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Energy Express

  • Editor: Christian Seassal
  • Vol. 21, Iss. S6 — Nov. 4, 2013
  • pp: A977–A990
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An image processing approach to approximating interface textures of microcrystalline silicon layers grown on existing aluminum-doped zinc oxide textures

Kai Hertel, Jürgen Hüpkes, and Christoph Pflaum  »View Author Affiliations


Optics Express, Vol. 21, Issue S6, pp. A977-A990 (2013)
http://dx.doi.org/10.1364/OE.21.00A977


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Abstract

We present an algorithm for generating a surface approximation of microcrystalline silicon (μc-Si) layers after plasma enhanced chemical vapor deposition (PECVD) onto surface textured substrates, where data of the textured substrate surface are available as input. We utilize mathematical image processing tools and combine them with an ellipsoid generator approach. The presented algorithm has been tuned for use in thin-film silicon solar cell applications, where textured surfaces are used to improve light trapping. We demonstrate the feasibility of this method by means of optical simulations of generated surface textures, comparing them to simulations of measured atomic force microscopy (AFM) scan data of both Aluminum-doped zinc oxide (AZO, a transparent and conductive material) and μc-Si layers.

© 2013 OSA

1. Introduction

Optical simulations are an important part of the design process of efficient thin-film solar cells. They allow for a better insight into the inner workings of solar cells and help understand the design parameters involved in tweaking solar cells for higher performance.

The overall performance of thin-film solar cells depends to a large extent on the interface textures between the media layers it is composed of. This is because the interface textures cause scattering, refraction and reflection of incoming light and consequently influence the radiation management of the solar cell. For an accurate optical simulation of thin-film solar cells it is therefore crucial to be able to use accurate approximations of the texture characteristics of the layer interfaces involved.

To this end, one generally relies on AFM scan data of layer interfaces to feed into the simulation. These data are gathered by physically scanning surfaces of layers during the production of solar cells.

In most cases, AFM data of only one layer are collected though, as it turns out to be both cumbersome and time consuming to repeatedly scan a solar cell after successive deposition of each individual layer. It is even more difficult to measure the exact same surface area on the solar cell layers after each processing step. So, even in cases where AFM scans of several layers are available, they usually do not correlate well in terms of their position and orientation on the solar cell (cf. [1

1. M. Ermes, K. Bittkau, and R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.

]). Additionally, the scan process may introduce unwanted changes to the materials, as atmospheric and thermal conditions may change when removing the sample from vacuum for some time. So, the collection of AFM data introduces a high degree of extra effort to the production process and possible degradation of interface properties.

Furthermore, for research and development purposes it is not always desirable to manufacture and measure the full solar cell stack. One would rather be able to predict the influence of changes in the manufacturing and processing of a single layer on the resulting solar cell.

To this end, Linz et al. [2

2. S. J. Linz, M. Raible, and P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001). [CrossRef]

, 3

3. M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, and K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000). [CrossRef]

] presented a model for a-Si thin-film growth based on physical parameters, like e.g. surface tension of the medium. More recently, Jovanov et al. [4

4. V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, and D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013). [CrossRef]

, 5

5. V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, and D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013). [CrossRef]

] presented a more practical idea to model a-Si growth in normal direction of existing AZO surfaces. This model was subsequently used to generate a-Si surface textures from an underlying input texture. The same idea has been studied by Sever et al. [6

6. M. Sever, B. Lipovsek, J. Krc, and M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

] for a-Si thin-film solar cells and multi-junction cells using conformal growth for the μc-Si layer. The model was recently enhanced by directional growth factors for simulating columnar μc-Si growth while neglecting so-called nanofeatures (cf. [7

7. V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, and D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013). [CrossRef] [PubMed]

]). The distinction between columnar growth and nanofeatures is important, as the columnar film growth is directional and in principle covered by existing models, while nanofeatures arise in a less predictable fashion.

