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When combined with graphene, hexagonal boron nitride (h-BN) is an idealsubstrate and gate dielectric with which to build metalh-BN|graphenefield-effect devices. We use first-principles density functional theory (DFT)calculations for Cu|h-BN|graphene stacks to study how the graphene dopingdepends on the thickness of the h-BN layer and on a potential differenceapplied between Cu and graphene. We develop an analytical model that describesthe doping very well, allowing us to identify the key parameters that governthe device behaviour. A predicted intrinsic doping of graphene is particularlyprominent for ultrathin h-BN layers and should be observable in experiment. Itis dominated by novel interface terms that we evaluate from DFT calculationsfor the individual materials and for interfaces between h-BN and Cu orgraphene.

Electrostatic doping of graphene through ultrathin hexagonal boron nitride films