Coupled Monte Carlo–Deterministic simulation of thermal behavior of graphene on substrate

Abstract

The purpose of this paper is to study thermal effects in a graphene sheet on substrate. The temperature evolution of the phonon branches and of the crystal lattice is obtained when also the presence of the substrate is taken into account. The numerical strategy is based on the coupling of stochastic and deterministic numerical methods; Boltzmann equation for charge transport is treated by using the Direct Simulation Monte Carlo approach, whose results are treated as source terms for the phonon Boltzmann equation which is solved deterministically. The results are useful also for applications as correct design of graphene-based prototypes, when heating effects in the presence of a substrate are relevant.

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

“…For optical phonons, the Einstein approximation of constant ω LO,T O,K 's is adopted. We refer to [12] and [34] for further details. 3 Numerical results…”

“…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.…”