Dynamical modeling of transport in MOS structures containing silicon nanocrystals for memory applications

A compact model that can be used to reproduce both quasi-static and dynamic characteristics of basic MOS cells with embedded Si-nc is presented. The structure is modeled through a device-like complex matrix of tunnel junctions, resulting in a time-dependent non-linear system of differential equations that is numerically solved, including calculation of the capacitance matrix, analytical tunneling expressions (direct and Fowler-Nordheim) for electrons/holes, and derivation of the effective tunneling area. The threshold evolution is calculated by monitoring the charge at each Si-nc as a function of time. The model is successfully validated against experimental data, showing its applicability to predict program/erase characteristics of nanocrystal memories as well as threshold voltage bit-to-bit dispersion as a consequence of geometrical non-uniformities in the nanocrystal layer position and/or gate areal coverage.