Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 77, Issue 2, Pages 593-613Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1052573
Keywords
graphene; hydrodynamical models; heating effects; maximum entropy principle
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Funding
- P.R.A. of the University of Calabria
- Progetto Giovani INDAM
- project FIR, Charge Transport in Graphene and Low Dimensional Structures: Modeling and Simulation, University of Catania, Italy
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In this paper we present a hydrodynamical model for the description of the charge transport in graphene, including heating effects on the crystal lattice, and conversely the influence of crystal heating on charge transport. The state variables used for the physical system are moments of the electron, hole, and phonon occupation numbers, and their evolution equations are derived by integration from the respective Boltzmann equations. The closure of the system is obtained by means of the maximum entropy principle and all the main scattering mechanisms between charges and phonons and among phonons themselves are taken into account. Numerical simulations are presented in the case of a graphene monolayer, evaluating the influence of the optical and acoustical phonons dynamics on the current-voltage characteristics and the raise rate of the lattice temperature.
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