Special k points for performing integrals over the Brillouin zone of [001] and [111] superlattices are obtained and discussed. If the superlattice period is taken properly, the number of special points required in order to reach suitable convergence can be greatly reduced. Twelve and ten special points will give the same accuracy for N×M [001] and [111] superlattices, respectively, as Chadi’s and Cohen’s ten special points for bulk semiconductors, provided we have N+M=4n, with n an integer. These special points can also be used to calculate the corresponding integrals for strained bulk semiconductors.

• Received 17 December 1987

DOI:https://doi.org/10.1103/PhysRevB.38.1999