Pauli principle and the Monte Carlo method for charge transport in graphene

Abstract

An attempt to include the Pauli principle in the Monte Carlo method by also acting 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 a test case. The results are compared with those obtained with the standard ensemble Monte Carlo technique and with the updated 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.

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene

“…( 13) until ∆t is reached. The selection of the scattering type and of the final state after collisions are based on the generation of other random numbers uniformly distributed in [0, 1]; we refer the interested reader to [11], in which the inclusion of Pauli's exclusion principle is discussed as well.…”

“…A lot of studies were devoted to the understanding of its electronic properties and to the simulation methods for semiconductor applications. Particular attention was paid by Monte Carlo techniques, which were already established for semiconductor devices [1,2,3], and above all by the correct inclusion of the Pauli exclusion principle in the standard Ensemble Monte Carlo approach [4], which in graphene is no longer negligible due to its high electronic degeneracy; a new Direct Simulation Monte Carlo scheme (DSMC) was developed in [5] while in the literature [6,7,8,9] it remained open a discussion about the classical liouvillian or quantum-like interpretation of the free flight step [10], whose study was addressed in [11].…”

“…The computational modeling of phonon's anisotropy addressed in this paper together with the correct inclusion of the Pauli principle [11] and the coupling of the DSMC simulations with deterministic solutions of the phonon Boltzmann equations [12,34] can constitute a complete and coherent simulation tool for the study of electrons and phonons transport processes in graphene. Its advantages could be extended to all applications dealing with electronic devices and also to other physical phenomena when such a kind of simulation's procedures are needed.…”