A computational model of thermoelectric and thermomagnetic semiconductors

We present a theoretical and computational framework for calculating transport properties of thermoelectric and thermomagnetic semiconductors and relating them to measurements. Assuming a multiple-band model with generally nonparabolic band structures, we numerically integrate the Boltzmann equation with a relaxation time approximation to obtain the electric conductivity and the Hall, Seebeck, Nernst, and Righi-Leduc coefficients under magnetic fields. These "bare" (microscopic) transport coefficients are used to calculate quantities that can be compared with measurements by numerically solving macroscopic differential equations in two dimensions with appropriate boundary conditions. It is shown that, for finite-geometry samples, there is considerable coupling between thermoelectric and thermomagnetic effects, which can make the magnetic-field dependence profile of measured values quite different from that of bare values.