Galvanomagnetic Properties of a Nonellipsoidal, Nonparabolic Band Model. I. Hall Coefficient

Abstract

The factor $r$, defined in the weak-field Hall-coefficient formula $R_0=\frac{r}{\mathrm{Ne}}$, is computed for the case of de-degenerate statistics using Morrel Cohen's nonellipsoidal, nonparabolic band model. An isotropic scattering time is assumed, but otherwise no approximations are made, despite the complexity of the energy-momentum relationship. Numerical results are presented and discussed for a wide range of values of the two parameters characterizing Cohen's model. The calculations are applied to degenerate $p$-type SnTe, for which the unusual value $r=0.6\mathrm{}$ has been found experimentally. Agreement is obtained using parameter values which correspond to a prolate dumbbell-shaped constant-energy surface. Such a shape had already been inferred from the Shubnikov-de Haas oscillations observed in SnTe.