Carrier statistics and quantum capacitance of graphene sheets and ribbons

In this work, fundamental results for carrier statistics in graphene two-dimensional sheets and nanoscale ribbons are derived. Though the behavior of intrinsic carrier densities in two-dimennsional graphene sheets is found to differ drastically from traditional semiconductors, very narrow (sub-$10nm$⁠) ribbons are found to be similar to traditional narrow-gap semiconductors. The quantum capacitance, an important parameter in the electrostatic design of devices, is derived for both two-dimensional graphene sheets and nanoribbons.