Accurate determination of optical constants of textured

JOURNAL OF APPLIED PHYSICS

VOLUME 96, NUMBER 10

15 NOVEMBER 2004

Accurate determination of optical constants of textured SnO2 using low incidence angle spectroscopic ellipsometry P. D. Paulsona) and Steven S. Hegedus Institute of Energy Conversion, University of Delaware, Newark, Delaware 19716

(Received 22 March 2004; accepted 2 August 2004) Accurate optical constants (n and k) of textured SnO2 films were obtained in the range of 0.85– 4.6 eV using spectroscopic ellipsometry. The angular dependence of the spectroscopic ellipsometer measurement was determined at incident angles 30°, 50°, and 70° from normal to the sample surface. Depolarization components due to texturing and substrate backside reflection were separately analyzed using the measurement on polished and unpolished samples. Depolarization due to substrate backside reflection was modeled accurately. By performing the measurements at a low angle of incidence (30°), where the depolarization due to texturing is at a minimum and therefore can be neglected in the optical model, one can obtain the accurate values of n and k. © 2004 American Institute of Physics. [DOI: 10.1063/1.1797544] I. INTRODUCTION

information about the texture parameters. Previously reported ellipsometric measurements were limited to a small spectral range of optical constants and did not analyze the depolarization resulting from the texturing.14 Additionally, selecting an appropriate incident angle for ellipsometry measurement is very critical due to the textured surface. Nevertheless, there is no work reported so far optimizing the incident angle for measurement of the textured TCO films. In this article, we investigate the effect of the incident angle on depolarization and its impact on the quality of the data. A self-consistent measurement procedure has been developed for the accurate determination of the optical constants of the textured TCO films on glass and applied to the specific case of SnO2.

Light trapping using textured transparent conductive oxides (TCO) is well known to enhance the light absorption in amorphous Si solar cells.1–4 A fluorine-doped tin oxide 共SnO2兲 is frequently used for this purpose.5 These films are typically deposited on glass substrates by an atmospheric pressure chemical-vapor deposition. The degree of texturing depends on the deposition conditions6 and is commonly characterized by the haze or ratio of diffuse to total transmission. The haze is strongly affected by the root-mean-square (rms) height and angle of the texture. The texture leads to the scattering of light as well as the increased self-absorption in the TCO due to multiple reflections. The light-absorption enhancement due to the texturing can be modeled and eventually used to vary the deposition conditions to optimize the light trapping.7–10 This requires the knowledge of accurate values of SnO2 optical constants, namely, the index of refraction “n” and extinction coefficient “k.” However, the scattering and self-absorption due to texturing lead to inaccurate results when the standard thin-film optical characterization techniques are applied. Results have been reported by several groups on one type of the textured SnO2 (made by Asahi Corp.) but differ considerably from one another. The techniques were based on both intensity11–13 (reflection and transmission) as well as phase14 (ellipsometry and polarimetry) measurement. The intensity method measures the ratio of the intensity of the reflected and transmitted light to the incident light and requires a topographical information of the texturing to model the data. The determination of the optical constants using this technique has a limited accuracy because of the unlimited number of adjustable parameters required in the optical modeling. On the other hand, the ellipsometry method measures the ratio of the p- and s-complex reflectance of the sample rather than the absolute reflectance of the sample and can be used to characterize the textured films without significant

II. MEASUREMENT AND MODEL APPROACH

Figure 1 shows a simplified form of the various optical processes that occurred during the ellipsometry measurement. In general, the surface feature size on the SnO2 films are less than or equal to the probing wavelength. For the spectral range we used for the ellipsometry, the surface feature size was comparable to the short wavelengths and very small for the remaining part of the spectrum. If the feature size is ⬃0.1 ␭ or less, the effect of surface roughness is to reduce the refractive index of the material, which can be modeled with an effective medium theory. If the feature size is comparable to the wavelength, it can be assumed that the texturing mainly causes the intensity reduction, provided that the detector geometry is such that it preferentially sees the specular reflection. This can be seen from Fig. 1(a), where the reflection from SnO2 surfaces parallel to the substrate cause specular reflections. On the other hand, the nonparallel surface causes a reflection, which cannot reach the detector if the detector is placed far from the sample. Nevertheless, some scattered light, which has no identifiable polarization state, can still reach the detector. Moreover, macroscopic roughness on SnO2 surface causes reflections with partial polarization. Also, cross polarization can occur in nominally isotropic systems due to texturing (s-polarized light goes to

a)

