Semiconductor current-flow equations (diffusion and degeneracy)

The correct form for the current-flow equation in semiconductors in the presence of density and temperature gradients, as well as electric fields, is derived from a perturbation solution of Boltzmann's equation. The conditions under which the various widely used approximate forms of the current-flow equation are valid are clearly discussed. A new term that occurs if the relaxation time depends on position is derived, and is shown to be comparable in magnitude to the other terms in the current-flow equation.