An image processing approach to approximating interface ... · with 3d optical modelling by...

An image processing approach toapproximating interface textures of

microcrystalline silicon layers grown onexisting aluminum-doped zinc oxide

textures

Kai Hertel,1,2,? Jurgen Hupkes,3 and Christoph Pflaum1,2

1 Lehrstuhl fur Systemsimulation, Universitat Erlangen-Nurnberg, Germany2 Graduate School of Advanced Optical Technologies, Universitat Erlangen-Nurnberg,

Germany3 Institut fur Energie- und Klimaforschung, IEK5 — Photovoltaik, Forschungszentrum Julich,

[email protected]

Abstract: We present an algorithm for generating a surface approximationof microcrystalline silicon (µc-Si) layers after plasma enhanced chemicalvapor deposition (PECVD) onto surface textured substrates, where data ofthe textured substrate surface are available as input. We utilize mathematicalimage processing tools and combine them with an ellipsoid generatorapproach. The presented algorithm has been tuned for use in thin-filmsilicon solar cell applications, where textured surfaces are used to improvelight trapping. We demonstrate the feasibility of this method by meansof optical simulations of generated surface textures, comparing them tosimulations of measured atomic force microscopy (AFM) scan data of bothAluminum-doped zinc oxide (AZO, a transparent and conductive material)and µc-Si layers.

© 2013 Optical Society of America

OCIS codes: (100.0100) Image processing; (160.6000) Semiconductor materials; (240.5770)Roughness; (350.6050) Solar energy.

References and links1. 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. Hanggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid

State Phys. 41, 391–403 (2001).3. M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hanggi, and K. Samwer, “Amorphous thin-film growth: theory

compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).4. V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hupkes, M. Zeman, and D. Knipp, “Influence of interface mor-

phologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. EnergyMater. Sol. Cells 112, 182–189 (2013).

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

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#193619 - $15.00 USD Received 9 Jul 2013; revised 27 Sep 2013; accepted 3 Oct 2013; published 9 Oct 2013(C) 2013 OSA 4 November 2013 | Vol. 21, No. S6 | DOI:10.1364/OE.21.00A977 | OPTICS EXPRESS A977

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

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

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

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

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

18. R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, and R. Schropp, “Understanding light trapping by lightscattering 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-filmsilicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn and A. Gombert, eds., Proc.SPIE 7725, 772516 (2010).

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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 thedesign 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 causescattering, refraction and reflection of incoming light and consequently influence the radiationmanagement of the solar cell. For an accurate optical simulation of thin-film solar cells it istherefore crucial to be able to use accurate approximations of the texture characteristics of thelayer interfaces involved.

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

In most cases, AFM data of only one layer are collected though, as it turns out to be bothcumbersome and time consuming to repeatedly scan a solar cell after successive depositionof each individual layer. It is even more difficult to measure the exact same surface area onthe solar cell layers after each processing step. So, even in cases where AFM scans of severallayers are available, they usually do not correlate well in terms of their position and orientationon the solar cell (cf. [1]). Additionally, the scan process may introduce unwanted changes tothe materials, as atmospheric and thermal conditions may change when removing the samplefrom vacuum for some time. So, the collection of AFM data introduces a high degree of extraeffort to the production process and possible degradation of interface properties.

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

To this end, Linz et al. [2, 3] presented a model for a-Si thin-film growth based on phys-ical parameters, like e.g. surface tension of the medium. More recently, Jovanov et al. [4, 5]presented a more practical idea to model a-Si growth in normal direction of existing AZO sur-faces. This model was subsequently used to generate a-Si surface textures from an underlyinginput texture. The same idea has been studied by Sever et al. [6] for a-Si thin-film solar cellsand multi-junction cells using conformal growth for the µc-Si layer. The model was recentlyenhanced by directional growth factors for simulating columnar µc-Si growth while neglect-ing so-called nanofeatures (cf. [7]). The distinction between columnar growth and nanofeaturesis important, as the columnar film growth is directional and in principle covered by existingmodels, while nanofeatures arise in a less predictable fashion.

We present an algorithm based on a different approach, rooted in mathematical imageprocessing. This algorithm models the changes in texture morphologies of µc-Si thin-filmsgrown on underlying textured AZO surfaces under deposition conditions where the forma-tion 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, 9, 10, 11]). 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 seemedlike a natural idea. The main difference between existing film growth methods, and our methodof modeling µc-Si textures is that the film growth models try to explain the growth process ofsilicon in terms of its physical characteristics, while our approach is primarily driven by visualfeatures of µc-Si surfaces.

