Generation of superlattice bandstructure using a wavefunction matching technique

Abstract

The bandstructure for complex wavevector for bulk semiconductors in the [100] and [111] directions has been calculated using a layer method — a technique that utilises empirical pseudopotentials. In addition to the usual Bloch type solutions, information is also obtained about the evanescent solutions. By using all these bulk solutions as a basis for the wavefunction in the superlattice, and by constraining the wavefunction to satisfy the relevant boundary conditions at the superlattice interfaces, the electronic bandstructure of the superlattice has been generated. This paper describes the method, and uses it to examine the electronic bandstructure of GaAs AlAs superlattices in the [100] direction. In particular, the in-plane bandstructure of the superlattice conduction bands has been examined, as has the variation of the energy gap of the superlattice with AlAs mole fraction.