Virtual-crystal approximation and alloy broadening of intersubband transitions inp-type SiGe superlattices

Abstract

The predictions of quantized state energies as calculated by the empirical pseudopotential method (EPM) and by the $6\ifmmode\times\else\texttimes\fi{}6\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model, both within the virtual-crystal approximation (VCA), are compared for the case of SiGe based quantum wells grown in the [001] direction. Furthermore, the accuracy of the VCA is tested by performing the EPM calculation with enlarged supercells comprising a number of minimal-volume supercells with a number of different configurations of pure Si or Ge atoms over the lattice sites. The accuracy of the VCA is found to be excellent (with errors less than 1 meV), and the agreement between the EPM and $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ is very good for energies up to a few hundred meV away from the valence band top. Finally, the influence of alloy disorder on the transition matrix elements, and the broadening of intersubband transitions due to fluctuations of the alloy composition and atomic configuration, are discussed.