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J. Appl. Phys., Vol. 96, No. 10, 15 November 2004

FIG. 1. Various optical processes occurring during the ellipsometry measurement: 1 and 2 are the coherent reflections from the film surface and the film/glass interface; 3 is the reflection leading to intensity loss; 4 and 5 are the coherent reflections (incoherent with 1 and 2) resulting from the backside reflection from the glass; 6 is the scattering, leading to the depolarization loss.

p-polarized light and vice versa).15 Additional depolarization results from the incoherent glass backside reflections. Figure 1(b) shows the coherent reflection from the film and filmglass interface along with the incoherent reflection from the glass backside. The incoherent reflection from the backside of the glass substrate, which is also detected along with the specular reflection from the film, causes depolarization. For our ellipsometry configuration, it was calculated and then experimentally tested that a glass substrate ⬎5 mm was necessary to avoid an incoherent reflection. Since the SnO2 films were on a 1 mm-thick glass substrate, the incoherent backside reflection has an influence on our data. A major emphasis of this work is to account for this effect. Typically, spectroscopic ellipsometry measurements are carried out at incident angles near the Brewster angle,16 because the difference in the p-wave and the s-wave intensities are maximum at these angles. This is particularly important for very thin films with thickness of ⬍100 Å. Also, for dielectric films, the poor sensitivity of a rotating analyzer for the ellipsometry parameter ⌬ near 0° (above the Brewster angle) and 180° (below the Brewster angle) makes the measurement of the dielectric constants meaningful only near to the Brewster angle region, where delta changes from 180° to 0°. This is because the rotating analyzer-type ellipsometer

P. D. Paulson and S. S. Hegedus

measures the cos ⌬, and it cannot distinguish between 0° and 180° or between 180° and 360°, causing great uncertainty in the ellipsometry measurement. The texturing can significantly affect the Brewster angle ellipsometric measurement. Conventionally, higher incident angles were used when the samples had highly textured surfaces. This is because the effective rms roughness value follows a cosine dependence; the films appear less rough at a higher incident angle.17 Also, the forward reflection increases with increasing incident angle. However, for films on a transparent substrate, higher incident angle measurement leads to a significant amount of depolarization from the substrate backside reflection. In this situation, a low-angle measurement would be an alternative to be considered. In order to study the effect of the incident angle, we selected three incident angles, Brewster angle (50°), smaller angle (30°), and higher angle (70°). The angle of incidence is defined relative to the sample normal. Thus, a higher incident angle beam is closer to the sample surface. In reality, the Brewster angle is a psuedo-Brewster angle because it depends on the wavelength. We selected the Brewster angle in such a way that the majority of the wavelength (used for this study) satisfies this condition. The higher and lower incident angles were selected in such a way that both the incident angles have a similar sensitivity in the SE measurement, i.e., the ratio of the s- and p-polarized reflection is nearly the same. The basic rotating polarizer-type ellipsometer can fully describe a nondepolarizing sample using two ellipsometric parameters, ␺ and ⌬. However, if the sample is isotropic but depolarizing, the two parameters are insufficient to fully describe an ellipsometric measurement. Using a retarder in the incident beam circumvents the problems associated with the depolarization and poor sensitivity of the rotating analyzer spectroscopic ellipsometer. Thus, the sensitivity of the ellipsometry is no longer limited to the Brewster angle measurements. A retarder introduces a known phase delay into one of the orthogonal components of the electric-field vector. The amount of retarding varies with the wavelength of the light. The ellipsometer we used for the present work is equipped with an autoretarder, which automatically varies the retarding delay with the wavelength. The addition of the retarder permits separate measurements of three quantities: ␣ = cos共2␺兲, ␤ = sin共2␺兲cos共⌬兲, and ␥ = sin共2␺兲sin共⌬兲. The amount of depolarization is obtained from the relation percentage of depolarization= 100* 共1 − ␣2 − ␤2 − ␥2兲.18 A. Optical modeling

The texturing on Asahi SnO2 films was designed to scatter the light in the subsequently deposited a-Si film to enhance its absorption. This implies that the texture feature size should be of the order of wavelength of the relevant illumination spectrum. For a-Si-based solar cells, this is ⬃500– 1000 nm. Effective-medium approximations (EMA) generally used for characterizing the roughness assume that the feature size is less than 0.1 ␭. Tompkins and McGahan16 and Azzam and Bashara17 have shown that certain class of macroscopic roughness can be modeled with EMA. It assumes that any depolarization generated by the macroscopic




