A physics-based strategy for choosing initial iterate for solving drift-diffusion equations

The drift-diffusion equations are a class of nonlinear systems in the application of semiconductor devices. High efficient solution methods for solving these equations play a significant role in numerical simulations. Some nonlinear iterative methods, including Newton method and Gummel method, are usually used to solve the discretized drift-diffusion equations. Therefore, a nonlinear initial iterate should be given. The nonlinear initial iterate has a strong influence on the solution method. Typically, the related physical values in the equilibrium state, including the potential, the electron concentration, and the hole concentration, are used as the initial iterate for solving the equations with a given bias voltage. Due to the strong nonlinearity, by using the typical initial iterate, the nonlinear iterate converges slowly or even can not converge when the given bias voltage is large. In this paper, an efficient initial iterate is constructed by exploiting the application features of the drift-diffusion equations. The key idea is to construct an approximate equation of the drift-diffusion equations by neglecting the recombination effect and casting the effects of the bias voltage on carriers' quasi-Fermi potential. And the initial iterate is obtained by solving the approximate equation. Some physical interpretations and theoretical analyses for the proposed method are given. Numerical results show that the proposed initial iterate is effective, and the number of nonlinear iterations can be reduced by about 90% at most compared to the typical initial iterate. In some cases, the nonlinear iteration can not converge when the typical initial iterate is used, while the iteration converges if the new initial iterate in this paper is used.