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

Self-consistent solutions of the Poisson and Schrodinger equations have been obtained in two-dimensions and are used to describe the behavior of electron states in narrow semiconductor channels. Numerical techniques employed for solving the individual Poisson and Schrodinger equations, as well as the outer iteration for self-consistency, will be discussed. The resultant computer implementation is quite robust and runs efficiently on a vector processor: a single solution typically requires 5-15 cpu minutes on an IBM 3090 vector machine with an 80% vector utilization; scalar execution requires 2.5-3 x more epu time.