<i>k⋅p</i>theory of semiconductor superlattice electronic structure. I. Formal results

Abstract

This is the first of a two-paper series in which we present a complete k\ensuremath{\cdot}p theory of semiconductor superlattices. Here we present the formal theoretical results. In the second paper, numerical impleed to derive an eigenvalue equation for the superlattice wave vector and eigenfunctions. The formalism has the advantage of involving only small-dimensionality matrices (typically, 12\ifmmode\times\else\texttimes\fi{}12). It is well suited to optical and transport property calculations.