Unified analytical modeling of GAA nanoscale MOSFETs

An analytical model is presented for the 3D subthreshold electrostatics of low-doped gate-all-around MOSFETs with circular and square cross sections. The model is based on a solution of the 3D Laplace equation utilizing the high symmetry of the devices and assuming near-parabolic potential distributions in the directions perpendicular to the gates for the central regions. To account for short-channel effects, additional functional forms are used near source and drain. High precision is made possible by utilizing auxiliary boundary conditions obtained from a conformal mapping analysis. Combining this model with a long-channel approximation for strong inversion, the drain current in the full range of bias voltages is calculated. The model compares very well with numerical calculations obtained from the ATLAS device simulator.