Theory of heterostructures: A reduced Hamiltonian method with evanescent states and transfer matrices

Abstract

A new theoretical technique for calculating the electronic properties of heterostructures is presented. This method is computationally more efficient than any current technique and has physically intuitive clarity. Furthermore, it can be applied to heterostructures with arbitrary perturbations varying in the direction perpendicular to the interface, such as smoothly varying electrostatic potentials caused by doping, compositional grading disruptions, and long range lattice relaxations. Using this method, we have studied several semiconductor surfaces, interfaces, and superlattices, including doping and relaxation effects in a realistic tight-binding model. The results for the Si (111)–(2×1) surface and the GaAs/AlAs interface with doping are presented.