.

For each sample type, pre and post flight average transmission was calculated from coincident spectralregions. This enabled the changes which may have occurred in both the exposed and control samples to bequantified over the complete spectrum, and give an indication of the change in energy throughput of thecomponents as a result of the exposure. Bandpass filter measurements were compared by measuring the centrewavenumber and 50% full width half-power points, and correlating the wavenumber displacement between preand post flight measurements. All the spectral features were corrected for instrument wavenumber andtransmission calibration prior to analysis.

Correlations of pre/post flight average transmissions, were analysed statistically to ensure both localisedand wideband regions the changes were seen in the context of their equivalent samples. Statistical comparisonsbetween pre and post flight data use the correlation coefficient (r), mean deviation and standard deviation (SD). Thecorrelation coefficient (r) is defined as;

( )( )( ) ( )

rx x y y

x x y y=

− −

− −

∑∑∑ 2 2

(6-1)

The size of the coefficient provides an indication of how well the pre and post flight data setscorrespond, where ;

r = +1 = perfect direct correlationr = -1 = perfect inverse correlation, and

-0.5 < r < + 0.5 = no correlation

6.6.1 Uncoated crystal materials

Samples of uncoated crystal materials, selected for evaluation of their long wavelength multi-phononand/or Reststrahl absorption properties included; CaF2, MgF2, Ge, Si, CdTe, TlBrI (KRS-5), TlClBr (KRS-6),Al2O3 (sapphire), and Y & Z-cut quartz.

Figure 6-16 shows the results of the pre-launch and post-recovery transmission correlation for thesematerials. The correlation of average transmittances from equivalent coincident spectral regions for the uncoatedcrystals gave a correlation coefficient (r) of 0.9962. The mean deviation, however, indicated a consistent loss in


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transmission of -0.765%, this was within the accuracy envelope permitted, inferring that no noticeable changes wereobserved. Controls for these crystals were unavailable.

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Figure 6-16 Average transmission correlation of uncoated crystal materials

6.6.2 Soft substrate / coating materials

“Soft” multilayer coating and substrate materials principally comprised KRS-5 (TlBrI) based multilayerquarter-wave stacks deposited on KRS-5 and KRS-6 (TlClBr) substrates. These were designed to utilize, bymultilayer action, the long-wavelength Reststrahl blocking properties of the materials. All of these componentswere originally fabricated for use in the Galileo-Jupiter probe[114].

Three different types of material combinations were employed to produce the various spectral responsecharacteristics available for this category using KRS-5 with a choice of As2S3/CdTe/ZnS and ZnSe alternatelayer materials. Each material combination produced a high region of transparency throughout the infraredspectrum containing periodic interference fringes which resulted at long-wavelength (~ 40µm) with a deepreststrahl absorption edge. All of the designs possessed the same basic multilayer structure containingalternative quarter-wavelength (λ/4) thickness layers reproduced at regular periods.

Substrate / (LH)n / Airwhere L = low index, H = high index material and n = number of repeating periods.

The resulting structure produced a periodic highly transparent interference spectrum containing areflection zone (notch) where the interference between layers add together to produce a region of destructiveinterference. The size of this zone being dependent upon the index contrast of the multilayer materials. Thisregion is particularly sensitive to thickness, index or absorption changes in the structure. Figure 6-17 shows theresults of the pre-launch and post-recovery transmission correlation for this group of filters.


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Soft (Volatile) Materials (KRS-5/KRS-6) Correlation (T%)(Correlation of 6 co-incident regions)

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Figure 6-17 Mean transmission correlation of “soft” substrate / coating materials

Comparisons of pre and post flight average transmittance were made between the soft (volatile) exposedsamples from both sites, the correlation coefficient (r) was -0.168, indicating no correlation pre/post flight for thesesamples. This was also evident from visual inspections, where gross physical degradation / delamination of thecoatings and substrate material was observed. Considerably less degradation in both spectral and physical propertieswas observed in samples located on the Earth-facing tray (G12) compared to equivalent samples located on theleading edge (B08). As a result of this experiment, the use of these materials in unprotected environments should beconsidered highly unsuitable in space borne IR instruments.

6.6.3 Hard substrate / coating materials

The selection of “hard” multilayer coating and substrate material flight specimens comprised spectrallyselective filters from the following atmospheric remote-sensing and weather forecasting satellite researchprojects; NIMBUS 4, 5, 6, 7, ITOS, TIROS-N, PIONEER and GALILEO. The substrates were Ge, Al2O3, Siand ZnSe based with combinations of PbTe based multilayers in alternating combinations with ZnS and ZnSe or,in the case of Al2O3 and Si, with SiO. The multilayer structures were principally bandpass filters with differingnumbers of cavities at various wavelengths between 4.4 and 15µm and bandwidths (FWHH) between 0.7 and6%. Additionally there was an 8-12µm long-wave pass edge filter and two antireflection coatings at 4.4 and10.6µm. The following design bandpass configurations were used :-i) Single cavity Fabry-Perot design

Substrate (Ge) / LHLHLHLLHLHLH / Air Where LL is λ/2Selected for highly sensitive transparent side bands

ii) H-Spaced double cavity half-wave designSubstrate (Ge) / LHLHHLHLHLHHLHL / AirSelected for sensitivity to absorption or index changes in the passband

iii) H and L-Spaced triple cavity half-wave designa. Substrate (Ge) / LHLHLLHLHLHLLHLHLHLLHL / Airb. Substrate (Ge) / LHHLHLHHLHLHHL / Airc. Substrate (Ge) / XLLHLHLLHLHLLX / Air Where X is a fractional simulated matching Herpin stack.

These designs were selected as they are all sensitive to changes in their passband profiles resulting fromabsorption or refractive index changes. iv) Split-cavity Fabry-Perot design

Substrate (Ge) / LHLHLH

2

L

2

H

2LHLHL

In this Fabry-Perot configuration the single cavity is sub-divided into three alternate layers each with athickness of λ/8; considered for better stability and microstructure of the cavity.


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Pre and post flight comparisons between the exposed and control hard multilayer coating / substratematerials produced an extremely good set of correlation data. The correlation coefficient obtained from 48coincident spectral regions was very high at 0.9967 from the exposed samples compared with the equivalentcontrol samples where a correlation coefficient of 0.9988 was obtained for comparisons between 19 similarcoincident regions. These values verified the correlations made to be valid and well matched. The meandeviations obtained from the exposed and equivalent control samples were -1.376% and -1.302% respectively.This indicates a small consistent loss in transmission for both data sets but is still within the transmission budgetdefined for the measurement accuracy from the two spectrophotometers. These filters are therefore consideredto be particularly stable with no degradation occurring as a result of the exposure. Figures 6-18 and 6-19 showsthe results of the pre-launch and post-recovery transmission correlation for both the exposed and controlsamples for this group of filters.

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Figure 6-19 Average transmission correlation of control "Hard" substrate / coating material filters

6.6.4. Results summary

The uncoated materials average transmittance correlation was very high between pre- and post flightmeasurements. A consistent loss in transmission was indicated but this was sufficiently small within the transmissionaccuracy envelope permitted to infer no changes had occurred. Comparison of pre- and post-flight averagetransmittance values from the soft-coated materials produced a poor correlation indicating no correlation betweenpre- and post-flight sample spectra. This was also evident from visual inspections, where gross physical degradation


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of the coatings and substrate materials was evident, having occurred as a result of excess space exposure and theeffects of atomic oxygen bombardment. Figures 6-20 and 6-21 show the effects of these changes on an uncoatedsample of KRS-5 material. X-ray composition analysis on this sample showed that free thallium ions haddisassociated and migrated to the surface (Figure 6-22) causing the material to become opaque. Post-flight visualand spectral analysis of these materials showed that less degradation had occurred in the Earth-facing tray (G12)than on the leading edge tray (B08).

Figure 6-20 Pre-Flight uncoated KRS-5 Figure 6-21 Post-Flight uncoated KRS-5

Figure 6-22 Post-Flight X-ray spectrum of KRS-5. Histograms show abundance of free thallium at thesurface and indicate no other contamination materials

From the hard-coated (II-VI/PbTe based) materials flown, comparisons of pre- and post-flight averagetransmission were well correlated. They showed a small and consistent loss in transmission for both the exposed


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and control samples (~1.3%), but within the transmission envelope measurement accuracy of thespectrophotometers. These samples are considered stable, showing no degradation as a result of the exposure. APbTe/ZnS-based sample was cleaned in 1,1,1-Trichloroethane and Propan-2-ol and re-measured. The spectrumremained unchanged indicating the surface was not contaminated during exposure to space.

6.7 LDEF Orbital meteoroid and debris impacts

Any spaceflight vehicle travelling in low Earth orbit will encounter meteoroids and orbital debris.Meteoroids are natural in origin, originating from comets or asteroids, whilst debris is the result of manmadematerials remaining in the Earth orbit. Either object can pose serious damage to the vehicle and exposedsurfaces. On the LDEF, the space facing experiment tray B08 provided some of the best examples of secondaryejecta from all of the impact sites recorded[115], and the various possible effects on a variety of differentexperimental samples. Several impacts occurred into the sides and edges of sample holders, leaving secondaryejecta spray patterns on the base plate, experiment samples and experiment-tray walls. Impacts into many of thecoated specimens created deep well-like depressions in the centre of the impact feature with a highly-definedouter spallation zone. Although complete substrate cleavage occurred from an impact on the uncoated sample ofcalcium fluoride, most of the other impacts produced only localized coating delamination around the peripheryof the impact site. One impact occurred into the side of the experiment base-plate (in the separation between theexperiment base-plate and experiment-tray wall), creating an ejecta spray pattern onto the inside of theexperiment-tray wall across from the crater. This crater is one of only a few found on LDEF which could begeometrically shown to have been produced by a highly oblique impact.

A total of 787 impact crater sites were recorded from the four experiments (S0001, A0056, A0147)contained in tray B08; approximately 26 of these sites being distributed over the surface area containing opticalmaterials (Figure 6-23). The majority of the impact craters were found on the base-plate and sample holderswere evenly distributed over the complete tray. In contrast, only one impact crater was found on samples fromthe Earth facing tray G12, with an estimated diameter of 0.5mm.

Figure 6-23 Post-flight inspection observations and impact cratering distribution


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6.7.1 Micrometeorite impact characteristics

Four impact sites are of particular interest from the cratering phenomena observed from optical surfacesof tray B08. The impact on the uncoated calcium fluoride (B8-2) occurred near to the edge of the sample holder.The impact crater was ~1mm diameter with a spallation zone diameter of ~5.5mm. The substrate cleaved in twodirections from the impact site at an angle of ~75° to the opposite sides of the sample, breaking the sample into 3pieces, as shown in Figure 6-24.

Although other samples had impact craters of this size with large spallation diameters and smallfractures, this was the only sample which showed evidence of complete substrate fracture, showing the fragileand brittle nature of calcium fluoride as a substrate material, whilst remaining functional. The crater itselfconsists of finely shattered material, as shown in Figure 6-25, and contains no visible remaining impact debris.

Figure 6-24 CaF2 Impact crater Figure 6-25 Localized CaF2 impact site

A large impact feature on an exposed PbTe/ZnS coated Ge substrate (B8-37) occurred close to the edgeof the substrate and holder interface with a spallation diameter of ~4.5 mm (Figure 6-26). The sample consistedof a 1mm thick Germanium substrate coated with a lead telluride/zinc sulphide based multilayer. Delaminationas a result of the impact has occurred around the localized periphery of the spallation zone (Figure 6-27),extending the impact area by approximately 1mm. The impact has not induced any further coating damagebeyond the localized delamination area, or added stress to the surrounding coating material so validating theadherence integrity of the coating.