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roughness is completely random. Our scatterometry measurement on these samples confirmed the random nature of the scattering from the Asahi SnO2 films. Thus, we model the texturing with the Bruggeman effective medium approximation consisting of SnO2 and void. Rovira and Collins14 also used a similar model successfully for characterizing textured SnO2 films. The optical modeling was carried out using the WVASE® software from J. A. Woollam Company.

amplitude is proportional to the thickness and refractive index of the materials. Cauchy dispersion relation [Eq. (2)] is used to generate the SnO2 optical constants in the high transparency region, where the extinction coefficient k is negligibly small. For a SnO2 film, this region corresponds to the energy range nearly between 2 and 3 eV.

1. Optical modeling of glass

where n is the refractive index and A, B, and C are the parameters known as the Cauchy coefficients. Since the extinction coefficient is negligibly small in this wavelength region, there are only two unknowns to be determined, the thickness of SnO2 and the refractive index parameter A (other fit parameters B and C in the Cauchy dispersion relation are kept constant). The global fit for the refractive index and thickness over a wide range of possible values was performed to prevent the mean-squared error (MSE) from falling into a local minimum. The thickness of the SnO2 film, hence obtained, was used in the optical model of the sample. In the next step, the starting values of the optical constants in the whole measurement region were determined. By using the known refractive index values determined in the transparent region 共k = 0兲, a wavelength-by-wavelength fit was performed over the entire spectral region. The n and k starting spectra obtained from this fit are close to the bulk optical spectra and are called the “initial spectra.” The general oscillator layer consisting of two oscillators was then constructed using the initial spectra. The oscillator strength, center energy, and broadening values are fitted to match the initial spectra. The ellipsometry parameters for the sample were generated with the general oscillator layer in the optical model. The difference between the generated and the measured ellipsometry parameters are reduced by regression analysis. For this, the software employs the LevenbergMarquardt algorithm, and the MSE was obtained from the equation16

In order to separate the glass absorption from the absorption in SnO2 film, optical constants of the glass were determined first after etching off the SnO2 film. The optical analysis used a two-phase glass/ambient model. The index of refraction for glass, ng, was determined by fitting the ellipsometry parameter ␺ and depolarization (due to back side reflection) in the transparent region, where the extinction coefficient, kg, is negligibly small. Then, ng is used to generate the normal transmission of the glass. Since kg is negligibly small, both transmission data are expected to match very well in the transparent region. However, in the absorbing region, the generated data differ from the measured data due to the glass absorption, and the glass extinction coefficient kg is extracted using a point-by-point fit on the measured transmission data starting from the transparent region. 2. Optical modeling of glass/ SnO2

The optical model used for the spectroscopic ellipsometry analysis on the glass/ SnO2 sample consists of a surface roughness layer, a SnO2 layer, an interface layer, and a glass substrate. The surface roughness layer is modeled with a Bruggeman EMA model consisting of void and SnO2. The volume fraction of void is a fitting variable in the model. It is also possible to model the surface roughness layer with a graded structure with increasing void volume fraction toward the surface. The optical constants of SnO2 films are generated using a general oscillatorlayer consisting of two oscillators, a Lorentz oscillator to generate the optical absorption due to the electronic transitions at higher energies and a Drude oscillator (Lorentz oscillator with a zero energy) to generate the free-carrier absorption. The Lorentz oscillator is a classical oscillator, which can be used to describe the interaction of atoms with electromagnetic waves.19 A simple form of the Lorentz oscillator can be described using the relation ␧共hv兲 =

A , E − 共hv兲2 − iBhv 2

共1兲

where A is the amplitude, E is the center energy, B is the broadening of the oscillator, and hv is the photon energy in eV. The interface layer is modeled with, again, a Bruggeman EMA model, which consists of 50% SnO2 and 50% glass with a variable thickness. The construction of the general oscillator model and the data fit strategy is described in the following section. The data fitting starts with the determination of the SnO2 thickness. The thickness of the SnO2 films was determined from the interference fringes. The number of fringes and its

