From Poisson Analysis to Padé Approximation: An Electrostatic Saturation Current Correction Factor for MOSFETs Under Minimized Secondary Effects

The classical one-dimensional long-channel equation for a MOSFET’s drain current can show very noticeable errors when applied to nanoscale devices, reaching a peak percentage error of 31.78% at a channel length of 50 nm. This paper investigates the discrepancy between the classical long channel equation and technology computer aided design (TCAD) simulations in the saturation region over a range of channel lengths and oxide thicknesses. As device dimensions vary, the threshold voltage rolls off. To counter this effect, the overdrive voltage was kept at a value of 0.436 V through the use of a TCAD simulation algorithm that continuously adjusted the gate bias. This approach helped to control variations in overdrive voltage, which usually resulted from threshold voltage roll-off, and, in turn, helped to facilitate the investigation of geometry dependent discrepancies. A very high saturation velocity was used to reduce the influence of carrier velocity saturation on the simulated drain current, allowing geometry dependent electrostatic deviations between the classical model and TCAD simulated drain current to be investigated with reduced interference from this transport limitation. A dimensionless correction factor which multiplies the drain current directly is developed from a quasi-static Poisson equation and represented using a Padé [4/4] approximation, with its coefficient calibrated against the TCAD result. This new correction factor greatly reduces the percentage error across every channel length. The resulting expression for the correction factor is pole free and avoids singularities for any device dimension.