Fluctuation model of the high-frequency hopping electrical conductivity of moderately compensated semiconductors with hydrogenic impurities

A model is developed according to which a hop of an electron (or hole) between two hydrogenic donors (or acceptors) occurs only when their energy levels become equal due to thermal and/or electrostatic fluctuations in a doped crystal. The main contribution to the real part of the high-frequency hopping electrical conductivity is assumed to come from acceptor pairs in which the time of hole tunneling is equal to the half-period of the external electric field and the phase of tunneling coincides with that of the field. In this case, the imaginary and real parts of the hopping conductivity are approximately equal. The results of calculations based on this model are compared to the experimental data for p-Ge: Ga with an intermediate degree of compensation of the main doping impurity.