Influence of substrate composition and crystallographic orientation on the band structure of pseudomorphic Si-Ge alloy films

Abstract

An analysis of the pseudomorphic ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ band-structure variation with substrate composition and crystallographic orientation is reported. A method is presented for determining all six independent elements of the strain tensor in a strained epitaxial film grown on a substrate of arbitrary orientation. The substrate orientation is found to be an important factor in determining the band-structure properties of the epitaxial film. The strain-dependent band-structure properties investigated are the following: (1) The conduction band ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\ensuremath{'}}$, ${\mathrm{\ensuremath{\Delta}}}_{1}$, and ${\mathrm{L}}_{1}$ valleys' shifts and degeneracy splittings, (2) the k=0 valence-band energy levels' shifts and degeneracy splittings, (3) the valence-band-state mixing, (4) the variation in the conduction- and valence-band-edge effective densities of state, (5) the variation in the intrinsic Fermi energy, and (6) the variation of the intrinsic-carrier concentration. It is shown that many aspects of the band structure---including the band gap, the density of states, and the position of the ${\mathrm{\ensuremath{\Delta}}}_{1}$-${\mathrm{L}}_{1}$ conduction-band-edge crossover---are each controllable through proper selection of film and substrate composition and crystallographic orientation.