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 (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{T}\text {)}$ </tex-math></inline-formula> during data retention (high-temperature baking after program/erase (P/E) cycling) was developed. This method involves monitoring the transients of threshold-voltage (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {th}}\text {)}$ </tex-math></inline-formula> shift and transconductance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${G}_{m}\text {)}$ </tex-math></inline-formula> recovery simultaneously. It is observed that the scatter relation between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${G}_{m}$ </tex-math></inline-formula> recovery and the corresponding <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {th}}$ </tex-math></inline-formula> 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, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {th}}$ </tex-math></inline-formula> decreases but <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${G}_{m}$ </tex-math></inline-formula> remains almost constant. In the subsequent stage, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${G}_{m}$ </tex-math></inline-formula> increases in proportion to the decrease in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text {th}}$ </tex-math></inline-formula>. To describe this characteristic, two different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{T}$ </tex-math></inline-formula> 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, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{T}$ </tex-math></inline-formula> in the NI region tunnels out, and simultaneously <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{T}$ </tex-math></inline-formula> in the BO region supplements it via transport mechanisms. The transition point between the first and second stages occurs when all the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{T}$ </tex-math></inline-formula> in the BO region dissipated. Results show good agreement between measured and simulated retention transients.