A New Method to Compute Subband Energy States of Low-Dimensional Systems by using Feynman Path Integrals

Abstract

When the dimensions of the semiconductor devices become small enough, the quantum effects, characteristic for the so called nanoelectronic devices (ND), open a new range of possibilities for various unconventional device applications. These are very interesting and have been the subject of many explorations recently. The operation of the two major ND — the resonant tunneling diode and the resonant tunneling transistor is based on the use of an applied control voltage to modulate the energy difference between the subband energy states of the low-dimensional electron or hole system in the quantum well of ND and the energy of the incident electron. Therefore, it is important to develop efficient methods for computation of subband states in ND. Most of the methods, used till now, are based on the solution of the Schrodinger equation with appropriate boundary conditions depending on the problem under consideration [1-15]. This approach, however, has limitations and it is desirable to create alternative techniques for modelling of ND especially for the case of resonant tunneling. It is the purpose of this work to outline an original computational technique to calculate numerically electron and hole subband states in ND with arbitrary shape of the potential of the quantum well and arbitrary band-structure. This method is based on the use of Feynman path integrals in real space and time and it accounts directly the quantum interference effect for the important case when the subband states of the conduction and the valence bands are mixed by the surface potential of the quantum well or the space-charge layer.