# Analysis of Channel Potential Recovery According to the Back Pattern in 3D NAND Flash Memory
## 3 DCP Recovery Time  
At the end of the verify operation, when the WL voltage decreased from \(V_{\text{pass}}\) to zero, the amounts of down-coupling voltage in WL 7, 8, and 9 were modeled as follows [15]: \begin{table}
\begin{tabular}{c c} \hline \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 (3D NAND) & 80 nm \\ Poly-Si channel thickness (3D NAND) & 10 nm \\ Selected WL (WL\({}_{\text{select}}\)) & WL8 \\ \(V_{hl}\) & 0.7 V \\ \(V_{\text{pass}}\), \(V_{\text{r}nd}\) & 6 V \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Device parameters and bias condition used in the TCAD simulation. Figure 1: **(a)** 3D NAND string structure used in TCAD simulation with 16 WLs, string select line (SSL), ground select line (GSL) and common source line (CSL). Values of the device parameter are listed in Table 1. **(b)** Cell pattern for each WL. **(c)** The timing diagram of DCP and recovery time. Each voltage bias condition is also listed in Table 1.  
\[\Delta V_{down-couple}\coloneqq-V_{th,neighbrocells}\]  
Figure 2a shows the channel potential recovery for each pattern. The channel potential, which dropped to \(-V_{th,neighbrocells}\), recovered over time in all patterns. In addition, channel potential recovered quickly in the early stage. However, the amount of potential recovery was not very different for each pattern. The variation of potential recovery from 0 s is shown in Figure 2b. The lower the programmed state of all adjacent WLs was, the faster the channel potential recovery in the early stages of recovery was. The amount of potential recovery was similar in all patterns after a sharp change. The amount of potential recovery after 1 us, 5 us, and 10 us compared to that after 100 ms is shown in Figure 2c. P1, P2, and P3 conditions mean that adjacent WLs were programmed to P1, P2, and P3, respectively. The recovery percentage of P1 in the early stage compared to the total recovery amount was 12.4%, which was larger than that of the other patterns. The amount of potential recovery after 5 us in the P1 pattern and after 10 us in pattern P2 and P3 are similar. This indicates that the boosting efficiency could be increased by adjusting recovery time before the program operation according to the pattern. The channel potential dropped owing to the DCP, being recovered as time elapsed when the trapped holes recombined with electrons while the holes diffused toward the center of the string [24]. In addition to electron-hole pair (EHP) recombination, a decrease of the electron concentration of the floating channel and the hole diffusion from the adjacent WLs region can cause the recovery of channel potential [25; 26; 27; 28; 29; 30; 31]. Therefore, we analyzed this phenomenon by using the EHP recombination in the floating channel and the carrier diffusion between the floating channel and the adjacent WLs region by the patterns. The electron concentration of the floating channel at 0 s and after 5 us are shown in Figure 3a,b, respectively. When the adjacent WLs were programmed in a low state, the  
Figure 2: (**a**) Channel potential recovery in the floating channel for each pattern. (**b**) Variation of potential recovery for each pattern compared to 0 s with linear and log plots. (**c**) The amount of potential recovery after 1 us, 5 us, and 10 μs and the percentage of it compared to that of 100 ms.  
electron concentration of the floating channel was low. In addition, the electron concentration of the floating channel decreased in all patterns. Furthermore, electron diffusion from the floating channel to the adjacent WLs region occurred as a result of the electron concentration of the floating channel being higher than that of the adjacent WLs. Diffusion is a phenomenon wherein carriers move from a relatively high concentration to a low concentration [29; 30; 31]. The flow of the carrier caused by diffusion is called flux.