We present an algorithm based on a different approach, rooted in mathematical image processing. This algorithm models the changes in texture morphologies of μc-Si thin-films grown on underlying textured AZO surfaces under deposition conditions where the formation of nanofeatures is dominant. Image processing is used in a wide range of applications, encompassing image reconstruction, segmentation, (de)blurring and face aging among others (cf. e.g. [8

8. R. M. Haralick, S. R. Sternberg, and X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987). [CrossRef] [PubMed]

, 9

9. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990). [CrossRef]

, 10

10. A. Lanitis, C. J. Taylor, and T. F. Cootes, “Modeling the process of ageing in face images,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (Kerkyra, Greece, 1999) 1, pp. 131–136. [CrossRef]

, 11

11. R. Malladi and J. A. Sethian, “Image processing: flows under min/max curvature and mean curvature,” Graph. Model. Image Process. 58(2), 127–141 (1996). [CrossRef]

]). As all these applications aim at analyzing or modifying existing images, trying some of the tools found in image processing and applying them to our problem seemed like a natural idea. The main difference between existing film growth methods, and our method of modeling μc-Si textures is that the film growth models try to explain the growth process of silicon in terms of its physical characteristics, while our approach is primarily driven by visual features of μc-Si surfaces.

Nonetheless, our approach has one concept in common with Jovanov’s method: Growth in normal direction is essentially equivalent to overlapping spheres of the same radius in every point of the surface. This relates to the method we will present below, to grow ellipsoids in certain positions on the surface, though in a less uniform fashion.

The model is applied to predict the surface morphology of a μc-Si film with a thickness in the sub-micron range deposited on an AZO layer that exhibits large surface features. In this regime, the formation of nanofeatures is more pronounced than the effects of columnar growth, which in turn begins to exhibit an increasing influence at higher layer thicknesses. To our knowledge, no methods have been published yet to address this problem.

We will compare the performance of the algorithm presented by means of rigorous optical simulations to both simulations using separately measured AFM data of both AZO and μc-Si interfaces, and simulations using a single interface texture combined with conformal growth of successive layers. The quantity of reference will be the short circuit current density JSC resulting from external quantum efficiencies (EQE) computed by optical finite difference frequency domain (FDFD) simulations. The simulations consider the full cell layer stack which incorporates the measured and computer generated interface textures respectively. The FDFD scheme rigorously models the back contact (cf. [12

12. C. Pflaum and Z. Rahimi, “An iterative solver for the finite-difference frequency-domain (FDFD) method for the simulation of materials with negative permittivity,” Numer. Linear Algebra Appl. 18(4), 653–670 (2011). [CrossRef]

]), including the metal back surface reflector (BSR), with its corresponding wavelength dependent material parameters and is fully capable of taking into account plasmonic effects (cf. [13

13. S. Yan, J. Krantz, K. Forberich, C. Pflaum, and C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

]). This is a crucial prerequisite for obtaining accurate results, as the back contact morphology causes surface plasmon resonances that influence both absorption losses in the back contact and light trapping in the silicon layer (cf. [14

14. H. Sai, H. Jia, and M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

, 15

15. V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013). [CrossRef]

]). The excitation of localized surface plasmon polaritons (LSPP) is influenced by the nanofeature sizes, both lateral and vertical, of the textures that describe the interface of the metal BSR with the adjacent AZO interlayer as well as the magnitude of the refractive index change on the layer interface (cf. [16

16. J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, and B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

, 17

17. U. Pätzold, E. Moulin, B. Pieters, R. Carius, and U. Rau, “Design of nanostructured plasmonic back contacts for thin-film silicon solar cells,” Opt. Express 19, A1219–A1230 (2011). [CrossRef]

, 18

18. R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, and R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

]. The simulation software and its components have been validated against analytical solutions as well as EQE and JSC measurements of manufactured solar cells in various scenarios in the past (cf. [19

19. C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, and H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III , R. B. Wehrspohn and A. Gombert, eds., Proc. SPIE 7725, 772516 (2010). [CrossRef]

, 20

20. C. Jandl, W. Dewald, C. Pflaum, and H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

, 21

21. C. Jandl, K. Hertel, C. Pflaum, and H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, and P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011). [CrossRef]

]).

