Landauer equation in three-dimensional amorphous materials

Abstract

We use the Boltzmann transport equation to calculate the three-dimensional (3D) version of the Landauer equation for incoherent electrons diffusing in a slab of amorphous material. We use the P-1 approximation to calculate the multiple-scattering transmission coefficient as a function of the diffusion coefficient. The 3D transmission coefficient is, apart from numerical coefficients, similar to that for 1D. The result is valid only for positions far away from the boundaries and for slabs having a thickness much greater than one mean free path.