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

Abstract

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.

Three‐dimensional analytical modeling and performance analysis of triple material trigate silicon‐on‐insulator MOSFET

“…As the thickness of channel film is reduced below 10 nm, quantum effects give rise to strong subband splitting, and energy quantization is mainly structural along the channel thinness (z-direction) whereas charge confinement occurs due to transverse electric field. 20,21 The energy quantization reduces the inversion charge concentration in the channel and hence degrades the current drive of the device. 22 The charge distribution in the trigate MOSFET accounting for quantization effects is determined by solving two-dimensional Schrodinger's equation for envelop wave function ψ(y, z).…”

Tunneling Current Variations in Small-Sized Devices Based on a Compact Threshold Voltage Model

“…However, a one-dimension method cannot meet the requirement of threshold voltage accuracy for scaled devices. To improve the threshold voltage accuracy, two-dimensional and quasi-two-dimensional analysis methods are often used [8,9]. When solving a twodimensional Poisson equation in the depletion region utilizing a two-dimensional method, the physical meaning of model parameters is deficient due to some approximations made on boundary conditions.…”