Scattering mechanisms and Boltzmann transport in graphene

TL;DR

This paper investigates various scattering mechanisms affecting graphene's electrical conductivity using Boltzmann transport theory, providing analytical models and highlighting Coulomb scattering's dominance at low carrier densities.

Contribution

It introduces a comprehensive analysis of scattering effects in graphene, including Coulomb, short-range, and surface roughness, with analytical expressions for conductivity dependence on substrate dielectric constant.

Findings

Coulomb scattering dominates near the Dirac point.

Conductivity scales as n^1 for Coulomb, n^0 for short-range, and n^-2 for surface roughness.

Analytical formulas relate conductivity to substrate dielectric properties.

Abstract

Different scattering mechanisms in graphene are explored and conductivity is calculated within the Boltzmann transport theory. We provide results for short-range scattering using the Random Phase Approximation for electron screening, as well as analytical expressions for the dependence of conductivity on the dielectric constant of the substrate. We further examine the effect of ripples on the transport using a surface roughness model developed for semiconductor heterostructures. We find that close to the Dirac point, \sigma \sim n^\beta, where \beta=1,0,-2 for Coulomb, short-range and surface roughness respectively; implying that Coulomb scattering dominates over both short-range and surface roughness scattering at low density.