Effect of random defect density fluctuations on the Fermi level in highly compensated semiconductors

A statistical model of random defect density fluctuations is proposed to determine the Fermi level distribution in compensated semiconductors. The model is based on the assumption for Gaussian defect distribution. It is shown that highly compensated materials convert into multi-component systems, containing regions with different types of conductivity. Thus an effective potential barrier in the sample appears, which is related to the degree of compensation. It is shown that this model is appropriate for materials which contain inhomogeneously distributed shallow as well as deep levels. The model is illustrated for the case of semi-insulating GaAs:Cr at 300 K.