2. Problem setting

The surface textured layers, deposited on a plane substrate, for the kind of solar cells we are interested in are commonly, in order: AZO as a front contact, μc-Si as an absorber layer, AZO as a back contact, and a back reflector made of silver (Ag). Due to the layer deposition process, the interface texture at the back side of the μc-Si layer depends both on the front side texture and the modifications introduced by the layer growth of μc-Si. The interface textures used in this study are based on a sample substrate of Corning borosilicate glass. On this substrate, a layer of AZO was sputter deposited using 2Wcm2 RF power, a heater temperature of 420°C, a pressure of 0.1Pa as well as an Ar gas flow rate of 100sccm. After deposition, the AZO layer was processed in diluted hydrochloric acid (0.5%) for an etching time of 40s, removing on average about 0.15μm of the AZO layer. The μc-Si absorber consists of a 0.5μm layer of device grade material deposited under a temperature of 200°C and a pressure of 133Pa (for further details cf. [27

27. X. Xu, “Nanotexturierte Grenzflächen in Silizium-Dünnschichtsolarzellen,” unpublished master’s thesis, Forschungszentrum Jülich, Germany (2011).

]). The μc-Si layer used in this study is relatively thin compared to typical texture layer thicknesses as they are used in thin-film solar cells. This allows us to study the impact of nanofeatures on the texture morphology more closely, as they are more pronounced in thin layers, while the effect of columnar growth is small in comparison. For the purpose of the method we describe, let us assume that we have available AFM data that characterize the texture of the AZO front contact in terms of a height map. We will then use this texture of the front AZO μc-Si interface to generate an approximation of the μc-Si back AZO interface.

3. Texture generation

Fig. 1 AFM texture data of AZO surface (a) with corresponding AFM μc-Si texture (b) courtesy of Forschungszentrum Jülich [27], and, for comparison, a texture generated from the AZO surface using our algorithm (c). Intensity corresponds to height in this depiction, with a range of 0.8μm.

The algorithm thus generates μc-Si like textures (cf. Fig. 1(c)) in a number of iterations that involve the following steps:
  1. Determine the curvature of the texture surface to identify ridges
  2. Apply ellipsoids on the ridges to form cloud-like patterns with constant radius and an elevation that linearly relates to the curvature
  3. Determine the gradient of the texture surface to find areas of steep slope
  4. Apply smaller ellipsoid spots in a vicinity of approximately 0.5μm (the layer thickness) around steep slopes

In principle, nanofeature sizes visible on the AFM textures are expected to increase with increasing film thicknesses. To account for this in the texture algorithm, the largest ellipsoid sizes as well as the probabilistic distribution radius are set to match the layer thickness, or at least roughly correlate with it. The increase of the distribution radius accounts for the increased area of larger spots on the texture in order to avoid increasing local spot densities.

3.1. Deterministic ellipsoid growth

The effects of steps 1 and 2 of the algorithm are illustrated in a simple test case: A flat texture with one peak in its center (cf. Fig. 2(a)). In cases where multiple ellipsoids are generated in close proximity to one another, they will overlap as shown in Fig. 2(b). The remaining steps 3 and 4 will be detailed further below, once the limitations of this first part of the algorithm become apparent.

Fig. 2 One peak benchmark with corresponding ellipsoid (a) and, for comparison, two peaks of elevation 1μm and 12μm respectively, with a resulting overlap of ellipsoids (b).

