Separation of coherent and incoherent contributions to reflectance difference spectraK. Schmidegg and P. Zeppenfeld Citation: Applied Physics Letters 90, 231903 (2007); doi: 10.1063/1.2746421 View online: http://dx.doi.org/10.1063/1.2746421 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/90/23?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Femtosecond laser fabrication of high reflectivity micromirrors Appl. Phys. Lett. 97, 041104 (2010); 10.1063/1.3467846 Bragg reflector enhanced attenuated total reflectance J. Appl. Phys. 106, 113109 (2009); 10.1063/1.3265436 Tunable reflectance Mg–Ni–H films Appl. Phys. Lett. 80, 2305 (2002); 10.1063/1.1463205 Mixed metal films with switchable optical properties Appl. Phys. Lett. 80, 1349 (2002); 10.1063/1.1454218 Characterization of multilayer reflective coatings for extreme ultraviolet lithography AIP Conf. Proc. 521, 108 (2000); 10.1063/1.1291768

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Separation of coherent and incoherent contributions to reflectancedifference spectra

K. Schmidegga� and P. ZeppenfeldInstitut für Experimentalphysik, Johannes Kepler Universität Linz, Altenbergerstr. 69, A-4040 Linz, Austria

�Received 12 February 2007; accepted 12 May 2007; published online 5 June 2007�

The authors present a method for the analysis of azimuthal dependent reflectance differencespectroscopy data that enables a separation of coherent and incoherent contributions to reflectancedifference spectra. The latter can originate from back side reflections of transparent films if theirthickness is larger than the coherence length of the light. Furthermore, instrument artifacts can besuppressed and additional contributions with different optical eigenaxes can be identified. © 2007American Institute of Physics. �DOI: 10.1063/1.2746421�

Reflectance difference spectroscopy �RDS�, also termedreflectance anisotropy spectroscopy �RAS�,1 is a nondestruc-tive optical technique which measures the normalized reflec-tance difference �r /r of light polarized along two perpen-dicular directions of the surface in normal incidencegeometry:

�r

r= 2

r1 − r2

r1 + r2. �1�

Here, r1 and r2 denote the complex reflectivities alongthe two orthogonal in-plane polarization axes of the incidentlight beam. Due to the normal incidence geometry, RDS isonly sensitive to an in-plane optical anisotropy. Usually, thesample position is chosen in a way that the directions 1 and2 coincide with the optical eigenaxes of the sample, in whichcase the resulting RDS signal is at its maximum. RDS hasfrequently been used to characterize metals and semiconduc-tors with cubic crystal symmetry,1,2 for which the isotropicbulk contribution cancels upon subtraction. In this case, theRDS signal originates from regions of reduced symmetrysuch as surfaces and interfaces only.

Recently, RDS has received wider attention and its fieldof application has been extended toward the characterizationof thin films of organic molecules,3 liquid crystals4 andpolymers.5 In contrast to metals and most investigated semi-conductors, such materials are transparent in the visibleand/or near UV spectral range and can possess multiple con-tributions to the RDS signal with more than one set of opticaleigenaxes. A few years ago, Macdonald et al. have devel-oped a generalized version of RDS, termed azimuth-dependent reflection anisotropy spectroscopy �ADRAS�,6,7

which addresses several of these issues. ADRAS relies on thefact that a rotation of the sample around its surface normal,which does not violate normal incidence conditions, leads toa modulation of the RDS amplitude due to the appearance ofoff-diagonal elements in the reflection Jones matrix of thesample. An analysis of the azimuthal dependence allows thedetermination of the position of the optical eigenaxes in thesurface plane as well as an identification of several contribu-tions to the RDS signal with different optical eigenaxes.

In this letter, we would like to present an extension to theabove approach. In contrast to the original work,6,7 where

azimuthal scans were only performed at several interestingspectral positions, we perform such a scan for each photonenergy, i.e., the data consist of RDS amplitudes as a functionof both photon energy and azimuth angle. A similar approachhas also been reported by Brinkley et al.,8 albeit less com-plete and for a very specific purpose. From this three-dimensional data set, we can then extract a coherent partoriginating from the surface reflection of the sample and anincoherent part, which may result from the back side reflec-tion of a birefringent transparent film, for instance. To dem-onstrate the capabilities of our method, we present ADRDSmeasurements of biaxially oriented poly�ethyleneterephtha-late� �PET� films, both with and without coating.

It is well known1,7 that the functional dependence of aRDS spectrum can be described by a fundamental reflectionanisotropy F�E� which depends only on the photon energy,and an azimuthal part which depends only on the azimuthalangle between the incident polarization and the direction ofthe optical eigenaxes. F�E� is given by Eq. �1�, if directions1 and 2 are parallel to the optical eigenaxes of the sample.For an arbitrary azimuthal orientation, the coherent RDS sig-nal can be written as:8

S�E,�� = F�E�cos 2�� − �0� , �2�

where � denotes the sample azimuth in the laboratory frameand �0 the value of � at which S�E�=0. Although this resultseems trivial, it can be used to precisely determine the angle�0 and thus the position of the optical eigenaxes ��0+45° �of the sample, if they are not already given by crystallo-graphic directions.

