A Charge Density Model of Silicon-nanowire GAA MOSFET Incoroperating the Source-drian Tunneling Effect for IC Design

One numerical compact model for one-dimensional electron charge density of n-type silicon ballistic nanowire gate-all-around metal-oxide-semiconductor field-effect transistors with ultra-short channel incorporating the source-drain tunneling is proposed. When establishing the AC model in practical device applications, compact models describing transient analysis of the carrier behaviors in the device channel are needed. When focusing on the charge density of carriers within GAA MOSFET devices, carriers transporting along the channel direction induced by the source-drain tunneling effect should also be taken into account in the subthreshold region. In this study, transmission coefficients of the source-drain tunneling effect are evaluated through expressing energy level of the lowest subband with bringing in the exact boundary conditions and using the Wentzel-Kramers-Brillouin approximation. Then, the carrier density can be derived from the charge profile in the channel using quantum statistics theory. Finally, comparisons of the calculations of the carrier densities between the source-drain tunneling and the thermionic modes in ballistic transport are demonstrated.