n共␭兲 = A +

B C + , ␭2 ␭4

N

1 MSE = 2N − M i=1

兺

2

+

冉

共2兲

冋冉

␺mod − ⌿exp i i ␴exp ⌿j

⌬mod − ⌬exp i i

␴exp ⌬j

冊册

冊

2

2

,

共3兲

where N is the number of measured parameters, M is the exp number of fitted parameters, and ␴exp ⌿j and ␴⌬j are the standard deviation in the measurement data. By using the experimental standard deviation as the weighing parameter in the fit, the contributions due to the noise in the MSE are reduced significantly. Also, a nearly constant and low standard deviation is obtained by using a dynamic averaging, which ensures that the fit is weighed equally over the whole spectrum of the data. To make the optical modeling easier, the SE data for a polished SnO2 film was modeled first. The optical model hence obtained was used to model the textured films. When modeling textured SnO2 films, the two surface roughness parameters, thickness and void fraction, were fitted first. The oscillator parameter will be adjusted later if needed to im-


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prove the fit. This helps to avoid using complex optical models involving several layers to fit the SE data. The measurement and optical modeling was performed at three incident angles, and the results were compared with the polished SnO2 films. III. EXPERIMENT

The textured SnO2 glass substrates used in this study were obtained from the Asahi Glass Corporation (Type U). The others have studied the optical properties of this type of SnO2 as well.3,7,10,13,14 The SE measurements were carried out using the J. A. Woollam variable angle spectroscopic ellipsometer (VASE) over the range of 0.85– 4.6 eV. It is a rotating analyzer-type ellipsometer fitted with an autoretarder. The detector in the present SE configuration is placed away from the sample surfaces (iris is 14 cm away from the center of the sample) so that it preferentially detects the specular reflection. The error caused by the p-s cross scatter from the surface roughness is measured by the four zone averaging during the measurement.20 Zone averaging causes the measured data to be averaged over the data acquired with the input polarizer positioned in each of the four quadrants. This can also help to eliminate the systematic errors due to the polarizer calibration offset. The SE measurements were performed at the polarizer tracking mode and also with the dynamic averaging to facilitate the constant minimum standard deviation in the measurement data. In addition to the measurement of ⌬, ␺, and depolarization, the normal specular transmission of the samples is obtained using the same setup. All four of these parameters are used to extract and verify the true optical constants of the glass and SnO2 (for comparison) films. Requiring the optical model to fit the multiple measurements (three incident angles and four different parameters) in a self-consistent manner strengthens the confidence in the results. Some of the textured SnO2 films were mechanically polished to significantly reduce the texture size, giving nearly specular smooth films. The atomic force microscopy (AFM) measurement shows that these films have an average rms roughness of about 42 nm, consistent with the reported values on this same brand of SnO2.13,14 Mechanical polishing reduced the rms roughness to nearly 10 nm. The SE measurements were also made on bare glass substrates after etching the SnO2 film. Nascent hydrogen generated from the reaction between Zn powder and hydrochloric acid was used to etch the SnO2 film. The SE measurement on a bare glass substrate is used to obtain the true glass optical constants as well as to compare the effect of the back surface reflection.

FIG. 2. Measurement and fit of the ellipsometry parameter ⌿ for the glass substrate after etching SnO2. The inset shows the measurement and the fit of the corresponding depolarization spectra for the same glass substrate. For both figures, the continuous line shows the fitted curve.

tical constants n and k obtained for the glass substrate from the best fit to the ellipsometry parameters and transmission data, respectively. It also shows the glass normal transmission data along with the best fit used for obtaining the glass absorption coefficient. B. Depolarization analysis of SnO2 / glass

Figures 4(a) and 4(b) show the measured depolarization map with a varying incident angle and energies for a polished and unpolished SnO2 film on glass, respectively. The depolarization was measured at an incident angle varying from 25 to 75 with the step of 0.1°. At every incident angle, the depolarization is measured for the energy range 1 – 4.5 eV with an energy step of 0.05 eV. The x axis shows the spectral energy of the probing light and the y axis shows the incident angle. The shading indicates the percentage of depolarization at a particular incident angle and energy. The shaded bands seen in the depolarization map are due to the interference effect (explained in a later section). For the polished SnO2 films, the depolarization in Fig. 4(a) is negligibly small 共⬍5 % 兲 at a lower angle 共⬍30° 兲 and gradually increases with the incident angle. Nearly 90% of the area depolarization map shows a value of less than 8%. For an unpolished SnO2 film, the depolarization in Fig. 4(b) is small again at the lower angle but increased significantly with the

IV. RESULTS AND DISCUSSION A. Characterization of glass substrate

Figure 2 shows the measured ␺ and depolarization for the glass substrate along with the best fit. The step in the ␺ spectra at 3.5 eV is due to the incoherent reflection from the backside of the glass substrate. This incoherent reflection causes the depolarization, which is shown in the graph. The depolarization is negligibly small at 50° and increased significantly for higher incident angles. Figure 3 shows the op-

FIG. 3. Measurement and fit of the transmission measured on the glass substrate. The inset shows the optical constants n and k spectra from the glass substrate.




