Implementation of piecewise-linear model for self-consistent calculation of resonant tunnelling current

Abstract

A piecewise-linear model is developed for calculating the resonant tunnelling current when the potential profile is non-linear and has a non-uniform mesh size. This model is apparently better suited for an arbitrary user-specified grid or mesh points generally used in heterostructure semiconductor device modelling programs for solving the one-dimensional Poisson equation. We have implemented the Airy function solutions and transfer matrix technique in this model to calculate the electron transmission probability and charge distribution. The use of a non-uniform mesh size can improve accuracy and reduce computational time for self-consistent calculations of the tunnelling current.