New approach to the problem of lattice dynamics of modulated structures: Application to superlattices

Any structure can be described in terms of a multiple cell instead of its primitive one. In the former case, a larger dynamical matrix is needed to describe the lattice vibrations. It is shown that this matrix can be obtained from the known one (written for a primitive cell in the latter case) in different points of the first Brillouin zone, by a similarity transformation, which is also derived. By choosing a convenient multiple cell, the effect of modulation can be introduced into the larger matrix by appropriate modifications to its elements. Some general conclusions are drawn for thick-layer superlattices of binary compounds and numerical results are given, as an example, for GaAs-AlAs monolayer superlattices.