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FIG. 4. Energy vs incident angle depolarization map for (a) polished and (b) unpolished Asahi SnO2 films. The bands are due to the interference effect resulting from the multiple reflection of the glass backside reflected light undergoing in the SnO2 film, coherent reflections 4 and 5 in Fig. 1. The darker region indicates a higher depolarization.

incident angle. The higher depolarization bands extended to the lower incident angles. The depolarization is caused by both the incoherent reflections from the substrate backside reflection as well as by the texturing on the SnO2 surface. The purpose of Figs. 5(a)–5(c) is to identify the depolarization contribution due to the substrate backside reflection and SnO2 texturing. Figure 5(a) shows the measured depolarization at three incident angles for the polished SnO2 films, in which the depolarization measured at the 30° incident angle is negligibly small compared to the depolarization measured at 50° and 70°. Since the film is very smooth, no depolarization is expected from texturing. From Fig. 2, we know that the reflection from the glass backside and hence, the depolarization increases with the incident angle. The depolarization in Fig. 5(a) also increases with the incident angle, indicating that the depolarization could be due to the backside reflection. Also note that the depolarization due to the glass substrate in Fig. 2 is flat and much less than that for a glass substrate with SnO2 films, as shown in Fig. 5(a). In order to study this, we generated depolarization for a smooth SnO2 film on a glass substrate. Figure 5(c) is the generated depolarization for a glass substrate at an incident angle of 70° for three thicknesses of smooth SnO2 films. It systematically shows how the glass backside reflection generates interference fringes in depolarization spectra, starting from the film-free glass to the film on glass with an increasing thickness. In the absence of a film, the depolarization is similar to

FIG. 5. Measured depolarization spectra at three incident angles for (a) polished and (b) unpolished Asahi SnO2 film on glass along with (c) the simulated depolarization spectra for a glass substrate with three thicknesses of smooth SnO2 films at the 70° incident angle. For both the polished and unpolished SnO2 films, the total depolarization is negligibly small at the 30° incident angle.

Fig. 2 that forms a step at the energy where the glass becomes transparent. There are no interference fringes in the depolarization spectra because the reflected light is due to the incoherent reflection from the backside of the glass substrate. In the presence of a very thin film 共8 nm兲, the depolarization is enhanced, and still, there are no interference fringes. As the film thickness increases, the depolarization component increases. The thickest film (800 nm, which is comparable to the Asahi SnO2 film thickness) shows very pronounced interference fringes. These interference fringes are the result of the multiple reflections that the substrate backside reflected light undergoes in the film [reflection 4, 5


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in Fig. 1(b)]. This phenomenon is similar to the interference fringes caused by the frontside reflections from film and film/substrate interface, except that in the present situation, it is happening in the transmission mode. Interference fringes resulting from both the frontside reflection and the glass backside reflection is clearly shown in Fig. 1(b). This result contradicts the model proposed by Rovira and Collins.14 They believe that the interference fringes in the polarization (depolarization) are due to the thickness nonuniformity. Our model clearly suggests that the depolarization at a higher angle is due to the backside reflection from the glass substrate and can be modeled accurately. The amount of substrate backside reflection collected at the detector increased from zero at a low incident angle (30°) to 85% at the higher incident angle (70°). The depolarization caused by the light scattering from the frontside reflection is negligibly small because of the ellipsometry configuration we used. Figure 5(b) shows the measured depolarization at three incident angles for an unpolished SnO2 film. Similar to Fig. 5(a), Fig. 5(b) also shows the depolarization due to the substrate backside reflection. However, different from the depolarization for a polished film, Fig. 5(b) shows a higher depolarization for the 50° incident angle. This is consistent with the depolarization map shown in Fig. 4(b), where the high depolarization bands are shifted to the low incident angles due to texturing. The depolarization for the textured SnO2 is a combination of both texturing and the substrate backside reflection. Thus, the resultant depolarization is expected to be higher than that for a polished film. In contrast, the depolarization for the textured SnO2 films at a 70° incident angle is lower and appears to be truncated at the higher-energy side. A possible explanation for this truncated depolarization could be that the substrate backside reflected light might not be reaching the detector because of scattering and/or refraction from the textured surfaces (nonparallel film surfaces-air interface). Since our ellipsometer is configured to predominantly detect the specular reflections, these reflections are undetected. The significant scattering by the textured SnO2 is evident from the wavelength-dependent decrease in the truncation. It may be useful to mention that while the textured SnO2 enhances the trapping in a-Si thin film solar cells, this also leads to the enhanced absorption in the SnO2.3,4,8 This means that a considerable amount of the substrate backside reflected light may be trapped by the total internal reflection and went undetected. Thus, at larger incident angles, the texturing leads to an increased loss of the depolarization information. Figure 5(b) also reveals the angular dependence of the depolarization. The depolarization at a 50° incident angle is higher than for a polished film because of the depolarization from the texturing as well as the backside reflection. On the other hand, this indicates that the backside reflected light is less scattered/reflected at the film-air interface and hence, reaches the detector. Also notice that the interference fringes become sharper compared to the depolarization fringes resulting from a purely backside reflected light [refer to Fig. 5(c)]. This sharp feature is an indication of the dominant texture effect we observed in several measurements. More scattered light (front reflected) with a partial polarization are


