Electrostatics of Graphene: Charge Distribution and Capacitance

TL;DR

This paper explores how electric charge distributes in graphene, revealing size-dependent edge charge enhancement and layer effects, which help explain experimental phenomena like electron emission and doping in 2D nanostructures.

Contribution

It introduces a combined atomic model and analytical approach to analyze charge distribution and capacitance in various graphene geometries, highlighting size and layer effects.

Findings

Charge density can be enhanced up to 13 times at edges.

Edge charge enhancement increases with graphene size.

Charge enhancement ratio scales linearly with the number of layers.

Abstract

The distribution of net electric charge in graphene is investigated, using both a constitutive atomic charge-dipole interaction model and an approximate analytical solution to Laplace's equation. We demonstrate a strong size dependence of the charge distributions in finite-size, infinitely-long and multi-layered rectangular graphene sheets, respectively. We found that the charge density can be naturally enhanced up to 13 times at graphene's geometry edges. This edge charge enhancement effect becomes more significant when the length or the width of graphene increases. The charge enhancement ratio is found to follow a linear relationship with the number of layers. These results can be used to understand the newly experimentally observed electron emission, charge impurity and chemical doping phenomena in 2-dimension nanostructure.