Statistics for a Semiconductor with an InSb-Type Valence Band

InSb is a semiconductor which has a linear term in its highest-lying valence-band energy-wave-vector relationship, with the net result that the valence band has an extremum at a position other than at $k=0\mathrm{}$. The effect of the linear term on the hole density, density-of-states mass, conductivity, and conductivity mass has been calculated. Each of these quantities has been evaluated by a series expansion in the extremum energy and is accurate to approximately 0.3%. Both the hole density and the density-of-states mass have a shallow maximum followed by a rapid decrease as the magnitude of the reduced extremum energy is increased. The conductivity and conductivity mass are qualitatively the same. When the calculations are applied to InSb, it is found that the linear term is important only at low temperatures. This conclusion is consistent with the experimentally determined band parameters.