# Inhibited Channel Potential of 3D NAND Flash Memory String According to Transient Time
## 3 Results  
The advantage of NLSB is that the potential of the selected WL channel is higher than that of the unselected WL channel. However, Figure 3 confirms that the selected WL channel potential decreases over time. Figure 3 shows the channel potential changing over time after the NLSB phenomenon. Time(t) was measured at t = 0 s, 30 ms, 100 ms, 300 ms, and 1 s. Here, (t = 0 s) was set as the time at which the program pulse was applied, and the channel potential over time was observed. In the results in Figure 3a-c, the channel potential is the highest when the time is 0 s. Additionally, the channel potential gradually decreases over time. Eventually, the channel potential reaches its lowest value at 1 s. However, the rate at which the channel potential decreases in Figure 3a-c is different. The rate at which the channel potential decreased was the fastest in Figure 3c, whereas that in Figure 3a was the slowest. In Figure 3c, the selected WL channel potential became like unselected WL, but Figure 3a showed little change compared to Figure 3c, with a difference of approximately 1V. Figure 3d is a graph showing the \(\Delta\) potential of Figure 3a-c. The graph in Figure 3d confirms that, the higher the \(V_{th}\) of the adjacent cell becomes, the faster the channel potential decreases. \begin{table}
\begin{tabular}{c c} \hline
**Quantity** & **Value** \\ \hline Gate length (WL) & 40 nm \\ Gate length (SSL, GSL) & 150 nm \\ Gate spacing & 30 nm \\ Gate dielectrics (O/N/O) & 4/8/8 nm \\ Channel hole diameter & 80 nm \\ Poly-Si channel thickness & 10 nm \\ Selected WL & WL8 \\ \(V_{CC}\) & 2 V \\ Doping (Arsenic/Boron) & \(1\times 10^{20}/\text{cm}^{3}/1\times 10^{18}/\text{cm}^{3}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Device parameters used in the simulation. During NLSB, the electrons from the floated channels gather in the selected WL channel because of the potential difference. However, the gathered electrons spread out over time. Figure 4 shows the results 0 s and 100 ms after NLSB occurred at P1 and P3. This figure shows the differences in the electron concentration of the selected WL, observed at P1-P3 during the same time, result from the difference in the concentration of electrons trapped in the nitride and the holes in the spacer. The electrons trapped in nitride attract holes in the spacer and channel. These spacers and channel holes attract electrons in the selected WL channel. Owing to the influence of the holes in the channel and in the spacer, the electrons gathered under the selected WL channel spread to WL7 and WL9. There are more electrons in the nitride of P3 than in P1, resulting in P3 attracting more holes to channels and spacers than P1. Therefore, the electrons in the selected WL of P3 spread faster than those of P1. As a result, the channel potential of P3 decreases faster than that of P1 owing to the faster electron movement. Figure 3: NLSB effect analysis according to transient time (**a**) \(V_{th}\) = P1, (**b**) \(V_{th}\) = P2, (**c**) \(V_{th}\) = P3 and (**d**) is the \(\Delta\) potential of selected WL at P1, P2, and P3. This can be proved in the electron concentration graph in Figure 5. Figure 5 is a graph of electron concentration according to transient time. Figure 5a shows no change in electron concentrations in the WL7 and WL9 channels, which increase over time for P1. However, Figure 5b shows that, for P3, the electrons spread to both sides over time, and the electron concentration in the WL7 and WL9 channels increase over time. Through this result, it can be confirmed that the explanation in Figure 4 is correct. Additionally, in Figure 5b, it can be seen that the electrons spread to WL7 and WL9, but not to the adjacent WL. This movements of electrons can be better confirmed when only one side of the WL is programmed. In Figure 5b, the \(V_{th}\) of WL7 and WL9 are E, and the other cells are P3. So, electrons spread to WL7 and WL9, which do not have electrons in nitride, and do not spread to the other cells that have electrons.