Electronic surface states and miniband structure of superlattices with multiple layers per period

Abstract

The electronic structure of a semi-infinite complex-basis superlattice (SL) with $N$ layers per period is investigated, with emphasis placed on the effect of the SL surface (i.e., the SL/substrate interface). The bulk dispersion relation as well as the energy expression and existence condition for surface states are derived using the transfer-matrix method within an envelope-function approximation. Some common properties of a symmetric termination of the SL potential (i.e., when the substrate is identical to the last layer of the SL basis) are discussed and it is shown that---contrary to binary SL's---surface states can appear in complex-basis SL's also without perturbing the SL potential at the surface. These general results are illustrated by application to ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ SL's with four-layer (two-well and two-barrier) bases.