Impact of Quantum Mechanical Correction in Surface Potential Based Compact Model on the Drain Current of Nanoscale MOSFETs”

Abstract

Impact of the Quantum Mechanical (QM) correction in surface potential based compact model on the drain current of nanoscale MOSFETs is studied. We have considered a QM correction model to the surface potential (l/ls) based compact model of M. A. Karim and A. Haque which has been proposed recently. This model does not use the bandgap widening approach. It directly adds the correction term to the semiclassicall/ls. It accounts for the wave function penetration effect into the gate dielectric. The validity of this model has been demonstrated through the modeling of the gate C - V characteristics. In our work we have studied the effect of this correction on the drain current characteristics of nanoscale MOSFETs. The results have been compared with two other models, PSP and Pregaldiny et al. both these methods incorporate QM correction through the bandgap widening approach. QM correction to l/ls in PSP is derived from triangular well approximation while Pregaldiny uses the variational approach. When the wave function penetration effect is considered for a given semiconductor charge density the average distance of charges from the Si-gate oxide interface considering the QM effect is reduced. This leads to the lowering of l/ls also. So the models neglecting the wave function penetration effect tend to overestimate the l/ls. Hence both PSP and Pregaldiny which overestimate l/ls tend to underestimate the drain current. The Karim model shows higher current than the two existing models and predicts a lower, more accurate threshold voltage. The percentage deviation of the drain current of the QM corrections of the PSP and Pregaldiny models has been observed with respect to Karim model. The percentage deviation is around 10 - 50% at higher gate voltage but the situation is extreme around 80 - 90% in moderate inversion (VGS ~ VT ) whose effect is more pronounced. Comparison between them shows that the wave function penetration effect into the gate dielectric plays an important role in modeling the drain current of nanoscale MOSFETs.