Real-space Hamiltonian method for low-dimensional semiconductor heterostructures

TL;DR

This paper introduces a simple, accurate real-space Hamiltonian method for calculating electronic states in low-dimensional semiconductor heterostructures, applicable to various k·p models and addressing unphysical solutions.

Contribution

The paper presents a novel, straightforward real-space Hamiltonian approach for low-dimensional heterostructures, capable of handling multiple band models and resolving issues with unphysical solutions.

Findings

Method accurately computes subband energies and envelope functions.

Applicable to 6-, 8-, and one-band models with demonstrated accuracy.

Provides strategies to identify and eliminate spurious solutions.

Abstract

We present a new method for calculating electronic states in low-dimensional semiconductor heterostructures, which is based on the real-space Hamiltonian in the envelope function approximation. The numerical implementation of the method is extremely simple; all subband energy levels and envelope functions are directly obtained by a single evaluation of the heterostructure Hamiltonian matrix. We test the method in the 6- and 8-band k \cdot p models as well as in a simple parabolic one-band model and demonstrate its great accuracy. The method can be straightforwardly generalized to a general n-band k \cdot p model. We describe three different approaches within the method which make it possible to investigate the origin and removal of the spurious or unphysical solutions, which has long been an important issue in the community.