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Oct 5, 2017 - Asman Tamang, Hitoshi Sai, Vladislav Jovanov, Koji Matsubara, and Dietmar Knipp* ..... [7] H. Sai, K. Saito, M. Hozuki, M. Kondo, Appl. Phys.
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Tiling of Solar Cell Surfaces: Influence on Photon Management and Microstructure Asman Tamang, Hitoshi Sai, Vladislav Jovanov, Koji Matsubara, and Dietmar Knipp* optical losses.[8–14] Hence, both the Microcrystalline silicon thin-film solar cells prepared on hexagonal tiled quantum efficiency (QE) and short-circuit current density of the solar cells can surfaces exhibit record short-circuit current densities and energy conversion potentially be enhanced when properly efficiencies. However, it remains unclear if hexagonal textured substrates implemented. Several experimental and represent the best possible substrate tiling. In this study, hexagonal tiled subsimulation approaches have been carried strates are compared with square and triangular tiled substrates in terms of out to derive the optimal textured interphoton management and microstructure. The 3D interface morphology of the faces.[4,7,9,15] However, realization and modeling of the optimal textured interindividual layers of the solar cells is calculated and used as input parameters faces are complex because several factors for the prediction of microcracks in the film and the simulation of 3D optical have to be considered.[4,7,9,15] In order to wave propagation. A comparison of the calculated interface morphologies realize the solar cells with high energy with experimental results exhibits a good agreement for solar cells on hexconversion efficiency, it is necessary to agonal textured substrates, permitting calculations for solar cells on square maximize the product of short-circuit and triangular textured substrates. The investigation of the crack formation current density, open-circuit voltage, and fill factor. Texturing the interfaces affects process indicates that the square and the triangular textured substrates are not only the short-circuit current density. superior to the hexagonal textured substrates. Finally, crack-free triangular The open-circuit voltage and fill factor textured solar cells exhibit increased short-circuit current densities compared are affected too by changing the surface to hexagonal and square textured solar cells. texture of microcrystalline silicon thinfilm solar cells.[2,7,16–26] Microcrystalline silicon films grown on textured surfaces exhibit a high concentration of microstructure-induced recom1. Introduction bination centers, while the silicon films prepared on smooth surfaces do not exhibit such microstructure-induced recomPhoton management and light trapping hold the capacity to bination centers.[16,18,23–26] A high concentration of recombiimprove the short-circuit current density and conversion efficiency of solar cells while reducing both material usage and nation centers is observed in regions with reduced structural reflection losses.[1–5] Light trapping is of particular interest for order, often called “cracks” or “voids.” The concentration of cracks increases with increasing roughness of the subthin-film solar cells, where the absorption depth is larger than strate.[14,16,18,23–26] As a result, the crack formation affects the the solar cell thickness. However, the absorption of light can [2–7] be improved by texturing the interfaces of the solar cells. charge collection efficiency of the solar cells. Furthermore, the open-circuit voltage and fill factor are affected.[7,16,18,22–26] The front textured interface improves the incoupling of incident light followed by scattering of the light, while the back Hence, these electrical properties of the microcrystalline silicon textured interface elongates the optical path length of the solar cell have to be considered when optimizing its light-traplight that is reflected from the back contact with minimal ping properties. The microcrystalline silicon (µc-Si:H) solar cells fabricated on hexagonal textured substrates exhibit the highest short-cirA. Tamang, Dr. V. Jovanov, Prof. D. Knipp cuit current density of up to 32.9 mA cm−2, and energy converJacobs University Bremen sion efficiency up to 11.8%.[3,6] The highest short-circuit current Campus Ring 1, 28759 Bremen, Germany E-mail: [email protected] density of 32.9 mA cm−2 is obtained for a 4 µm thick solar cell Dr. H. Sai, Dr. K. Matsubara on a hexagonal textured substrate with period of 4 µm, while Research Center for Photovoltaic Technologies the highest energy conversion efficiency is obtained for a solar National Institute of Advanced Industrial Science and Technology (AIST) cell with a thickness of 1.7 µm on a hexagonal textured subAIST Tsukuba Central 2, 1-1-1 Umezono, Tsukuba strate with a period of 2.0 µm.[3,6] However, it remains unclear Ibaraki 305-8568, Japan if hexagonal textured substrates represent the best possible subProf. D. Knipp Geballe Laboratory for Advanced Materials strate. Hence, in this study, the influence of different textured Department of Materials Science and Engineering substrates on the QE, short-circuit current density, and formaStanford University tion of cracks is studied. Stanford, CA 94305, USA In the following, the µc-Si:H solar cells with different substrate textures are compared in respect of the optical properties DOI: 10.1002/admi.201700814