Nonetheless, our approach has one concept in common with Jovanov’s method: Growth innormal direction is essentially equivalent to overlapping spheres of the same radius in everypoint of the surface. This relates to the method we will present below, to grow ellipsoids incertain 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 thesub-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, whichin 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-Siinterfaces, and simulations using a single interface texture combined with conformal growth ofsuccessive layers. The quantity of reference will be the short circuit current density JSC result-ing from external quantum efficiencies (EQE) computed by optical finite difference frequencydomain (FDFD) simulations. The simulations consider the full cell layer stack which incorpo-rates the measured and computer generated interface textures respectively. The FDFD schemerigorously models the back contact (cf. [12]), including the metal back surface reflector (BSR),with its corresponding wavelength dependent material parameters and is fully capable of takinginto account plasmonic effects (cf. [13]). This is a crucial prerequisite for obtaining accurateresults, as the back contact morphology causes surface plasmon resonances that influence bothabsorption losses in the back contact and light trapping in the silicon layer (cf. [14, 15]). The ex-citation 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 theadjacent AZO interlayer as well as the magnitude of the refractive index change on the layerinterface (cf. [16, 17, 18]. The simulation software and its components have been validatedagainst analytical solutions as well as EQE and JSC measurements of manufactured solar cellsin various scenarios in the past (cf. [19, 20, 21]).

2. Problem setting

The production of thin-film silicon solar cells typically begins with a glass substrate or su-perstrate, on which several layers are deposited successively. Work on layers may involve addi-tional processing after deposition, like etching, annealing, or other methods aimed at modifyingthe surface texture of the respective media layers (cf. [22, 23, 24, 25, 26]). In principle, after thefinalization of each layer, AFM data can be collected to record the surface characteristics of therespective media layer, which will afterwards become the interface to the next layer. Repeateddata collection of the surface characteristics is not always a viable option though for reasonsoutlined above.

The surface textured layers, deposited on a plane substrate, for the kind of solar cells we areinterested in are commonly, in order: AZO as a front contact, µc-Si as an absorber layer, AZOas 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 textureand the modifications introduced by the layer growth of µc-Si. The interface textures used inthis study are based on a sample substrate of Corning borosilicate glass. On this substrate, alayer of AZO was sputter deposited using 2 W

cm2 RF power, a heater temperature of 420◦C, apressure of 0.1Pa as well as an Ar gas flow rate of 100sccm. After deposition, the AZO layerwas processed in diluted hydrochloric acid (0.5%) for an etching time of 40s, removing onaverage about 0.15µm of the AZO layer. The µc-Si absorber consists of a 0.5µm layer ofdevice grade material deposited under a temperature of 200◦C and a pressure of 133Pa (forfurther details cf. [27]). The µc-Si layer used in this study is relatively thin compared to typicaltexture layer thicknesses as they are used in thin-film solar cells. This allows us to study theimpact of nanofeatures on the texture morphology more closely, as they are more pronouncedin thin layers, while the effect of columnar growth is small in comparison. For the purpose ofthe method we describe, let us assume that we have available AFM data that characterize thetexture of the AZO front contact in terms of a height map. We will then use this texture of thefront AZO µc-Si interface to generate an approximation of the µc-Si back AZO interface.


(a) (b)

(c)

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

3. Texture generation

Looking at the AZO surface texture in Fig. 1(a), one can clearly identify sharp ridges andsmooth inclines next to them. The µc-Si surface in Fig. 1(b), on the other hand, exhibits spher-ical or, more generally, ellipsoid shaped growth that accumulates in cloud-like structures inthe corresponding places. These rounded patterns occur on both larger and smaller scales in thetexture, and reach down in size to relatively fine-grained spots of only about 0.1µm in diameter.We will try to imitate and approximate these patterns in our algorithm by means of a superposi-tion of ellipsoid shapes that can be parameterized to range from spherical to disc-like patterns.As input data we will use the AFM data of the AZO texture and transform them by applyingellipsoids on the ridges and in surrounding areas of steep slopes.