Figure 6-26 B8/37 Impact feature Figure 6-27 B8/37 Localized impact site

An antireflection coated silicon sample (B8-47) received a small impact directly at the edge positionbetween the specimen and its holder (Figure 6-28), producing an ejecta spray pattern of molten aluminium whichback-reflected across the sample surface. The component comprised a 1mm thick silicon substrate coated with asingle antireflection layer of silicon monoxide. Photographs obtained by scanning electron microscopy in Figure6-29 show the detailed impact damage sustained in the collision. This SEM was taken at 175x magnification atan angle of 30° and shows the nature of the aluminium surface-deposit ejected out of the impact area. The figurealso shows the high granularity of the deposited material, which gives a visual indication of the impact forcedistribution of material ejected.


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Figure 6-28 B8/47 Edge position impact Figure 6-29 B8/47 impact site 175x

The impact at this site exposed the edges of crystal cleavage planes running parallel to the surface ofthe substrate. The surface fragmented at the crater edge without damaging the coating around the periphery ofthe impact site.

Sample B8-25 received three impact craters over a small localized area of the exposed aperture. Thesample comprised a germanium/silicon monoxide multilayer coating deposited on a 1 mm thick sapphiresubstrate. Observing two of the sites by optical microscopy (Figures 6-30 & 6-31) showed that two differenttypes of impact damage had been sustained. Two of the sites were similar in form with uniform concentric ringsextending out at various radii from the centre. The other site was larger in size and not so concentricallyuniform. The various colours observed are reflections from different thicknesses of layer materials, broken byradial fractures in the concentric rings.

Figure 6-30 B8/25 Ge/SiO on Al2O3 (1) Figure 6-31 B8/25 Ge/SiO on Al2O3 (2)

SEM micrographs obtained from these sites (Figures 6-32 & 6-33) show the nature and form of twodifferent types of impact cratering.

Figure 6-32 B8/25 Ge/SiO on Al2O3 (1) Figure 6-33 B8/25 Ge/SiO on Al2O3 (2)


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SEM Figure 6-32 shows a region of the original uncoated substrate material around the centre of thesite. A small ring of very fine debris, and the uniform circular nature of the first concentric ring, indicate apossible shock-wave extending from the centre radially upon impact. The coating material, fragmenting radiallyon the first elevated concentric ring, produced the different colours observed optically. Material further awayfrom the centre appears less fragmented and more molten, possibly due to the radial propagation of heat from thecentre. Further magnification from the centre of the impact sites show possible residual micrometeorite debris.

Figure 6-33 is a larger impact site on that same sample magnified by 190x. Here the impact hasproduced a central circular area of the original uncoated substrate material, surrounded by which is a uniforminner concentric ring of coating material shaped from a possible shock-wave extending radially on impact fromthe centre of the site. Material beyond the interface between the uncoated substrate and coating has fragmentedin a non-uniform single concentric area. Possible impact debris is visible at the centre of the impact crater.

As a result of these impacts, no further delamination of the coating material has occurred beyond theimmediate periphery of the impacted area. This could have been produced by either induced stress in thecoating, or by general mechanical fatigue. Subsequently the effects of these impacts have produced nosignificant degradation on either the performance, usage or environmental adhesion integrity of the coatings orsubstrate materials.

6.8 Experiment conclusions

The effects of space exposure on the infrared filters and materials flown on LDEF were minor. Nosignificant changes were found either in transmission or spectral position of any hard coated II-VI / PbTe-basedmultilayers on Germanium substrates, or in uncoated crystal substrates. The softer materials however wereadversely affected in their physical and optical properties by the long exposure in space, from exhibiting areduced transmission to complete opacity. Although impacts by micrometeorites damaged some samples, thesedid not detract from their function and performance as an optical component. Likewise, atomic oxygen and spaceradiation caused no spectral effects which could be detected, other than in soft material samples which wereexposed beyond that intended for these types of components.


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SUMMARY AND CONCLUSIONS

This thesis has described the results of the research carried out into the optical properties of a selectionof infrared materials, and their implementation into filter and optical systems design. The analysis methodsdeveloped in this work have been applied to spectral transmission measurements of a comprehensive set ofinfrared materials typically used in the manufacture of filters. This analysis has provided a concise set ofdispersive n and k values across a wide range of temperatures and wavelengths, which can now be included as anintegral part of future filter design calculations. By incorporating these values into the putative multilayerdesigns of the filters and antireflection coatings and into the models of spectral characteristics of the lens andwindow materials in the optical train, a predicted performance model has been constructed for the HIRDLSradiometer instrument. This model is used in a process of establishing a spectral requirement for the filters,working from the known spectral characteristics of the other optical elements in the system together with theknowledge of the spectral requirements of the instrument. Further, by using this model working with actualspectral measurements of the filters and coated elements it has been demonstrated that the spectral design of theinstrument as a whole has complied with the requirements demanded by the formal instrument specification. At alater date, the overall spectral response of the instrument as predicted by the model will be correlated with theradiometric calibration of the instrument. Additionally, as a result of the spectral and physical analysis performedon the exposed filters and materials from the LDEF experiment, an increased confidence in their use in satelliteborne optical remote sensing instrumentation has been established.

FUTURE RESEARCH

This research has primarily been concerned with the optical characterisation of the materials currentlyin use for the design and manufacture of infrared filters and coatings at Reading. An investigation into theproperties of alternative substrate and coating materials would be of interest, in extending the selection ofinfrared materials currently available and providing advantages to the multilayer design methods by improvedrefractive index matching. Indeed some work has already started but not reported here on GeSe, There may alsobe additional mechanical advantages in the disposition of alternative materials within a multilayer, by eitherreducing the intrinsic stress or providing better adhesion of the multilayer to the substrate.

The accuracy of the temperature-dependent dispersion models derived in this thesis may be furtherenhanced by the increased control and stability offered by the use of a total helium immersion cryostat in thecold spectral measurements. This equipment was not available during the course of my research, however, ourlaboratory has recently acquired this apparatus to which the application of this characterisation method is wellsuited. Research into further refining both the stoichiometric PbTe and II-VI layer material dispersion andabsorption models is required, particularly for operation at reduced temperatures, this will enable more precisemultilayers to be deposited. A further examination of the deposition parameters in an attempt to provide betterfilms for optical characterisation would be invaluable, particularly how the rate of deposition, pressure,temperature, and cooling rate may affect the quality of the thin-film properties. The implementation of ion-beamassisted deposition techniques should help to improve the mechanical and optical properties of the layermaterials, by densifying the deposited films. This may assist with the optical characterisation of these materialsby providing more reproducible and dense films, and also increase the environmental durability and spectralstability of the materials. The further work of verifying the predicted spectral performance models with themeasured instrument throughput when the HIRDLS instrument radiometric calibration is carried out shouldestablish the integrity of the instrument system model.


148

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152

APPENDICES

Appendix A Temperature-dependent complex refractive indicesAppendix B Thickness-dependent polynomial regression coefficientsAppendix C Absorption program algorithmAppendix D Multilayer matrix calculation with absorptionAppendix E Publications listAppendix F Refractive Index Data Sources

Appendix A.Refractive index (n) values for Germanium (Ge) 2-20µµµµm

Wl (µµµµm) 300 250 200 150 100 502.0 4.1069 4.0867 4.0655 4.0433 4.0200 3.99572.5 4.0674 4.0470 4.0259 4.0041 3.9816 3.95853.0 4.0472 4.0267 4.0057 3.9843 3.9623 3.93993.5 4.0353 4.0149 3.9940 3.9728 3.9511 3.92914.0 4.0278 4.0073 3.9866 3.9655 3.9441 3.92234.5 4.0227 4.0022 3.9815 3.9605 3.9393 3.91775.0 4.0190 3.9986 3.9779 3.9570 3.9359 3.91455.5 4.0164 3.9959 3.9753 3.9545 3.9334 3.91216.0 4.0143 3.9939 3.9733 3.9525 3.9315 3.91036.5 4.0127 3.9923 3.9717 3.9510 3.9300 3.90897.0 4.0114 3.9910 3.9705 3.9497 3.9288 3.90787.5 4.0104 3.9900 3.9695 3.9488 3.9279 3.90698.0 4.0095 3.9891 3.9686 3.9479 3.9271 3.90618.5 4.0088 3.9884 3.9679 3.9473 3.9264 3.90559.0 4.0082 3.9878 3.9673 3.9467 3.9259 3.90499.5 4.0076 3.9873 3.9668 3.9462 3.9254 3.9045

10.0 4.0072 3.9868 3.9663 3.9457 3.9250 3.904110.5 4.0067 3.9864 3.9659 3.9453 3.9246 3.903711.0 4.0063 3.9860 3.9656 3.9450 3.9243 3.903411.5 4.0060 3.9857 3.9652 3.9447 3.9240 3.903112.0 4.0057 3.9854 3.9649 3.9444 3.9237 3.902912.5 4.0054 3.9851 3.9647 3.9441 3.9234 3.902613.0 4.0051 3.9848 3.9644 3.9439 3.9232 3.902413.5 4.0049 3.9846 3.9642 3.9436 3.9230 3.902214.0 4.0046 3.9843 3.9639 3.9434 3.9228 3.902014.5 4.0044 3.9841 3.9637 3.9432 3.9226 3.901815.0 4.0041 3.9839 3.9635 3.9430 3.9224 3.901715.5 4.0039 3.9837 3.9633 3.9428 3.9222 3.901516.0 4.0037 3.9834 3.9631 3.9426 3.9220 3.901416.5 4.0035 3.9832 3.9629 3.9424 3.9219 3.901217.0 4.0033 3.9830 3.9627 3.9423 3.9217 3.901017.5 4.0030 3.9828 3.9625 3.9421 3.9215 3.900918.0 4.0028 3.9826 3.9623 3.9419 3.9214 3.900818.5 4.0026 3.9824 3.9621 3.9417 3.9212 3.900619.0 4.0024 3.9822 3.9619 3.9415 3.9211 3.900519.5 4.0022 3.9820 3.9617 3.9414 3.9209 3.900320.0 4.0020 3.9818 3.9616 3.9412 3.9207 3.9002


