Two-dimensional models for quantum effects on short channel electrostatics of lightly doped symmetric double-gate MOSFETs

Analytical Verilog‐A compatible 2D model including quantum short channel effects and confinement for the potential, threshold voltage and the carrier charge sheet density for symmetrical lightly doped double‐gate metal‐oxide‐semiconductor field effect transistors (MOSFETs) is developed. The proposed models are not only applicable to ultra‐scaled devices but they have also been derived from 2D Poisson and 1D Schrödinger equations including 2D electrostatics, in order to incorporate quantum mechanical effects. Electron and hole quasi‐Fermi potential effects were considered. The models are continuous and have been verified by comparison with COMSOL and BALMOS numerical simulations for channel lengths down to 7 nm at 1 nm oxide thicknesses; very good agreement within ±5% has been observed for silicon thicknesses down to 3 nm