Thin Solid Films xxx (2011) xxx–xxx

TSF-29704; No of Pages 6

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Thin Solid Films

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Extraction of optical properties of flat and surface-textured transparent conductiveoxide films in a broad wavelength range

J.A. Sap, O. Isabella⁎, K. Jäger, M. ZemanDelft University of Technology, Laboratory of Photovoltaic Materials and Devices, Mekelweg 4, 2628 CD Delft, The Netherlands

⁎ Corresponding author. Tel.: +31 15 27 89546; fax:E-mail address: O.Isabella@TUDelft.nl (O. Isabella).

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Please cite this article as: J.A. Sap, et al., Th

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 October 2010Received in revised form 28 July 2011Accepted 4 August 2011Available online xxxx

Keywords:Thin-film solar cellsTransparent conductive oxideSurface roughnessScatteringRefractive index

An accurate characterization method is developed to determine the refractive index of smooth and surface-textured transparent conductive oxide (TCOs) films. The properties are obtained from simultaneous fitting ofsimulated specular reflectance/transmittance spectra to spectroscopic measurements for different polariza-tions and angles of light incidence. The simulations are based on a combination of physical models describingdielectric function of TCO films. Besides the refractive index also other material properties of TCO films areobtained, such as the band gap and free carrier absorption. A light scattering model is implemented into thesimulations to take into account the diffused part of the light scattered at randomly-textured surfaces of TCOfilms.

+31 5 26 22463.

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in Solid Films (2011), doi:10.1016/j.tsf.2011.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Transparent conductive oxide (TCO) layers have become animportant part in a variety of consumer devices, such as flat paneldisplays and solar cells. In thin-film silicon solar cells they serve as thetop transparent electrode and/or as intermediate layers to manipulatelight propagation in the cell. The TCO layers have to fulfill severalstringent requirements, such as high optical transmission in thespectrum of interest, low sheet resistance, temperature durability andgood chemical stability. In addition, the TCO layer has to be surface-textured in order to enhance light absorption inside the solar cell dueto the scattering at internal rough interfaces [1]. In multi-junctionthin-film silicon solar cells with different silicon-based absorbers thehigh transparency is required in the wavelength region from 300 nmto 1100 nm [2,3]. The accurate determination of TCOs opticalproperties in such a broad wavelength region is very important. Theknowledge of the accurate properties is necessary for the optimizationof the solar cell structures using the optoelectronic device simulators[4,5].

In order to determine the complex refractive index of the TCO filmsin a broad wavelength range an extraction method is developed inwhich the simulated reflectance and transmittance (R/T) spectra ofthe TCO films are fitted on the spectroscopic measurements. Thesimulation of the R/T spectra is based on the existing physical modelsthat describe the dielectric function of the TCO films. From matchingthe simulated andmeasured R/T spectra themodel parameters can be

extracted. This approach for extracting material properties has beendemonstrated in the past for different TCOmaterials. Mergel and Qiao[6] obtained the properties of tin-doped indium oxide (ITO) layers byfitting only one transmittance spectrum per sample. This wasrepeated for aluminium-doped zinc oxide (AZO) films by Qiao et al.[7]. Solieman and Aegerter [8] carried out simultaneous fits onreflectance and transmittance for ITO layers at normal incidence. In allthese cases the layers were optically flat, i.e. the surface roughnesswas small in comparison to the wavelength.

In this article we present an extractionmethod that is extended byincluding a simultaneous fit on a large amount of measured R/Tspectra, which enhances the accuracy of the extracted materialproperties. Further a light scattering model is introduced in themethod allowing the characterization of surface-textured TCO layers.The R/T spectra were measured with variable angle spectroscopy(VAS) [9]. SCOUT simulation software [10] was used to simulate andfit the spectra in order to extract the material properties. Threedifferent TCO materials were characterized and treated with theimproved method: aluminium-doped zinc oxide (AZO) [11], tin-doped indium oxide (ITO) [12] and fluorine-doped tin oxide (FTO)[13].