reaching the detector. Thus, it can be inferred that the SE measurement becomes more sensitive to the texturing at the Brewster angle. Finally, for the incident angle of 30°, the depolarization for the textured films is again higher than the polished films. This suggests that similar to the incident angle of 50°, there is no depolarization loss due to texturing, and the measurements are sensitive to the texturing. However, the total depolarization is always negligibly small at 30° because the depolarization due to the backside reflection is almost zero. This depolarization result was further tested by performing the measurement on the textured glass substrate. After roughening and blackening the backside of the glass, the measurement showed that the depolarization reduced to almost zero, confirming the role of backside reflection in generating the depolarization. The following conclusions were drawn from the discussions: (1) Both the SnO2 texturing and glass backside reflection causes the depolarization, and the total depolarization is the sum of these two. The truncated depolarization leads to an information loss. (2) The depolarization due to the glass backside reflection increases with the incident angles. Texturing causes an information loss in both the frontside reflection (partial polarization) and substrate backside reflection (truncated depolarization). With an increasing incident angle, the substrate backside reflection increases, leading to a larger information loss. (3) For both the polished and unpolished SnO2 sample, the total depolarization is minimum at low incident angles. Also, the low-angle measurement has a less depolarization loss due to texturing. Modeling the depolarization contribution due to texturing is very complex, especially when the feature size reaches the wavelength of the probing light. This suggests that a measurement with a minimum depolarization without truncation would be ideal for the optical modeling. C. Optical constants of textured SnO2

Optical modeling was performed on the ellipsometric data measured at three different incident angles, as described in the previous section. Table I shows the summary of the results obtained from the optical modeling. The thickness of the film obtained from the fitting is in excellent agreement with the values determined from the electron microscopy. Also, the roughness values are in good agreement with the AFM measurement for both the polished and textured SnO2. This suggests that the EMA model is successful in modeling the textured surface. The introduction of an interface layer in the optical model significantly improved the MSE value. The presence of such an interface layer is reported in the literature, and it could be due to the incomplete space filling by coalescing grains during the initial phase of film deposition14 or could be due to a deposited barrier-layer-like silicon oxycarbide. The void fraction in the surface roughness layer drastically reduces from 40% to 14% as the result of polishing.




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TABLE I. Comparison of the optical model data for the polished and unpolished Asahi SnO2 films. The unpolished and polished SnO2 films have surface roughnesses of the order of 42 and 11 nm, respectively, measured by AFM. Incident angle (°)

SnO2 thickness (nm)

Polished SnO2 30 50 70 Unpolished SnO2 30 50 70

Roughness layer thickness (nm)

Void fraction (%)

Interface layer thickness (nm)

Void fraction (%)

