Abstract: A graphene device includes a graphene layer and a back gate electrode connected to apply a global electrical bias to the graphene from a first surface of the graphene. At least two graphene device electrodes are each connected to a corresponding and distinct region of the graphene at a second graphene surface. A dielectric layer blanket-coats the second graphene surface and the device electrodes. At least one top gate electrode is disposed on the dielectric layer and extends over a distinct one of the device electrodes and at least a portion of a corresponding graphene region. Each top gate electrode is connected to apply an electrical charge carrier bias to the graphene region over which that top gate electrode extends to produce a selected charge carrier type in that graphene region. Such a carbon structure can be exposed to a beam of electrons to compensate for extrinsic doping of the carbon.