In this chapter we study the mechanisms for carrier transport in two dimensional graphene sheets. We demonstrate that at high carrier density, graphene's transport properties depend both on the type of impurities present and on graphene's screening properties. Treating different impurity potentials within the Boltzmann transport formalism, and including screening within the random phase approximation, we calculate the dependence of graphene conductivity on carrier density, dielectric constant of the substrate and properties of the impurity potential providing results for charged impurities, short-range scatterers, Yukawa-like impurities, Gaussian-correlated impurities and mid-gap resonant states. At low carrier density, we show that disorder causes the Dirac point to be highly inhomogeneous. When the local fluctuations in carrier density exceed the average density, the system is in the electron-hole puddle-regime. We describe the self-consistent theory to capture the ensemble averaged properties of the puddles and an effective medium theory that computes the conductivity of this inhomogeneous medium. We also briefly discuss graphene conductivity in a weak magnetic field and at finite temperature and discuss the crossover from this semi-classical picture to the regime of fully quantum phase-coherent transport. Finally, we select a few representative experiments that provide a rigorous test of the accuracy and validity of this transport theory.
Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications
Graphene Carrier Transport Theory, Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications, Springer, New York, NY, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=906994
(Accessed May 29, 2023)