In an earlier study, we applied this technique to biaxiallyoriented polymer films, whose optical eigenaxes do not nec-essarily coincide with the machine direction of the film.5

Furthermore, if the sample consists of several layers withindependent optical anisotropies which are spectrally sepa-rated, the position of both optical eigenaxes can be deter-mined by looking at the azimuthal dependence of the respec-tive spectral feature.6

Equation �2� is, however, only valid for semi-infiniteopaque materials or very thin films, where the film thicknessis much smaller than the wavelength. If the sample consistsof a transparent film with sufficiently large birefringence anda thickness much larger than the wavelength of light, the twopolarization components of the light beam reflected at theback side of the film experience quite different retardances

a�Present address: Hueck Folien GmbH, Gewerbepark 30, A-4342 Baumgar-tenberg, Austria; electronic mail: k.schmidegg@hueck-folien.at

APPLIED PHYSICS LETTERS 90, 231903 �2007�

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upon traversing the film and thus become incoherent. Thespectrometer then measures the anisotropy of the reflectedintensities rather than the anisotropy of the reflected ampli-tudes. This incoherent contribution to the RDS signal is char-acterized by a 4� azimuthal dependence.7 As a consequence,S�E� is no longer only a harmonic function of 2�, but con-tains contributions with both 2� and 4� dependence fromthe front side �coherent� and the back side �incoherent� re-flections, respectively. We can thus rewrite Eq. �2� as

S�E,�� = Fc�E�sin 2�� − �0� + Fi�E�sin 4�� − �0� + C ,

�3�

where Fc�E� and Fi�E� denote the fundamental coherent andincoherent contributions to the RDS signal, and C is a con-stant offset resulting from first order instrument artifacts. Ananalysis of S�E ,�� at each measured photon energy by fittingEq. �3� to the experimental data yields the magnitudes ofboth coherent and incoherent contributions to the RDS signal�Fc�E�, Fi�E��, the position of the optical eigenaxes ��0�, andfirst order instrument artifacts �C�.

Note that, in contrast to Eq. �2�, Eq. �3� contains sineinstead of cosine functions due to the fact that the two oscil-lations share a common zero transition instead of a commonmaximum. �0 in Eq. �3� thus differs by 45° from �0 in Eq.�2�. We should further point out that �0 is dependent on theoptical setup of the RDS spectrometer. If we consider de-vices based on the polarizer–photoelastic modulator–sample–analyzer �PMSA� setup, it is decisive for the valueof �0 if the photoelastic modulator is located before or afterthe sample in the optical path, i.e., if the instrument is eitherof the PMSA or the PSMA type. PMSA-type instrumentsgive a maximum RDS signal, if the polarization direction ofthe polarizer �i.e., the incident light beam� is parallel to oneof the optical eigenaxes of the sample.9 However, PSMAsystems show a maximum RDS amplitude if the polarizationdirection of the incident beam is at 45° with the optical ei-genaxes of the sample.10,11 Since our instrument is of thePMSA type, we have assumed this measurement geometry inall considerations of this letter.

So far, we have quietly assumed that �0 is the same forcoherent and incoherent components. However, in generalthe orientation of the eigenaxes may differ for both contribu-tions due to birefringence gradients in the sample and canalso be dependent on the photon energy. In this case, �0 hasto be replaced by �0,c�E� and �0,i�E� in Eq. �3�, respectively.A spectral analysis of �0,c�E� and �0,i�E� can then be used todistinguish different contributions with different positions ofthe optical eigenaxes.

In conventional RDS experiments, C can be determinedby acquiring two spectra at �=0° and �=90° sample azi-muth, thus reversing the sign of �r /r �Eq. �2��. A nonzeroaverage of these two spectra then corresponds to an �energydependent� instrumental offset induced by imperfections inthe optical path �such as window strain�, and it can be usedto correct the acquired RDS spectra.12 Actually, this methodworks for any two spectra taken at azimuth angles separatedby 90°, but the precision is best for 0° and 90°, since �r /rhas its maximum amplitude at these positions. From Eq. �3�,we can also see that a measurement at an azimuth angle of�−�0=45° should not contain any incoherent contribution,but since a perfect alignment is quite difficult, its presence inRDS spectra can never be ruled out completely.

