Full Analytical Evaluation of the Einstein Relation for Disordered Semiconductors

We present a simple analytical method for the evaluation of the Einstein relation for disordered semiconductors with exponential distribution of tail states. The proposed analytical method is based on the binomial expansion theorems, and the calculation result permitted an accurate evaluation of the validity of the analytical approximation, as well as further improvement of the theoretical formulas. The accuracy and the efficiency of the obtained formulas of the Einstein relation for disordered semiconductors are demonstrated with the comparison of the numerical and analytical results. The formulas can be used to analyze the experimental results.