Modeling of Threshold Voltage Distribution in NAND Flash Memory: A Monte Carlo Method

Abstract

NAND flash reliability (both endurance and retention) degrades with the scaling of NAND flash memory technology and the introduction of multilevel cell (MLC) and triplelevel cell (TLC) technologies. As a result, stronger error correction code (ECC) methods are required in the solid-state drive application, especially for MLC and TLC flash memory devices. Modeling of the threshold voltage (Vt) distribution in the NAND flash memory can make the ECC simulations more effective and efficient. In this paper, we show a semiphysical and Monte Carlo method to generate a reallike V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> distribution by mimicking the NAND flash programming and data retention (DR) processes. Probability distributions used in the Monte Carlo method are obtained by the measurements of the NAND devices and data interpolation or extrapolation. Simulations by this model can obtain reallike V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> distribution for any given Program/Erase cycle and DR time. Excellent results have been obtained and confirmed by comparing the simulations with the measured data from 16-nm NAND flash devices.