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

Abstract

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-Fermilevel 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 zerotemperature 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.

Landauer‐QFLPS Model for Mixed Schottky‐Ohmic Contact Two‐Dimensional Transistors

“…To overcome this, in this work a zero‐temperature‐limit algorithm with one‐shot convergence was developed in ref. [68] in order that the influence becomes negligible and the theory genuinely stands as a powerful basis for incorporating contact‐effect into the model.…”

“…The functional relations of the electron ( n ) and hole ( p ) densities with their QFLs (ε Fn and ε Fp , respectively) are implicitly determined according to the electrostatic–statistic relations (ESRs), which include three equations given as follows. [ 41,68 ]…”

“…Algorithms to solve the ESRs defined by Equations ()–() and the integrals in Equations () and () have been reported previously. [ 68 ]…”