Optimized Hydrodynamical Model for Charge Transport in Graphene

Starting from the Boltzmann equations and employing the moment method, hydrodynamical models for charge transport in suspended monolayer graphene have been devised. In particular in Camiola and Romano (J Stat Phys 157:1114-1137, 2014), Luca and Romano (Ann Phys 406:30-53, 2019), Luca and Romano (Int J Non-Linear Mech 104:39-58, 2018), Luca and Romano (Ann Phys 406:30-53, 2019), Luca et al. (J Comput Theoret Trans 49(7), 2020), and Camiola et al. (Charge transport in low dimensional semiconductor structures, the maximum entropy approach. Springer, 2020) closure relations have been obtained by adopting the Maximum Entropy Principle (MEP). Stemming from the kinetic equations, some physical parameters appear in the production terms such as the acoustic phonon, the optical phonon and the K-phonon coupling constants. Their values have been estimated by experimental data and fundamental approach, e.g. the density functional theory. However, they depend on the modelling of the energy band and scattering terms. Here, we try to improve the hydrodynamical model proposed in Camiola and Romano (J Stat Phys 157:1114-1137, 2014) by an optimisation of the parameters above through a minimisation of the difference between velocity and energy, found with the considered hydrodynamical models and the direct solution of the Boltzmann equation obtained with a Discontinuous Galerkin (DG) method (Coco et al., Ricerche mat 66:201-220, 2017; Majorana et al., Commun Comput Phys 26, 114-134, 2019).