Diffusivity-mobility ratio for heavily doped semiconductors

Abstract

For heavily doped semiconductors, the diffusivity-mobility ratio is shown to be dependent on the Thomas-Fermi screening length squared. Within the Thomas-Fermi approximation and by means of the Sommerfeld expansion, we show that the diffusivity-mobility ratio at finite temperatures can be expressed as a series expansion of some function of the density of states. Furthermore, we show that the diffusivity-mobility ratio, in extremely degenerate case, is the same from the empirical result. We present numerical calculations of the diffusivity-mobility ratio as a function of net carrier concerntration, by taking n-type heavity doped GaAs and using Kane's density of states as an example.