Analytical modeling of metal gate granularity based threshold voltage variability in NWFET

Abstract

Estimation of threshold voltage VT variability for NWFETs has been computationally 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 VT variability. Here, an analytical model is proposed to estimate VT variability caused by MGG. We extend our earlier FinFET based MGG model to a cylindrical NWFET by satisfying three additional requirements. First, the gate dielectric layer is replaced by Silicon of electro-statically equivalent thickness using long cylinder approximation; Second, metal grains in NWFETs satisfy periodic boundary condition in azimuthal direction; Third, electrostatics is analytically solved in cylindrical polar coordinates with gate boundary condition defined by MGG. We show that quantum effects only shift the mean of the VT distribution without significant impact on the variability estimated by our electrostatics-based model. The VT distribution estimated by our model matches TCAD simulations. The model quantitatively captures grain size dependence with σ(VT) 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× faster compared to commercial TCAD simulations.