Accurate modelling of the accumulation region of a double barrier resonant tunnelling diode

Abstract

We have developed a computer program which calculates the electron concentration, potential profile and sub-band energies in the accumulation region of a double barrier resonant tunnelling diode. The calculations employ a local density approximation to calculate the 3D electron density and an expansion in orthogonal functions for the 2D wave functions. The total potential is separated into two parts: one part originating from 2D electrons and the other part due to 3D electrons and doping effects. The numerical profile of the latter part is modelled by a simple analytical function in a satisfactory way even for non-uniform doping profiles. Also, the potential caused by 2D electrons may be written in an appropriate functional form. With the help of both potential models, we are able to build an electron Hamiltonian in which the effects of 2D and 3D electrons, as well as the doping, are taken into account. In this way, the wave functions of the 2D electrons may be obtained semi-analytically by diagonalizing the Hamiltonian and solving Poisson's equation to a restricted degree of self-consistency. Tunnelling of electrons through the barrier is taken into account. The routine is combined with an analysis of the tunnelling process and a model for the depletion region to give an accurate description of the current-voltage characteristics of double barrier resonant tunnelling diodes.