The generated ellipsoid exhibits low and smooth curvature on its surface with higher jumps occurring on the edges. The curvature of the ellipsoid is defined in each point in space as the reciprocal of the radius 1r of a virtual sphere whose tangent locally matches that of the ellipsoid under consideration. In general, the curvature can be determined locally for any surface structure regardless of its actual shape. Obviously, pitfalls of occurring singularities (r → 0) need to be avoided for numerical processing. This is accomplished by evaluating a sufficiently regularized version of the mean curvature expression
f(u)=uu
for a scalar quantity u(), in this case the height map of the texture (∇ denotes the gradient; for an introduction to mean curvature refer e.g. to Colding et al. [28

28. T. H. Colding and W. P. Minicozzi, “A Course in Minimal Surfaces” in Graduate Studies in Mathematics (American Mathematical Society, 2011), Vol. 121.

]). The discretization of the curvature operator in our implementation is based on Mondelli and Ciomaga’s publication on mean curvature motion [29

29. M. Mondelli and A. Ciomaga, “Finite difference schemes for MCM and AMSS,” Image processing on line 2011, http://dx.doi.org/10.5201/ipol.2011.cm_fds.

]. Of course, discretization of any operator introduces inaccuracies, here in the way how curvature is perceived locally. In general, the discrete curvature map of a rotationally invariant object is not necessarily rotationally invariant itself. This is not a problem in the kind of application we are interested in though, as irregularities tend to make the texture more cloud-like, and thus make the algorithm more easily applicable in practice.

In principle, we can iterate over this process repeatedly with decreasing ellipsoid sizes to generate multi-scale cloud patterns that visually resemble the μc-Si texture. This is demonstrated in Fig. 3 by means of the peak benchmark from above with up to four iterations of a curvature based ellipsoid generator. Starting with a curvature map of some input interface, we cascade and superimpose ellipsoids to form cloud-like textures by iterating the ellipsoid generation with decreasing vertical scaling. In essence, the first iteration creates a rough approximation of μc-Si cloud patterns, while repeated iterations of the algorithm can be used to refine the result. Ellipsoids attached to the ridges of AZO textures will avert a repeated superposition of ellipsoids centered in the same regions, while jumps in curvature on the ellipsoid boundaries cause a cloud-like overlap of ellipsoids. Despite a lack of experimental data to verify against, we would assume that the initial scaling factor of the ellipsoid radius and height on the texture plane scales linearly with the layer thickness, within reasonable ranges of thickness as they occur in thin-film solar cell applications.

Fig. 3 One peak benchmark: Input data (a), and outputs of the sphere generator (top: plot over line with depiction of normalized curvature below) as well as resulting superimposed spheres (bottom half) after 1 (b), 2 (c), 3 (d) and 4 (e) iterations.

3.2. Probabilisitic spot placement

Fig. 4 Section of the input layer AZO AFM data (a), and 1 (b), 2 (c) and 3 (d) iterations of the sphere generator applied to it.
Fig. 5 Superposition of 2 (a) and 3 (b) sphere generator iterates from Figs. 4(b)–4(c) and 4(b)–4(d), respectively.
Fig. 6 Enhanced section of the AFM scan of the μc-Si texture from Fig. 1(b) for reference. This section corresponds to the AZO section used as input in Figs. 4, 5, and 7.
Fig. 7 Generated spheres (a) and roughness applied to it by means of a distribution of additional ellipsoids, ranging from 5nm (b) to 20nm (d) in vertical peak size. The corresponding root mean square roughness added by this step ranges from 21nm to 31nm.

The steps of this algorithm can be applied iteratively with variations in scale and linearly combined to generate the types of structures that resemble μc-Si textures. In our experience, no more than two iterations are required to obtain texture patterns that closely resemble any reference μc-Si layers we experimented with.

3.3. Optional pre- and post-processing

Depending on the quality of the input AFM data, additional preprocessing may be advisable for getting the best results: As both curvature and gradient operators are prone to picking up on noise, generation of ellipsoids based on curvature and slope information may generate spurious cloud structures in positions where one would not expect any. Fortunately, noise can be reduced very efficiently by means of a smoothing operator. In numerical experiments we have successfully used isotropic diffusion of the kind
ut=u
for this purpose. Even minimal smoothing applied to curvature and gradient maps leads to favorable results. This is, because diffusion type smoothing processes quickly suppress sharp edges and peaks, while slowing down exponentially in time.

