2-D threshold voltage model for short-channel MOSFET with quantum-mechanical effects

A threshold condition different from the classical one is proposed for MOSFET with quantum effects, by means of self-consistent numerical solution of the Schrdinger's and Poisson's equations, and thus an accurate 1-D threshold-voltage model is obtained with good agreements between simulated results and measurement data. Based on this 1-D model, an accurate 2-D quantum-modified threshold-voltage model for small-scale MOSFET is developed by solving the quasi-2D Poisson's equation and taking short-channel effects and quantum-mechanical effects into consideration. The model can also be used for simulation of electrical properties and design of structural parameters for deep-submicron MOSFETs with high-k materials as gate dielectric.