## 3 Results and Discussions  
Figure 2a shows the transfer characteristics with different \(\kappa\) values of spacers while keeping their thickness of 10 nm. The \(\kappa\) values of spacers are 3.9, 7.0, 9.0, 15.0, and 25.0, which correspond to SiO\({}_{2}\), Si\({}_{3}\)N\({}_{4}\), Al\({}_{2}\)O\({}_{3}\), Y\({}_{2}\)O\({}_{3}\), and HfO\({}_{2}\), respectively [28]. In the subthreshold region (0.0 V \(<\) V\({}_{\text{GS}}\)\(<\) 0.35 V), drain current is independent of \(\kappa\) values because tunneling mainly occurs between the source and tunnel region under the gate, without the effects of the fringing field through spacers. From V\({}_{\text{GS}}\) = 0.35 V, drain current starts to increase with increasing \(\kappa\) value. Improved current drivability can be also observed in the output characteristics as shown in Figure 2b. At V\({}_{\text{DS}}\) = 1.0 V, drain current with the spacer \(\kappa\) = 25.0 is enhanced more than two times compared to that with the spacer \(\kappa\) = 3.9. In order to check the performance improvement by high-\(\kappa\) spacer, BTBT rates are analyzed in the channel region underneath the spacer. Figure 3a describes the two-dimensional (2D) contour on the electron tunneling rate with the spacer of \(\kappa\) = 3.9 and 25 at V\({}_{\text{DS}}\)/V\({}_{\text{GS}}\) = 1.0 V/1.0 V. In case of \(\kappa\) = 3.9, the tunneling occurrence is negligible in the channel under the spacer region (dashed red square). That means silicon oxide does not give strong fringing field enough to improve tunneling probabilities. On the other hand, high tunneling rates can be seen by increasing the fringing field under the spacer region when the spacer of \(\kappa\) = 25 is used. Figure 3b indicates the averaged electron tunneling rate in the specific region under the spacer. In case of \(\kappa\) = 25, tunneling induced by the fringing field starts to occur from V\({}_{\text{GS}}\) = 0.31 V and continues to increase. However, when \(\kappa\) values become smaller, tunneling is generated by the fringing field at the larger V\({}_{\text{GS}}\). For \(\kappa\) = 3.9, it even starts from V\({}_{\text{GS}}\) = 0.9 V by the low fringing field. The difference of the tunneling turn-on voltage between \(\kappa\) = 3.9 and \(\kappa\) = 25 is almost 0.6 V. Based on these results, it is obvious that high-\(\kappa\) spacer is more suitable for low power and high performance devices. Averaged electric fields under the spacer are also checked according to different \(\kappa\) values in Figure 3c, where the electric fields linearly increase as a function of V\({}_{\text{GS}}\), regardless of \(\kappa\) values. Compared to the electric field with \(\kappa\) = 3.9, the absolute electric field is more than doubled for \(\kappa\) = 25, leading to higher current drivability. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Definition** & **Parameter** & **Value** \\ \hline Gate Length & \(\text{L}_{\text{gate}}\) & 100 nm \\ Equivalent Oxide Thickness & \(\text{T}_{\text{ox}}\) & 1 nm \\ Spacer Thickness & \(\text{L}_{\text{spc}}\) & 0–10 nm \\ Spacer Dielectric Constant & \(\kappa_{\text{spc}}\) & 3.9–25 \\ Body Thickness & \(\text{T}_{\text{body}}\) & 20 nm \\ Tunnel Region Thickness & \(\text{T}_{\text{tunnel}}\) & 4 nm \\ Drain Underlap Length & \(\text{L}_{\text{under}}\) & 10 nm \\ Tunnel Region Doping & \(\text{N}_{\text{tunnel}}\) & \(1\times 10^{17}\) cm\({}^{-3}\) \\ Source Doping & \(\text{N}_{\text{source}}\) & \(2\times 10^{20}\) cm\({}^{-3}\) \\ Drain Doping & \(\text{N}_{\text{drain}}\) & \(1\times 10^{20}\) cm\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structure dimensions used in technology computer-aided design (TCAD) simulation. Figure 3: (**a**) Two-dimensional (2D) contour mapping of electron tunneling rate at V\({}_{\rm{GS}}\) = 1.0 V for the spacers with \(\kappa\) = 3.9 and \(\kappa\) = 25. (**b**) Averaged electron tunneling rate, and (**c**) averaged electric field at V\({}_{\rm{DS}}\) = 1.0 V in the channel region under the spacer.