## 3 Analysis of Program and Erase Window
### Program Window Effect
When the area of the gate is reduced compared to the substrate, the effective program voltage decreases in the space area due to a decrease in the fringing field, causing a decrease in the electron concentration, especially in the gate edge area. Therefore, to maximize the effect of reducing the gate edge electron concentration, it is important to make the gate edge shape as right-angled as possible rather than rounding it, as shown in Figure 4a,b. Figure 4c compares quantitative e-trapped charge values by cutting the a-a' of Figure 4a,b. Even though the ON pitch is the same, there is a clear difference in the electron concentration in the edge area due to the gate edge rounding effect at the 2 nm level. Thus, as the ON mold pitch decreases, it becomes necessary to closely examine the structural shape of the edge area in contact with the oxide and precisely control the related processes. For example, modifying the material composition of the silicon nitride layer to control the etching rate can be a key solution for creating angled corners [11]. During the CVD deposition process of the nitride material in the ON (oxide/nitride) mold formation, adjusting the flow rate of SiH\({}_{4}\) can vary the composition ratio of the nitride material adjacent to the oxide. This adjustment increases the etching rate of the adjacent nitride material during wet etching, thus facilitating the creation of angled corners. These methods are practical solutions for forming the desired corner shapes while reducing process complexity. Figure 3: Electron-trapped charge distribution in charge trap layer during program operation in (**a**) reference, (**b**) Lg scaling, (**c**) Ls scaling, and (**d**) both Lg/Ls scaling. (**e**) Comparison of e-trapped charge in CTL by cutting a-a’ area in (**a,b**). Meanwhile, as confirmed in Figure 2a,b, it can be seen that the threshold voltage decreases even in the Ls scaling structure, although to a lesser extent compared to Lg scaling. To analyze the cause of program speed reduction in the Ls scaling structure, the e-trapped charge according to the Ls change was compared to when Lg was fixed, as shown in Figure 5a,b. Figure 5b is the result of a quantitative comparison of the electron-trapped charge by cutting a-a' of the CTL in Figure 5a. Similar to the decrease in Lg, it shows that as Ls decreases, the e-trapped charge distribution becomes narrower. Figure 5c shows the electric field value confirmed by cutting the b-b' area in Figure 5a. As the Ls value decreases, the influence of the pass voltage applied to the adjacent WL on the electric field of the selected WL increases. Therefore, the program voltage on the selected WL becomes more concentrated in the cell area of the selected WL, which forms a narrow distribution of e-trapped charges in the charge trap layer of the selected WL. On the other hand, when Ls is larger, the program voltage applied to the selected WL is distributed toward the surrounding WL, showing a relatively wide distribution. Thus, it can be inferred that when Ls decreases, the programmed Vth is read as smaller due to the relatively narrow distribution of electrons. Additionally, we examined how the program would change if the program voltage applied to the selected WL was as high as 22 V. Figure 5d shows the change in the programmed Vth with an increased program voltage applied to the selected WL during Ls scaling. The results show that as the program voltage increases, the reduction effect of the programmed Vth due to Ls reduction decreases. Figure 5e confirms the e-trapped charge distribution in the CTL when programmed at 22 V. As seen in Figure 5a, with 17 V programming, the electron concentration distribution is still narrow when scaling Ls compared to the reference. This difference in the distribution of electron concentration in the space region will have a greater impact on the change in channel resistance during the read operation, so the difference in the programmed Vth is expected to be maintained or the gap may widen further.