Analysis and Optimization of Threshold Voltage Variability by Polysilicon Grain Size Simulation in 3D NAND Flash Memory

Abstract

The impact of linear correlation between lognormal distribution grain size mean and sigma along the polysilicon channel on threshold voltage (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> ) variability has been investigated in three dimensional (3D) NAND flash. The variety of grain size mean and sigma results in the unstable V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> variability. To obtain a stable V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> distribution with various grain size mean, the grain size mean dependent V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> variability sensitivity to the grain size sigma was used to optimize the linear correlation between grain size mean and sigma via TCAD simulation. The optimized linear correlation with stable V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> variability is obtained except for the “unbalance region” affected by the combination of grain boundaries and positions with these grain size mean and sigma values resulting in the slightly shrinking V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> variability. Our results strongly suggest that this approach could guide the direction of polysilicon crystallization optimization to obtain stable V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> distribution with the predicted linear correlation between grain size mean and sigma.