2. Modelling dielectric functions

The transmittance and reflectance of a TCO layer can be simulatedwith a set of physical models. Each model provides susceptibility as afunction of wavelength and is most accurate in a specific part of thespectrum. Combining the separate models yields the dielectricfunction of the TCO layer from which the refractive index in a broadwavelength range can be determined. The wavelength dependent

08.023

Energy

Den

sity

of S

tate

s Valence band Conduction band

EV EC E0

~exp[(E-EV)/γ γV] ~exp[(E-EC)/ C]

Fig. 1. Schematic representation of the density of states functions of the valence andconduction band in the OJL interband transitions model.

2 J.A. Sap et al. / Thin Solid Films xxx (2011) xxx–xxx

reflectance and transmittance are calculated according to thisrefractive index. For TCOs, the Extended Drude model[14,15], theO'Leary–Johnson–Lim (OJL) interband transitions model [16] and aBrendel oscillator[17] are used. The scattering effects from the surfaceare modelled with either a Bruggeman effective medium approach foroptically flat layers or a roughness model based on scalar scatteringtheory.

All physical models are effective in the entire consideredwavelength range. However, the underlying equations cause theeffects of each single model to be strong in a specific part of thespectrum. Superposition of the physical models creates a combinedmodel that includes all effects that occur in the thin TCO film. Thismethod of superposition has also been demonstrated by Ehrmann andReineke-Koch [18] in combination with ellipsometry measurementsof AZO thin films.

2.1. Extended Drude model

The Drude model, proposed in 1900 [14,15], describes thetransport properties of electrons in materials and is used to modelfree carrier absorption that is observed in the infrared (IR) part of thespectrum. With the classical Drude formula the susceptibility of freeelectrons is given by

χ ωð Þ = ω2p

−ω2−i⋅Γω= −

ω2p

ω2−Γ 2 + i⋅Γω2

p

ω3 + ωΓ 2 ð1Þ

with frequency ω, damping factor Γ and plasma frequency ωp. In theextendedDrudemodel the damping factor is not constant but a functionof frequency. This extension provides better results when fitting dopedlayers because it accounts for the effects of ionized impurity scattering[6]. The frequency-dependent damping factor is given by

Γ ωð Þ = ΓL−ΓL−ΓH

π ⋅ arctanω−ωcross

ωwidth

� �+

π2

� �ð2Þ

with high and low frequency damping constants ΓH and ΓL, crossoverfrequency ωcross and width of the transition region, ωwidth. These fourparameters together with the plasma frequency ωp provide theextended Drude model with a total of five possible fitting parameters.

2.2. O'Leary–Johnson–Lim (OJL) bandgap model

The empirical OJL model [16] describes the effect of interbandtransitions on the dielectric function. This model is therefore mostinfluential in the energy range near the bandgap energy of the TCOmaterial. The OJL model was originally developed for amorphousmaterials. Even though TCO films are amorphous or polycrystalline[19], this model provided the closest fitting results on the measuredspectra. In comparison, the Tauc–Lorentz [20] and Campi–Coriasso[21] models provided worse fits. Since we are mainly interested in therefractive indices of the TCO layers, a good fit to the measured spectrais vital. We therefore decided to work with the OJL model.

The OJL model uses expressions for the density-of-states (DOS) forboth the conduction and valence band. These DOS functions can berepresented by a parabolic function with tail states that exponentiallydecay into the bandgap as schematically drawn in Fig. 1.

The DOS of the conduction band is then given by [16]

NC =

ffiffiffi2

pm�3 = 2

C

π2ℏ3 ⋅

ffiffiffiffiffiffiffiffiffiffiffiffiffiE−EC

p; E≥EC +

γC

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiγC

2exp −1

2

� �⋅ exp

E−ECγC

� �s; E<EC +

γC

2

8>>><>>>:

ð3Þ

where mC* represents the effective mass associated with the conduc-tion band. EC is the disorderless band edge and γC is the Urbach energy.

