Three dimensional multi-grid Poisson solver

Abstract

The Newton multigrid method was shown to be an effective method for solving the nonlinear Poisson equation for semiconductor devices under thermal equilibrium conditions. This technique can also be used to solve problems involving reverse bias junctions. Assuming an insignificant concentration of minority carriers, such that no leakage current is present, and fixing the quasi-Fermi potential as a constant for majority carriers, the nonlinear Poisson equation can be used to simulate such situations.