Compact unified modeling of multigate MOSFETs based on isomorphic modeling functions

A compact analytical model is presented for the 3D electrostatics of nanoscale gate-all-around MOSFET with a square and rectangular cross sections perpendicular to the source-drain axis. The model is based on solutions of the 3D Laplace equation (subthreshold) and Poisson's equation (above threshold), where suitable 2D isomorphic modeling functions are utilized to describe the potential distribution in the cross sections. From this, the device capacitances and the drain current can be calculated in the full range of bias voltages. The model compares well with numerical calculations obtained from the ATLAS device simulator. This model can be readily extended to include double gate and trigate MOSFETS and FinFETs.