Microscopic description of confinement in quantum well and sawtooth semiconductor superlattices

Abstract

We have studied GaAs–GaAlAs superlattices with quantum well and sawtooth structures and InAs–GaSb quantum well superlattices. Our Hamiltonian is H=H0+V where H0 represents, for example, the perfect (bulk) GaAs and V is the difference between the potential of the atoms in the alloy layers and that of the atoms of GaAs in those layers. We expand the wave function of the superlattice system in terms of the eigenfunctions of H0 and solve the Schrodinger equation numerically by direct diagonalization. We use nonlocal relativistic pseudopotentials adjusted to reproduce the bulk band structures. We recover the states lying deep in the confining potential, in accord with the existing experimental and theoretical results. We also find new well localized states which have large amplitudes in the confining layers or at the interfaces. In particular, we report the existence of a series of confined levels of X and L character. We present charge density plots along the full length of the superlattice period in 〈100〉 direction which show that in a number of cases the microscopic picture of confinement differs significantly from the predictions of simpler models. Our tests indicate that the rapidly varying terms in the potential must be explicitly accounted for in quantitative studies of systems whose characteristic dimensions are of order 100 Å or less.