A generalized Einstein relation for semiconductors

The Einstein relation relates the diffusion coefficient to the mobility and is frequently used in semiconductor device analysis and design. A flux equation governing the behavior of mobile particles in semiconductor material is derived from the Boltzmann transport equation. The particles are assumed to obey quantum statistics. The flux equation provides the formal means for defining the transport parameters D and μ.A generalized Einstein relation valid for any particle density under equilibrium as well as non-equilibrium conditions is derived. The relation is given in terms of Fermi integrals and a scattering parameter. Once the scattering parameter is specified, the Einstein relation can be easily evaluated. The asymptotic limit for degenerate material is also given.