Finite Element Modeling of Fowler–Nordheim Program-Erase Process in High- $k$ Interpoly Dielectric Flash Memories

The program/erase process in floating gate (FG) flash memory devices is modeled by considering sequential quantum tunneling of electrons and taking into account quantum confinement in the channel and FG. We precisely determine location of quasi-bound or decaying quantum states in the inversion layer and in FG comprising a nanocrystal (NC) layer, and compute their lifetime by finding the complex eigenenergy of the resonance transmission problem. Self-consistent solutions to Poisson and Schrödinger equations are obtained for the quantum states of electrons in the inversion layer of MOS devices, and subsequently, sequential Fowler-Nordheim tunneling current to the spherical NCs is obtained using finite-element method considering open boundary conditions. The method described here is capable of determining the tunneling current accurately for arbitrary potential profiles, and can be applied for composite tunnel dielectric stacks. Our results show good agreement with the experimental data for high-k interpoly dielectric flash memory devices.