▎ 摘　　要

A disorder based analytical carrier density for graphene is presented here. The carrier density, a basic property of all semiconductors, is obtained based on exponential distribution describing the potential fluctuations induced by impurities and shows good agreement with numerical results. The quantum capacitance is subsequently derived from the carrier density, with a good agreement with experimental measurements. A method for extracting the gate coupling function is also proposed, which relates the internal surface potential with the external applied gate voltage. The essential properties of graphene device physics, such as the temperature, material disorder, and surface potential dependences, are captured in these analytical equations. (C) 2016 AIP Publishing LLC.