Auto-correlation of velocity-fluctuations and frequency-dependent diffusion constant for hot electrons

Abstract

A method has been developed for determining the auto-correlation functions of the fluctuations in the transverse and the parallel components of hot carrier-velocity in a semiconductor by Monte Carlo simulation. The functions for electrons in InSb are determined by this method for applied electric fields of 50 V/cm, 75 V/cm, and 100 V/cm. With increasing value of the time interval the transverse auto-correlation function falls nearly exponentially to zero, but the parallel function falls sharply to a negative peak, then rises to positive values and finally becomes zero. The interval beyond which the auto-correlation function is zero and the correlation time are also evaluated. The correlation time is found to be approximately 1.6 times the relaxation time calculated from the chord mobility. The effect of the flight sampling time on the value of variance of the displacement, is investigated in terms of the low frequency diffusion constants, determined from the variation of the correlation functions. It is found that the diffusion constants become independent of the sampling time if it is of the order of one hundred times the relaxation time. The frequency-dependent diffusion constants are calculated from the correlation functions. The transverse diffusion constant falls monotonically with frequency for all the field strengths studied. The parallel diffusion constant has similar variation for the lower fields (50 V/cm and 75 V/cm) but it has a peak at about 44 GHz for the field of 100 V/cm.