A drain current formula for two-dimensional field-effect transistors with one-shot convergence algorithm

Two-dimensional material-based field-effect transistors (2DM-FETs) exhibit both ambipolar and unipolar carrier transports. To physically and compactly cover both cases, a quasi-Fermi-level phase space (QFLPS) approach was proposed, but it still involves complicated integration operations. This article aims at improving the numerical efficiency of the QFLPS model by several orders of magnitude so that it can readily be implemented in a standard circuit simulator. We first rigorously derive the integral-free formula for the drain-source current to achieve this goal. Besides computationally benign, it explicitly gives the correlation terms between the electron and hole components. Secondly, to work out the boundary values required by the new expressions, we develop an algorithm for the channel electrostatic potential based on the zero-temperature limit property of the 2DM-FET system. By calibrating the model with the realistic device data of black phosphorus and monolayer molybdenum disulfide FETs, the algorithm is tested against practical cases. Two orders of magnitude improvement in time consumption can be achieved compared with the integral-form QFLPS approach, and it is even four orders of magnitude faster than the traditional continuity-equation based approach.