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.