Theory of carrier density in multigated doped graphene sheets with quantum correction

TL;DR

This paper presents an exact, efficient quantum capacitance model for calculating spatially varying carrier density in multigated doped graphene sheets, accommodating complex geometries and doping profiles.

Contribution

It introduces a novel exact solution for carrier density in doped graphene with quantum corrections, applicable to arbitrary gating geometries and doping configurations.

Findings

Exact solution matches self-consistent Poisson-Dirac method

Enables fast computation of carrier density and quantum capacitance

Applicable to complex gating geometries and doping profiles

Abstract

The quantum capacitance model is applied to obtain an exact solution for the space-resolved carrier density in a multigated doped graphene sheet at zero temperature, with quantum correction arising from the finite electron capacity of the graphene itself taken into account. The exact solution is demonstrated to be equivalent to the self-consistent Poisson-Dirac iteration method by showing an illustrative example, where multiple gates with irregular shapes and a nonuniform dopant concentration are considered. The solution therefore provides a fast and accurate way to compute spatially varying carrier density, on-site electric potential energy, as well as quantum capacitance for bulk graphene, allowing for any kind of gating geometry with any number of gates and any types of intrinsic doping.