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1 Calculatg Haze Parameter Textured Transparent Conductive Oxides A. Čampa * and M. Topič University Ljubljana, Faculty Electrical Engeerg *Correspondg author: Tržaškaa 25, 1000 Ljubljana, Slovenia, andrej.campa@fe.uni-lj.si Abstract: In th-film solar cells (a-si:h, µcvery Si:H, CIGS, ) scatterg light is important to crease absorption light the active layers solar cells. Today the most efficient th-film solar cells are designedd or deposited on random textured transparent conductive oxides (TCO). In order to study the scatterg properties the surface texture we have developed a numerical model COMSOL, which calculates the scatterg parameters from atomic force microscopy scan surface texture/topography. This way we can study and evaluate the texture capabilities to scatter the light before producg such a texture, thus reducg time and cost for studyg new types textured surfaces. The simulation results obtaed from the numerical model were compared to measured values. (1) The haze parameter is measured by means Total Integratg Scatterg measurements (TIS) [ 1]. The prciple measurement haze reflectance is shown Fig 1. Keywords: Solar cells, surface scatterg parameters textures, 1. Introduction Optical characterization complex structures and textures terfaces between two layers presents one the important issues the design th-film solar cells. The rough surface texture between two materials scatters part the light to oblique angles ( transmittance and reflectance), thus creasg the light path through layers. By prolongg the light path active layers th-film solar cells the absorptance light and efficiency solar cell creases. By creasg the absorptance side active layers, the overall th-film thickness can be decreased, therefore the deposition times and costss related to deposition processes are reduced. To study different surface textures or morphologies we have set up a numerical model to study the scatterg capabilities such a surface. The scatterg is determed by the Haze parameter, Eq. 1. Haze parameter (H) determes the fraction light that is scattered (diffused light (I dif )) at the terface compared to total tensity light (II tot, specular (II spec ) and diffused light) ). Figure 1. The prciple measurg I tot and I dif usg a total tegratg sphere. The haze reflectance is determed directly from measurements total and diffused light. To gather the scattered light the detector a total tegratgg sphere (also called Ulbricht sphere) is used. Puttg on or f the spectralon reflector at the openg the sphere, the specular beam signal can be captured or left out. This way the total and diffused reflectance can be measured, from which the haze can be calculated accordg to Eq. 1. For our measurements we have used Perk Elmer Lambda 950 spectrophotometer. The design and optimization the surface texture is maly regulated by the solar spectrum and the absorption coefficients the layers. It is important to achieve a good scatterg the wavelength region 500 nm to 1000 nm, where a part the light is transmitted through the

2 absorptive layers. By prolonggg the light path the absorptive layer the quantum efficiency solar cells creases and thus the solar cell efficiency improves. The haze parameter at a specific wavelength is calculated from the farand field doma. Two different approaches models obtag the haze parameters are shown. mesh the surface is required, sce the small details surface roughness already affect the scatterg properties. However, the surface generation and transformation is slow, therefore we have generated only one surface with the same approximation for all wavelengths. It was generated for the worst case scenario (good approximation for the shortest wavelength). 2. Numerical Model The numerical models were prepared for a COMSOL simulation stware version 4.2a with a Radio Frequency (RF) module. Two types numerical models are presented, one model with an air-perfect electric conductor (PEC) terface and one model with a realistic terface between two custom materials. 2.1 Numerical model for air-pec terface The approach taken when buildg a numerical model is similar to the approach taken when measurg the haze parameter. The idea behd the model is to calculate the far-field tensity the specular and diffused light separately. The easiest way to achieve this is by surroundg the studied surface by a sphere. Assumg the transmittance through the layer or reflectance from the subsequent terfaces is negligible, we can then surround the sample only by half the sphere. Assumg the directions x and y the sample are symmetrical, the model can be reduced to one eighth the sphere, as shown Fig. 2. The atomic force microscopy (AFM) scan the textured TCO surface [2, 3] was imported to the numerical model. In Fig. 3 the AFM scan widely used Asahi U type TCO is presented [4]. The imported png image was constructed or approximated with a parametric surface, the maximum number knots was set to 800. The imported surface was meshed with a triangular mesh, the maximum size was set to 20 nm, while the mimum size was set to 5 nm. The maximum m size corresponds to the size the pot the AFM scan. Reducg the size the mesh would not produce better results from an optical pot view, while a larger size the mesh may not take to account all the details the morphology, therefore the creased size the mesh may fluence the scatterg the short wavelength region. For shorterr wavelengths a more detailed Figure 2. Numerical model for the air-pec terface, showg the imported surface TCO and boundary conditions at different edges the model. Figure 3. AFM scan a textured TCO (Asahi U). The numerical error can be decreased by settg more pots mesh resolution at the boundary condition and settg fewer pots mesh resolution at the ner boundary the far- from the boundary conditionn can be reduced and field doma. This way unwanted reflectance the relatively slow post processg calculation haze from the far-field can be sped up. By settg enough pots at the textured surface and boundary condition, the rest the doma can

