Quantum mechanical effects on the threshold voltage of surrounding-gate MOSFETs

In this work, we investigate analytically quantum mechanical (QM) effects on the threshold voltage (VTH) shift of the surrounding-gate (SG) metal-oxide-semiconductor field-effect transistors (MOSFETs). We show how VTH is influenced by QM effects with the considerations of (110)-silicon (Si) orientation and (100)-Si orientation. Both doped and undoped models are presented. The analytical results of the undoped model are compared with those obtained by Yu et al., and good agreement is observed. We show how VTH is influenced with the doping level. When the radius of an SG MOSFET is small (<5 nm), the VTH shift will be significant, and one should be careful in the use of the device with an extremely small silicon body radius. We find that at very high doping levels (>1018 cm−3), the VTH shift will be large.