Two-dimensional distributed effects in graphene SymFETs

The perfect symmetry in the band structure of graphene has motivated the investigation of single-particle inter-layer tunneling in finite area two-terminal graphene-insulator-graphene hetero-structures. Based on this transport mechanism, Zhao et al. [1] recently proposed a symmetric graphene tunneling field-effect transistor (SymFET), where current flows by resonant tunneling between an n-type graphene electrode and a p-type graphene electrode. This device was analyzed in previous works employing a single particle tunneling model and assuming a 1-D approximation of the device. However, two-dimensional effects can be important in tunneling devices based on 2-D materials and alter the predicted characteristics of such devices. In this work, we introduce a rigorous 2-D electrostatic model that takes into consideration: (a) the intra-graphene-layer potential distributions, and (b) the internal current flows through the device, as suggested in the work of Zhao et al. [1] as a proposed future element to be considered in further work.