Diffusion can also be employed to counteract some of the adverse effects of an exaggerated application of roughness. This is, because the type of roughness presented here is made of spots consisting of additional ellipsoids. Consequently, sharp edges emerge on their boundaries, especially where several ellipsoids form in close proximity to one another. As with input noise, these edges are effectively reduced by the smoothing operator, while the overall elevation of the ellipsoids remains largely intact.

4. Validation and numerical results

For the validation of the method above, we consider four scenarios of solar cells with matching layer thicknesses in accordance with Table 1. The thickness considered in the following scenarios is the effective thickness of the media, meaning the average height of each layer across the layer area. This way, the volume of the layers is constant across simulations of different surface textures. The glass substrate layer is included only for the purpose of allowing for refraction to occur at the air glass interface. The glass layer thickness is not representative of any physical solar cell, which are made on top of glass substrates about 3mm thick. This discrepancy is however irrelevant for the following discussion, as the same conditions apply to all setups under consideration. The results shown in this section were obtained using one step of curvature based ellipsoids with a horizontal diameter of 500nm and a maximum vertical height of 15nm, and one step of gradient based spots with a horizontal spot diameter of 200nm and a height of 20nm.

Table 1. Layer specifications of the simulated solar cells

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Table 2. Simulation results: Output current in the lower and higher parts of the optical regime, as well as combined values for the full spectrum. The resulting output of the shorter wavelengths is caused by incoupling, while light of longer wavelengths benefits from light trapping by means of the scattering properties of the bottom interface texture. Mean value and standard deviations correspond to simulations (1) through (5) with algorithm generated textures. Results are based on EQE results as depicted in Fig. 10 and the air mass 1.5 solar spectral irradiance (AM1.5).

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Fig. 8 Histogram of the relative frequency of angle occurrences throughout the textures: A comparison of the AZO (red), μc-Si (green) and algorithmically generated textures (yellow). Angles are measured in degrees against the horizontal plane and quantized to integer values.

The dimensions of the simulated domain are 5.5μm×5.5μm×1.9μm including 0.5μm regularized periodic boundary layers along the horizontal axes. Mesh sizes are uniform and chosen in a way to approximate electromagnetic waves by at least 20 Cartesian Yee cells per wavelength in each medium. Table 2 shows simulations results which demonstrate that the generated textures accomplish a better approximation of the reference solar cell stack than in cases where identical front and rear textures are used. All five simulations with algorithm-generated textures turn out to be closer to the reference result than the more simplistic baseline setups. The volatility of the results introduced by the randomness in our algorithm is comparatively low, and consequently we have high confidence in the results obtained. Not only do the JSC results better match those of the reference simulation, but even the external quantum efficiency plots are more consistent with the reference setting (cf. Fig. 10), and the same holds for absorption losses in the back contact (cf. Fig. 11). Taking a closer look at Table 2, we see that in the shorter wavelength part of the spectrum is not as sensitive to variations in texture morphology. In this part of the spectrum, absorption is mainly dominated by the incoupling performance of the front textures, as most absorption occurs before any light reaches the bottom end of the μc-Si absorber layer. The μc-Si texture appears to perform almost as well in this position as the AZO texture. For longer wavelengths however, the scattering behavior of the rear textures is a decisive factor in absorption performance, so the difference in texture morphologies has a much higher impact. In this part of the spectrum, we clearly see that the combination of front and rear textures is relevant. As a trend, the μc-Si texture performs better as a front layer interface than the AZO texture does when applied to the rear layers, but modelling non-conformal layer growth is clearly necessary to allow for more accurate predictions of cell performance. The algorithm we presented appears to deliver this increase in accuracy, at least for the samples we investigated so far.
Fig. 9 Input AZO (A) with textures generated by the algorithm corresponding to simulation results (1) and (2) in Table 2, and μc-Si AFM scan for comparison (S).

