Numerical method for solving the semiclassical Boltzmann equation on multilayer heterogeneous structures


We adapt the method developed by D.R. Penn and M. D. Stiles to implement a numerical solution to the semi-classical Boltzmann Equation on multilayer heterogeneous systems. This involves discretization of the linearized spin-independent Boltzmann Equation where the solution for each layer, considered as a bulk material, is obtained. The solutions for the different layers are then joined using boundary conditions at the interfaces to get the result for the whole multilayer structure. This method does not exploit the relaxation time approximation thus produces wider applicability especially to materials that cannot be considered to have a free-electron structure. The resulting distribution function is then used to calculate for the current density for a multi-layered material under a constant external electric field.