Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices

摘要

Several formulations of the system of nonlinear elliptic partial differential equations modeling semiconductor devices are presented. The equations are discretized using finite difference techniques, and a class of Newton-like methods based on splittings of the Jacobians are developed. Sufficient conditions for convergence of these methods are stated and proved. A multigrid method for solving the nonlinear semiconductor equations is also described, and numerical examples are presented illustrating its efficiency and utility. (ERA citation 09:015758)