NUMERICAL SOLUTION OF THE PERTURBED BOLTZMANN EQUATION IN FREQUENCY AND TIME DOMAINS

We present two original methods which yield the small-signal response around the d.c. bias in bulk semiconductors, using direct numerical resolutions of the perturbed Boltzmann equation. The first method operates in the frequency domain. An a.c. sinusoidal electric field perturbation superimposed to the d.c. field produces an a.c. perturbation of the distribution function which is computed at each frequency. The second method operates in the time domain. A step electric field perturbation is superimposed at time t=0 to the d.c. field. The resulting perturbations of the distribution function and of the average velocity are then computed as a function of time. These methods are applied to the case of holes in silicon at T=300 K under hot-carrier conditions and used to compute the differential-mobility spectrum. I