Layer-by-Layer Insight into Electrostatic Charge Distribution of Few-Layer Graphene

In few-layer graphene (FLG) systems on a dielectric substrate such as SiO₂, the addition of each extra layer of graphene can drastically alter their electronic and structural properties. Here, we map the charge distribution among the individual layers of finite-size FLG systems using a novel spatial discrete model that describes both electrostatic interlayer screening and fringe field effects. Our results reveal that the charge density in the region very close to the edges is screened out an order of magnitude more weakly than that across the central region of the layers. Our discrete model suggests that the interlayer charge screening length in 1-8 layer thick graphene systems depends mostly on the overall gate/molecular doping level rather than on temperature, in particular at an induced charge density >5 × 10¹² cm^-2, and can reliably be determined to be larger than half the interlayer spacing but shorter than the bilayer thickness. Our model can be used for designing FLG-based devices, and offers a simple rule regarding the charge distribution in FLG: approximately 70%, 20%, 6% and 3% (99% overall) of the total induced charge density reside within the four innermost layers, implying that the gate-induced electric field is not definitely felt by >4th layer.