153

Extinction coefficients (k) for Germanium (Ge) 12-35µµµµm

Wl (µµµµm) 300K 250K 200K 150K 100K 50K12.0 4.00E-05 3.00E-05 4.00E-05 4.00E-05 3.00E-05 4.00E-0512.5 4.00E-05 4.00E-05 4.00E-05 4.00E-05 3.00E-05 4.00E-0513.0 5.00E-05 4.00E-05 4.00E-05 4.00E-05 4.00E-05 4.00E-0513.5 5.00E-05 5.00E-05 4.00E-05 4.00E-05 4.00E-05 4.00E-0514.0 5.00E-05 4.00E-05 4.00E-05 4.00E-05 4.00E-05 4.00E-0514.5 6.00E-05 6.00E-05 3.00E-05 7.00E-05 2.00E-05 4.00E-0515.0 6.00E-05 1.00E-04 6.00E-05 8.00E-05 4.00E-05 4.00E-0515.5 1.40E-04 7.00E-05 1.00E-04 8.00E-05 6.00E-05 7.00E-0516.0 1.00E-04 8.00E-05 7.00E-05 6.00E-05 6.00E-05 6.00E-0516.5 9.00E-05 8.00E-05 7.00E-05 7.00E-05 7.00E-05 7.00E-0517.0 1.50E-04 1.30E-04 1.30E-04 1.30E-04 1.30E-04 1.20E-0417.5 2.90E-04 2.70E-04 2.50E-04 2.40E-04 2.10E-04 2.10E-0418.0 3.30E-04 2.90E-04 2.70E-04 2.40E-04 2.20E-04 2.00E-0418.5 3.60E-04 3.10E-04 2.80E-04 2.60E-04 2.30E-04 2.30E-0419.0 3.80E-04 3.40E-04 3.20E-04 2.80E-04 2.50E-04 2.30E-0419.5 3.90E-04 3.40E-04 3.10E-04 2.70E-04 2.30E-04 2.20E-0420.0 3.70E-04 2.90E-04 2.70E-04 2.20E-04 1.90E-04 1.70E-0420.5 3.20E-04 2.70E-04 2.40E-04 2.00E-04 1.60E-04 1.60E-0421.0 3.90E-04 3.40E-04 2.80E-04 2.40E-04 2.00E-04 1.90E-0421.5 4.50E-04 3.70E-04 3.50E-04 2.90E-04 2.60E-04 2.30E-0422.0 6.10E-04 5.00E-04 4.60E-04 3.90E-04 3.50E-04 3.10E-0422.5 7.50E-04 6.50E-04 5.80E-04 4.90E-04 4.00E-04 4.10E-0423.0 9.50E-04 8.30E-04 7.60E-04 6.30E-04 5.50E-04 5.30E-0423.5 1.39E-03 1.28E-03 1.14E-03 9.60E-04 8.10E-04 7.30E-0424.0 1.34E-03 1.13E-03 9.30E-04 7.70E-04 6.40E-04 5.30E-0424.5 8.60E-04 6.80E-04 5.70E-04 4.80E-04 3.70E-04 3.10E-0425.0 8.80E-04 7.00E-04 6.60E-04 6.90E-04 5.30E-04 4.40E-0425.5 1.62E-03 1.49E-03 1.33E-03 1.14E-03 9.50E-04 7.80E-0426.0 1.93E-03 1.64E-03 1.44E-03 1.19E-03 9.30E-04 7.80E-0426.5 2.19E-03 1.85E-03 1.67E-03 1.33E-03 1.13E-03 9.10E-0427.0 2.71E-03 2.42E-03 2.12E-03 1.79E-03 1.40E-03 1.13E-0327.5 3.40E-03 2.81E-03 2.52E-03 2.02E-03 1.57E-03 1.19E-0328.0 4.04E-03 3.85E-03 3.71E-03 3.23E-03 2.88E-03 2.38E-0328.5 6.81E-03 5.69E-03 4.74E-03 3.88E-03 2.93E-03 2.20E-0329.0 6.56E-03 5.60E-03 5.29E-03 4.21E-03 3.28E-03 2.57E-0329.5 6.54E-03 5.00E-03 4.16E-03 3.06E-03 2.18E-03 1.73E-0330.0 3.95E-03 3.24E-03 2.80E-03 2.04E-03 1.64E-03 1.20E-0330.5 3.24E-03 2.76E-03 2.28E-03 1.77E-03 1.45E-03 1.12E-0331.0 3.18E-03 2.62E-03 2.33E-03 2.02E-03 1.62E-03 1.11E-0331.5 3.37E-03 2.78E-03 2.40E-03 1.84E-03 1.52E-03 1.12E-0332.0 3.12E-03 2.68E-03 2.18E-03 1.74E-03 1.49E-03 1.04E-0332.5 2.90E-03 2.45E-03 2.08E-03 1.75E-03 1.38E-03 9.80E-0433.0 2.87E-03 2.43E-03 2.33E-03 1.99E-03 1.70E-03 1.01E-0333.5 3.12E-03 2.58E-03 2.32E-03 1.84E-03 1.51E-03 1.10E-0334.0 3.34E-03 2.67E-03 2.46E-03 1.90E-03 1.52E-03 1.15E-0334.5 3.33E-03 3.21E-03 2.54E-03 1.78E-03 1.42E-03 1.00E-0335.0 3.52E-03 2.95E-03 2.73E-03 1.98E-03 1.45E-03 1.13E-03


154

Refractive index (n) values for Silicon (Si) 0.5-12µµµµm

Wl (µµµµm) 300 250 200 150 100 500.50 3.4669 3.4589 3.4509 3.4429 3.4349 3.42691.00 3.4567 3.4487 3.4407 3.4327 3.4247 3.41671.50 3.4482 3.4402 3.4322 3.4242 3.4162 3.40822.00 3.4411 3.4331 3.4251 3.4171 3.4091 3.40112.50 3.4354 3.4274 3.4194 3.4114 3.4034 3.39543.00 3.4308 3.4228 3.4148 3.4068 3.3988 3.39083.50 3.4272 3.4192 3.4112 3.4032 3.3952 3.38724.00 3.4244 3.4164 3.4084 3.4004 3.3924 3.38444.50 3.4223 3.4143 3.4063 3.3983 3.3903 3.38235.00 3.4207 3.4127 3.4047 3.3967 3.3887 3.38075.50 3.4195 3.4115 3.4035 3.3955 3.3875 3.37956.00 3.4187 3.4107 3.4027 3.3947 3.3867 3.37876.50 3.4181 3.4101 3.4021 3.3941 3.3861 3.37817.00 3.4177 3.4097 3.4017 3.3937 3.3857 3.37777.50 3.4174 3.4094 3.4014 3.3934 3.3854 3.37748.00 3.4171 3.4091 3.4011 3.3931 3.3851 3.37718.50 3.4169 3.4089 3.4009 3.3929 3.3849 3.37699.00 3.4167 3.4087 3.4007 3.3927 3.3847 3.37679.50 3.4164 3.4084 3.4004 3.3924 3.3844 3.3764

10.00 3.4162 3.4082 3.4002 3.3922 3.3842 3.376210.50 3.4160 3.4080 3.4000 3.3920 3.3840 3.376011.00 3.4159 3.4079 3.3999 3.3919 3.3839 3.375911.50 3.4159 3.4079 3.3999 3.3919 3.3839 3.375912.00 3.4160 3.4080 3.4000 3.3920 3.3840 3.3760


155

Extinction coefficient (k) values for Fz Silicon (Si) 6.5-30µµµµm

Wl (µµµµm) 300 250 200 150 100 506.5 4.02E-06 3.16E-06 2.74E-06 4.61E-06 7.01E-06 7.10E-067.0 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-057.5 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-058.0 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-058.5 4.00E-05 4.00E-05 3.00E-05 4.00E-05 4.00E-05 4.00E-059.0 3.00E-04 3.10E-04 3.10E-04 2.70E-04 1.80E-04 8.00E-059.5 5.00E-05 4.00E-05 3.00E-05 4.00E-05 5.00E-05 4.00E-05

10.0 7.00E-05 7.00E-05 6.00E-05 7.00E-05 8.00E-05 9.00E-0510.5 1.30E-04 1.20E-04 1.10E-04 1.10E-04 1.10E-04 1.10E-0411.0 1.80E-04 1.70E-04 1.60E-04 1.60E-04 1.60E-04 1.70E-0411.5 2.00E-04 1.80E-04 1.60E-04 1.50E-04 1.50E-04 1.60E-0412.0 1.60E-04 1.40E-04 1.30E-04 1.20E-04 1.10E-04 1.30E-0412.5 1.70E-04 1.50E-04 1.30E-04 1.20E-04 1.10E-04 1.30E-0413.0 2.30E-04 2.00E-04 1.70E-04 1.50E-04 1.40E-04 1.60E-0413.5 3.20E-04 2.90E-04 2.60E-04 2.20E-04 2.10E-04 2.30E-0414.0 1.70E-04 1.50E-04 1.20E-04 1.00E-04 8.00E-05 1.00E-0414.5 1.20E-04 1.10E-04 9.00E-05 8.00E-05 7.00E-05 9.00E-0515.0 1.30E-04 1.20E-04 1.00E-04 9.00E-05 8.00E-05 1.00E-0415.5 1.60E-04 1.40E-04 1.20E-04 1.00E-04 9.00E-05 1.10E-0416.0 6.80E-04 6.40E-04 5.80E-04 5.20E-04 4.60E-04 4.70E-0416.5 1.03E-03 9.00E-04 7.50E-04 6.20E-04 5.30E-04 5.30E-0417.0 4.40E-04 3.80E-04 3.10E-04 2.50E-04 2.10E-04 2.40E-0417.5 4.00E-04 3.50E-04 3.00E-04 2.50E-04 2.20E-04 2.50E-0418.0 4.00E-04 3.50E-04 2.90E-04 2.40E-04 2.00E-04 2.30E-0418.5 3.40E-04 3.00E-04 2.50E-04 2.00E-04 1.70E-04 2.10E-0419.0 3.30E-04 2.90E-04 2.40E-04 2.10E-04 1.90E-04 2.20E-0419.5 3.70E-04 3.20E-04 2.70E-04 2.30E-04 2.00E-04 2.60E-0420.0 3.00E-04 2.60E-04 2.10E-04 1.70E-04 1.40E-04 1.50E-0420.5 2.70E-04 2.30E-04 1.80E-04 1.40E-04 1.20E-04 1.80E-0421.0 2.20E-04 1.80E-04 1.50E-04 1.10E-04 9.00E-05 1.10E-0421.5 1.90E-04 1.50E-04 1.20E-04 9.00E-05 7.00E-05 1.00E-0422.0 1.60E-04 1.30E-04 1.00E-04 8.00E-05 6.00E-05 8.00E-0522.5 1.40E-04 1.20E-04 9.00E-05 7.00E-05 5.00E-05 7.00E-0523.0 1.30E-04 1.00E-04 8.00E-05 6.00E-05 5.00E-05 6.00E-0523.5 1.30E-04 1.00E-04 8.00E-05 6.00E-05 4.00E-05 4.00E-0524.0 1.20E-04 1.00E-04 7.00E-05 5.00E-05 4.00E-05 4.00E-0524.5 1.10E-04 9.00E-05 7.00E-05 5.00E-05 4.00E-05 3.00E-0525.0 1.10E-04 9.00E-05 6.00E-05 5.00E-05 3.00E-05 3.00E-0525.5 1.10E-04 9.00E-05 7.00E-05 5.00E-05 3.00E-05 3.00E-0526.0 1.20E-04 9.00E-05 7.00E-05 5.00E-05 3.00E-05 3.00E-0526.5 1.20E-04 1.00E-04 8.00E-05 5.00E-05 3.00E-05 3.00E-0527.0 1.20E-04 1.00E-04 7.00E-05 5.00E-05 3.00E-05 2.00E-0527.5 1.20E-04 1.00E-04 7.00E-05 5.00E-05 3.00E-05 2.00E-0528.0 1.20E-04 1.00E-04 7.00E-05 5.00E-05 3.00E-05 2.00E-0528.5 1.30E-04 1.00E-04 7.00E-05 5.00E-05 4.00E-05 2.00E-0529.0 1.30E-04 1.00E-04 7.00E-05 5.00E-05 4.00E-05 2.00E-0529.5 1.30E-04 1.00E-04 7.00E-05 5.00E-05 4.00E-05 2.00E-0530.0 1.30E-04 1.00E-04 7.00E-05 5.00E-05 3.00E-05 2.00E-05


156

Refractive index (n) values Zinc Selenide (ZnSe) 1.5-20µµµµm

Wl (µµµµm) 300 250 200 150 100 501.5 2.4447 2.4384 2.4320 2.4257 2.4194 2.41302.0 2.4424 2.4364 2.4304 2.4244 2.4185 2.41252.5 2.4402 2.4346 2.4289 2.4232 2.4176 2.41193.0 2.4381 2.4328 2.4274 2.4220 2.4166 2.41133.5 2.4361 2.4310 2.4259 2.4208 2.4157 2.41064.0 2.4341 2.4293 2.4244 2.4196 2.4147 2.40984.5 2.4322 2.4276 2.4229 2.4183 2.4137 2.40905.0 2.4303 2.4258 2.4214 2.4170 2.4126 2.40815.5 2.4283 2.4241 2.4198 2.4156 2.4114 2.40716.0 2.4263 2.4223 2.4182 2.4141 2.4101 2.40606.5 2.4243 2.4204 2.4165 2.4126 2.4087 2.40487.0 2.4222 2.4185 2.4147 2.4109 2.4072 2.40347.5 2.4200 2.4164 2.4128 2.4091 2.4055 2.40198.0 2.4177 2.4142 2.4107 2.4072 2.4037 2.40028.5 2.4153 2.4119 2.4085 2.4051 2.4017 2.39839.0 2.4128 2.4095 2.4062 2.4029 2.3996 2.39639.5 2.4100 2.4068 2.4036 2.4004 2.3972 2.3941

