A note on the semiconductor current flow equations

The current flow equations for nondegenerate and degenerate semiconductors at low temperature are discussed in terms of the Boltzmann transport equation. It is shown that the diffusion current in an inhomogeneous but isotropic semiconductor must be expressed as q.D(r). ∇n(r) where n(r) is the carrier (electron) concentration and D(r) is a spatially varying diffusion "constant." Some formulas which have been given for semiconductor device parameters, i.e., the emitter efficiency for heavily doped transistors when expressed as a ratio of resistivities, could be rigorously developed if the diffusion current were expressible as q.∇[D(r)n(r)]. However, this form is not consistent with the transport equation from which D(r) can be defined and evaluated.