Transfer-matrix algorithm for the calculation of the band structure of semiconductor superlattices

Abstract

A new compact algorithm has been developed for the calculation of the band structure of III-V or II-VI compound semiconductor superlattices. Within the envelope-function approximation, the procedure yields a transfer matrix of dimension 2n\ifmmode\times\else\texttimes\fi{}2n for an n-band k\ensuremath{\cdot}p model. The boundary conditions for the wave functions at the interfaces between layers are built into the calculation in a natural manner. The method readily adapts itself to the case where an external magnetic field is present along the superlattice axis. The effects of strain, due to lattice mismatch or an applied external stress, can also be taken into account. This extended transfer-matrix method enjoys the advantages of the usual one-band transfer-matrix method which is employed in solving the Kronig-Penney model. The standard eight-band k\ensuremath{\cdot}p description of the band structures of the individual layers is used in obtaining results for specific superlattices. Our results are in excellent agreement with earlier calculations which have used the k\ensuremath{\cdot}p and the tight-binding approximations.