The Application of the Single-Band Envelope-Function Model in the Entire Brillouin Zone for Electronic Structure and Optical Properties Calculations

Abstract

The object of this paper is to analyze the electronic and optical properties of semiconductor nanostructures made of semiconductors with more than one significant minimum in the conduction band by applying the single-band envelope-function model in the entire Brillouin zone. We have developed a method of calculating the eigenvalues and eigenfunctions of the corresponding Hamiltonian and explored the possibility of forming a single-zone model for the entire Brillouin zone by taking the exact dependence of the conduction band energy on the wave vector E(k). Since the crystalline potential is periodic, an expansion of the electron energy band can be made in terms of vectors of the direct lattice. This method is applied to GaAs and Si quantum wells and quantum wires with square and rectangular cross sections of [001] and [110] orientation, and its accuracy is examined by comparing it with other numerically more complex and demanding methods.