A SPICE Compact Model for Ambipolar 2-D-Material FETs Aiming at Circuit Design

Abstract

We report a charge-based analytic and explicit compact model for field effect transistors (FETs) based on two-dimensional materials (2DMs), for the simulation of 2DMbased analog and digital circuits. The device electrostatics is handled by invoking 2D density of states and Fermi-Dirac statistics, that are later combined with Lambert-W function and Halley's correction, so to eventually obtain explicit expressions for the electron and hole charges, which are exploited in the calculation of drift-diffusion currents for both carriers. Further, the charge model is extended to obtain characteristics of 2DMbased negative capacitance FETs. The model is benchmarked against experimental MoS2 FET measurements, and experimental ambipolar characteristics of narrow band-gap materials such as black phophorous. Its soundness for SPICE circuit-level simulations is also demonstrated.

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

“…However, this method omits the realistic Coulomb interaction between electrons and holes coexisting in the channel, which results in coupling terms in the electrostatics equations. On account of this issue, Ahsan21 [29] chooses to discard the terms, reducing the model back to Ygd20 again (in the meaning that they share the surface potential model). They justify the approximation by claiming that the coupling term is nearly eliminated by the strong negative exponential dependence on bandgap.…”

“…However, this topic actually has less been touched. Besides ZTL method reported in this work, another frequently reported method is Halley's method [28,29,40]. In contrast with ZTL method, Halley's method mainly cares about the iterative formula for a general purpose, rather than tuning initial guess for a specific system, thus employing less physical benefit than ZTL does.…”

“…The as-derived equations ( 12)-( 16) contain polylogarithm functions, which can be approximated by the standard Chebyshev rational polynomial technique achieving a relative error accuracy of up to 10 −10 on a global scale [39]. It is worth noting that some previous works adopted a truncated Taylor's expansion method [26,29] or empirical estimation method [40].…”

“…Without detailed research on the coupling relationship, certain pragmatic methods have to be adopted to overcome this problem, such as the equivalent circuit model [27], which equates ambipolar FETs to the parallel connection of n-type and p-type transistors or simply ignoring the QFL splitting that should exist [28]. Although an article intentionally discussed this issue [29], an ansatz of simply discarding the coupling term was adopted without any further explanations.…”

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

“…[41] The QFLPS theory features ambipolar integrity and diagram representability compared with the early reported driftdiffusion formula-based models. [61][62][63][64][65][66][67] Ambipolar integrity means that the Coulomb coupling between electrons and holes in a semiconductor system is effectively included by the quasi-equilibrium approximation (QEA) derived from the QFLPS theory, which was usually missed in previous works. Simply discarding the terms can yield significant difference compared with the exact continuity equation-based solutions.…”