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

TL;DR

This paper models charge transport in graphene on different substrates using a semiclassical approach, emphasizing the importance of the Pauli Exclusion Principle and substrate roughness effects on mobility.

Contribution

It introduces a stochastic model for impurity distance in charge-impurity scattering, improving the accuracy of high-field mobility predictions in graphene.

Findings

h-BN substrate enhances high-field mobility compared to SiO2.

Random impurity distance accounts for substrate roughness effects.

Inclusion of PEP is crucial for accurate charge transport simulation.

Abstract

The aim of this work is to simulate the charge transport in a monolayer graphene on different substrates. This requires the inclusion of the scatterings of the charge carriers with the impurities and the phonons of the substrate, besides the interaction mechanisms already present in the graphene layer. As physical model, the semiclassical Boltzmann equation is assumed and the results are based on Direct Simulation Monte Carlo (DSMC). A crucial point is the correct inclusion of the Pauli Exclusion Principle (PEP). Two different substrates are investigated: SiO$_2$ and hexagonal boron nitride (h-BN). In the adopted model for the charge-impurities scattering, a crucial parameter is the distance $d$ between the graphene layer and the impurities of the substrate. Usually $d$ is considered constant. Here we assume that $d$ is a random variable in order to take into account the roughness of the substrate and the randomness of the location of the impurities. We confirm, where only the low-field mobility has been investigated, that h-BN is one of the most promising substrate also for the high-field mobility on account of the reduced degradation of the velocity due to the remote impurities.