Comprehensive Characterization Method for Modeling Retention Transients in NAND Flash Memory

A comprehensive characterization method and a physically based model for profiling the evolution of the trapped oxide charge ( ${Q}_{T}\text {)}$ during data retention (high-temperature baking after program/erase (P/E) cycling) was developed. This method involves monitoring the transients of threshold-voltage ( ${V}_{\text {th}}\text {)}$ shift and transconductance ( ${G}_{m}\text {)}$ recovery simultaneously. It is observed that the scatter relation between ${G}_{m}$ recovery and the corresponding ${V}_{\text {th}}$ reduction for different baking temperatures can be effectively merged over a universal curve. This curve consists of two stages. In the first stage of retention, ${V}_{\text {th}}$ decreases but ${G}_{m}$ remains almost constant. In the subsequent stage, ${G}_{m}$ increases in proportion to the decrease in ${V}_{\text {th}}$ . To describe this characteristic, two different ${Q}_{T}$ distribution regions were indispensably introduced; one is a near-interfacial (NI) region close to the Si surface and the other is a bulk oxide (BO) region. During retention, ${Q}_{T}$ in the NI region tunnels out, and simultaneously ${Q}_{T}$ in the BO region supplements it via transport mechanisms. The transition point between the first and second stages occurs when all the ${Q}_{T}$ in the BO region dissipated. Results show good agreement between measured and simulated retention transients.