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The aim of this work is to simulate the charge transport in a monolayergraphene on different substrates. This requires the inclusion of thescatterings of the charge carriers with the impurities and the phonons of thesubstrate, besides the interaction mechanisms already present in the graphenelayer. As physical model, the semiclassical Boltzmann equation is assumed andthe results are based on Direct Simulation Monte Carlo (DSMC). A crucial pointis the correct inclusion of the Pauli Exclusion Principle (PEP). Two differentsubstrates are investigated: SiO$_2$ and hexagonal boron nitride (h-BN). In theadopted model for the charge-impurities scattering, a crucial parameter is thedistance $d$ between the graphene layer and the impurities of the substrate.Usually $d$ is considered constant. Here we assume that $d$ is a randomvariable in order to take into account the roughness of the substrate and therandomness of the location of the impurities. We confirm, where only thelow-field mobility has been investigated, that h-BN is one of the mostpromising substrate also for the high-field mobility on account of the reduceddegradation of the velocity due to the remote impurities.

High-field mobility in graphene on substrate with a proper inclusion of the Pauli exclusion principle