A 2D analytical electrostatics analysis for the cross-section of a FinFET (or tri-gate MOSFET) is performed to calculate the threshold voltage.The analysis results in a modified gate capacitance with a coefficient H introduced to model the effect of tri-gates and its asymptotic behavior in 2D is that for double-gate MOSFET.The potential profile obtained analytically at the cross-section agrees well with numerical simulations.A compact threshold voltage model for FinFET,comprising quantum mechanical effects,is then proposed.It is concluded that both gate capacitance and threshold voltage will increase with a decreased height,or a decreased gate-oxide thickness of the top gate,which is a trend in FinFET design.
The analytical solutions to 1D Schrdinger equation (in depth direction) in double gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non uniform potential in the channel is concerned with an arbitrary depth so that the analytical solutions agree well with numerical ones.Then,an implicit expression for electron density and a closed form of threshold voltage are presented fully comprising quantum mechanical (QM) effects.This model predicts an increased electron density with an increasing channel depth in subthreshold region or mild inversion region.However,it becomes independent on channel depth in strong inversion region,which is in accordance with numerical analysis.It is also concluded that the QM model,which barely considers a box like potential in the channel,slightly over predicts threshold voltage and underestimates electron density,and the error increases with an increasing channel depth or a decreasing gate oxide thickness.
A new approach,gate-capacitance-shift (GCS) approach,is described for compact modeling.This approach is piecewise for various physical effects and comprises the gate-bias-dependent nature of corrections in the nanoscale regime.Additionally,an approximate-analytical solution to the quantum mechanical (QM) effects in polysilicon (poly)-gates is obtained based on the density gradient model.It is then combined with the GCS approach to develop a compact model for these effects.The model results tally well with numerical simulation.Both the model results and simulation results indicate that the QM effects in poly-gates of nanoscale MOSFETs are non-negligible and have an opposite influence on the device characteristics as the poly-depletion (PD) effects do.
