The Einstein relation94 is one rela

The Einstein relation94 is one relation between the conductivity and Fermi level properties (in this case the density of states ρ(E) and the diffusion constant D, both evaluated at EF). The Landauer formula4 [Eq. (1.22)] is another such relation (in terms of the transmission probability at the Fermi level rather than in terms of the diffusion constant).The Einstein relation (1.11) for an electron gas at zero temperature follows on requiring that the sum of the drift current density −σE/e and the diffusion current density−D∇ns vanishes in thermodynamic equilibrium, characterized by a spatially constant electrochemical potential μ: