Physical mechanisms underlying band gap narrowing

When the band gap, electron affinity or density of states in a material vary gradually with position, the carrier densities and carrier transport equations contain terms in addition to those found in the conventional Shockley model. Generally there are two effects responsible for these changes, viz., the rigid-band effect, and the density-of-states effect. Besides in heavily doped semiconductors there are modifications due to the degeneracy. This paper emphasizes the physical concepts underlying these various effects. The consequences for device analysis are discussed.