A modeling of the retention characteristics of non-volatile memories embedded with metallic nanoparticles

In this paper, three dimensional calculations of the potential distribution inside previously fabricated non-volatile memory (NVM) devices consisting of platinum nanoparticles (NPs) embedded in the SiO₂/HfO₂ matrix were performed to examine whether the barrier for tunneling is seriously affected by the discharge of one electron from one of the metallic NPs. To do this, the Poisson equation inside the device was numerically solved and the device was simulated by a standard finite elements method with the assumption that the NPs are spherical and approximately arranged in a simple square lattice. First order tetrahedral elements have been used while, by exploiting the problem symmetries and using 80,000 unknowns, the expected discretization error is less than 1%. A band diagram was constructed from the potential calculations. Results show that when all four spheres in the unit cell are charged, the potential on the spheres is 0.14 eV, and when one sphere discharges, this value changes by 45 meV. The calculations also show that the barrier changes by approximately 1%, hence, almost constant. This leads theoretically to an exponential decrease in the charge and an exponential increase in the number of neutral NPs. Calculations of the transmission coefficient agree well with the decay constant T.