A dedicated circuit for charged particles simulation using the Monte Carlo method

Abstract

We present a dedicated integrated circuit for the simulation of charged particles based on Monte Carlo method. The Monte Carlo method leads to the solution of a particular form of the integro-differential Boltzmann equation (non-linear charge transport in semiconductors) permitting a direct statistical computation of the simulated particles distribution function in the phase space. This circuit should be the building block of a semiconductor device hardware simulator. Because of the complexity of microdynamical transport in semiconductors, the physical model used needs to be simplified in order to achieve a more simple circuit of small size. Starting from a chosen model we describe here how all the arithmetics involved in the problem has been set up for resolving the Boltzmann equation. Moreover, the binary format for the various physical quantities involved is discussed in view of the desired result accuracy: mainly, the drift velocity in a static uniform electric field taking into account all hot carrier effects.