10.0 2.4071 2.4040 2.4009 2.3978 2.3947 2.391610.5 2.4040 2.4010 2.3979 2.3949 2.3919 2.388911.0 2.4006 2.3977 2.3948 2.3918 2.3889 2.386011.5 2.3970 2.3942 2.3913 2.3885 2.3857 2.382812.0 2.3931 2.3904 2.3876 2.3849 2.3821 2.379412.5 2.3890 2.3863 2.3836 2.3810 2.3783 2.375713.0 2.3845 2.3819 2.3794 2.3768 2.3742 2.371713.5 2.3797 2.3772 2.3748 2.3723 2.3698 2.367414.0 2.3745 2.3722 2.3698 2.3675 2.3651 2.362814.5 2.3690 2.3668 2.3645 2.3623 2.3601 2.357815.0 2.3631 2.3610 2.3589 2.3568 2.3547 2.352515.5 2.3568 2.3548 2.3529 2.3509 2.3489 2.346916.0 2.3501 2.3483 2.3464 2.3446 2.3428 2.340916.5 2.3429 2.3413 2.3396 2.3379 2.3362 2.334617.0 2.3353 2.3338 2.3323 2.3308 2.3293 2.327817.5 2.3272 2.3259 2.3246 2.3233 2.3220 2.320718.0 2.3185 2.3174 2.3164 2.3153 2.3142 2.313118.5 2.3094 2.3085 2.3077 2.3068 2.3060 2.305119.0 2.2997 2.2991 2.2985 2.2979 2.2973 2.296719.5 2.2894 2.2891 2.2888 2.2884 2.2881 2.287820.0 2.2785 2.2785 2.2785 2.2785 2.2785 2.2784


157

Extinction coefficient (k) values Zinc Selenide (ZnSe) 10-33µµµµm

Wl (µµµµm) 300 250 200 150 100 5010.0 8.30E-07 1.20E-06 6.80E-07 3.50E-07 4.00E-07 5.20E-0710.5 9.20E-07 1.48E-06 8.63E-07 5.45E-07 1.08E-06 1.73E-0611.0 1.21E-06 1.50E-06 8.43E-07 4.45E-07 1.21E-06 2.84E-0611.5 1.40E-06 1.70E-06 9.31E-07 5.40E-07 1.60E-06 4.21E-0612.0 1.77E-06 1.90E-06 1.00E-06 5.63E-07 1.87E-06 5.20E-0612.5 1.80E-06 1.90E-06 1.00E-06 4.80E-07 1.90E-06 5.70E-0613.0 2.10E-06 1.91E-06 8.06E-07 2.52E-07 1.53E-06 5.64E-0613.5 2.58E-06 2.46E-06 1.28E-06 6.98E-07 1.79E-06 5.53E-0614.0 4.24E-06 4.07E-06 2.64E-06 1.77E-06 2.52E-06 5.55E-0614.5 7.97E-06 8.78E-06 7.58E-06 6.69E-06 7.29E-06 1.00E-0515.0 2.00E-05 2.00E-05 2.00E-05 1.00E-05 1.00E-05 2.00E-0515.5 3.00E-05 3.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-0516.0 5.00E-05 4.00E-05 4.00E-05 3.00E-05 2.00E-05 2.00E-0516.5 6.00E-05 4.00E-05 3.00E-05 2.00E-05 2.00E-05 1.00E-0517.0 7.00E-05 5.00E-05 4.00E-05 3.00E-05 2.00E-05 2.00E-0517.5 9.00E-05 7.00E-05 5.00E-05 3.00E-05 2.00E-05 2.00E-0518.0 9.00E-05 7.00E-05 5.00E-05 3.00E-05 2.00E-05 2.00E-0518.5 1.10E-04 8.00E-05 6.00E-05 4.00E-05 3.00E-05 2.00E-0519.0 1.60E-04 1.20E-04 1.00E-04 7.00E-05 5.00E-05 4.00E-0519.5 2.50E-04 2.10E-04 1.70E-04 1.20E-04 1.00E-04 8.00E-0520.0 4.40E-04 3.70E-04 3.00E-04 2.30E-04 1.90E-04 1.60E-0420.5 6.50E-04 5.40E-04 4.20E-04 3.10E-04 2.40E-04 1.90E-0421.0 8.40E-04 6.70E-04 5.20E-04 3.80E-04 2.80E-04 2.20E-0421.5 1.13E-03 9.60E-04 8.30E-04 7.30E-04 6.90E-04 6.00E-0422.0 2.46E-03 2.44E-03 2.45E-03 2.47E-03 2.44E-03 2.27E-0322.5 5.57E-03 5.38E-03 5.11E-03 4.84E-03 4.49E-03 4.12E-0323.0 8.36E-03 7.92E-03 7.67E-03 7.07E-03 5.77E-03 5.24E-0323.5 9.42E-03 8.53E-03 7.87E-03 7.43E-03 6.89E-03 6.20E-0324.0 1.02E-02 8.62E-03 8.23E-03 6.01E-03 3.97E-03 3.32E-0324.5 9.51E-03 6.94E-03 4.83E-03 3.12E-03 2.17E-03 1.80E-0325.0 6.39E-03 4.80E-03 3.56E-03 2.59E-03 2.03E-03 1.70E-0325.5 5.85E-03 4.85E-03 4.08E-03 3.37E-03 2.84E-03 2.42E-0326.0 6.99E-03 6.14E-03 5.39E-03 4.60E-03 3.88E-03 3.36E-0326.5 9.00E-03 7.76E-03 6.75E-03 5.66E-03 4.71E-03 4.05E-0327.0 1.05E-02 8.56E-03 7.49E-03 5.97E-03 4.70E-03 4.03E-0327.5 9.47E-03 7.95E-03 6.49E-03 4.90E-03 3.69E-03 3.09E-0328.0 8.51E-03 6.95E-03 5.50E-03 4.08E-03 3.02E-03 2.43E-0328.5 7.81E-03 6.19E-03 4.92E-03 3.62E-03 2.62E-03 2.04E-0329.0 7.51E-03 5.96E-03 4.66E-03 3.38E-03 2.41E-03 1.83E-0329.5 7.16E-03 5.74E-03 4.43E-03 3.19E-03 2.26E-03 1.71E-0330.0 6.95E-03 5.55E-03 4.29E-03 3.11E-03 2.23E-03 1.66E-0330.5 7.01E-03 5.65E-03 4.41E-03 3.30E-03 2.44E-03 1.81E-0331.0 7.54E-03 6.19E-03 5.02E-03 3.96E-03 3.00E-03 2.22E-0331.5 8.58E-03 7.15E-03 5.91E-03 4.69E-03 3.53E-03 2.58E-0332.0 1.46E-02 8.85E-03 7.17E-03 5.78E-03 4.53E-03 3.30E-0332.5 1.22E-02 1.13E-02 8.91E-03 7.66E-03 6.36E-03 4.75E-0333.0 1.29E-02 1.30E-02 9.50E-03 9.88E-03 9.16E-03 6.76E-03


158

Refractive index (n) values for Zinc Sulphide (ZnS) 1.5-20µµµµm

Wl (µµµµm) 300 250 200 150 100 501.5 2.2759 2.2737 2.2715 2.2692 2.2670 2.26482.0 2.2700 2.2679 2.2658 2.2638 2.2617 2.25972.5 2.2647 2.2628 2.2609 2.2589 2.2570 2.25513.0 2.2600 2.2582 2.2564 2.2546 2.2528 2.25103.5 2.2557 2.2540 2.2523 2.2506 2.2490 2.24734.0 2.2517 2.2502 2.2486 2.2470 2.2454 2.24384.5 2.2481 2.2466 2.2451 2.2435 2.2420 2.24055.0 2.2446 2.2431 2.2417 2.2402 2.2387 2.23735.5 2.2412 2.2397 2.2383 2.2369 2.2355 2.23406.0 2.2378 2.2363 2.2349 2.2335 2.2321 2.23076.5 2.2343 2.2328 2.2314 2.2300 2.2286 2.22717.0 2.2306 2.2292 2.2277 2.2263 2.2248 2.22347.5 2.2268 2.2253 2.2238 2.2223 2.2208 2.21928.0 2.2226 2.2211 2.2195 2.2179 2.2163 2.21488.5 2.2181 2.2165 2.2148 2.2131 2.2115 2.20989.0 2.2132 2.2115 2.2097 2.2079 2.2061 2.20449.5 2.2079 2.2060 2.2041 2.2022 2.2003 2.1983

10.0 2.2020 2.1999 2.1979 2.1958 2.1938 2.191710.5 2.1955 2.1933 2.1911 2.1889 2.1867 2.184411.0 2.1885 2.1861 2.1837 2.1813 2.1789 2.176511.5 2.1808 2.1782 2.1756 2.1730 2.1704 2.167812.0 2.1724 2.1696 2.1668 2.1640 2.1611 2.158312.5 2.1634 2.1603 2.1572 2.1542 2.1511 2.148113.0 2.1535 2.1502 2.1469 2.1436 2.1403 2.137013.5 2.1430 2.1394 2.1358 2.1322 2.1287 2.125114.0 2.1316 2.1278 2.1239 2.1201 2.1162 2.112314.5 2.1195 2.1153 2.1112 2.1070 2.1029 2.098715.0 2.1065 2.1020 2.0976 2.0932 2.0887 2.084315.5 2.0927 2.0880 2.0832 2.0784 2.0737 2.068916.0 2.0781 2.0730 2.0680 2.0629 2.0578 2.052716.5 2.0627 2.0573 2.0519 2.0465 2.0411 2.035717.0 2.0464 2.0407 2.0350 2.0292 2.0235 2.017717.5 2.0294 2.0233 2.0172 2.0112 2.0051 1.999018.0 2.0115 2.0051 1.9987 1.9923 1.9859 1.979418.5 1.9929 1.9861 1.9794 1.9726 1.9659 1.959119.0 1.9735 1.9664 1.9593 1.9522 1.9451 1.938019.5 1.9534 1.9459 1.9385 1.9310 1.9236 1.916120.0 1.9325 1.9247 1.9169 1.9092 1.9014 1.8936