Please cite this article as: J.A. Sap, et al., Thin Solid Films (2011), doi:10

TheUrbach energy determines the shape of the exponential tail and isameasure for the disorder in thematerial. The expressions byO'Learyshow that the DOS approaches the band edge when the Urbachenergy goes to zero. The DOS of the valence band (NV) is described byas similar expression. These DOS functions are used to compute thejoint-density-of-states (JDOS) function with

J ℏωð Þ = ∫∞

−∞NC Eð ÞNV E−ℏωð ÞdE ð4Þ

This JDOS function is then applied to determine the absorptioncoefficient according to

α ℏωð Þ = D2 ℏωð ÞJ ℏωð Þ ð5Þ

whereD2(ħω) is the optical transitionmatrix element [22]. The relationfor the absorption coefficient can be used to determine the imaginarypart of the refractive index through:

k = α⋅λ4π

ð6Þ

This can be converted to the imaginary susceptibility. The Kramers–Kronig relations [23,24], that are valid for response functions in physicalsystems, are then used to obtain the real part of this susceptibility. Theobtained complex susceptibility function can be added to those of theother models for correct implementation of the OJL model. The OJLexpressions give also other material properties such as the Urbachenergy and the bandgap of the material E0=EC−EV.

2.3. Brendel oscillator

A Brendel oscillator [17] is added to improve the fitting result inthe proximity of the bandgap. Brendel proposed a model that uses thedielectric function of a damped harmonic oscillator with a Gaussiandistribution of resonance frequencies. This expanded version of aharmonic oscillator can be used in the entire range of the spectrumand improved the fitting result on the measured R/T spectra. Thesusceptibility is given by

χ ωð Þ = 1ffiffiffiffiffiffiffiffiffiffi2πσ

p ∫∞

−∞e

− x−ω0ð Þ2σ 2

h i⋅

ω2p

x2−ω2−iΓωdx ð7Þ

with the Gaussian distribution width σ and the resonance frequencyω0.

2.4. Surface roughness

The effects of light scattering on specular reflectance and transmit-tance are not contained in the dielectric function of the TCOmaterial. Toincorporate these effects in the model a distinction is made between

.1016/j.tsf.2011.08.023

n ε= 1 ii

ε χ= + Σ

Importmeasured

spectraFit satisfying?

Materialproperties

yes

no

R/T spectrafrom Fresnel’s

equations

Adjust parameters ofthe sub models

Fig. 2. Feedback loop for fitting simulated R/T spectra on spectroscopic measurements.

3J.A. Sap et al. / Thin Solid Films xxx (2011) xxx–xxx

opticallyflat layers,with a roughnessmuchsmaller than thewavelengthof the incident light, and rough layers. For opticallyflat layers an effectivedielectric function is composed according to the Bruggeman effectivemedium model [25]:

1−fð Þ⋅εh−εeff

εh + 2εeff+ f ⋅

εp−εeffεp + 2εeff

= 0: ð8Þ

The effective dielectric function εeff is related to the dielectricfunctions of the twomaterials that make up the interface, εh and εp. Theparameter f represents the volume fraction. For higher roughness, thedecrease in specular reflectance and transmittance (R/T) is described bytwo relations that are based on scalar scattering theory. The etchingprocess to obtain rough surfaces may have caused thickness inhomo-geneities along the thin film. It is however considered that the thicknesschanges smoothly along the sample in comparison with the surfaceroughness such that these thickness inhomogeneities donot significantlyinfluence the R/T spectra on the measured spot. The drop in specularreflectance is then given by Eq. (9) that was proposed by Bennett andPorteus [26]. In a similar way the drop in specular transmittance is givenby Eq. (10) that was developed by Carniglia [27].

Rspec = R0 exp − 4πσR cosψλ

� �2� �ð9Þ

Tspec = T0 exp − 2πσR

λ

� �2n1 cosψ1−n2 cosψ2ð Þ2

� �ð10Þ

In these equations, R0 and T0 are the reflectance and transmittancefor an identical flat layer, σR is the root-mean-square (RMS) roughnessof the surface and ψ1 and ψ2 are the angles of the incident andtransmitted light respectively.