MSE

639.0 639.8 643.8

11.0 11.1 11.1

8.5 14.4 14.4

51.8 51.8 51.9

48 52 55

2.5 6.8 9.8

669.1 670.4 668.3

34.7 38.3 43.4

37 40 40

51.5 51.2 50.8

43 47 48

4.3 14.6 17.5

Figures 6(a) and 6(b) show the measured ⌿ and ⌬, respectively, for the 30° incident angle along with the fit for the polished SnO2 films. Figure 6(c) is the normal transmission generated from the optical constants obtained from the fit and the normal specular transmission measured using the same set up. That means that the generated transmission curve was calculated from the optical constants obtained from the SE performed at the 30° incident angle without adjusting the fit parameters, and the measured data is obtained at a normal incident. The closeness of the generated and measured transmission data shows the accuracy of the data obtained from the fit. The ellipsometry measurement and optical modeling at three different incident angles were carried out to check the angular dependence of the optical constants determination for a smooth film. Figure 7 shows the optical constants for a polished film obtained at three different incident angles. The optical constants measured at different angles are found to be nearly identical below 4 eV. However, the fit statistics from Table II show that the fit is best at the 30° incident angle. This difference may be because of the residual texturing in the polished SnO2 films, which can influence the higher incident angle measurements (by the reasons explained in the depolarization section). For a perfectly polished SnO2 film, we do not expect any angle dependence. This exercise shows that it is possible to do a sensitive ellipsometry measurement on smooth films at the incident angle away from the Brewster angles. Figures 8(a) and 8(b) show the measured ⌿ and ⌬, respectively, for the 30° incident angle along with the fit for the textured SnO2 films. Fits are not as good as for the polished films. However, the fit with the 30° angle is better than the fit with the 50° and 70° incident angles, as confirmed by the MSE values shown in Table I. The depolarization is almost six times higher than for a polished film at the same incident angle. The higher depolarization is due to the texturing, which could not be modeled properly. Figure 8(c) is the normal transmission generated from the optical constants obtained from the fit and the normal specular transmission measured using the same set up. Unlike the polished SnO2 films [Fig. 6(c)], the measured and generated transmission data for the textured film are not in good agreement. This is because the generated data does not account for the intensity

FIG. 6. Experimental and fit of ellipsometry parameters (a) ⌿ and (b) ⌬ for the polished SnO2 films at an incident angle 30°; (c) is the normal transmission generated from this data along with the measured transmission.


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FIG. 7. Comparison of the optical constants n and k spectra for the polished Asahi SnO2 films measured at the three different incident angles.

loss due to the scattering. For modeling the intensity loss due to the scattering, one needs adjustable parameters like statistical distribution of local slopes or Fourier roughness coefficients.21 On the other hand, this experiment clearly shows the advantage of the ellipsometry technique over the intensity measurement for determining the optical constants of the highly textured surface. Figure 9 shows the optical constants for the unpolished textured SnO2 films measured at the 30°, 50°, and 70° incident angles along with the optical constants of the polished SnO2 films measured at the 30° incident angle. The index of refraction is found to be very similar for all the measurements. However, the extinction coefficient shows an angular dependence, and the optical absorption edge seems to be shifting toward a lower energy with higher incident angles. This is an artifact caused by the depolarization, which is dominant at a higher incident angle. A similar effect of depolarization due to texturing on Si has been reported in the literature.22 The extinction coefficients for the unpolished film approach the same value of the polished film as the incident angle decreases. At 30°, they are almost the same, thus validating the measurement approach. The error in the determination of the true extinction coefficient (based on the measurement on polished SnO2) samples at 3.2 eV are as high as 395% and 275% for 70° and 50°, respectively, compared to the 29% for the 30° incident angle. This suggests that the low-angle SE measurement provides sufficient phase information to model the optical constants accurately. This TABLE II. Drude and Lorentz oscillator parameter values obtained from best fit for the polished and unpolished SnO2 films. Incident angle (°)

Drude Oscillator A

Polished 30 27.698 50 29.25 70 30 Unpolished SnO2 30 27.698 50 29.25 70 30.505

Lorentz Oscillator

B

A

E (eV)

B

0.036 0.034 0.033

0.552 0.904 0.66

4.509 4.536 4.499

0.399 0.318 0.371

0.036 0.034 0.033

0.694 0.770 0.725

4.434 4.484 4.462

0.336 0.684 0.719

FIG. 8. Experimental and fit of ellipsometry parameters (a) ⌿ and (b) ⌬ for the unpolished SnO2 films at an incident angle 30°; (c) is the normal transmission generated from this data along with the measured transmission.