The algorithm thus generates µc-Si like textures (cf. Fig. 1(c)) in a number of iterations thatinvolve 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 anelevation 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


(a) (b)

Fig. 2. One peak benchmark with corresponding ellipsoid (a) and, for comparison, twopeaks of elevation 1µm and 1

2 µm respectively, with a resulting overlap of ellipsoids (b).

In principle, nanofeature sizes visible on the AFM textures are expected to increase withincreasing film thicknesses. To account for this in the texture algorithm, the largest ellipsoidsizes as well as the probabilistic distribution radius are set to match the layer thickness, or atleast roughly correlate with it. The increase of the distribution radius accounts for the increasedarea 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 texturewith one peak in its center (cf. Fig. 2(a)). In cases where multiple ellipsoids are generated inclose proximity to one another, they will overlap as shown in Fig. 2(b). The remaining steps3 and 4 will be detailed further below, once the limitations of this first part of the algorithmbecome apparent.

The generated ellipsoid exhibits low and smooth curvature on its surface with higher jumpsoccurring on the edges. The curvature of the ellipsoid is defined in each point in space as thereciprocal of the radius 1

r of a virtual sphere whose tangent locally matches that of the ellip-soid under consideration. In general, the curvature can be determined locally for any surfacestructure 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 sufficientlyregularized version of the mean curvature expression

f (u) =−∇ · ∇u‖∇u‖

for a scalar quantity u(x), 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]). The discretization of thecurvature operator in our implementation is based on Mondelli and Ciomaga’s publication onmean curvature motion [29]. Of course, discretization of any operator introduces inaccuracies,here in the way how curvature is perceived locally. In general, the discrete curvature map of arotationally invariant object is not necessarily rotationally invariant itself. This is not a problemin the kind of application we are interested in though, as irregularities tend to make the texturemore 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 togenerate multi-scale cloud patterns that visually resemble the µc-Si texture. This is demon-


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

strated in Fig. 3 by means of the peak benchmark from above with up to four iterations ofa 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 ellipsoidgeneration with decreasing vertical scaling. In essence, the first iteration creates a rough ap-proximation of µc-Si cloud patterns, while repeated iterations of the algorithm can be used torefine the result. Ellipsoids attached to the ridges of AZO textures will avert a repeated super-position of ellipsoids centered in the same regions, while jumps in curvature on the ellipsoidboundaries cause a cloud-like overlap of ellipsoids. Despite a lack of experimental data to ver-ify against, we would assume that the initial scaling factor of the ellipsoid radius and height onthe texture plane scales linearly with the layer thickness, within reasonable ranges of thicknessas they occur in thin-film solar cell applications.

3.2. Probabilisitic spot placement

However, when applied to a real AZO texture, steps 1 and 2 of this algorithm yield increasinglyplateau-like surfaces with increasing numbers of iterations (cf. Fig. 4). In the case of the 0.5µmthick µc-Si layer depicted in Fig. 1, we picked a scaling factor, so the largest occurring ellipsoidgrain diameter is about 0.6µm, and thus in the same order of magnitude as the layer thickness.In each consecutive iterate we used half the scaling factor of the previous iterate. Their super-position can be used reasonably up to the point where plateaus dominate the textures (Fig. 5),but real µc-Si structures contain additional, more fine-grained spot-like components, as well


(a) (b)

(c) (d)

Fig. 4. Section of the input layer AZO AFM data (a), and 1 (b), 2 (c) and 3 (d) iterations ofthe sphere generator applied to it.

(a) (b)

Fig. 5. Superposition of 2 (a) and 3 (b) sphere generator iterates from Figs. 4(b)-4(c) and4(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.

(cf. Figs. 1 and 6). In order to place these fine-grained spots on the slopes of the generatedspheres, we can use the gradient magnitude. Numbers and accumulation of these additionalspots can be steered by using a threshold for the gradient magnitude to trigger spots, a gradientdependent spot radius or both. In real-world AZO type textures, places of steep gradient occuraccumulated in areas which are too dense to directly resemble the more diffuse spot distributionin µc-Si textures. In order to avoid an accumulation of spots in these dense areas, which wouldcertainly look unnatural, we use an additional random element. Employing a random number


(a) (b)

(c) (d)

Fig. 7. Generated spheres (a) and roughness applied to it by means of a distribution of addi-tional ellipsoids, ranging from 5nm (b) to 20nm (d) in vertical peak size. The correspondingroot mean square roughness added by this step ranges from 21nm to 31nm.

generator, we distribute the spots around the position they would deterministically be placed inwithin a given range in the order of magnitude of the layer thickness, and thus correspondingto the ellipsoid sizes used in the deterministic part of the algorithm in step 2. Once the positionand radius of the spot in the texture plane has been determined, the roughness can be adjustedby means of the vertical spot height. In Fig. 7, this effect is illustrated for a spot diameter of160nm and a set of different vertical sizes of roughness.

