Small-signal ac conductivity and velocity overshoot in semiconductor materials

We consider the response of a semiconductor to small perturbations in the applied electric field away from a steady uniform dc field. Both ac conductivity and time-dependent velocity response are calculated for a relaxation model described by moment equations for the average electron velocity and energy. Our model involves only three parameters determined by the energy and momentum relaxation rates and their derivatives. Two of them, the momentum relaxation rate Γm which sets the frequency and time scales and the ratio (dJ/dE)/(J/E), are easily obtained from dc conductivity measurements. The third can be obtained from a measurement of the value of the peak ac conductivity in the case where the peak occurs at a nonzero frequency. The form of the conductivity is explored as a function of these parameters, and consistency tests are suggested to determine the applicability of the model. The cutoff frequency where the ac conductivity drops to half its zero-frequency value is shown to be determined largely by the dc parameters Γm and (dJ/ dE)/(J/E). Precise restrictions on the parameters are given for the existence of velocity overshoot in the presence of the dc bias field. It is shown that observation of a peak ac conductivity at a nonzero frequency always implies the presence of velocity overshoot. The cutoff frequency for a spatially uniform system is shown to be insensitive to the presence of velocity overshoot.