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Comparison of the FMM, FEM and FDTD methods for the modeling of absorption in nanowire arrays by Nicklas Anttu, Aalto University

Semiconductor nanowire arrays have received substantial interest for solar cells and photodetectors. Successful design of such devices relies typically on numerical modeling and optimization of the absorption of light. Here, we benchmark the performance, benefits, and drawbacks of three of the of the most popular optics modeling methods: the Fourier modal method (FMM), the finite element method (FEM), and the finite-difference time-domain (FDTD) method. We validate that each of the methods solves the problem successfully, both with regard to spectral response as well as to electric field distributions. After that, we continue to test how much computational time and random-access memory — the two limiting factors in numerical modeling — the methods need.
As a summary, two very similar looking nanowire arrays can show very different behavior in the modeling – for example depending on the materials, geometry, the width of the wavelength range of interest, or even the type of output such as total absorption or spatially resolved absorption. A single method is not an optimum choice in general. Instead, for a successful design process, we propose to use a combination of all three methods. We give a guideline for how to choose the appropriate modeling method, which can speed up the calculation by up to a factor of 1000.