The steps of this algorithm can be applied iteratively with variations in scale and linearlycombined 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 anyreference 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 advisablefor getting the best results: As both curvature and gradient operators are prone to picking upon noise, generation of ellipsoids based on curvature and slope information may generate spu-rious cloud structures in positions where one would not expect any. Fortunately, noise can bereduced very efficiently by means of a smoothing operator. In numerical experiments we havesuccessfully used isotropic diffusion of the kind

∂u∂ t

= ∇ ·∇u

for this purpose. Even minimal smoothing applied to curvature and gradient maps leads tofavorable results. This is, because diffusion type smoothing processes quickly suppress sharpedges and peaks, while slowing down exponentially in time.

Diffusion can also be employed to counteract some of the adverse effects of an exaggeratedapplication of roughness. This is, because the type of roughness presented here is made ofspots 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 ofthe ellipsoids remains largely intact.

4. Validation and numerical results

For the validation of the method above, we consider four scenarios of solar cells with matchinglayer thicknesses in accordance with Table 1. The thickness considered in the following scenar-ios is the effective thickness of the media, meaning the average height of each layer across thelayer area. This way, the volume of the layers is constant across simulations of different surfacetextures. The glass substrate layer is included only for the purpose of allowing for refractionto occur at the air glass interface. The glass layer thickness is not representative of any physi-cal solar cell, which are made on top of glass substrates about 3mm thick. This discrepancy ishowever irrelevant for the following discussion, as the same conditions apply to all setups un-der consideration. The results shown in this section were obtained using one step of curvaturebased 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 of20nm.

Table 1. Layer specifications of the simulated solar cells

Layer Medium Effectiveposition thickness [µm]

1 air 0.22 glass 0.23 AZO 0.34 µc-Si 0.55 AZO 0.16 Ag 0.45

The first two scenarios represent the baseline set of data that are commonly available for atypical simulation conducted with our simulation code. In these scenarios, we use AFM dataof only one single layer surface and apply multiple copies of it to essentially all interfaces thatare assumed to be textured. This means that conformity is assumed for the growth process inthese cases. Thus, the first constellation, the most commonly encountered case, uses the AFMscan of the front AZO layer, while the second one uses that of the µc-Si layer. The texturedata of one AFM scan are applied to all rough interfaces in this context, i.e. to the rear sidesof the front AZO, µc-Si and back AZO layers. For the third setup we use both AFM scans,the one of the front AZO layer and the one of the µc-Si layer, simultaneously. The µc-Si layertexture is used for both the rear interface of the µc-Si layer and that of the following AZOback contact. This double use of the µc-Si layer texture is mainly for lack of AFM data ofthe back AZO layer. As the back AZO layer is thin compared to both µc-Si and front AZOlayers, its texture is assumed to be relatively close to the adjacent interface texture in termsof morphology. The JSC results of this third setup represent the frame of reference for theother simulation setups to be compared against (cf. Table 2). In the fourth setup we use theAFM measured AZO texture and an approximation of the µc-Si texture that has been generatedwith the texture algorithm. As the placement of roughness introduces at least a minor randomelement to the texture generation, for demonstration purposes we run five simulations, eachwith a different texture generated from the same AZO AFM data. This allows us to assess theextent to which these variations influence simulation results. Subjectively, the visual appearance


of the generated textures more closely resembles the µc-Si texture than the AZO texture does(cf. Fig. 9). But to compare the textures quantitatively, we need to introduce some metric thatturns the height information of the textures into a more manageable format. So, in order to getan idea of how the generated interface textures relate to real µc-Si textures, we compare themby means of a histogram of their angles (cf. Fig. 8). This histogram depicts the relative numberof occurrences, the so-called empirical probability, of slope angles in each texture and is relatedto the light trapping of the interfaces. This comparison neglects the shape of texture patternsand their slope graphs, which are hard to quantify, but allows us to, at least roughly, relatethe textures to one another. This is only one of many conceivable ways to compare interfacetextures. Its advantage is a dimensionality reduction of geometric interface data, so they canbe compared to one another more easily than the original dataset. Figure 8 shows that thehistogram profiles of the algorithmically generated textures resemble the histogram of µc-Sitexture much better than the AZO layer texture. After these preliminary considerations, we willnow take a look at the corresponding optical simulation results.

