Effective masses and sum rules in strained Si/Ge structures

Valence-band effective masses in strained Si/Ge semiconductor structures have been calculated using empirical pseudopotentials with spin-orbit coupling. By separating different terms within the effective-mass sum rule, it is shown explicitly that numerous couplings via the momentum operator between orbital components across the fundamental band gap play a crucial role in establishing the strained-layer effective masses. The neglect of these matrix element effects, involving conduction states lying within about 8 eV from the band edge, can lead to significant errors in determining the valence-band effective masses. These results indicate the necessity for a reappraisal of the formulation of effective-mass-type models employing a limited number of bands as applied to strained-layer heterosystems because the important couplings are not just those between states lying close to the band edges.