For correct implementation of Eqs. (9) and (10) in SCOUT, themodel for flat layers has to be multiplied with the exponential termsin Eqs. (5) and (6). SCOUT does not support the option to feed therefractive index back as input for these equations. This problem ispartly circumvented by measuring the samples with the TCO layerfacing the incoming light. In this case n1 is equal to 1.0. The refractiveindex of the TCO n2 is approximated as a linear function. Theparameters of this linear function are used as fitting parameters. Alinear approximation is chosen because the SCOUT model only allowsthe use of two fitting parameters for the rough layer.

2.5. High frequency permittivity and layer thickness

The high frequency permittivity ε∞ and layer thickness are alsotaken into account by the simulation of the R /T spectra but are notdirectly related to any of the models mentioned before. The dielectricfunction of a semiconductor material as a function of energy levels outto a constant and real value in themid-infrared. This vertical offset canbe describedwith a constant dielectric function referred to as the highfrequency permittivity.

The thickness of the layer does not influence the dielectric functionbut describes the amount and distribution of the interference fringesin the R/T spectra.

2.6. Calibration of the glass substrate

Glass is used as substrate carrier for the layers. SCOUT provides adielectric function of microscope slide glass over a wavelength rangeof 200–2000 nm. This dielectric function is composed of a number ofBrendel oscillators and is useful for rough estimations. For moreaccurate characterization this standard glass model is calibrated tomatch the Corning Eagle 2000TM glass substrates thatwere used in theexperiments. This is done by fitting the standard glass model on R/Tmeasurements of the Corning Eagle 2000TM substrates.

Please cite this article as: J.A. Sap, et al., Thin Solid Films (2011), doi:10

2.7. Fitting procedure

The process of fitting simulated R/T spectra to spectroscopicmeasurements is schematically drawn in Fig. 2. The accuracy of the fitdepends on the models used to provide the susceptibilities, χi.

3. Experimental details

3.1. Sample preparation

The TCO materials that are characterized with SCOUT are AZO, ITOand FTO. The AZO samples with a thickness of approximately 1 μm areRF-magnetron sputtered on Corning Eagle 2000TM glass substrates.The target that was used for sputtering contained 98 wt.% ZnO and2 wt.% Al2O3. Randomly-textured surfaces are introduced by wetchemical etching in a 0.5% HCl solution where the etching timecontrols the roughness of the surface [11]. For AZOmaterial, a batch ofnine samples is preparedwith etching time ranging from 0 to 50 s. TheITO sample with a thickness of approximately 500 nm is alsodeposited with RF-magnetron sputtering [12]. The target used forITO sputtering was composed of 90 wt.% In2O3 and 10 wt.% SnO2. ForITO no roughness is chemically induced on the surface and thereforeonly optically flat samples are available. The analysed FTO sample is astandard Asahi U-type substrate where FTO is deposited usingatmospheric pressure chemical vapour deposition [13]. The thicknessof the FTO is approximately 800 nm and the RMS surface roughness(σR) is close to 40 nm. For FTO the roughness originates naturally fromthe deposition process and therefore also no flat FTO samples areavailable. The carrier concentrations of all samples were determinedwith Hall measurements and are reported in Table 1.

3.2. R/T measurements

The R/T measurements at different angles of illumination wereperformed with a Perkin Elmer Lambda 950 spectrophotometer. Anaccessory called Angular Reflectance/Transmittance Analyzer (ARTA)[9,28] was available to carry out the VAS measurements. The ARTAcontains automated detector and sample holder rotation stages.Only the specular component of the transmitted or reflected light ismeasured, which requires the detector to be right behind thesample for transmittance and at twice the angle of incidence of thelight for reflectance measurements. R /T spectra are obtained withARTA over awavelength range of 300–1500 nm for AZO, ITO and FTOat angles of incidence: 0°, ±15°, ±30°, ±45° and±60° and both forp- and s-polarized light. The average is taken over positive and negative

.1016/j.tsf.2011.08.023

Table 1Measured free carrier density of the AZO, ITO and FTO samples.

Material Free carrier density

[1020 cm−3]

AZO 2.9±0.3ITO 6.5±0.4FTO 1.6±0.2

Fig. 4. Sub-set of fitting results for rough TCO layers.

