Abstract
The attempt to include the Pauli principle in the Monte Carlo method by acting also on the free flight step and not only at the end of each collision is investigated. The charge transport in suspended monolayer graphene is considered as test case. The results are compared with those obtained in the standard Ensemble Monte Carlo technique and in the new Direct Simulation Monte Carlo algorithm which is able to correctly handle with Pauli's principle. The physical aspects of the investigated approach are analyzed as well.
Highlights
The Monte Carlo approach is nowadays widely used in simulations of charge transport in semiconductor devices
It can be noted that the Pauli principle is always fulfilled in the NEMC case for each value of the particle number nP, while the numerical distribution function obtained with the standard ensemble Monte Carlo (SEMC) approach is compatible with the Pauli principle only for nP 8 × 104
In the presence of an applied electric field E, the mean energy and velocity calculated with the SEMC and NEMC approaches are in good agreement, while they are totally different with the free-flight-based Monte Carlo (FFMC) approach
Summary
The Monte Carlo approach is nowadays widely used in simulations of charge transport in semiconductor devices. When the simulations involve degenerate materials, the inclusion of the Pauli principle becomes essential; to this aim, Lugli and Ferry [4] improved the EMC method and included the Pauli principle by means of a rejection technique at the end of each scattering process. With this procedure the charge distribution can exceed the maximum value of 1, leading to unphysical results. An important issue which we address in this paper arises when degenerate materials are considered In this case, there is an ongoing debate in the literature about whether the Pauli principle should be applied to the free-flight step or not.
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