Monte-Carlo method to analyze the small signal response of the semiconductor carriers

An approach for analysis of the small signal response of the carriers in semiconductors is presented. The integro-differential equation, describing the phenomenon in the time domain is transformed into a Fredholm integral equation of the second kind. The response of the carrier system to a small signal of a general time dependence can be calculated by the knowledge of the response to an impulse signal, defined by a delta function in time. For an impulse signal, the obtained integral equation resembles the basic structure of the integral form of the time dependent (evolution) Boltzmann equation. Due to this similarity a physical model of the impulse response process is developed. The model explains the response to an impulse signal in terms of a relaxation process of two carrier ensembles, governed by a Boltzmann equation. A Monte-Carlo method is developed which consists of algorithms for modeling the initial distribution of the two ensembles. The numerical Monte-Carlo theory for evaluation of integrals is applied. The subsequent relaxation process can be simulated by the standard algorithms for solving the Boltzmann equation. The presented simulation results for Si and GaAs electrons serve as a test of the Monte-Carlo method and demonstrate that the physical model can be used for explanation of the small signal response process.