Effect of temperature on the validity of the einstein relation in heavily doped semiconductors

An analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility ratio of the carriers in such semiconductors. It is found that, with increasing temperature from relatively low values, the ratio first increases in a nonlinear manner and then decreases till, at high temperatures, it approaches its value corresponding to the non-degenerate condition resulting in a peak over a narrow range of temperatures.