A Novel Quasi-3-D Threshold Voltage Model for Fully Depleted Quadruple-Gate (FDQG) MOSFETs: With Equivalent Number of Gates (ENG) Included

Instead of solving the three-dimensional (3-D) Poisson's equation, we present a novel quasi-3-D threshold voltage model for fully depleted quadruple-gate (QG) MOSFETs based on the minimum central potential derived from the quasi-3-D scaling equation. Accounting for short-channel effects (SCEs) on the device, the natural length of the QG FET in the scaling equation is obtained from the equivalent number of gate equation of 1/ λ
_QG
²
= 1/ λ
_DG1
²
+1/ λ
_DG2
²
, where the QG device working in x-y-z space with natural length of λ
_QG
can be broken into two equivalent double-gate (DG) FETs with natural lengths of λ
_DG1
and λ
_DG2
working in y-z and x-z planes, respectively. Numerical simulation data for threshold voltage roll-off and drain-induced barrier lowering effects (DIBL) were compared to the model to validate the formula. Among QG FETs with the same perimeters, one with a square cross section will show the worst immunity to SCEs due to the largest natural length. With the criterion of DIBL≤50 mV, an improvement of up to 30% is illustrated in the minimum channel length for the QG MOSFET in comparison to the DG MOSFET.