159

Extinction coefficient (k) values for ZnS (Cleartran) 10-33µµµµm

Wl (µµµµm) 300 250 200 150 100 5010.0 5.70E-10 8.20E-10 8.00E-08 7.10E-09 3.90E-08 2.90E-0810.5 8.91E-06 8.92E-06 7.92E-06 8.42E-06 7.62E-06 8.72E-0611.0 3.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-0511.5 2.00E-05 2.00E-05 1.00E-05 1.00E-05 9.52E-06 1.00E-0512.0 3.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-05 2.00E-0512.5 6.00E-05 6.00E-05 5.00E-05 4.00E-05 4.00E-05 4.00E-0513.0 1.10E-04 9.00E-05 7.00E-05 5.00E-05 4.00E-05 4.00E-0513.5 1.60E-04 1.30E-04 9.00E-05 8.00E-05 6.00E-05 5.00E-0514.0 2.60E-04 2.10E-04 1.60E-04 1.30E-04 9.00E-05 8.00E-0514.5 7.30E-04 6.80E-04 6.20E-04 5.80E-04 5.60E-04 5.60E-0415.0 2.23E-03 1.68E-03 1.00E-03 6.20E-04 4.00E-04 3.00E-0415.5 2.76E-03 2.24E-03 2.35E-03 2.54E-03 2.66E-03 2.92E-0316.0 3.52E-03 3.01E-03 3.64E-03 2.86E-03 2.80E-03 2.53E-0316.5 3.36E-03 3.81E-03 3.54E-03 3.50E-03 3.08E-03 3.63E-0317.0 3.51E-03 3.87E-03 3.55E-03 4.20E-03 3.61E-03 4.26E-0317.5 3.53E-03 3.72E-03 3.65E-03 3.48E-03 3.63E-03 3.21E-0318.0 3.34E-03 3.22E-03 2.65E-03 1.80E-03 1.43E-03 1.11E-0318.5 2.32E-03 1.63E-03 1.09E-03 8.00E-04 6.00E-04 4.90E-0419.0 2.96E-03 2.97E-03 2.24E-03 2.05E-03 1.86E-03 1.76E-0319.5 4.05E-03 3.96E-03 3.65E-03 3.49E-03 2.76E-03 3.22E-0320.0 4.06E-03 4.05E-03 4.02E-03 4.64E-03 4.06E-03 4.30E-0320.5 4.23E-03 4.15E-03 4.50E-03 3.96E-03 4.14E-03 3.64E-0321.0 3.89E-03 4.59E-03 4.37E-03 4.36E-03 4.62E-03 3.35E-0321.5 3.84E-03 4.66E-03 3.58E-03 3.30E-03 3.18E-03 2.50E-0322.0 3.85E-03 3.57E-03 3.63E-03 4.42E-03 3.63E-03 2.91E-0322.5 4.18E-03 3.93E-03 3.81E-03 4.38E-03 3.52E-03 2.66E-0323.0 3.42E-03 4.06E-03 4.26E-03 6.74E-03 3.72E-03 3.63E-0323.5 3.58E-03 3.06E-03 3.60E-03 4.84E-03 4.86E-03 3.74E-0324.0 5.64E-03 4.43E-03 3.33E-03 4.31E-03 5.97E-03 3.30E-0324.5 4.75E-03 3.84E-03 4.94E-03 5.87E-03 4.22E-03 4.58E-0325.0 3.50E-03 5.08E-03 4.74E-03 3.74E-03 6.56E-03 3.78E-0325.5 4.52E-03 3.65E-03 5.52E-03 5.00E-03 5.28E-03 3.96E-0326.0 4.07E-03 4.09E-03 5.13E-03 4.22E-03 3.95E-03 5.34E-0326.5 3.82E-03 4.04E-03 3.83E-03 6.71E-03 3.72E-03 3.83E-0327.0 4.66E-03 3.55E-03 5.64E-03 4.14E-03 5.57E-03 4.90E-0327.5 4.33E-03 4.13E-03 3.91E-03 3.99E-03 4.42E-03 4.28E-0328.0 3.33E-03 4.42E-03 5.27E-03 9.03E-03 4.24E-03 3.90E-0328.5 5.23E-03 4.43E-03 4.46E-03 4.41E-03 3.62E-03 4.12E-0329.0 3.80E-03 4.54E-03 3.84E-03 4.32E-03 7.72E-03 4.31E-0329.5 5.11E-03 3.33E-03 4.06E-03 3.72E-03 4.07E-03 4.73E-0330.0 4.75E-03 3.65E-03 4.64E-03 4.25E-03 4.66E-03 4.25E-0330.5 3.76E-03 3.92E-03 4.32E-03 5.50E-03 3.24E-03 3.70E-0331.0 3.75E-03 4.15E-03 3.57E-03 4.31E-03 4.41E-03 6.25E-0331.5 3.71E-03 4.20E-03 3.97E-03 3.56E-03 3.30E-03 4.65E-0332.0 4.42E-03 4.15E-03 5.81E-03 4.35E-03 3.61E-03 3.91E-0332.5 4.18E-03 4.09E-03 6.46E-03 6.21E-03 7.02E-03 5.17E-0333.0 3.27E-03 3.77E-03 4.40E-03 3.88E-03 4.63E-03 3.23E-03


160

Refractive index (n) values for Cadmium Telluride (CdTe) 1-24µµµµm

Wl (µµµµm) 300 250 200 150 100 501.0 2.8015 2.8004 2.7992 2.7980 2.7967 2.79541.5 2.7337 2.7302 2.7268 2.7233 2.7197 2.71622.0 2.7122 2.7082 2.7041 2.7000 2.6959 2.69172.5 2.7025 2.6982 2.6939 2.6895 2.6852 2.68083.0 2.6972 2.6927 2.6883 2.6838 2.6793 2.67483.5 2.6938 2.6892 2.6847 2.6801 2.6756 2.67104.0 2.6914 2.6868 2.6822 2.6776 2.6730 2.66834.5 2.6895 2.6849 2.6803 2.6756 2.6710 2.66635.0 2.6880 2.6833 2.6787 2.6740 2.6693 2.66465.5 2.6866 2.6819 2.6773 2.6726 2.6679 2.66326.0 2.6854 2.6807 2.6760 2.6713 2.6666 2.66196.5 2.6842 2.6795 2.6748 2.6701 2.6653 2.66067.0 2.6830 2.6783 2.6736 2.6688 2.6641 2.65947.5 2.6818 2.6771 2.6724 2.6676 2.6629 2.65828.0 2.6806 2.6759 2.6712 2.6664 2.6617 2.65698.5 2.6794 2.6746 2.6699 2.6652 2.6604 2.65579.0 2.6781 2.6734 2.6686 2.6639 2.6591 2.65449.5 2.6768 2.6721 2.6673 2.6626 2.6578 2.6530

10.0 2.6754 2.6707 2.6659 2.6612 2.6564 2.651710.5 2.6740 2.6693 2.6645 2.6598 2.6550 2.650211.0 2.6726 2.6678 2.6631 2.6583 2.6535 2.648711.5 2.6710 2.6663 2.6615 2.6568 2.6520 2.647212.0 2.6694 2.6647 2.6599 2.6552 2.6504 2.645612.5 2.6678 2.6630 2.6583 2.6535 2.6487 2.643913.0 2.6661 2.6613 2.6566 2.6518 2.6470 2.642213.5 2.6643 2.6595 2.6548 2.6500 2.6452 2.640414.0 2.6624 2.6577 2.6529 2.6482 2.6434 2.638614.5 2.6605 2.6558 2.6510 2.6463 2.6415 2.636715.0 2.6585 2.6538 2.6491 2.6443 2.6395 2.634715.5 2.6565 2.6518 2.6470 2.6422 2.6374 2.632716.0 2.6544 2.6496 2.6449 2.6401 2.6353 2.630516.5 2.6521 2.6474 2.6427 2.6379 2.6331 2.628317.0 2.6499 2.6452 2.6404 2.6357 2.6309 2.626117.5 2.6475 2.6428 2.6381 2.6333 2.6286 2.623818.0 2.6451 2.6404 2.6357 2.6309 2.6262 2.621418.5 2.6426 2.6379 2.6332 2.6284 2.6237 2.618919.0 2.6400 2.6353 2.6306 2.6259 2.6211 2.616319.5 2.6373 2.6327 2.6280 2.6233 2.6185 2.613720.0 2.6345 2.6299 2.6253 2.6206 2.6158 2.611020.5 2.6317 2.6271 2.6225 2.6178 2.6130 2.608321.0 2.6288 2.6242 2.6196 2.6149 2.6102 2.605421.5 2.6257 2.6212 2.6166 2.6119 2.6072 2.602522.0 2.6226 2.6182 2.6136 2.6089 2.6042 2.599522.5 2.6194 2.6150 2.6104 2.6058 2.6011 2.596423.0 2.6161 2.6118 2.6072 2.6026 2.5979 2.593223.5 2.6128 2.6084 2.6039 2.5993 2.5947 2.590024.0 2.6093 2.6050 2.6005 2.5960 2.5913 2.5866


161

Extinction coefficient (k) values for Cadmium Telluride (CdTe) 20-40µµµµm

Wl (µµµµm) 300 250 200 150 100 5020.0 4.10E-08 4.70E-08 7.00E-08 2.20E-07 7.90E-07 3.90E-0820.5 7.03E-07 3.97E-07 5.13E-07 3.05E-07 7.99E-07 3.47E-0721.0 2.34E-06 7.11E-07 1.90E-06 9.05E-07 1.42E-06 7.86E-0721.5 4.98E-06 2.89E-06 3.44E-06 2.75E-06 2.61E-06 1.48E-0622.0 1.00E-05 8.15E-06 9.56E-06 7.21E-06 6.96E-06 5.71E-0622.5 2.00E-05 1.00E-05 2.00E-05 1.00E-05 9.87E-06 8.50E-0623.0 3.00E-05 2.00E-05 2.00E-05 1.00E-05 9.40E-06 7.00E-0623.5 3.00E-05 3.00E-05 2.00E-05 1.00E-05 1.00E-05 7.26E-0624.0 4.00E-05 3.00E-05 3.00E-05 2.00E-05 1.00E-05 1.00E-0524.5 4.00E-05 3.00E-05 2.00E-05 2.00E-05 1.00E-05 7.28E-0625.0 6.00E-05 5.00E-05 5.00E-05 3.00E-05 2.00E-05 2.00E-0525.5 7.00E-05 6.00E-05 4.00E-05 3.00E-05 2.00E-05 1.00E-0526.0 8.00E-05 6.00E-05 5.00E-05 3.00E-05 2.00E-05 1.00E-0526.5 9.00E-05 7.00E-05 5.00E-05 3.00E-05 2.00E-05 1.00E-0527.0 1.00E-04 8.00E-05 5.00E-05 3.00E-05 2.00E-05 2.00E-0527.5 1.20E-04 9.00E-05 6.00E-05 4.00E-05 2.00E-05 2.00E-0528.0 1.60E-04 1.30E-04 1.10E-04 7.00E-05 5.00E-05 4.00E-0528.5 2.30E-04 2.00E-04 1.60E-04 1.10E-04 8.00E-05 6.00E-0529.0 3.50E-04 2.80E-04 2.20E-04 1.40E-04 9.00E-05 5.00E-0529.5 5.10E-04 4.10E-04 3.30E-04 2.30E-04 1.60E-04 1.10E-0430.0 7.30E-04 6.20E-04 4.90E-04 3.40E-04 2.40E-04 1.70E-0430.5 9.80E-04 8.30E-04 6.50E-04 4.40E-04 3.00E-04 2.10E-0431.0 1.29E-03 1.06E-03 8.10E-04 5.30E-04 3.60E-04 2.50E-0431.5 1.64E-03 1.38E-03 1.09E-03 8.50E-04 7.30E-04 7.00E-0432.0 2.52E-03 2.34E-03 2.22E-03 2.09E-03 2.00E-03 2.05E-0332.5 4.38E-03 4.26E-03 4.24E-03 4.60E-03 4.71E-03 4.85E-0333.0 6.38E-03 5.95E-03 6.01E-03 6.53E-03 6.61E-03 4.87E-0333.5 7.77E-03 5.68E-03 1.04E-02 6.60E-03 8.88E-03 4.52E-0334.0 6.97E-03 6.83E-03 6.52E-03 7.24E-03 7.85E-03 7.09E-0334.5 6.68E-03 7.16E-03 6.43E-03 7.93E-03 7.23E-03 4.19E-0335.0 7.04E-03 7.00E-03 6.25E-03 5.46E-03 3.10E-03 1.85E-0335.5 6.45E-03 6.46E-03 5.25E-03 3.40E-03 1.90E-03 1.15E-0336.0 6.23E-03 6.53E-03 4.06E-03 2.58E-03 1.66E-03 1.06E-0336.5 5.99E-03 5.23E-03 3.75E-03 2.50E-03 1.84E-03 1.40E-0337.0 5.99E-03 4.41E-03 3.90E-03 2.81E-03 2.29E-03 1.71E-0337.5 6.38E-03 4.69E-03 4.54E-03 3.52E-03 2.75E-03 2.11E-0338.0 7.42E-03 5.08E-03 5.17E-03 4.29E-03 3.25E-03 2.50E-0338.5 8.82E-03 3.63E-03 1.01E-02 5.35E-03 5.13E-03 2.90E-0339.0 6.63E-03 4.54E-03 7.54E-03 4.90E-03 5.09E-03 3.38E-0339.5 5.88E-03 4.77E-03 4.88E-03 3.79E-03 4.84E-03 3.49E-0340.0 6.74E-03 3.71E-03 3.40E-03 2.31E-03 5.93E-03 3.86E-03


