Band-Edge Calculations for Bismuth and Bismuth-Antimony Alloys

The Lax ellipsoidal-nonparabolic (ENP) and the Cohen nonellipsoidal-nonparabolic (NENP) dispersion relations have been used to calculate the band-edge parameters for Bi_1-xSbₓ (0≤x≤0.18) for a number of plausible band models. These calculations provide a self-consistent picture of the band-edge configuration of the Bi-Sb alloy system which is compatible with reported experimental data. The minima which have been observed in the thermoelectric-power-vs-temperature curves for a range of Bi-Sb alloys are accounted for by our calculations. We find that the semimetal-semiconductor transition point lies in the range $0.07<x<0.10$ and that the magnitude of the direct L-point gap Eg varies with temperature at a rate 0.1<(∂Eg∂T)<0.35 meV/^∘{}K, the most likely value being 0.19 meV/^∘{}K. For semimetallic alloys with 0≤x≤0.04, we find that 15≤mₕ*mₑ*≤26 for the ENP model, and 9≤mₕ*mₑ*≤15 for the NENP model, where mₕ* and mₑ* are, respectively, the density-of-states effective masses of holes in the T-point band and electrons in the L-point band. Corresponding ratios calculated for T>0^∘K and for semiconductive Bi-Sb alloys are less accurate, but are consistent with the results for the semimetallic alloys at T=0^∘K.