4 J.A. Sap et al. / Thin Solid Films xxx (2011) xxx–xxx

angles of incidence to reduce misalignment errors. This gives a total ofseventeen spectra when taking into account that it is not possible tomeasure reflectance at 0° with ARTA and that there is no differencebetween the transmittance at 0° for p- and s-polarized light.

3.3. Surface morphology characterization

Atomic force microscopy (AFM) was used to analyse the surfacemorphology andmeasure the RMS surface roughness of the TCO films.An NT-MDT nTegra atomic force microscope was deployed. Themeasurements were carried out in semi-contact mode at a frequencyscan of 1 line/s and resolution 512×512 pixels over areas of 5×5 μm2

and 10×10 μm2. The cantilever was a whisker type (NT-MDT NSC 05)with a radius of curvature of 10 nm.

4. Results

For each TCO sample a simultaneous fit is done on all seventeenmeasured spectra. A subset of the fitting results of the simulated spectrafrom SCOUT on the R/Tmeasurements is shown in Fig. 3 for the flat ITOsample at 45° angle of incidence and s-polarized light. For flat layers theBruggeman effective medium approach is used to simulate thescattering effects of the surface. There is a good agreement betweensimulationsandmeasurements. Tests have shown that thismodel is alsoable to fit R/T spectra of flat AZO layers with comparable fittingaccuracy. This model can thus be used to characterize different types ofTCO materials with flat surfaces.

Similarly a subset of the results for rough TCO layers, at 45°ands-polarization, are presented in Fig. 4 for AZO and FTO where thescatteringmodel is used (Eqs. (9)–(10)). Thefits on the transmittance ofrough TCO layers are less accurate compared to the reflectance. This ismainly due to Eq. (10) that provides only limited accuracy as alsoobserved by Zeman et al. [29]. The loss of coherence of the light due toscattering is in reality stronger than predicted by themodel. To ensure agoodoverallfitting result aweight factor of 0.1 is applied to thefit on thetransmittance spectra. This optimum value of 0.1 is determinedexperimentally by closely monitoring the optimal fit on reflectancespectra and the fit on transmittance near the band gap energy and in theNIR part of the spectrum where the scattering effects are less strong.

Fig. 3. Sub-set of fitting results for flat TCO layers.

Please cite this article as: J.A. Sap, et al., Thin Solid Films (2011), doi:10

The obtained refractive indices of the three TCO materials areshown in Fig. 5a–c. Note that for the AZO the refractive index is givenfor both the flat sample and the rough sample. Table 2 summarizesothermaterial properties used in themodels obtained from the fitting.The good agreement between the obtained properties for rough andflat AZO layers is an indication that the model for rough interfaces isworking properly because the material properties are not expected tochange due to the etching process.

Fig. 5.Obtained refractive indices for (a) flat and rough AZO, (b) ITO and (c) FTO samples.

.1016/j.tsf.2011.08.023

Table 2Obtained fitting parameters for the analysed AZO, ITO and FTO samples.

AZO AZO (rough) ITO FTO (rough)

Bandgap energy [eV] 3.727 3.671 4.231 4.261Urbach energy [meV] 143.1 141.4 178.6 132.7Plasma frequency [eV] 1.200 1.217 1.830 1.145Brendel oscillatorresonance frequency

[eV] 3.062 2.964 3.341 3.670

Layer thickness [nm] 1269 722.2 485.8 833.4RMS roughness [nm] – 70.40 – 39.88Surface mix volume fraction [−] 0.383 – 0.447 –

5J.A. Sap et al. / Thin Solid Films xxx (2011) xxx–xxx

5. Verification

The bandgap energy of AZO was found to be approximately 3.7 eV.This corresponds to values found in literature where the bandgap ofAZO is typically between 3.4 and 4.0 eV [7,30,31]. The same holds forthe bandgap of ITO where the obtained bandgap energy of 4.2 eV iswithin the range of reported values (3.5–4.3 eV) [32–34]. Thebandgap of FTO can be justified when looking at the transmittancespectra in Figs. 3 and 4. The wavelength at which the transmittance ofFTO decreases to zero due to bandgap absorption is comparable tothat of ITO, which implies that the bandgap energies are comparable.For the AZO sample this wavelength is longer implying that itsbandgap is lower than that of FTO. The obtained bandgap energies aretherefore in agreement with the shape of the measured transmittancespectra.