The dimensions of the simulated domain are 5.5µm×5.5µm×1.9µm including 0.5µm regu-larized periodic boundary layers along the horizontal axes. Mesh sizes are uniform and chosenin a way to approximate electromagnetic waves by at least 20 Cartesian Yee cells per wave-length in each medium. Table 2 shows simulations results which demonstrate that the gener-ated textures accomplish a better approximation of the reference solar cell stack than in caseswhere identical front and rear textures are used. All five simulations with algorithm-generatedtextures 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 comparativelylow, and consequently we have high confidence in the results obtained. Not only do the JSCresults better match those of the reference simulation, but even the external quantum efficiencyplots are more consistent with the reference setting (cf. Fig. 10), and the same holds for absorp-tion losses in the back contact (cf. Fig. 11). Taking a closer look at Table 2, we see that in theshorter 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 ofthe front textures, as most absorption occurs before any light reaches the bottom end of theµc-Si absorber layer. The µc-Si texture appears to perform almost as well in this position as

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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 (yel-low). Angles are measured in degrees against the horizontal plane and quantized to integervalues.


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Fig. 9. Input AZO (A) with textures generated by the algorithm corresponding to simulationresults (1) and (2) in Table 2, and µc-Si AFM scan for comparison (S).

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%]

AZO

µc−Si

Reference

alg(1)

alg(2)

alg(3)

alg(4)

alg(5)

Fig. 10. Simulation results: External quantum efficiencies across the optical spectrum. Re-sults are based on FDFD optical simulations.


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

λ [µm] range [0.3,0.6) [0.6,1.1] total [0.3,1.1]Textures: Short circuit current density JSC[

mAcm2 ]:

AFM AZO on all interfaces 8.927 8.727 17.654AFM µc-Si on all interfaces 8.872 9.033 17.905Reference: AFM AZO, AFM µc-Si 8.886 9.457 18.343AFM AZO, algorithmic µc-Si (1) 8.940 9.468 18.407AFM AZO, algorithmic µc-Si (2) 8.925 9.439 18.364AFM AZO, algorithmic µc-Si (3) 8.924 9.412 18.336AFM AZO, algorithmic µc-Si (4) 8.921 9.365 18.286AFM AZO, algorithmic µc-Si (5) 8.931 9.424 18.355Mean value and standard deviation 18.350±0.039

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

5

10

15

20

25

30

35

40

45

50

wavelength [µm]

ab

so

rpti

on

[%

]

AZO

µc−Si

Reference

alg(1)

alg(2)

alg(3)

alg(4)

alg(5)

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


the AZO texture. For longer wavelengths however, the scattering behavior of the rear texturesis a decisive factor in absorption performance, so the difference in texture morphologies has amuch higher impact. In this part of the spectrum, we clearly see that the combination of frontand rear textures is relevant. As a trend, the µc-Si texture performs better as a front layer inter-face than the AZO texture does when applied to the rear layers, but modelling non-conformallayer 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 sampleswe investigated so far.

5. Conclusion

We have demonstrated the viability of an image processing based algorithm to generate tex-tures that simulate and predict the effect of µc-Si depositions on AZO surfaces. For this, wecompared algorithm generated textures with measured textures of real µc-Si depositions. Thetextures were fed into an optical FDFD simulation for comparison and resulting short circuitcurrent densities were compared, showing a favorable outcome for the method presented. Sofar, we have successfully applied this method to one set of µc-Si textures, with their specificmaterial parameters of thickness and cristallinity, and further investigations will be necessary tosee how well the method can be generalized to other µc-Si parameter sets. In principle, the pa-rameters that affect the horizontal and vertical spot sizes as well as their shapes, quantities anddistribution can be adjusted in a wide range of manners. However, for the generation of accu-rate texture morphologies, a visual inspection of the effects of the deposition conditions on thetexture morphologies will be necessary for a specific deposition process, as long as there is noa priori knowledge available on how certain deposition parameters correlate with nanofeaturecharacteristics.

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

Acknowledgments

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


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