A Numerical Method for the Calculation of Transient Response in Mesoscopic Devices

Abstract

The transient behavior in 1-D quantum devices such as the resonant tunneling diode are commonly modeled using numerical Wigner Function methods (Ravaioli et al, 1985; Frensley, 1987). However, modeling 2-D and 3-D mesoscopic devices, such as T-structure (Sols et al, 1989) and Aharonov-Bohm effect (Datta et al., 1985) transistors, presents a problem: for an n dimensional structure: Wigner function calculations are 2n dimensional and thus the computational time required quickly becomes prohibitive. As an alternative, direct solution of Schrödinger’s equation remains n dimensional, and while a summation over incident states is required, this summation often will be limited in momentum space. In this paper, we present preliminary results of numerical calculations based on the solution of the 2-D Schrödinger equation which include absorbing boundary conditions for the proper simulation of the device as an open system.