[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