figure is a crucial result for this work, demonstrating that it is possible to obtain optical constants on textured films provided that a low incident angle is used. Figure 10 shows the comparison of the data obtained from our analysis and the optical data reported in the literature for this material. Since our thickness agrees well with the thickness obtained by electron microscopy, we believe that the index of refraction obtained from our fit is accurate, and it is consistent with the values reported by Rovira and Collins.14,23 However, the extinction coefficient reported by Rovira and Collins in Ref. 14 is much higher than the value reported in Ref. 23. It can be seen that the lower value reported by them in Ref. 23 is consistent with our measurement and also agrees well with the value reported by Zeman et al.7 The slight difference in the shape of the curve may be due to the difference in the oscillator models used for the




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SnO2 obtained at a 30° angle were in close agreement with the data obtained from the polished samples. Also, a comparison with the reported values in the literature shows the usefulness of this technique. Optical constants obtained on the textured films from the low-angle measurements are found to be more accurate than those obtained at the Brewster angle or higher, as typically done. ACKNOWLEDGMENTS

The authors would like to thank Dan Ryan for the spectrophotometer measurements. This work was supported by the National Renewable Energy Laboratory Subcontract No. ADJ-1-30630-12. FIG. 9. Comparison of the optical constants n and k spectra for a textured Asahi SnO2 glass measured at three different angles. Also shown for comparison is the spectra obtained for a 30° incident angle measurement on a polished SnO2 sample.

data fit. Alternatively, the samples may have different properties because the SnO2 manufacturer may have changed their process conditions over the past several years. V. CONCLUSION

Spectroscopic ellipsometric measurements were carried out on textured and polished SnO2 film on glass. A systematic study of the effect of the measurement angle on the depolarization shows that the low incident angle results in the least depolarization. The optical constants on the textured

FIG. 10. Comparison of the optical constants n and k spectra obtained from a 30° incident angle measurement on a polished Asahi SnO2 film with results reported in the literature for the similar glass.

1

H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, Appl. Phys. Lett. 42, 968 (1983). 2 J. Morris, R. R. Arya, J. G. O’Dowd, and S. Wiedman, J. Appl. Phys. 67, 1079 (1990). 3 S. S. Hegedus and R. Kaplan, Prog. Photovoltaics 10, 257 (2002). 4 Y. Hishikawa, E. Maruyama, S. Yata, M. Tanaka, S. Kiyama, and S. Tsuda, Sol. Energy Mater. Sol. Cells 49, 143 (1997). 5 P. F. Gerhardinger and R. J. McCurdy, Mater. Res. Soc. Symp. Proc. 426, 399 (1996). 6 R. G. Gordon, J. Proscia, F. B. Ellis, Jr., and A. E. Delahoy, Sol. Energy Mater. 18, 263 (1989). 7 M. Zeman, R. A. C. M. M. van Swaaij, and J. W. Metselaar, J. Appl. Phys. 88, 6436 (2000). 8 S. S. Hegedus, B. Sopori, and P. D. Paulson, Proceedings of the 29th IEEE Photovoltaic Specialists Conference (IEEE, New York, 2002), 1122. 9 M. Zeman, J. A. Willemen, L. L. A. Vosteen, G. Tao, and J. W. Metselaar, Sol. Energy Mater. Sol. Cells 46, 81 (1997). 10 F. Leblanc, J. Perrin, and J. Schmitt, J. Appl. Phys. 75, 1074 (1994). 11 G. Tao and J. W. Metselaar, Proceedings of the SPIE Conference 242 (1995). 12 J. Wallinga, J. Daey Ouwens, R. E. I. Schropp, and W. F. van der Weg, Mater. Sci. Forum 173–174, 331 (1995). 13 J. Wallinga, D. Nilsson, W. F. van der Weg, and R. E. I. Schropp, Sol. Energy Mater. Sol. Cells 69, 69 (2001). 14 P. I. Rovira and R. W. Collins, J. Appl. Phys. 85, 2015 (1999). 15 “Guide to Using WVASETM” (J. A. Woollam Co., Inc., NE, USA). 16 H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (John Wiley & Son’s Inc., 1999). 17 R. M. A. Azzam and N. M. Bashara, Phys. Rev. B 5, 4721 (1972). 18 “Short Course 2001 Technical Notes,” (J. A. Woollam Co., Inc., NE, USA). 19 F. Wooten, Optical Properties of Solids (Academic, New York, 1972), p. 42–52. 20 R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 233. 21 C. L. Mitsas and D. I. Siapkas, Appl. Opt. 34, 1678 (1999). 22 U. Rossow, Thin Solid Films 97, 313 (1998). 23 G. M. Ferreira et al., Mater. Res. Soc. Symp. Proc. 762, 515 (2003).
