Valence band averages in silicon: Anisotropy and non-parabolicity

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Abstract
The density of states in the valence band of silicon has been calculated numerically using 6*6 and 30*30 k.p Hamiltonians with two different sets of band parameters. The bands are highly anisotropic and non-parabolic due to the small size of the spin-orbit splitting. The accuracy of the calculations is limited by the uncertainty in the band parameters. Because the bands are non-parabolic, the thermal average masses are temperature dependent. The thermal density of states effective mass varies by about a factor of two between low temperature and room temperature, while the thermal velocity mass is nearly temperature independent. It is shown that the dependence of the optical cross sections of deep levels on photon energy should extrapolate to 15 meV below the valence band edge, giving rise to systematic errors in determining thresholds. The additional non-parabolicity found with the 30*30 Hamiltonian is significant for optical cross sections, but not for thermal averages.