Computational Design of Random Rough Surfaces in Thin-film Solar Cells by Stochastic Gradient Methods

Abstract

We present an efficient numerical algorithm to solve for the optimal random structure in maximizing the absorptance for thin-film solar cells. Random rough texture can increase the absorbing efficiency of solar cells by trapping the optical light and increasing the optical path of photons. The thim-film solar cells consist of several different layers. The interfaces separating the layers are modeled as random profiles. The Karhunen-Loeve Expansion is used to represent the random profiles. Two parameters, the root mean square to the average height and the correlation length, delicate the shape of the random interface statistically with the help of Karhunen-Loeve Expansion. In maximizing the absorptance, we formulate the design problem as a optimization problem with PDE constraint to solve for the optimal parameters. The stochastic gradient method is applied to solve the random optimization problem, which leads to significant savings in computational cost compared to the full gradient method. The adjoint state method is employed to calculate the gradient of the objective function at each sample. The convergency of the stochastic gradient method in optimizing the proposed objective function is proved. Numerical examples are performed which demonstrate the accuracy and convergence of the algorithm. It is shown that the optimally obtained random textures yield absorption enhancement of the solar cells. In addition, the computational cost is reduced dramatically compared to the full gradient method.