3 be meshed with a lower number pots. The mesh size can be reduced even below the recommended mimum 10 pots per wavelength to obta good results. At the edge, where the surface and the sphere tersect, we can expect a high, unwanted reflectivity from the PML, sce a part the cident field is reflected at the perpendicular angle back from the surface. Most this light is then reflected back to the structure, the angle cidence backscattered light on the PML is close to 90 degrees. In order to reduce unwanted reflectance, we have generated a Gaussian beam stead the plane wave. The Gaussian beam has a much lower tensity at the tersectionn the studied surface and the sphere. The model was solved for scattered field and the Gaussian beam was generated for the background field accordg to Eq. 2. / / / x, y and z are coordates and w is the width the Gaussian beam. In most cases the w was set to the same number as the radius the doma. 2.2 Numerical model for the air-material terface In most cases we are terested how the light is scattered between two materials. We will show another model that takes to account two materials ( our case an air-realistic metal terface). Becausee we have a complex terface between two materials, we have decidedd to switch to a total field calculation, sce the backscattered field cannot be simply defed. This time the cident Gaussian beam is defed at the scatterg boundary condition and therefore the studied doma is not enclosed by the PML doma, Fig 4. At the bottom, bellow the studied material doma, the material was termated by the scatterg boundary condition. Other settgs are the same, compared to the first model. In Fig. 4 we can see how the far-field doma is divided to the specular and the diffused surface. The surface tegration far-field tensity (tensity is proportional to emw.normefar 2 ) is performed on these surfaces to obta the specular and the diffused tensity light, from which the haze parameterr is calculated. The width the specular surface (2) corresponds to the width the cident aperture the Lambda 950 spectrophotometer. Figure 4. Numerical model for air-material terface, showg the specular and diffused far-field doma from which the haze parameter is calculated. 3. Results Both models were tested on the same sample with the same isotropic morphology the surface. The structures for verification consisted the Asahi U TCO covered by a th layer alumum. Thickness the alumum layer was around 100 nm. Alumum has high reflectivity the wide wavelength range (more than 90%), thus the air-pec model might be utilized. The measured wavelength dependent complex refractive dex alumum was imported to COMSOL order to obta good results. The haze parameter was calculated the range between 500 and 1000 nm with the step size 50 nm, measurements weree done every 10 nm. However, the haze parameter does not change rapidly, thus fewer steps were taken the simulations. In Fig. 5 the results the simulation for air- PEC (symbols) and the air-material (black curve) model are shown and compared to the measured values (red curve). Good agreement is obtaed between the measurements and the simulations for both numerical models. The wavelength dependent complex refractive dex (N( ) = n( ) ik( )) values for alumum, used the model, are summarized Table 1.

