Compact Modeling of Cross-Sectional Scaling in Gate-All-Around FETs: 3-D to 1-D Transition

We model the effects of cross-sectional radius scaling on ${C}$ – ${V}$ and ${I}$ – ${V}$ characteristics of gate-all-around FETs (GAAFETs), capturing the continuous transition from a 3-D electron system to a 1-D electron system. We have obtained computationally efficient models for effective mass, bandgap, and subband energies as functions of the cross-sectional radius and gate voltage based on simple approximate analytic expressions. Together, they provide a compact model for VLSI circuit simulation, especially for analog and RF circuits that will be seriously affected by the new humps and peaks in ${C}$ – ${V}$ and ${I}$ – ${V}$ introduced by the subbands. The model has been validated with ${k}\cdot {p}$ -based technology computer aided design simulations as well as measured data. To the best of our knowledge, this is the first compact model capturing cross-sectional size-dependent dimensional crossover (3-D to 1-D) in ${I}$ – ${V}$ and ${C}$ – ${V}$ for GAAFETs.