Physics-based analytical model of quantum-mechanical electron wave function penetration into thin dielectric films and capacitance evaluation

We propose an analytical expression of the electron distribution function inside silicon and SiO2 films under the surface-accumulation condition, to simulate the capacitance of a metal-oxide-semi conductor system. We assume a three-dimensional electron gas system and discuss the penetration of the electron wave function into SiO2 or high-k material films. It is demonstrated that the penetration of the wave function into the insulator film slightly influences the, capacitance-voltage characteristics. It is also demonstrated that the penetration of the wave function into high-k materials is deeper than that into SiO2 film for identical equivalent oxide thickness (EOT).