Surface electronic structure of a step-well-basis superlattice

Abstract

Surface electronic structure of a semi-infinite polytype superlattice (SL) with period consisting of three different layers (the so-called step-well basis) is investigated using a transfer-matrix approach within an effective-mass approximation. Explicit analytical formulas for the bulk dispersion relation as well as the energy expression and existence condition for surface states are given for arbitrary terminating medium and their simplification for particular SL terminations by a substrate identical to one of the SL constituents is discussed. Dependence of surface-state properties (i.e., its energy position and the degree of localization) on SL parameters (i.e., layer thicknesses and potential barrier heights) and different surface configurations (depending on a sequence of SL layers approaching the surface as well as on the choice of substrate) is studied for a triple-constituent ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$-based SL. Additionally, surface-state wave functions are plotted in order to examine the associated space-charge distributions.