Theory of phonon dispersion relations in semiconductor superlattices

Abstract

In this paper we study the phonon dispersion in superlattices consisting of alternating layers of semiconductors. First the parameters in the adiabatic bond-charge model are obtained. Then it is shown that an excellent approximation to the dispersion curves of the bulk semiconductors can be obtained first by a zeroth-order calculation which includes only short-range forces and Coulomb interactions between ions and bond charges in the same and neighboring layers, then by a first-order perturbation to include the effect of the remaining forces. Thus it is possible to obtain the complex phonon dispersion relations via the eigenvalue method in the zeroth-order calculation. The eigenmode displacements of the superlattice are obtained by matching the eigenvectors associated with complex phonon branches at the interfaces, and the superlattice phonon dispersion curves including the effect of interlayer Coulomb interactions are calculated in the first-order approximation. The results for the superlattice phonon frequencies compare very favorably with the existing experimental data.