Dept of Mathematical Sciences, University of Delaware

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Title: Optimization of Thin Film Solar Cells

Abstract: We describe an ongoing project to develop a flexible and rigorously justified software tool for optimizing the design of thin film solar cells. To optimize a design, we use the differential evolution algorithm (DEA) to improve the efficiency of the solar cell. To evaluate the efficiency there are two steps:

1) Photonic Model: Maxwell's equations need to be solved in the solar cell to find the generation rate of electrons and holes. We restrict ourselves to the 2D case when Maxwell's equations decouples into s-polarized and p-polarized waves that satisfy different Helmholtz equations. To solve the Helmholtz equations rapidly we use the Rigorous Coupled Wave Analysis (RCWA) method. This method is based on using Fourier series in the horizontal (quasi-periodic) direction. Since the technique is meshless, it is easy to change both the geometry of the device and the material parameters for each simulation. Furthermore the method is fast. We prove convergence.

2) Electron transport: We use the standard drift-diffusion model to simulate electron transport in the semiconductor layers of the device. This model predicts the density of mobile electrons and holes in the device as well as the static electric field generated by these entities. Using the Hybridizable Discontinuous Galerkin (HDG) method or a finite difference scheme, we can discretize the model. The resulting system of nonlinear equations is solved by Newton's method, and by using different biasing voltages the optimal efficiency for a given design can be computed. Convergence of HDG is proved for a related time domain problem.

We have used the above algorithm to optimize several solar cell designs. In particular using graded semiconductor layers we predict substantial improvements in efficiency compared to homogeneous layers. Future work will include implementing a two and three dimensional models.