Origin of the anomalous size-dependent increase of capacitance in boron nitride–graphene nanocapacitors

The anomalous size-dependent increase in capacitance in boron nitride–graphene nanocapacitors is a puzzle that has been initially attributed to the negative quantum capacitance exhibited by this particular materials system. However, we show in this work that the anomalous nanocapacitance of this system is not due to quantum effects but has pure electrostatic origin and can be explained by a parallel-plate (square) nanocapacitor model filled with a dielectric film characterized by a size/thickness-dependent relative permittivity. The model presented here is in excellent agreement with the experimentally measured capacitance values of recently fabricated graphene and hexagonal boron nitride nanocapacitors. The results obtained seem to suggest that the size-dependent increase of capacitance in the above-mentioned family of nanocapacitors can be explained by classical finite-size geometric electrostatic effects.