Anisotropic transport for parabolic, non-parabolic, and linear bands of different dimensions

We have developed a robust analytical methodology for modeling the anisotropic transport distribution function, which can be then used to describe various transport properties of anisotropic systems, including the electrical conductivity, carrier mobility, Seebeck coefficient, and thermal conductivity. Our methodology has considered the general cases for 3-, 2-, and 1-dimensional systems with parabolic, non-parabolic, and linear dispersion relations. Calculations are made using both the relaxation time approximation and the mean free path approximation. We have found that the Onsager relation can be violated under certain conditions. Furthermore, the methodology developed in the present work is compared with the traditionally used numerical methodology.