In this work, fundamental results for carrier statistics in graphene2-dimensional sheets and nanoscale ribbons are derived. Though the behavior ofintrinsic carrier densities in 2d graphene sheets is found to differdrastically from traditional semiconductors, very narrow (sub-10 nm) ribbonsare found to be similar to traditional narrow-gap semiconductors. The quantumcapacitance, an important parameter in the electrostatic design of devices, isderived for both 2d graphene sheets and nanoribbons.
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