Electrostatics of Graphene: Charge Distribution and Capacitance

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.