A Dedicated Circuit for Charged Particles Simulation Using the Monte Carlo Method


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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, associated with a Poisson's equation solver. 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 one-particle 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.

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