Modeling Quantum Effects on MOSFET Channel Surface Potential

Quantum mechanical (QM) effects are playing a significant role in MOSFET (metal-oxide-silicon field-effect transistor) device channel surface potential characteristics due to the ever shrinking feature size such as thin gate dielectric (below 4nm). An increase of the channel surface potential from the classical result due to the QM effects at strong inversion is reported in the simulation results of [1, 2]. In a recent paper, [3], we derived the QM correction analytical models for the device inversion charge and currentvoltage (I-V) characteristics. These models are suitable for applications in SPICE (simulation program with integrated circuit emphasis) simulator. The correction formulae are derived from the density-gradient (DG) model, [4-6], using asymptotic methods [710]. However due to insufficient information in the DG model concerning boundary conditions, in [3] we used the asymptotic outer charge density surface potential parameter, qs w , as a fitting parameter in comparing our final analytical I-V model with the numerical data. In this paper we extend the work of [3] and derive a compact analytical surface potential model with QM effects for a device operating at strong inversion. This new model gives excellent results compared with the numerical data.