Analytical Modeling of the Subthreshold Electrostatics of Nanoscale GAA Square Gate MOSFETs

An analytical model is presented of the 3-D subthreshold electrostatics of low-doped nanoscale squaregate MOSFETs operating in the subthreshold domain. The model is based on a solution of the 3-D Laplace equation utilizing the four-fold symmetry of the cross sections perpendicular to the channel axis and assuming parabolic potential distributions in the directions perpendicular to the gates for the central regions. Near source and drain other functional forms are used to precisely account for the transition to a flat potential at the two contacts. From the resulting electrostatics, capacitances, drain current, and scaling properties are obtained. The model compares very well with numerical calculations obtained from the ATLAS device simulator.