162

Appendix B

Polynomial regression coefficients for the determination of Germanium (Ge) transmittance profilefor uncoated substrate material of thickness t at 293K

T = A0 + A1t + A2t2 + A3t

3 + A4t4 + A5t

5 + A6t6

cm-1 A0 A1 A2 A3 A4 A5 A6

800 0.47223 -0.01230 0.00471 -0.00225 0.00058 -7.8x10-5 4.1x10-6

780 0.47388 -0.01658 0.00984 -0.00503 0.00138 -0.00019 1.1x10-5

760 0.47006 -0.01078 0.00077 -0.00066 0.00026 -4.6x10-5 3.0x10-6

740 0.47235 -0.01609 0.00388 -0.00154 0.00034 -3.9x10-5 1.8x10-6

720 0.47650 -0.02464 0.01697 -0.00871 0.00239 -0.00033 1.8x10-5

700 0.46977 -0.00597 -0.00081 0.00023 -6.6x10-6 -5.5x10-6 5.9x10-7

680 0.47190 -0.02076 0.00427 -0.00195 0.00051 -6.8x10-5 3.6x10-6

660 0.46884 -0.02584 -0.00262 0.00185 -0.00049 6.6x10-5 -3.6x10-6

640 0.46738 -0.02998 -0.00462 0.00280 -0.00064 7.1x10-5 -3.0x10-6

620 0.47327 -0.03198 0.00728 -0.00305 0.00077 -0.00010 5.3x10-6

600 0.46754 -0.01497 -0.00727 0.00406 -0.00110 0.00015 -8.2x10-6

580 0.47114 -0.06963 0.00817 -0.00126 0.00021 -2.3x10-5 1.2x10-6

560 0.47236 -0.12541 0.02529 -0.00524 0.00089 -9.2x10-5 4.1x10-6

540 0.47530 -0.12802 0.03161 -0.00904 0.00199 -0.00025 1.3x10-5

520 0.47075 -0.13511 0.02768 -0.00575 0.00105 -0.00012 6.5x10-6

500 0.47169 -0.11416 0.02143 -0.00470 0.00096 -0.00013 7.1x10-6

480 0.47272 -0.11222 0.02264 -0.00557 0.00117 -0.00015 7.7x10-6

460 0.46690 -0.14945 0.02568 -0.00157 -4.8x10-4 1.2x10-4 -8.3x10-6

440 0.46168 -0.21637 0.05537 -0.00905 0.00078 -8.6x10-6 -2.4x10-6

420 0.45580 -0.35116 0.14571 -0.04046 0.00735 -0.00077 3.5x10-5

400 0.46944 -0.21993 0.06641 -0.01637 0.00294 -0.00032 1.5x10-5

380 0.43915 -0.41076 0.19133 -0.05540 0.01007 -0.00104 4.7x10-5

360 0.37981 -0.51848 0.31588 -0.10775 0.02132 -0.00229 0.00010340 0.25050 -0.44422 0.33111 -0.13152 0.02917 -0.00341 0.00016320 0.41226 -0.48433 0.26548 -0.08496 0.01631 -0.00174 7.9x10-5

300 0.42033 -0.45112 0.22850 -0.06823 0.01231 -0.00124 5.3x10-5

280 0.41922 -0.47644 0.25459 -0.07979 0.01500 -0.00156 6.9x10-5

260 0.45579 -0.35116 0.14570 -0.04046 0.00735 -0.00077 3.5x10-5

240 0.46357 -0.20478 0.05100 -0.00863 0.00089 -0.00004 2.2x10-15

220 0.47035 -0.21094 0.06246 -0.01554 0.00287 -0.00032 1.5x10-5

200 0.46545 -0.24272 0.07495 -0.01718 0.00276 -0.00027 1.1x10-5

180 0.47053 -0.20939 0.06105 -0.01475 0.00262 -0.00028 1.3x10-5

160 0.47378 -0.16236 0.04188 -0.01032 0.00193 -0.00021 1.0x10-5

140 0.47116 -0.11158 0.01929 -0.00348 0.00056 -0.00006 2.9x10-6

120 0.46707 -0.12958 0.01770 0.00035 -0.00077 0.00014 -8.8x10-6

100 0.46800 -0.13403 0.02054 -0.00066 -0.00058 0.00012 -8.3x10-6

80 0.46932 -0.10393 0.01378 -0.00102 -6.7x10-5 2.5x10-5 -1.8x10-6

60 0.47061 -0.03658 0.00125 0.00049 -0.00021 3.7x10-5 -2.4x10-6

40 0.46995 -0.03705 0.00138 -2.6x10-5 6.8x10-5 -2.1x10-5 1.8x10-6


163

Polynomial regression coefficients for the determination of Fz Silicon (Si) transmittance profilefor uncoated substrate material of thickness t at 293K

T = A0 + A1t + A2t2 + A3t

3 + A4t4 + A5t

5 + A6t6

cm-1 A0 A1 A2 A3 A4 A5 A6

1500 0.53794 -0.00428 -7.9E-04 4.5E-04 -1.3E-04 1.9E-05 -1.1E-061480 0.53812 -0.01175 -9.3E-05 1.3E-04 -3.4E-05 4.5E-06 -2.4E-071460 0.53869 -0.02710 2.0E-03 -6.4E-04 1.7E-04 -2.3E-05 1.3E-061440 0.53821 -0.03029 1.0E-03 1.4E-05 -1.1E-05 1.4E-06 -5.9E-081420 0.53854 -0.02413 1.3E-03 -3.1E-04 7.4E-05 -9.4E-06 4.7E-071400 0.53838 -0.02073 6.8E-04 -6.7E-05 6.8E-06 1.4E-07 -5.9E-081380 0.53808 -0.02062 -2.3E-04 4.3E-04 -1.3E-04 1.9E-05 -1.1E-061360 0.53834 -0.02052 4.9E-04 2.6E-05 -1.8E-05 3.4E-06 -2.4E-071340 0.53792 -0.01858 -6.3E-04 5.5E-04 -1.5E-04 2.1E-05 -1.1E-061320 0.53821 -0.02503 4.0E-04 1.9E-04 -6.1E-05 9.1E-06 -5.3E-071300 0.53861 -0.03025 1.7E-03 -3.7E-04 8.4E-05 -1.1E-05 5.3E-071280 0.53799 -0.02475 2.7E-05 3.2E-04 -8.0E-05 9.8E-06 -4.7E-071260 0.53857 -0.02021 1.1E-03 -3.5E-04 9.8E-05 -1.4E-05 8.3E-071240 0.53813 -0.01539 -3.1E-04 3.0E-04 -7.9E-05 1.0E-05 -5.3E-071220 0.53849 -0.01614 5.3E-04 -9.8E-05 1.9E-05 -1.8E-06 5.9E-081200 0.53859 -0.02362 1.2E-03 -3.0E-04 7.4E-05 -9.9E-06 5.3E-071180 0.53816 -0.03255 6.1E-04 3.3E-04 -1.1E-04 1.5E-05 -8.3E-071160 0.53777 -0.04038 3.9E-04 8.0E-04 -2.4E-04 3.4E-05 -1.9E-061140 0.53834 -0.05458 3.2E-03 1.1E-06 -5.7E-05 9.8E-06 -5.9E-071120 0.53828 -0.06262 4.4E-03 -1.6E-04 -2.7E-05 5.8E-06 -3.6E-071100 0.53863 -0.05822 4.4E-03 -4.4E-04 5.7E-05 -5.5E-06 2.4E-071080 0.53838 -0.04398 2.3E-03 -9.1E-05 -8.8E-07 7.6E-07 -5.9E-081060 0.53831 -0.03257 8.4E-04 2.1E-04 -7.2E-05 1.0E-05 -5.9E-071040 0.53833 -0.02944 6.6E-04 1.9E-04 -6.7E-05 1.0E-05 -5.9E-071020 0.53867 -0.03832 2.2E-03 -2.9E-04 5.3E-05 -5.7E-06 2.4E-071000 0.53900 -0.05655 5.0E-03 -9.1E-04 1.9E-04 -2.5E-05 1.3E-06980 0.53836 -0.08082 7.4E-03 -3.8E-04 -4.8E-05 1.3E-05 -8.9E-07960 0.53812 -0.09451 1.0E-02 -6.9E-04 -1.9E-05 1.1E-05 -7.7E-07940 0.53801 -0.09160 8.9E-03 -3.2E-04 -1.1E-04 2.3E-05 -1.5E-06920 0.53821 -0.11238 1.4E-02 -1.5E-03 8.3E-05 2.4E-06 -4.7E-07900 0.53812 -0.14307 2.4E-02 -3.3E-03 3.6E-04 -2.5E-05 7.7E-07880 0.53823 -0.14528 2.5E-02 -3.7E-03 4.6E-04 -3.9E-05 1.5E-06860 0.53830 -0.12316 1.8E-02 -2.3E-03 2.5E-04 -1.9E-05 7.1E-07840 0.53871 -0.09739 1.2E-02 -1.6E-03 2.4E-04 -2.7E-05 1.4E-06820 0.53858 -0.13489 2.2E-02 -3.4E-03 4.6E-04 -4.4E-05 2.0E-06800 0.53860 -0.10659 1.4E-02 -1.7E-03 1.9E-04 -1.5E-05 5.9E-07780 0.53816 -0.13170 2.0E-02 -2.6E-03 2.6E-04 -1.6E-05 4.1E-07760 0.53822 -0.14450 2.4E-02 -3.6E-03 4.5E-04 -3.8E-05 1.5E-06740 0.53761 -0.18932 4.0E-02 -6.9E-03 8.8E-04 -7.0E-05 2.4E-06720 0.53832 -0.12979 2.0E-02 -2.5E-03 2.6E-04 -1.7E-05 4.7E-07700 0.53888 -0.05400 4.1E-03 -5.4E-04 9.5E-05 -1.1E-05 5.3E-07


164

Polynomial regression coefficients for the determination of Zinc Selenide tranmsittance profilefor uncoated substrate material of thickness t at 293K

T = A0 + A1t + A2t2 + A3t

3 + A4t4 + A5t

5 + A6t6

cm-1 A0 A1 A2 A3 A4 A5 A6

700 0.71556 0.00129 -0.00471 0.00245 -6.2E-04 7.5E-05 -3.6E-06690 0.72640 -0.01930 0.01014 -0.00325 5.6E-04 -5.0E-05 1.8E-06680 0.69029 0.03961 -0.02957 0.01028 -1.9E-03 1.9E-04 -7.7E-06670 0.74268 -0.05104 0.03158 -0.01152 2.3E-03 -2.4E-04 1.0E-05660 0.75169 -0.06739 0.03895 -0.01365 2.6E-03 -2.6E-04 1.1E-05650 0.72024 -0.01803 0.00302 -0.00120 2.8E-04 -3.5E-05 1.8E-06640 0.70713 -0.00054 -0.01265 0.00446 -8.3E-04 7.8E-05 -3.0E-06630 0.71890 -0.02480 4.0E-04 -6.9E-13 1.4E-13 -1.4E-14 5.8E-16620 0.72890 -0.04613 0.00858 -0.00215 2.8E-04 -1.4E-05 -2.1E-15610 0.75016 -0.08343 0.03584 -0.01248 2.4E-03 -2.4E-04 1.0E-05600 0.75929 -0.09515 0.04568 -0.01608 3.1E-03 -3.2E-04 1.3E-05590 0.77683 -0.12760 0.06526 -0.02290 4.4E-03 -4.5E-04 1.8E-05580 0.72965 -0.05259 0.00884 -0.00269 5.3E-04 -5.5E-05 2.4E-06570 0.72204 -0.04086 -0.00121 0.00097 -1.9E-04 1.7E-05 -5.9E-07560 0.75553 -0.09573 0.03755 -0.01281 2.5E-03 -2.5E-04 1.0E-05550 0.69840 0.00314 -0.03213 0.01226 -2.5E-03 2.5E-04 -1.1E-05540 0.75393 -0.09726 0.03273 -0.01064 2.0E-03 -1.9E-04 7.7E-06530 0.71763 -0.04890 -0.00778 0.00376 -7.5E-04 7.4E-05 -3.0E-06520 0.74412 -0.11791 0.02569 -0.00728 1.4E-03 -1.3E-04 5.3E-06510 0.72281 -0.11949 0.00486 0.00204 -5.7E-04 6.6E-05 -3.0E-06500 0.70863 -0.16634 0.00781 0.00395 -1.0E-03 1.0E-04 -4.1E-06490 0.74529 -0.29982 0.07104 -0.01323 1.8E-03 -1.5E-04 5.3E-06480 0.73072 -0.33978 0.08133 -0.01295 1.4E-03 -8.8E-05 2.4E-06470 0.72309 -0.39347 0.10574 -0.01792 2.0E-03 -1.3E-04 3.6E-06460 0.64562 -0.45551 0.13700 -0.02063 1.3E-03 2.4E-05 -4.7E-06450 0.55086 -0.63585 0.32015 -0.08887 1.4E-02 -1.2E-03 4.4E-05440 0.38716 -0.45440 0.22602 -0.06048 9.1E-03 -7.3E-04 2.4E-05


