Monotone Iterative Method for Parallel Numerical Solution of 3D Semiconductor Poisson Equation

Various self-consistent semiconductor device equations, such as drift diffusion, hydrodynamic and Boltzmann transport equations require solution of a multi-dimensional Poisson’s equation that describes the potential distribution in the device for a specified doping profile. In this paper, a three-dimensional semiconductor nonlinear Poisson’s equation is solved numerically with finite volume and monotone iterative methods. Based on the strong nonlinear property of the Poisson equation, the proposed new method converges monotonically for arbitrary initial guess. By comparing with Newton's iterative method, it is easy for implementation, relatively robust and faster with much less computation time, and its algorithm is inherently parallel in large scale computing. The presented method has been successfully implemented on a 16-processors Linux-Cluster with MPI. Furthermore, the developed parallel 3D 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. Key-Words: 3D Nonlinear Poisson’s Equation, Semiconductor Device Simulation, Monotone Iterative Technique, Parallel Computing, Domain Decomposition