As an application example, we present measurements onbiaxially oriented PET films, since they represent the idealcase of a birefringent film with a thickness large enough toexhibit the above-mentioned incoherence effects. Birefrin-gence in PET films is the result of orientation of the polymerchains in the production process.5 Furthermore, PET is trans-parent at photon energies below 4 eV, which is well withinthe spectral range of our RDS setup �1.5–5.5 eV�. This en-ables us to study both transparent and absorbing regions ofthe material at the same time. Our experimental setup con-sists of a commercial RDS system �supplied by ISA JobinYvon� equipped with a motorized sample rotation stage.

Figure 1 shows an angular RDS scan of a 50 �m PETfilm at a photon energy of 3.5 eV, i.e., in the transparentregime of the material, where the sample was rotated in stepsof 5°. The azimuthal dependence of Re��r /r� clearly exhib-its 2� and 4� contributions. A numerical fit of Eq. �3� to theexperimental data yields excellent correspondence. To illus-trate the individual contributions, the 2� and 4� componentsare shown explicitly in the graph.

A full ADRDS measurement consists of a set of spectraobtained for azimuth angles in the range of 0°�180° or anazimuthal scan at each photon energy. A fitting routine wasdeveloped, which extracts the numerical values of Eq. �3�from a full ADRDS data set. We can thus obtain two spectraof both signal components by plotting Fc�E� and Fi�E�, asshown in Fig. 2. The most noticeable fact is that the coherentspectrum is very similar to the spectrum obtained from thesame sample after deliberately roughening its back side, thuseliminating back side reflections and the majority of the in-coherent part. The spectrum of the 4� contribution is domi-nated by interference oscillations with a wavelength �energy�period inversely proportional to the product of birefringenceand sample thickness ��n ·d� below the absorption edge ofPET ��4 eV�, and looks similar to a birefringence spectrumobtained in transmission geometry. Since the incoherent con-tribution is mainly caused by light reflected from the backside of the sample, it almost completely vanishes above4 eV. There is, however, still a small fraction present, whichoriginates from incoherent reflection at the top surface in-duced by depolarization effects and roughness. For thinnerfilms and/or larger coherence length, one would expect to see

FIG. 1. Azimuthal dependent RDS scan of a 50 �m PET film at a photonenergy of 3.5 eV �squares� and numerical fit to Eq. �3� �solid line�. Theamplitudes of the 2� �dashed line� and 4� �dotted line� components are alsoshown.

231903-2 K. Schmidegg and P. Zeppenfeld Appl. Phys. Lett. 90, 231903 �2007�

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additional interference oscillations with a period proportionalto �n ·d�−1, which is considerably smaller than ��n ·d�−1.These fast oscillations, however, may also be averagedout due to instrument resolution and/or residual surfaceroughness.

As a second application example we have chosen a PETsample covered by silver clusters with a nominal thickness of4 nm. Silver clusters exhibit special optical properties due totheir finite size, namely, particle plasmon resonances, whosefrequencies are in the visible spectral range. In Fig. 3, thiscluster signature is most clearly revealed in the 2� compo-nent and expressed as a broad negative peak centered at2.4 eV. Plasmonic effects are also visible in the 4� compo-nent as a modulation of the birefringence oscillation, whichis due to the fact that both the incident and the back sidereflected beam traverse the cluster layer.

It is clear from Fig. 3 that a study of the plasmonicstructures in the RDS spectrum is much easier by analyzingthe coherent contribution only. Birefringence and interfer-ence oscillations, which are in practice always present in aRDS spectrum containing both contributions, can be effi-ciently suppressed. The above presented method is thus es-pecially well suited for samples where a deliberate roughen-ing of the back side is not possible.

In summary, we have shown that ADRDS �a� eliminatesthe need for precise azimuthal alignment of the sample, �b�allows an automatic correction for instrument artifacts, and�c� can be used to separate coherent and incoherent contri-

butions to the RDS signal for certain classes of samples, suchas oriented polymer films. While this method is certainlymore time consuming than a conventional single RDS mea-surement and thus not suited for situations where the signalvaries with time, it allows convenient and complete charac-terization of optically anisotropic, transparent samples.

The authors would like to thank M. Flores-Camacho forvaluable discussions and complementary ADRDS measure-ments. This work was partly supported by the AustrianNANO Initiative within the projects “0100: NanostructuredSurfaces and Interfaces” and “0154: PolyMet.”

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FIG. 2. Separation of coherent �thin solid line� and incoherent �dashed line�contributions to an ADRDS measurement of an uncoated 50 �m PET film.The thick solid line represents the RDS data acquired from the same filmwith a deliberately roughened back side.

FIG. 3. Coherent �solid line� and incoherent �dashed line� parts of ADRDSspectra of a 50 �m PET film covered by silver clusters with a nominalthickness of 4 nm. The optical signature of the clusters is revealed in thecoherent contribution as a broad negative peak at 2.4 eV.

231903-3 K. Schmidegg and P. Zeppenfeld Appl. Phys. Lett. 90, 231903 �2007�

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