4 to obta good results the long wavelength region, the Gaussian beam has to be greater than a few wavelengths. The dispersion the beam is directly related to the ratio between the wavelength and the Gaussian beam width. In order to elimate the dispersion due to the Gaussian beam, its width should be more than 5 wavelengths [5]. Figure 5. Simulated haze reflection for the air-pec terface (symbols) and for the air-al haze for the air-al textured terface (red curve). terface (black curve) and measured Table 1: Wavelength dependent refractive dex th-film alumum used the simulations Al/wavelength [nm] n( ) k( ) Sce the air-material model uses an ordary scatterg boundary condition and the not more advanced PML boundary condition as the air- with different widths the studied doma. In PEC model, we conducted a set simulations Fig. 6 results for 3 different doma widths are shown: 5000 nm, 6000 nm and 7500 nm, the width Gaussian beam was set to 5000 nm all three cases. If we crease the doma size we get better results, especially the long wavelength region. However, all simulations, we observe the same trend with a higher deviation the long wavelength region. In order Figure 6. Comparison simulation results for different widths the doma (reference 7500 nm) with the same width the Gaussian beam (5000 nm). In Fig. 7 two cases are shown with different widths the Gaussian beam (5000 nm and 7500 nm). In both cases we see bendg the electric field (encircled), which is the consequence a less than ideal boundary condition. The bendg is more pronounced for a wider Gaussian beam. The boundary condition does not work well for high cident angles, the part light is reflected back to the doma. At the tersectionn the doma with a studied surface the boundary condition acts as a waveguide for high cident angles, which is then translated to bendg the electric field. The error can be suppressed by a bigger doma or a narrower Gaussian beam. In most cases the width the Gaussian beam can be set to the width the doma to obta eligible results.

5 haze is the same compared to the measured haze as presented Fig. 6a [6]. In Fig. 8 the Haze for TE (green dashed curve) and TM wave (red dashed curve) are also shown, along with the haze for unpolarized light (black solid curve) for se shaped gratgs. The peak the Haze at 800 nm is related to the first diffraction order gratg, while the peak at 400 nm is related to the second diffraction order accordg to the gratg equation [7]. For comparison, the simulated unpolarized haze for a rectangular shape is presented (blue solid le). The ma deviation between the measured and the simulated haze is that we have used an approximated gratg shape (rectangular and se), however the tendency the haze was as expected for both approximations, compared to measured U- shaped gratgs. The described gratg structure could be solved with 2D simulations, however our purpose was to show the correctnesss the model used for anisotropic structures. Figure 7. Bendg electric field due to less than ideal boundary condition. In the second example (width Gaussian beam is 7500 nm) the bendg is more pronounced than the first case (width the Gaussian beam is 5000 nm). 3.1 Anisotropic surface In the case an anisotropic surface (directional dependent surface texture) the same model can be used. However, we have to make two setss simulations to take to account both polarizations (TE wave and TM wave). We conducted the simulation the surface as described by Heijna [6]. In this case the gratg surface was reproduced with an ideal se and rectangular gratgs width a period 1000 nm and an amplitude 300 nm. The results are shown Fig. 8. The tendency the simulated Figure 8. The calculated haze functions reflection for sus diffraction gratg (black solid curve) for the TE and TM wave (dashed curves) and for rectangular gratg (blue solid curve). 7. Conclusions The scatterg light from the textured surfaces is very important th-film solar cells. We have demonstrated that the relatively simple numerical model can be used for determation scatterg parameter haze provided the AFM scans textured surface are available. Two different models were shown and their differences were discussed. The possible errors from numerical modelg were suppressed

6 orderr to obta credible numerical results. The model was verified on a realistic isotropic TCO structure and on an anisotropic gratg structure. 8. References 1. J. M. Bennett, L. Mattsson, Introductionn to Surface Roughneess and Scatterg, Optical Society America, Washgtonn D.C. (1989) 2. S. Faÿ, J. Stehauser, N. Oliveira, E. Vallat- Sauva, C. Ballif, Opto-electronic properties rough LP-CVD ZnO:B for use as TCO th- film silicon solar cells, Th Solid Films, 515, p (2007) 3. J. Müller, B. Recha, J. Sprger, Milan Vanecek, TCO and light trappg silicon th film solar cells, Solar Energy, 77, p. 917 (2004) 4. Sato, K., Y. Gotoh, Y. Hayashi, K. Adachi, H. Naishimura, Highly Textured SnO 2 TCO Films for a-si Solar Cells, Reports the Research Laboratory, Asahi Glass Co., Ltd. 40, p. 129 (1992) 5. A. Čampa, Modellg and optimization advanced optical concepts th-film solar cells,, PhD Thesis, Ljubljana (2010) 6. M.C.R. Heijna, J. Löffler, B.B. Van Aken, W.J. Soppe, H. Borg, P. G.J.M. Peeters, Nanoimprt lithography light trappg patterns sol-gell coatgs for th film silicon solar cells, Proceedgs SPIE 7002, Strasbourg (2008) 7. C. Hee, R.H. Morf, Submicrometer gratgs for solar energy applications, Applied Optics, 34, p (1995)