Fig. 10 Simulation results: External quantum efficiencies across the optical spectrum. Results are based on FDFD optical simulations.
Fig. 11 Simulation results: Back contact absorption losses across the optical spectrum. Results are based on FDFD optical simulations.

5. Conclusion

We have demonstrated the viability of an image processing based algorithm to generate textures that simulate and predict the effect of μc-Si depositions on AZO surfaces. For this, we compared algorithm generated textures with measured textures of real μc-Si depositions. The textures were fed into an optical FDFD simulation for comparison and resulting short circuit current densities were compared, showing a favorable outcome for the method presented. So far, we have successfully applied this method to one set of μc-Si textures, with their specific material parameters of thickness and cristallinity, and further investigations will be necessary to see how well the method can be generalized to other μc-Si parameter sets. In principle, the parameters that affect the horizontal and vertical spot sizes as well as their shapes, quantities and distribution can be adjusted in a wide range of manners. However, for the generation of accurate texture morphologies, a visual inspection of the effects of the deposition conditions on the texture morphologies will be necessary for a specific deposition process, as long as there is no a priori knowledge available on how certain deposition parameters correlate with nanofeature characteristics.

In our opinion, this method can be applied to both generating μc-Si-like textures in situations where only AFM data of AZO textures are available, as well as situations where both μc-Si and AZO textures are in principle available, but measured in non-overlapping regions on the substrate. The latter application allows for better parameter tuning of the algorithm in terms of grain sizes, while in the former application still a rough approximation of μc-Si growth can be generated. Moreover, in scenarios where series of textures of different thickness are produced or other parameter studies are conducted, one possible option is to measure multiple layers of the first sample and use the measurement results to calibrate and fine-tune the algorithm parameters for use in successive samples.

Acknowledgments

We express our gratitude to Philipp Magnus, formerly Malibu GmbH & Co KG, for fruitful discussions on the matter in the early stages of development of the texture algorithm, and Xu Xu, formerly master student with Forschungszentrum Jülich, for performing extensive and time-consuming AFM measurements of the AZO and μc-Si samples that are used throughout this publication. We gratefully acknowledge funding through Bundesministerium für Umwelt (BMU) by means of the LIST project grant (contract no. 0325299), as well as the Erlangen Graduate School of Advanced Optical Technologies (SAOT) by means of the Deutsche Forschungsgemeinschaft (DFG) in the framework of the German excellence initiative.

References and links

1.

M. Ermes, K. Bittkau, and R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.

2.

S. J. Linz, M. Raible, and P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001). [CrossRef]

3.

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, and K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000). [CrossRef]

4.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, and D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013). [CrossRef]

5.

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, and D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013). [CrossRef]

6.

M. Sever, B. Lipovsek, J. Krc, and M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

7.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, and D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013). [CrossRef] [PubMed]

8.

R. M. Haralick, S. R. Sternberg, and X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987). [CrossRef] [PubMed]

9.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990). [CrossRef]

10.

A. Lanitis, C. J. Taylor, and T. F. Cootes, “Modeling the process of ageing in face images,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (Kerkyra, Greece, 1999) 1, pp. 131–136. [CrossRef]

11.

R. Malladi and J. A. Sethian, “Image processing: flows under min/max curvature and mean curvature,” Graph. Model. Image Process. 58(2), 127–141 (1996). [CrossRef]

12.

C. Pflaum and Z. Rahimi, “An iterative solver for the finite-difference frequency-domain (FDFD) method for the simulation of materials with negative permittivity,” Numer. Linear Algebra Appl. 18(4), 653–670 (2011). [CrossRef]

13.

S. Yan, J. Krantz, K. Forberich, C. Pflaum, and C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

14.

H. Sai, H. Jia, and M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

15.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013). [CrossRef]

16.

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, and B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

17.

U. Pätzold, E. Moulin, B. Pieters, R. Carius, and U. Rau, “Design of nanostructured plasmonic back contacts for thin-film silicon solar cells,” Opt. Express 19, A1219–A1230 (2011). [CrossRef]

18.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, and R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

19.

