3.7 Quantum Mechanical Effects

Effects that arise due to structural and electrical confinement in the multi-gate structures are dealt in this section. The threshold voltage shift arising due to bias-dependent ground state sub-band energy is already accounted for in the surface potential calculations (See Section 3.4). The reduction in width and bias-dependence in effective oxide thickness due to the inversion charge centroid being away from the interface is taken care of here. The section is evaluated only if $QMTCENIV_i$ or $QMTCENCV_i$ is non-zero. While a single equation with parameters $ETAQM$, $QM0$ and $ALPHAQM$ govern the motion of charge centroid w.r.t. bias, two different quasi-switches are introduced here for the purpose of effective width calculation and effective oxide thickness calculation. $QMTCENIV_i$ uses the above expression to account for the effective width in I−V calculations and $QMTCENCV_i$ uses the same expression for the effective width and effective oxide thickness for C−V calculations. The pre-calculated factor MTcen is for the geometric dependence (on $TFIN/HFIN/R$) of the charge centroid in subthreshold region.