Small-signal analysis of the Boltzmann equation from harmonic- and impulse-response methods

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