Current-voltage characteristics of a graphene nanoribbon field-effect   transistor
  We present an analytical device model for a field-effect transistor based on a heterostructure which consists of an array of nanoribbons clad between the highly conducting substrate (the back gate) and the top gate controlling the source-drain current. The equations of the model of a graphene nanoribbon field-effect transistor (GNR-FET) include the Poisson equation in the weak nonlocality approximation. Using this model, we find explicit analytical formulas for the spatial distributions of the electric potential along the channel and for the GNR-FET current-voltage characteristics (the dependences of the source-drain current on the drain voltages as well as on the back gate and top gate voltages) for different geometric parameters of the device. It is shown that the shortening of the top gate can result in a substantial modification of the GNR-FET current-voltage characteristics. 
V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji