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

摘要

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