Finite element modeling of retention process in high-k interpoly dielectric nanocrystal flash memories

Data retention is one of the reliability factor for flash memory devices. In this work, retention process of nanocrystal flash memory with high-k interpoly dielectrics is modeled considering inelastic trap assisted tunneling. The electronic level in nanocrystal and defect is obtained by solving Poisson and Schrodinger equation self-consistently over entire device using finite element method. Vibrational levels corresponding to optical phonon are considered in high-k. Capture and relaxation is modeled using vibronic coupling and emission is considered as quasi bound state decay from defect electronic level. Lifetime of defect level is calculated by computing complex eigenenergy of the modified inhomogeneous schrodinger equation under open boundary condition. Retention time is obtained by cumulatively adding capture and emission time for all the electrons inside nanocrystal. Cylindrical symmetry of the device is utilized in finite element method by mapping 3D problem into 2D space for enhancing computational efficiency. The result of the model is compared with the experimental data for HfO
₂
high-k interpoly dielectric flash memory.