Numerical methods for calculating self-consistent solutions of electron states in narrow channels.

Abstract

Self-consistent solutions of the Poisson and Schrodinger equations have been obtained in two dimensions and used to describe the behavior of electron states in narrow semiconductor channels. Numerical techniques used for solving the equations, as well as the outer iteration for self-consistency, are discussed. The resultant computer implementation is quite robust and runs efficiently on a vector processor: a single solution typically requires 5-15 CPU (central processing unit) min on an IBM 3090 vector machine with an 80% vector utilization; scalar execution requires 2.5-3 times more CPU time. A sample calculation shows qualitative differences between narrow channels of electrons (~60 nm in width) for the classical and semiclassical models for suitable bias and low ambient temperature.