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and potential formation of cracks. The solar cells are realized on three different substrates: hexagonal (also known as honeycomb[3–7,22]), square, and triangular texture. The solar cell structures investigated in this study are introduced in Section 2. In Section 3, the interplay of the device geometry on the light trapping of the solar cells and the crack formation is discussed. Finally, the optimal regular polynomial tiling is identified and the results are summarized in Section 4.

2. Modeling of Silicon Thin-Film Solar Cells To investigate the light trapping and formation of cracks, a description of the surface morphology of each layer of the solar cells is necessary. In this study, a simple 3D morphological algorithm is used to determine the interface morphology of each solar cell layer.

2.1. Interface Morphologies of Silicon Thin-Film Solar Cells The morphology for each interface of the solar cells is determined by its initial layer morphology and fabrication conditions. As a result, each solar cell layer exhibits different interface morphology.

A simple 3D morphological algorithm is developed for the calculation of the interface morphology of each layer of the solar cells.[4,9,16,22,27,28] The morphological algorithm is equally capable of modeling lithographic, etching, and deposition processes.[4,16,22,27,28] Further details on the modeling of the fabrication process of the solar cell are provided in the Supporting Information and literature.[27,28] The calculated interface morphologies of the hexagonal (Figure 1a), square (Figure 1b), and triangular (Figure 1c) textured substrates and film thicknesses are used as inputs to model the respective interface morphologies of the µc-Si:H solar cell layers. The surface morphologies of the silicon films are calculated for film thickness of 3 µm (Figure 1d–f). The thickness of 3.0 µm represents a standard or reference thickness. For this thickness, a large set of experimental results is available, so that we used this structure as our reference device.[4,7,22] The corresponding 3D side views of the surface morphologies of the solar cell layers are shown in Figure S1 in the Supporting Information. A direct comparison of the calculated with measured surface morphologies and cross-sections for the hexagonal textured solar cells exhibits a good agreement.[4] Further details on the comparison are provided in literature.[4] Hence, we can assume that the calculated surface morphology of the square and triangular textured solar cells provides a realistic description.

Figure 1.  Top views of a,d) hexagonal, b,e) square, and c,f) triangular textured substrates before a–c) and after d–f,) the deposition of a 3 µm thick microcrystalline silicon solar cell. The radius (R) of the structures is 1732 nm (see Figure 2). The direction lines A and B are shown in a–c) by white arrows and potential crack formation regions are shown in d–f) by white lines.

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Figure 2. Dimensions of the hexagonal (red), square (blue), and triangular (green) textured substrates normalized to the radius (R) of the circle (black). The period of hexagonal, square, and triangular textured substrates is given by Phex = √3 × R, Psqu = √2 × R, and Ptri = √3 × R, respectively.

For a direct comparison of different polynomial tiled patterns (hexagonal, square, and triangular), all the corners of the polygons are placed on a circumcircle with radius, R, as demonstrated in Figure 2. The period of hexagonal (Phex) and triangular (Ptri) textured substrates is given by √3 × R, while the period of square (Psqu) textured substrate is equated to √2 × R. The radii of the circumcircle are varied from 0 to 1732 nm. A radius of 0 nm corresponds to a flat substrate, while a radius of 1732 nm corresponds to a period of 3 µm for the hexagonal and triangular textured substrates and 2.45 µm for the square textured substrate. The height-to-radius ratio (H/R ratio) of all the textured substrates is kept constant at ≈0.43 for the radii >866 nm. For smaller radii, the H/R ratio is reduced due to constrains imposed on the device structure as a consequence of the fabrication process. The radius of the opening in the etch mask is assumed to be 400 nm for solar cells structures with a radii of 577 nm or larger, which is consistent with experimental results for the solar cells on hexagonal substrates.[4] For structures with smaller radii, the size of the opening in the resist is reduced. The size of the opening limits the H/R ratio for small radii. For hexagonal and triangular textured substrates, the H/R ratio is decreased to 0.26, while for the square textured substrates, the H/R ratio is decreased to 0.21 when radii