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 Optical Society of America
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. ). 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, 3] 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, 5] 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.  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. ). 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, 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 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. ), 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. ). 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, 15]). 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, 17, 18]. 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, 20, 21]).
2. Problem setting
The production of thin-film silicon solar cells typically begins with a glass substrate or superstrate, on which several layers are deposited successively. Work on layers may involve additional processing after deposition, like etching, annealing, or other methods aimed at modifying the surface texture of the respective media layers (cf. [22, 23, 24, 25, 26]). In principle, after the finalization of each layer, AFM data can be collected to record the surface characteristics of the respective media layer, which will afterwards become the interface to the next layer. Repeated data collection of the surface characteristics is not always a viable option though for reasons outlined above.
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 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. ). 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
Looking at the AZO surface texture in Fig. 1(a), one can clearly identify sharp ridges and smooth inclines next to them. The μc-Si surface in Fig. 1(b), on the other hand, exhibits spherical or, more generally, ellipsoid shaped growth that accumulates in cloud-like structures in the corresponding places. These rounded patterns occur on both larger and smaller scales in the texture, 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 superposition 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 applying ellipsoids 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 that involve the following steps:
- Determine the curvature of the texture surface to identify ridges
- Apply ellipsoids on the ridges to form cloud-like patterns with constant radius and an elevation that linearly relates to the curvature
- Determine the gradient of the texture surface to find areas of steep slope
- 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.
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 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 expression28]). The discretization of the curvature operator in our implementation is based on Mondelli and Ciomaga’s publication on mean curvature motion . 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.
3.2. Probabilisitic spot placement
However, when applied to a real AZO texture, steps 1 and 2 of this algorithm yield increasingly plateau-like surfaces with increasing numbers of iterations (cf. Fig. 4). In the case of the 0.5μm thick μc-Si layer depicted in Fig. 1, we picked a scaling factor, so the largest occurring ellipsoid grain 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 superposition 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 (cf. Figs. 1 and 6). In order to place these fine-grained spots on the slopes of the generated spheres, we can use the gradient magnitude. Numbers and accumulation of these additional spots can be steered by using a threshold for the gradient magnitude to trigger spots, a gradient dependent spot radius or both. In real-world AZO type textures, places of steep gradient occur accumulated in areas which are too dense to directly resemble the more diffuse spot distribution in μc-Si textures. In order to avoid an accumulation of spots in these dense areas, which would certainly look unnatural, we use an additional random element. Employing a random number generator, we distribute the spots around the position they would deterministically be placed in within a given range in the order of magnitude of the layer thickness, and thus corresponding to the ellipsoid sizes used in the deterministic part of the algorithm in step 2. Once the position and radius of the spot in the texture plane has been determined, the roughness can be adjusted by means of the vertical spot height. In Fig. 7, this effect is illustrated for a spot diameter of 160nm and a set of different vertical sizes of roughness.
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
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.
The first two scenarios represent the baseline set of data that are commonly available for a typical simulation conducted with our simulation code. In these scenarios, we use AFM data of only one single layer surface and apply multiple copies of it to essentially all interfaces that are assumed to be textured. This means that conformity is assumed for the growth process in these cases. Thus, the first constellation, the most commonly encountered case, uses the AFM scan of the front AZO layer, while the second one uses that of the μc-Si layer. The texture data of one AFM scan are applied to all rough interfaces in this context, i.e. to the rear sides of 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 layer texture is used for both the rear interface of the μc-Si layer and that of the following AZO back contact. This double use of the μc-Si layer texture is mainly for lack of AFM data of the back AZO layer. As the back AZO layer is thin compared to both μc-Si and front AZO layers, its texture is assumed to be relatively close to the adjacent interface texture in terms of morphology. The JSC results of this third setup represent the frame of reference for the other simulation setups to be compared against (cf. Table 2). In the fourth setup we use the AFM measured AZO texture and an approximation of the μc-Si texture that has been generated with the texture algorithm. As the placement of roughness introduces at least a minor random element to the texture generation, for demonstration purposes we run five simulations, each with a different texture generated from the same AZO AFM data. This allows us to assess the extent 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 that turns the height information of the textures into a more manageable format. So, in order to get an idea of how the generated interface textures relate to real μc-Si textures, we compare them by means of a histogram of their angles (cf. Fig. 8). This histogram depicts the relative number of occurrences, the so-called empirical probability, of slope angles in each texture and is related to the light trapping of the interfaces. This comparison neglects the shape of texture patterns and their slope graphs, which are hard to quantify, but allows us to, at least roughly, relate the textures to one another. This is only one of many conceivable ways to compare interface textures. Its advantage is a dimensionality reduction of geometric interface data, so they can be compared to one another more easily than the original dataset. Figure 8 shows that the histogram profiles of the algorithmically generated textures resemble the histogram of μc-Si texture much better than the AZO layer texture. After these preliminary considerations, we will now 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 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.
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.
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.
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