Current in semiconductors with position-dependent band gap and electron affinity

When the band gap, electron affinity, or density of states in a semiconductor vary gradually with position, the expressions for the electron and hole current densities contain terms in addition to those corresponding to the conventional drift and diffusion components. These expressions are developed with emphasis on the physical interpretation of each of the additional terms and on the definition of the electrostatic potential. The expressions can be used for a variety of materials including graded heterojunctions, graded band gap semiconductors, and semiconductors with high concentrations of shallow-level impurities.