The authors review the theory of semiconductor superlattice electronic structure. First a survey of theoretical methods is presented. These methods can be divided into two general classes: the supercell approach in which the superlattice is viewed as a material with a large unit cell, and the boundary-condition approach in which bulk wave functions in the constituent semiconductors are matched at the superlattice interfaces. Supercell approaches are essentially the same as conventional band-structure methods. They can only be applied to thin-layer superlattices because of numerical cost. The authors discuss problems of interface matching that occur in various boundary-condition methods and relate these methods to each other. A particular boundary-condition method is used to discuss the electronic structure of various III-V semiconductor superlattices. Emphasis is placed on discussing the qualitatively different behavior that can arise because of different energy-band lineups, strain conditions, and growth orientations. The authors compare the results of three commonly used boundary-condition methods and find generally good agreement.

DOI:https://doi.org/10.1103/RevModPhys.62.173