Analytical Modeling of Metal Gate Granularity based Threshold Voltage Variability in NWFET

TL;DR

This paper presents an analytical model to estimate threshold voltage variability in NWFETs caused by Metal Gate Granularity, significantly reducing computational effort while maintaining high accuracy compared to TCAD simulations.

Contribution

An extended analytical model for MGG-induced V T variability in cylindrical NWFETs, improving accuracy and speed over existing models and simulations.

Findings

Model matches TCAD simulation results with 6% error.

Captures grain size dependence of V T variability.

Model is 63 times faster than TCAD simulations.

Abstract

Estimation of threshold voltage V T variability for NWFETs has been compu- tationally expensive due to lack of analytical models. Variability estimation of NWFET is essential to design the next generation logic circuits. Compared to any other process induced variabilities, Metal Gate Granularity (MGG) is of paramount importance due to its large impact on V T variability. Here, an analytical model is proposed to estimate V T variability caused by MGG. We extend our earlier FinFET based MGG model to a cylindrical NWFET by sat- isfying three additional requirements. First, the gate dielectric layer is replaced by Silicon of electro-statically equivalent thickness using long cylinder approxi- mation; Second, metal grains in NWFETs satisfy periodic boundary condition in azimuthal direction; Third, electrostatics is analytically solved in cylindri- cal polar coordinates with gate boundary condition defined by MGG. We show that quantum effects only shift the mean of the V T distribution without sig- nificant impact on the variability estimated by our electrostatics-based model. The V T distribution estimated by our model matches TCAD simulations. The model quantitatively captures grain size dependence with {\sigma}(V T ) with excellent accuracy (6%error) compared to stochastic 3D TCAD simulations, which is a significant improvement over the state-of- the-art model with fails to produce even a qualitative agreement. The proposed model is 63 times faster compared to commercial TCAD simulations.