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, and H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III , R. B. Wehrspohn and A. Gombert, eds., Proc. SPIE 7725, 772516 (2010). [CrossRef]

20.

C. Jandl, W. Dewald, C. Pflaum, and H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

21.

C. Jandl, K. Hertel, C. Pflaum, and H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, and P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011). [CrossRef]

22.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, and V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011). [CrossRef]

23.

Y. Li, B. Qian, C. Li, J. Xu, and C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013). [CrossRef]

24.

P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass super-strates,” Adv. OptoElectron. 2007,24584-1–24584-7 (2007). [CrossRef]

25.

H. Sai and M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” Appl. Phys. 105(9), 094511 (2009).

26.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, and B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

27.

X. Xu, “Nanotexturierte Grenzflächen in Silizium-Dünnschichtsolarzellen,” unpublished master’s thesis, Forschungszentrum Jülich, Germany (2011).

28.

T. H. Colding and W. P. Minicozzi, “A Course in Minimal Surfaces” in Graduate Studies in Mathematics (American Mathematical Society, 2011), Vol. 121.

29.

M. Mondelli and A. Ciomaga, “Finite difference schemes for MCM and AMSS,” Image processing on line 2011, http://dx.doi.org/10.5201/ipol.2011.cm_fds.

OCIS Codes
(100.0100) Image processing : Image processing
(160.6000) Materials : Semiconductor materials
(240.5770) Optics at surfaces : Roughness
(350.6050) Other areas of optics : Solar energy

ToC Category:
Light Trapping for Photovoltaics

History
Original Manuscript: July 9, 2013
Revised Manuscript: September 27, 2013
Manuscript Accepted: October 3, 2013
Published: October 9, 2013

Citation
Kai Hertel, Jürgen Hüpkes, and Christoph Pflaum, "An image processing approach to approximating interface textures of microcrystalline silicon layers grown on existing aluminum-doped zinc oxide textures," Opt. Express 21, A977-A990 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S6-A977


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References

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  14. H. Sai, H. Jia, and M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys.108(4), 044505 (2010).
  15. V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells110, 49–57 (2013). [CrossRef]
  16. J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, and B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys.95(3), 1427–1429 (2004).
  17. U. Pätzold, E. Moulin, B. Pieters, R. Carius, and U. Rau, “Design of nanostructured plasmonic back contacts for thin-film silicon solar cells,” Opt. Express19, A1219–A1230 (2011). [CrossRef]
  18. R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, and R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys.102(1), 014503 (2007).
  19. C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, and H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn and A. Gombert, eds., Proc. SPIE7725, 772516 (2010). [CrossRef]
  20. C. Jandl, W. Dewald, C. Pflaum, and H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157
  21. C. Jandl, K. Hertel, C. Pflaum, and H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, and P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011). [CrossRef]
  22. J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, and V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett.99(13), 131114–131114 (2011). [CrossRef]
  23. Y. Li, B. Qian, C. Li, J. Xu, and C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci.265, 324–328 (2013). [CrossRef]
  24. P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass super-strates,” Adv. OptoElectron.2007,24584-1–24584-7 (2007). [CrossRef]
  25. H. Sai and M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” Appl. Phys.105(9), 094511 (2009).
  26. F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, and B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys.107(1), 013708 (2010).
  27. X. Xu, “Nanotexturierte Grenzflächen in Silizium-Dünnschichtsolarzellen,” unpublished master’s thesis, Forschungszentrum Jülich, Germany (2011).
  28. T. H. Colding and W. P. Minicozzi, “A Course in Minimal Surfaces” in Graduate Studies in Mathematics (American Mathematical Society, 2011), Vol. 121.
  29. M. Mondelli and A. Ciomaga, “Finite difference schemes for MCM and AMSS,” Image processing on line 2011, http://dx.doi.org/10.5201/ipol.2011.cm_fds .

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