| A numerical model for the three-dimensional quantum-mechanical simulation of nano-crystal Flash memories has been developed. A software program using numerical algorithms has been written for the detailed steady-state simulation of p-n junction and metal-oxide-semiconductor (MOS) structure with and without semiconductor nano-crystals embedded in the gate dielectric. The program can be expanded for metal-oxide-semiconductor field-effect transistors (MOSFETs) by introducing source and drain electrodes with transport theories. Information is encoded in the threshold voltage of the device, which depends on doping, size and shape of the nano-crystal layer. Such memories are promising in terms of shorter write-erase times and lower power consumption with respect to conventional nonvolatile memories.; In general the system of partial differential equations that forms the basic semiconductor equations together with appropriate boundary conditions cannot be solved explicitly. To facilitate the simulation of nanoscale devices, new modeling approaches, which are based on the solution of the Schrodinger equation, are being sought to complement existing techniques. Using classical seven-point discretization, the differential equations at the inner points have been replaced by difference equations where only the nearest neighboring points for each of the inner points are invoked. An iterative method was developed to solve the entire nonlinear device self-consistently. The simulation results provide the electron and hole concentration, electric potential for the entire device from where various electrical properties can be deduced. The quantum effects occurring at the oxide-silicon interface under the inversion condition have been investigated with this method for the ultra thin oxide MOS structure. Comparison data of different solver routines for the Poisson and Schrodinger equations have been reported also. Results obtained from the self-consistent solution of the Poisson-Schrodinger equations on a three-dimensional grid are compared to classical simulations as well as commercial simulators. Accurate results have been obtained with significantly short computational time. |
