Optical Modelling for Multilayer and Geometric Light-Trapping Structures for Crystalline Silicon Solar Cells Yang Li, Zhongtian Li, Zhong Lu, Jie Cui, Zi Ouyang, Alison Lennon The School of Photovoltaics and Renewable Energy Engineering, The University of New South Wales, Sydney NSW 2052, Australia. Abstract — The use of thinner wafers, new anti-reflection coating materials and rear passivation layers make necessary a generalized, flexible optical model that can simulate a wide wavelength range without excessive computation time and complexity. This paper presents an optical model based on the transfer matrix method. The crystalline silicon wafer with dielectric layers on both sides is modeled as an incoherent layer between coherent multilayer dielectric structures. In addition, an incident angle distribution from a geometric analysis was also used to extend the application of the model to textured surfaces. The model was validated by comparing simulated and experimental reflectance for a number of alkaline-textured surfaces including the coating materials of silicon nitride and anodic aluminum oxide (AAO). It was used to estimate that the optimum thickness for an AAO ARC was 100 nm and to predict the optimum (optical) combination of thicknesses of dielectric layers on the rear surface of a crystalline silicon solar cell. Index Terms — transfer matrix, light trapping, anti-reflection layer, simulation. I. INTRODUCTION Increasing optical absorption is a key objective in the evolution of solar cell designs, and it is increasingly becoming more critical. Since many PERC and PERL-like solar cell designs are emerging, an improved red response can be achieved by optimizing the thickness and materials used for the rear dielectric layer. This optimization becomes more critical as thinner wafers are used and new dielectric materials are investigated. Therefore, researchers need effective tools to evaluate the potential of these new structures and materials, understand the way they are incorporated into new solar cell designs and guide experiments. Different optical models have been reported for solar cells, however many lack flexibility and have practical drawbacks. Ray-tracing was widely employed to analyze the macro-sized morphology of light trapping structures for silicon solar cells [1]. The transfer matrix method (TMM) has been used to evaluate the optical performance for sub-wavelength multi- layered thin film solar cells [2]. There are also other sophisticated methods for more general structures, like finite difference time domain (FDTD), which can simulate plasmonic structures while at the cost of computational time and memory. An optical model based on TMM was presented earlier to optimize the optical properties of anodic aluminum oxide (AAO) layers on the rear surface of silicon solar cells [3]. The porous AAO layer was treated as an effective medium and its optimum thickness as a rear dielectric layer was predicted. However, this approach was only suitable for cells with a flat (i.e., polished) surface and it employed approximations regarding the silicon substrate’s incoherence. Another approximate technique has been used with TMM to optimize a triple layer antireflection coating (ARC) for acidic-textured solar cells [4]. However, it required time-consuming repetitive computation to average the coherent noise with longer wavelengths. Here, we present an updated model based on a more general form of TMM, which can integrate an incoherent layer into the coherent multilayer system natively. Additionally, by combining the TMM with an analyzed angle distribution of incident light on a pyramid surface, the updated model could simulate the optical response of an anisotropic textured solar cell with multiple dielectric layers on both sides. The theory will be explained in section II. Then, the simulation results were compared with different structures to confirm the effectiveness of the model. Finally, it was used to predict the optimum thickness for AAO as an ARC layer and for rear dielectric stack. II. MODEL A crystalline silicon solar cell with multiple dielectric layers on both front and rear surfaces can be modeled as a thick incoherent substrate between coherent layers. If the surface is textured, incident light will arrive at the surface with a distribution of angles. This distribution can be calculated by geometrical analysis for regular textures, and can then be used in the calculation of the layer and interface matrices for the TMM model. This represents a general approach for analyzing the light trapping properties of structures comprising a combination of macro-sized morphology, sub-macro film coating and incoherent absorbing materials. In the paper, normally-incident unpolarized light on regular upright pyramids was used as an example to demonstrate the method. The general approach for treating an incoherent layer in TMM is to calculate the transfer matrix for the coherent parts first, which can be treated as effective boundary conditions on both sides of the incoherent layer [5].