A Compact Carrier Quantization Model for Nanoscale MOSFETs Simulation

Due to the advanced fabrication technology, the oxide thickness is now in the regime of 1.0 nm for nanoscale MOSFETs. The quantization effects and inversion charge density displacement away from the interface of oxide and silicon can not be neglected. The most accurate model for such problem is solving the Schrödinger-Poisson (SP) equations with proper boundary condition in 1D structure. However, for 2D device characteristics and circuit dynamics, solution of the SP equations encounters numerical difficulty and is not ready for practical applications. Various quantum correction models have been proposed for theoretical exploration and verification. In this paper we study the quantization effects and for the first time develop a corresponding charge analytical model in terms of oxide thickness and applied voltage for ultrathin oxide MOSFETs. Based on a comprehensive investigation of charge peak location, peak value, averaged charge displacement, and charge density, the successfully derived compact model accounting for the quantization effects enables fast and accurate characterization of the effective charge density in nanoscale MOSFETs. This new model has computational superiority and can be directly applied for nanoscale device and circuit simulation without solving the SP equations. Compared with the measured C-V data of an ultrathin N-MOSFET, our simulation results demonstrate the model accuracy. Key-Words: Compact Model, Quantum Mechanical Effects, Ultrathin Oxide, MOS Devices, C-V Curves