A parallel monotone iterative method for the numerical solution of multi-dimensional semiconductor Poisson equation

Various self-consistent semiconductor device simulation approaches require the solution of Poisson equation that describes the potential distribution for a specified doping profile (or charge density). In this paper, we solve the multi-dimensional semiconductor nonlinear Poisson equation numerically with the finite volume method and the monotone iterative method on a Linux-cluster. Based on the nonlinear property of the Poisson equation, the proposed method converges monotonically for arbitrary initial guesses. Compared with the Newton's iterative method, it is easy implementing, relatively robust and fast with much less computation time, and its algorithm is inherently parallel in large-scale computing. The presented method has been successfully implemented; the developed parallel nonlinear Poisson solver tested on a variety of devices shows it has good efficiency and robustness. Benchmarks are also included to demonstrate the excellent parallel performance of the method.