[paper] Efficient Long-Channel MOSFET Model

Ananda Sankar Chakraborty

Efficient Long-Channel MOSFET Model 

with SPICE-enabled Lambert W Function for Universal Application

Silicon (2025): 1-10; DOI 0.1007/s12633-025-03576-1

1 ETCE, Indian Institute of Engineering Science and Technology, Shibpur (IN)

Abstract: A novel, accurate charge-based MOSFET long-channel computational model is presented, which is portable and can be used across the electrical engineering domains ranging from sensing to power electronics, both under sub-threshold as well as super-threshold regime of MOSFET operation. The proposed physics-based model can be universally used to any long-channel MOS-transistor, as it does not depend on any empirical factor and features extremely good computational efficiency. The model uses a novel two-step charge linearization, resulting into accurate drain current and charge model – valid for both the subthreshold and super-threshold regime of long-channel MOSFET operation. Another salient feature of the proposed model is a novel SPICE-compatible numerical solution strategy for the principal branch of the Lambert W function (W0(x) for {x ∈ R | x ≥ 0}). The algorithm is faster than present industry standard implementations, computationally efficient, accurate with maximum percentage error≈10−14% and therefore may be incorporated in a SPICE engine for electrical design and optimization. The proposed computationally efficient long channel MOSFET model is validated against thorough TCAD simulations upto the fourth derivative and has been found to have fast convergence along with much higher degree of accuracy compared to existing MOSFET models.

FIG: Bulk-MOSFET structure: its current (I_DS) and conductance (g_DS) vs Drain Voltage (V_DS)

(Line: proposed model, symbol: TCAD)

[paper] Compact IV Model for DG MoS2 FETs

Ahmed Mounir, Francois Lime, Alexander Kloes, Alexandros Provias, Theresia Knobloch, 

K. P. O’Brien, Tibor Grasser and Benjamin Iniguez

Compact I–V Model for Double-Gated MoS2 FETs Including Short-Channel Effects

IEEE TED, Vol. 72, No. 12, Dec 2025

DOI: 10.1109/TED.2025.3622099

Rovira i Virgili University, Tarragona (SP)
THM University of Applied Sciences, Giessen (D)
Technical University of Vienna (A)
Intel Foundry Technology Research, Hillsboro (US)

Abstract: This article presents a physics-based analytical compact model for double-gated molybdenum disulfide (MoS2) field effect transistors (FETs), incorporating key physical and short-channel effects (SCEs), such as mobility degradation and velocity saturation. The model is developed from a unified charge control model by evaluating the charge density within the 2D MoS2 layer, represented using the Lambert W function, which provides an analytical expression valid and continuous from the subthreshold to the above threshold regime. The drain current is then derived from this unified charge control model, and as a function of closed-form equations for the charge densities at the source and drain ends of the channel. Despite its simplicity, the model shows excellent agreement with experimental data for channel lengths down to 60nm, making it a powerful tool for accurately predicting the performance of downscaled devices. By including SCEs, this work extends previous modeling efforts and provides a more comprehensive framework for the simulation and optimization of 2D material-based FETs in circuit design.

FIG: Cross-sectional view of the double-gated MoS2 FET, showing the top gate oxide stack made of Al2O3 and HfO2, with the local back gate oxide consisting of HfO2. Validation of the compact model against experimental data for double-gate MoS2 FET L = 60nm (bottom line)

Acknowledgements: This work was supported in part by European Union Bayesian inference with flexible electronics for biomedical applications (BAYFLEX) under Contract 101099555 and in part by the Ministry of Science of Spain under Contract PID2021122399OB-I00

[paper] Lambert W function for nanoscale MOSFET modeling

A. Ortiz-Conde a, V.C.P. Silva b c, P.G.D. Agopian b c, J.A. Martino b, F.J. García-Sánchez a

Some considerations about Lambert W function-based nanoscale MOSFET charge control modeling

Solid-State Electronics (2025) 109080,

DOI:10.1016/j.sse.2025.109080

a Solid-State Electronics Lab, Universidad Simón Bolívar, Caracas 1080 (VE)
b LSI/PSI/USP, Universidade de São Paulo, São Paulo (BR)
c Department of Electronic and Telecom. Eng., Universidade Estadual Paulista, São João Da Boa Vista (BR)

Abstract: The unwanted low-level doping present in supposedly undoped MOSFET channels has a significant effect on charge control and Lambert W function-based inversion charge MOSFET models, as well as on subsequent drain current models. We show that the hypothetical intrinsic MOSFET channel approximation, often used to describe a nominally undoped channel, produces significant errors, even for the low-level concentrations resulting from unintentional doping. We show that the traditional charge control model, which mathematically describes the gate voltage as the sum of one linear and one logarithmic term of the inversion charge, is only valid for the hypothetically intrinsic case. However, it may still be used for nominally undoped but unintentionally low-doped channel devices within the region of operation where the majority carriers are the dominant charge. With this in mind, we present here a better approximation of the nominally undoped MOSFET channel surface potential. We also propose an improved, modified expression that describes the gate voltage as the sum of one linear and two logarithmic terms of the inversion charge. A new approximate drain current control formulation is also proposed to account for parasitic series resistance and/or mobility degradation. The new model agrees reasonably well with measurement data from nominally undoped vertically stacked GAA Si Nano Sheet MOSFETs.

FIG: The simulated transistor structural geometry and transfer characteristics of the three TCAD simulated nanosheet devices (symbols), together with the corresponding playbacks (lines) of the traditional model and modified model.

Data availability: Data will be made available on request.

Generalized EKV Compact MOSFET Model

On the Explicit Saturation Drain Current in the Generalized EKV Compact MOSFET Model

Francisco J. García-Sánchez, Life Senior Member, IEEE,

and Adelmo Ortiz-Conde, Senior Member, IEEE

IEEE TED Aug 9. 2021

DOI: 10.1109/TED.2021.3101186

*Solid State Electronics Laboratory, Universidad Simón Bolívar, Caracas 1080, Venezuela

Abstract: We present and discuss explicit closed-form expressions for the saturation drain current of short channel metal-oxide-semiconductorfield-effect transistors (MOSFETs) with gate oxide and interface-trapped charges, and including carrier velocity saturation, according to the generalized Enz-Krummenacher-Vittoz (EKV) MOSFET compact model. The normalized saturation drain current is derived as an explicit function of the normalized terminal voltages by solving the transcendental voltage versus charge equation using the Lambert W function. Because this special function is analytically differentiable, other important quantities, such as the transconductance and the transconductance-to-currentratio, can be readily expressed as explicit functions of the terminal voltages.

Fig: Comparison of simulated transfer characteristics with (red lines and symbols) and another without (black lines and symbols) radiation-induced oxide and interface-trapped charges. Calculation of V_GB versus ID_sat (lines) comes from denormalization and the explicit ID_sat versus V_GB (symbols) comes from denormalization of the proposed explicit expressions