165

Polynomial regression coefficients for the determination of Zinc Sulphide (Cleartran) transmittanceprofile for uncoated substrate material of thickness t at 293K

T = A0 + A1t + A2t2 + A3t

3 + A4t4 + A5t

5 + A6t6

cm-1 A0 A1 A2 A3 A4 A5 A6

1000 0.75324 -0.00241 4.0E-06 6.0E-08 -1.3E-08 1.3E-09 -5.3E-11990 0.75356 -0.00348 9.1E-06 -1.6E-07 2.7E-08 -2.7E-09 1.1E-10980 0.75389 -0.00609 2.6E-05 -7.3E-08 -3.4E-09 4.0E-10 -1.8E-11970 0.75422 -0.00716 3.6E-05 -4.6E-08 -2.0E-08 2.2E-09 -9.5E-11960 0.75456 -0.00850 5.1E-05 -1.6E-07 -1.5E-08 1.7E-09 -7.1E-11950 0.75491 -0.01210 1.0E-04 -7.4E-07 1.1E-08 -6.1E-10 2.4E-11940 0.75527 -0.01728 2.1E-04 -2.1E-06 3.3E-08 -1.5E-09 5.3E-11930 0.75564 -0.02067 3.0E-04 -3.7E-06 6.8E-08 -3.2E-09 1.1E-10920 0.75602 -0.02307 3.8E-04 -5.0E-06 8.7E-08 -3.3E-09 1.1E-10910 0.75639 -0.02492 4.4E-04 -6.1E-06 6.9E-08 5.9E-10 -6.5E-11900 0.75678 -0.02687 5.1E-04 -7.5E-06 6.5E-08 3.4E-09 -2.0E-10890 0.75718 -0.02799 5.6E-04 -8.7E-06 1.3E-07 -1.6E-09 2.6E-15880 0.75765 -0.02638 4.9E-04 -7.4E-06 1.2E-07 -3.1E-09 7.7E-11870 0.75813 -0.02335 3.9E-04 -5.0E-06 5.3E-08 4.9E-10 -5.3E-11860 0.75861 -0.02146 3.3E-04 -3.8E-06 3.1E-08 1.1E-09 -6.5E-11850 0.75911 -0.02055 3.0E-04 -3.4E-06 4.4E-08 -7.8E-10 1.2E-11840 0.75964 -0.02239 3.5E-04 -4.4E-06 5.1E-08 -2.0E-10 -1.8E-11830 0.76019 -0.02920 6.0E-04 -9.8E-06 1.7E-07 -4.2E-09 9.5E-11820 0.76081 -0.03657 9.4E-04 -1.9E-05 4.0E-07 -9.7E-09 2.0E-10810 0.76144 -0.04320 0.00131 -3.1E-05 7.3E-07 -1.6E-08 2.4E-10800 0.76209 -0.05345 0.00201 -5.9E-05 1.7E-06 -4.7E-08 8.4E-10790 0.76276 -0.06613 0.00307 -1.1E-04 3.9E-06 -1.2E-07 2.5E-09780 0.76345 -0.07579 0.00402 -1.7E-04 6.4E-06 -2.2E-07 4.5E-09770 0.76415 -0.08323 0.00484 -2.2E-04 9.1E-06 -3.3E-07 7.0E-09760 0.76415 -0.09234 0.00595 -3.0E-04 1.4E-05 -5.3E-07 1.2E-08750 0.76414 -0.10120 0.00714 -3.9E-04 1.9E-05 -7.8E-07 1.8E-08740 0.76413 -0.11502 0.00922 -5.6E-04 3.0E-05 -1.3E-06 3.1E-08730 0.76408 -0.14168 0.01393 -0.00103 6.4E-05 -3.1E-06 7.7E-08720 0.76399 -0.16668 0.01919 -0.00162 1.1E-04 -5.7E-06 1.5E-07710 0.76376 -0.19903 0.02717 -0.00266 2.0E-04 -1.1E-05 2.9E-07700 0.76240 -0.27974 0.05253 -0.00667 6.1E-04 -3.6E-05 1.0E-06690 0.75121 -0.45797 0.13515 -0.02454 2.8E-03 -1.9E-04 5.8E-06680 0.69483 -0.63110 0.26050 -0.06154 8.6E-03 -6.7E-04 2.2E-05670 0.15587 -0.21571 0.12428 -0.03804 6.5E-03 -5.9E-04 2.2E-05660 0.74337 -0.51095 0.16717 -0.03293 4.0E-03 -2.8E-04 8.8E-06650 0.57329 -0.63757 0.30938 -0.08281 1.3E-02 -1.1E-03 3.7E-05


166

Polynomial regression coefficients for the determination of Cadmium Telluride (CdTe) transmittanceprofile for uncoated substrate material of thickness t at 293K

T = A0 + A1t + A2t2 + A3t

3 + A4t4 + A5t

5 + A6t6

cm-1 A0 A1 A2 A3 A4 A5 A6

450 0.66618 -0.00565 0.00003 -1.7E-07 1.2E-08 -1.2E-09 5.3E-11440 0.66680 -0.00901 0.00007 -3.3E-07 -2.5E-08 2.9E-09 -1.2E-10430 0.66747 -0.01255 0.00014 -1.2E-06 3.4E-09 8.6E-10 -4.1E-11420 0.66819 -0.01346 0.00016 -1.6E-06 3.0E-08 -1.6E-09 6.5E-11410 0.66897 -0.01554 0.00021 -2.5E-06 3.9E-08 -1.4E-09 4.7E-11400 0.66982 -0.02336 0.00047 -8.3E-06 1.9E-07 -6.3E-09 1.8E-10390 0.67075 -0.02767 0.00065 -1.4E-05 3.0E-07 -7.0E-09 1.2E-10380 0.67176 -0.03131 0.00083 -1.9E-05 4.9E-07 -1.3E-08 2.4E-10370 0.67287 -0.03521 0.00105 -2.7E-05 7.4E-07 -1.8E-08 2.7E-10360 0.67409 -0.04613 0.00180 -6.1E-05 2.1E-06 -6.8E-08 1.3E-09350 0.67542 -0.08054 0.00545 -3.1E-04 1.7E-05 -7.6E-07 1.8E-08340 0.67661 -0.15090 0.01869 -1.8E-03 1.5E-04 -8.4E-06 2.3E-07330 0.67509 -0.26346 0.05383 -7.6E-03 7.7E-04 -4.9E-05 1.5E-06320 0.66561 -0.38973 0.11203 -2.0E-02 2.3E-03 -1.6E-04 4.9E-06310 0.51443 -0.56463 0.27117 -7.2E-02 1.1E-02 -9.2E-04 3.2E-05300 0.07954 -0.11287 0.06635 -2.1E-02 3.6E-03 -3.3E-04 1.2E-05


167

Appendix C


168


169

Appendix DMultilayer calculation matrix with absorption

in normal incidence illumination

Example single layer calculation

The layer phase factor is given byδπ θ

λ=

2 Nd cos where N is the complex refractive index, d is the physical

thickness (µm), θ is the angle of incidence, and λ is the evaluation wavelength (µm). In this case where normalincidence illumination θ = 0 then cosθ = 1 and is subsequently ignored, and as N= (n - ik), then δ becomes

( )δ

π

λ=

−2 d n ik.

The characteristic matrix for the recursive sequence is:

B

Cm i m m

i m m m sm

q

= ∏=1

1cos sin /

sin cos

δ δ ηη δ δ η

where :B is the normalised electric field amplitude, C is the normalised magnetic field amplitude, s is the substrate, m isthe individual layer being calculated and q is the total summation of layers.Using the complex trigonometric identity for cosδ given by:

cosδ = cos (x - iy) = cos(x) cosh(y) + isin(x) sinh(y)

then ( )cos cosδπλm

dnm ikm= −

2

in terms of x and y then :- xdnm=

2π

λand y

dkm=2π

λevaluation of the first term cos δm then becomes:

( )cos cos cos cosh sin sinhδπλ

πλ

πλ

πλm

m m m mx iy dn dk

idn dk

= − =

+

2 2 2 2

ηm =Y (nm – ikm),ηs = Y (ns – iks) where Y is the admittance of free space given by ;

Y = ε

µ0

0

= 0.002654 Ω-1 and ηm & ηs are the optical admittance of the layer and substrate.

Where the substrate is non-absorbing, iks = 0 therefore ηs = Y ns

(which in the case of germanium ηs = Y ns = Y 4.0).Using the complex trigonometric identity for sinδ given by :

sinδm = sin (x - iy) = sinx coshy + icosx sinhyand where cosh(-x) = cosh(x) and sinh(-x) = -sinh(x)

then ( )sin sin sin cosh cos sinhδπλ

πλ

πλ

πλm

x iydnm dkm

idnm dkm= − = −

2 2 2 2

From the initial characteristic matrix, B then becomes:

B =( )

cossin

δδ

ηηm

i m

ms+ =

( )( )cos

sinδ

δ

m

im

ns

iks

nm

ikm

+−

−

and C becomes j m m m sη δ δ ηsin cos+Returning to B, as cosδm = cos (x - iy) = cos(x) cosh(y) + isin(x) sinh(y), then:


170

( )( )

B =

cos cosh sin sinh

sin cosh cos sinh

2 2 2 2

2 2 2 2

π

λ

π

λ

π

λ

π

λ

η

η

π

λ

π

λ

π

λ

π

λ

dnm dkm idnm dkm

is

iks

mik

m

dnm

dkm i

dnm

dkm

+ +

−

−

−

where ks = 0, as in the case of the substrate in a non-absorptive region then ns - iks = ns .

Expanding B into real and imaginary parts then requires firstly separating in

snm

ikm

− into real

and imaginary parts by multiplying by its complex conjugate,

ins

nm ikm

ins

nm ikm

nm ikm

nm ikm

inskm nskm

nm km−=

−⋅

+

+=

−

+2 2 .

