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Multidimensional Fourier-Series Solution of the Quasi-Neutral Drift–Diffusion Equations

The semiconductor drift–diffusion equations describe the flow of electrons and holes in solar cells. When fully coupled using Poisson's equation, these equations are strongly nonlinear. However, with the exception of the first micrometer near each surface, the uniformly doped bulk in a solar cell is quasi-neutral, meaning that there is a nearly equal density of excess electrons and holes at each location. The drift–diffusion equations can then be reduced to two differential equations, one approximately linear in the excess carrier density and the other approximately linear in the excess electrostatic potential. The small deviations from linearity can be accommodated by initially treating the nonlinear terms as constant, updating the constants based on the solution result, and then iterating this cycle until convergence is achieved. When these linear differential equations are subject to reflective edge boundary conditions as typically occur when modeling solar cells, they can be solved efficiently using Fourier-series techniques. A specific numerical approach is described in detail and validated for the 2- and 3-D simulations of silicon-wafer solar cells with varying back contact parameters.