Discrete-Trap Effects on 3-D NAND Variability – Part I: Threshold Voltage

In this two-part article we discuss the difference between a continuous and a discrete approach to trap modeling in the simulation of 3-D NAND Flash memories with polysilicon channel. In Part I we focus on threshold voltage $({\mathrm { V}}_{\mathrm { T}})$ fluctuations induced by traps and show that lower values for the average and rms ${\mathrm { V}}_{\mathrm { T}}$ arise when the discrete nature of traps is accounted for. We explain such differences in terms of a stronger percolation that leads to a lower number of filled traps in the discrete-trap case, and investigate such differences as a function of cell parameters and temperature. Finally, we compare the two approaches showing that a continuous trap model cannot reproduce the correct dependences resulting from a discrete treatment.