Although the bandgap energies are in agreement with literatureand the shapes of the transmittance spectra, it must be pointed outthat the objective of this work is the determination of the refractiveindex. For this purpose a set of models is combined with the ambitionto obtain an optimal fit. The added Brendel oscillator may interferewith the OJL bandgap model, which can cause the obtained bandgapenergies to deviate from the real values. This will, however, notinfluence the obtained refractive indices since they are directly relatedto the accuracy of the fit on the R/T spectra.

To quantify the accuracy and reproducibility of the TCO model thefitting was repeated ten times; each time with different and randomstarting values of the fitting parameters. The fitting was donecompletely automatic without intervention and below a deviationthreshold of 0.005 the fitting was stopped. Fig. 6 presents the resultsof this analysis for the most important parameters of the rough TCOmodel. The standard deviation of the obtained value is for mostparameters within 5% meaning that the model is able to find anaccurate and unique fit. The model for flat layers is considered to bemore accurate since it forms the basis for the rough layer model.

Fig. 6. Standard deviation of fitting parameters obtained with the rough TCO model.

Fig. 7. AFM scans of (a) AZO after 10 s of etching, (b) AZO after 50 s of etching and (c)Asahi U-type FTO. The obtained RMS roughness is 34 nm, 100 nm and 37 nmrespectively.

Please cite this article as: J.A. Sap, et al., Thin Solid Films (2011), doi:10.1016/j.tsf.2011.08.023

Fig. 8. Comparison of themodelled RMS roughness with AFMmeasurements for all nineAZO samples and the FTO sample. The dashed line is the ideal agreement betweenmeasurements and modelling outcome.

6 J.A. Sap et al. / Thin Solid Films xxx (2011) xxx–xxx

With the aid of AFM measurements the RMS surface roughnessobtained with the fitting was verified. Fig. 7a–c shows the surfacetexture of the AZO samples with an etching time of 10 and 50 s andthe FTO sample.

The RMS roughness obtained from the AFM analysis is comparedwith that obtained from the models for all nine AZO samples and theFTO sample. This comparison is presented in Fig. 8. This graph showsthat for surface roughness up to 80 nm there is a good agreementbetween the modelled and measured results. This agreement alsoverifies the correct implementation of the model for rough surfaces.The sample with 50 s of etching shows a larger deviation. Moreresearch is therefore required to analyse the agreement for sampleswith surface roughness larger than 80 nm.

6. Conclusions

Optical characterization with variable angle spectroscopy is anaccurate method to determine the optical properties of TCO films.Optical measurements were performed over a broad wavelength range(300–1500 nm) with a Lambda 950 spectrophotometer equipped withthe ARTA accessory. The measurements, performed at different anglesand polarizations, provide seventeen R/T spectra per sample. Amathematical model is fitted simultaneously on these spectra. Thebasic model for optically flat layers showed the possibility tocharacterize AZO and ITO films and obtain, amongst other properties,the refractive index of these films.

Please cite this article as: J.A. Sap, et al., Thin Solid Films (2011), doi:10

The implementedmodel for rough interfaces allows also the charac-terization of randomly textured TCOs. The obtained material propertiesfor rough AZO films are close to the properties of flat AZO films.Furthermore the obtained roughness is comparable to AFM measure-ments fromwhich the conclusion canbedrawn that themodel for roughTCO is working properly. Besides rough AZO themodel is also tested forAsahi U-Type FTO with similar accuracy. The simultaneous fit onseventeen spectra provides a unique and accurate solution despite thelarge amount of fitting parameters. This addition make the composedSCOUT interface a valuable tool for characterizing TCO films with highaccuracy in a broad wavelength range.

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