Physics-Based Analytical Model of Quantum-Mechanical Electron Wave Function Penetration into Thin Dielectric Films for Capacitance Evaluation

摘要

We propose an analytical expression of election distribution function inside silicon and SiO{sub}2 film in the surface-accumulation condition to simulate capacitance of MOS system. We assume three-dimensional electron gas system and discuss the penetration of electron wave function into SiO{sub}2 or high-k materials film. It is demonstrated that penetration of wave functions into the insulator film slightly influences C-V characteristics. It is also demonstrated that the penetration of wave function of high-k materials is deeper than that of SiO{sub}2 film for identical equivalent oxide thickness (EOT).