The real parts of B become :

Re(B) =

cos cosh sin cosh

cos sinh

2 2 2 2

2 2

2 2

2 2

π

λ

π

λ

π

λπ

λ

π

λ

π

λ

dnm dkmn

skm

nm

km

dnm dkm

nskm

nm

km

dnm dkm

−+

+

+

and imaginary parts of B become ;

Im(B) =

sin sinh sin cosh

cos sinh

2 2 2 2

2 2

2 2

2 2

π

λ

π

λ

π

λπ

λ

π

λ

π

λ

dnm dkmn

skm

nm

km

dnm dkm

nskm

nm

km

dnm dkm

++

+

+

B is therefore represented by B = Re(B) + iIm(B)

Returning to C, where C = iηmsinδm + cosδmηs and δπ

λ

π

λmdnm

idkm= −

2 2,

using the trigonometric identities :sinδ = sin(x +iy) = sinx coshy + icosx sinhy, andcosδ = cos(x +iy) = cosx coshy + isinx sinhy, then

C

= − +

+

i mdnm dkm

idnm dkm

dnm dkmi

dnm dkms

ηπ

λ

π

λ

π

λ

π

λ

π

λ

π

λ

π

λ

π

λη

sin cosh cos sinh

cos cosh sin sinh

2 2 2 2

2 2 2 2

as iηm = i(nm - ikm),Y = iY nm + Y km and ηs = Y ns then separating out the real and imaginary parts of Cbecomes :

Y Re(C) = Y kmsin2π

λ

dnm

cosh

2π

λ

dkm

+Ynrcos

2π

λ

dnm

sinh

2π

λ

dkm

+

Y nscos2π

λ

dnm

cosh

2π

λ

dkm

and

Y Im(C) = Y nmsin2π

λdnm

cosh

2πλdkm

-Y kmcos

2πλdnm

sinh

2πλdkm

+


171

Y nssin2π

λdnm

sinh

2πλdkm

Inserting the real and imaginary parts to determine the reflection and transmission coefficients :

R =η

η

η

η0

0

0

0

B C

B C

B C

B C

−

+

−

+

*

and ( )

( )( )T =

4 0Reη η

η η

s

B C B C0 0+ +*

where * = complex conjugate, and η0 = Y

then for R, η

η0

0

B C

B C

B C i

i

−

+=

− +

Y Y

Y Y

Im(B) - Im(C))

Re(B) + Re(C) + ( Im(B) + Im(C))

Re( ) Re( ) (

denoting numerator coefficients Y Re( ) Re( ) (B C i− + Y Im(B) - Im(C)) as a+ib and denominator coefficients

Y Y Re(B) + Re(C) + ( Im(B) + Im(C))i as f+ig, and expanding by multiplying by its complex conjugate, then:

( )η

η0

02 2

B C

B C

a ib

f ig

f ig

f ig

af bg i bf ga

f g

−

+=

++

−− =

+ + −

+

*

is then equivalent to :

η

η0

02 2

2 2

B C

B C

B C B C B C B C

B C B C

iB C B C B C B C

B C B C

−

+=

− + + − +

+ + ++

− + − + −

+ + +

(

Y Y Y Y

Y Y

Y Y Y Y

Y Y

Re( ) Re( ))( Re( ) Re( )) ( Im( ) Im( ))( Im( ) Im( ))

( Re( ) Re( )) ( Im( ) Im( ))

( Im( ) Im( ))( Re( ) Re( )) ( Im( ) Im( ))( Re( ) Re( ))

( Re( ) Re( )) ( Im( ) Im( ))

The admittance of free spaceY between numerator and denominator cancel, and by denoting the equation in

the form v+iw then :

vB C B C B C B C

B C B C=

− + + − +

+ + +

(Re( ) Re( ))(Re( ) Re( )) (Im( ) Im( ))(Im( ) Im( ))

(Re( ) Re( )) (Im( ) Im( ))2 2, and

iwB C B C B C B C

B C B C=

− + − + −

+ + +

(Im( ) Im( ))(Re( ) Re( )) (Im( ) Im( ))(Re( ) Re( ))

(Re( ) Re( )) (Im( ) Im( ))2 2

The reflection coefficient inclusive of absorption is then calculated by R = v2 + w2.Returning to the transmission coefficient T, as η0 = Y and ηs = Y ns, then :

Tns

B C B C=

+ + +

42 2(Re( ) Re( )) (Im( ) Im( ))

Calculation of the absorptance can then be deduced from A = 1 - T - R

This calculation procedure has been verified by example using a single layer of refractive indexnm = 2.0 and extinction coefficient of km = 0.05 deposited on a loss free germanium substrate of indexns = 4.0. The film thickness was a single quarter-wave layer of physical thickness 1.25µm calculated for awavelength λ = 10µm. Using these parameters, values of T = 90.780%, R = 0.137% and A = 9.083% werecalculated and correctly verified by comparing with an industry standard thin-film software program.


172

Appendix EPublications

Principal Author1. G.J. Hawkins, R. Hunneman, J.J. Barnett, J.G. Whitney : “Spectral design and verification of HIRDLS filters

and antireflection coatings using an integrated system performance approach”, Proc SPIE Annual MeetingSan Diego 1998, (in press)

2. G.J. Hawkins, R. Hunneman, M.T. Gardner, G.T. Babcock : “An ultra-wide passband (5-30µm) filter for FTIRstudies of Photosystem II”, Infrared Physics & Technology, Vol 39. pp 297-306, (1998)

3. G.J.Hawkins, R. Hunneman, C.Cole : "Infrared filters for space-flight focal plane array applications",Proc. SPIE 2253, pp 333-347, (1994)

4. G.J.Hawkins, R.Hunneman : "Design and Fabrication of Infrared Filters for Remote SoundingInstrumentation", Proc. SPIE 2210, pp 639-65, (1994)

5. G.J.Hawkins, J.S.Seeley, R.Hunneman : "Exposure to space radiation of high performance infrared multilayerfilters and materials technology experiment (A0056)", NASA Conf. Proc. 3134 Pt 3 First LDEF post-retrievalsymposium pp 1477-1491, (1991)

6. G.J.Hawkins, R.Hunneman, J.S.Seeley : "Space Exposure of Infrared Filters and Materials on the NASA LongDuration Exposure Facility (LDEF)", University of Reading, ISBN 07049 04098 (1991).

7. G.J.Hawkins, J.S.Seeley, R.Hunneman SERC Final Report (GR/F/67990) on “Study of Effects of the SpaceEnvironment on Infrared Filters and Materials Flown on the NASA LDEF Mission.”PPARC Assessment offinal report graded Alpha-5 for scientific and/or technological merit.

8. G.J.Hawkins, J.S.Seeley, R.Hunneman : "Preliminary results from Infrared Filters and Materials". LDEFSpaceflight Environment Effects Newsletter, NASA Code 720. 1, No.5 (1990).

9. G.Hawkins, R.Hunneman, J.S.Seeley : "Preliminary results from Infrared Multilayer Filters and Materialsexposed to the space environment on the NASA LDEF mission", Proc. SPIE 1320, pp 407-419, (1990)

10. G.Hawkins, R.Hunneman, J.Seeley : "Spectral characterisation of cooled filters for remote sensing", Proc.SPIE 915, pp 71-78. (1988)

11. G.Hawkins, R.Hunneman, J.Seeley. : "Design and disposition of infrared optical multilayer coatings for theImproved Stratospheric and Mesospheric Sounder (ISAMS)", Proc. SPIE 868, pp 52-62, (1987)

Co-Author12. R. Hunneman, G.J. Hawkins : “The manufacture and spectral assessment of the filters and antireflection

coatings for use in the HIRDLS instrument”, Proc SPIE Annual Meeting San Diego 1998, (in press)13. R. Hunneman, G.J. Hawkins : “Infrared filters and dichroics for the advanced along track scanning radiometer

(AATSR)”, Applied Optics, Vol 35, No 28, pp 5524-5528, (1996).14. R. Hunneman, G.J. Hawkins : “Novel material combinations for enhanced infrared filter performance”, Proc

IOP Optoelectronics Conf, ISBN 07503 03824, pp 188-193 (1996).15. R.Hunneman, G.J.Hawkins : “Infrared filters and dichroics for the Advanced Along Track Scanning

Radiometer (AATSR)”, Proc OSA Optical Interference Coatings Conf, Vol 17, pp 358-360, (1995).16. R.Hunneman, J.J.Barnett, G.J.Hawkins : “High-Performance Infrared Filters for the HIRDLS 21-Channel

Focal Plane Detector Array”, Proc. SPIE 2210-49, pp 516-532, (1994).17. A.Zheng, J.S.Seeley, R.Hunneman, G.J.Hawkins : "Ultra-narrow Filters with Good Performance when Tilted

and Cooled", Applied Optics, Vol.31, No. 22, pp 4336-4338, (1992).18. A.Zheng, J.S.Seeley, R.Hunneman, G.J.Hawkins : "Design of narrowband filters in the infrared region",

Infrared Physics and Technology, Vol 31, No.3, pp 237-244, (1991).19. J.S.Seeley, R.Hunneman, G.J.Hawkins : "System performance in IR atmospheric radiometry", Proc. SPIE

1270, pp 244-249, (1990).20. K.Zhang, R.Hunneman, J.S.Seeley, G.J.Hawkins : "Investigation of ultra wideband multi-channel dichroic

beamsplitters from 0.3 to 52µm", Infrared Physics and Technology, Vol.30, pp 45-53, (1990).21. K.Zhang, J.Seeley, R.Hunneman, G.Hawkins : "Optical and semiconductor properties of lead telluride

coatings", Proc SPIE 1125, pp 45-52, (1989).22. J.Seeley, G.Hawkins, R.Hunneman : "Performance model for cooled IR filters", J. Inst. Phys. 'D'

optics-ECOOSA, pp S71-S74, (1988).


173

Appendix FRefractive Index Data Sources

F-1 N.P. Barnes, M.S. Piltch, : “Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium”, J.Opt.Soc.Am., Vol. 69, No. 1 pp 178-180 (1979)

F-2 D.F. Edwards, E. Ochoa, : “Infrared Refractive index of Silicon”,Applied Optics, Vol 19, (24), pp.4130-4131, (1980)

F-3 E.D. Palik, : “Cadmium Telluride (CdTe)”, Handbook of Optical Constants of Solids, Academic Press Inc, ISBN 0-12-544420-6, pp 409-427 (1985)

F-4 A. Feldman, : “Optical Materials Characterization Final Technical Report”, National Bureau of Standards Technical Note 933, pp53-54, (1978).

F-5 M. Debenham, : “Refractive Indices of Zinc Sulfide in the 0.405-13-µm Wavelength Range”, Applied Optics, Vol. 23, No. 14, pp 2238-2239, (1984).

F-6 S.S. Ballard, K.A. McCarthy, W.L. Wolfe, : “Optical Materials for Infrared Instrumentation”, The University of Michigan, Willow Run Laboratories, Report No. 2389-11-S, pp24-25 (1959)


F-8 D.F Bezuidenhout, : “Calcium Fluoride (CaF2)”, Handbook of Optical Constants of Solids II, AcademicPress Inc, ISBN 0-12-544422-2, pp 815-835 (1991)

F-9 D.R. Barron, : “Buchdahl’s chromatic co-ordinate concept applied to IR materials”, Thorn EMI Electronics, (1987).

F-10 W.L. Wolfe, A.G. DeBell, J.M. Palmer, : “Status of cryogenic refractive index measurements”, Proc. SPIE 245, pp 164-172 (1980)

F-11 N.P. Barnes, M.S. Piltch, : “Temperature-dependent Sellmeier coefficients for Cadmium Telluride”,J.Opt.Soc.Am Vol 67 No. 5 May 1977

F-12 J.S. Browder, S.S. Ballard, : “Thermal expansion data for eight optical materials from 60K to 300K”,Applied Optics, Vol. 16, No. 12, pp 3214-3217, (1977)

F-13 Commercially Published Data : Eagle Picher, Electro-Optic Materials, Germanium and Silicon Optics, Quapaw, Oklahoma 74363, USA.

F-14 D.F. Edwards, : “Silicon (Si)”, Handbook of Optical Constants of Solids,Academic Press Inc, ISBN 0-12-544420-6, pp 547-569 (1985)


spectral characterisation of infrared optical materials and filters

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