TEMPERATURE INFLUENCE ON THE GENERALIZED EINSTEIN RELATION FOR DEGENERATE SEMICONDUCTORS WITH ARBITRARY BAND STRUCTURES

Abstract

We present a systematic study of the temperature influence on the generalized Einstein relation for degenerate semiconductors with different band structures. The conventional Einstein relation is still a good approximation at very high temperatures for most carrier concentrations but becomes invalid at low temperatures for highly degenerate semiconductors. As the temperature rises, higher energy bands with small minimum energy separations (e.g., from GAMMA band to L band) and large density-of-state effective masses will have a larger fraction of carriers, because the minimum energy separations become comparable to the thermal energy. Thus, from 500 K to 1200 K, in n-type GaAs and n-type Ge, we observe kinks in the D/mu versus carrier concentration curves. However, no such kinks are observed in n-type Si due to its large minimum energy separations. Similarly, p-type Ge and p-type GaAs show no kinks, because the energy of the spin-orbit splitting in these semiconductors is large compared to the thermal energy.