# Repeater Insertion for Multi-Walled Carbon Nanotube Interconnects
## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**14 nm Node** & **Cu** & **MWCNT 1** & **MWCNT 2** & **MWCNT 3** \\ \hline Simulated \(n_{opt}\) & 44 & 21 & 12 & 11 \\ Estimated \(n_{opt}\) & 43 & 19 & 11 & 9 \\ Estimated \(h_{opt}\) & 10 & 17 & 10 & 10 \\ \(T_{\text{min}}\) (ns) & 0.974 & 0.651 & 1.538 & 1.522 \\ \hline
**7 nm Node** & **Cu** & **MWCNT 1** & **MWCNT 2** & **MWCNT 3** \\ \hline Simulated \(n_{opt}\) & 83 & 36 & 24 & 25 \\ Estimated \(n_{opt}\) & 79 & 31 & 24 & 19 \\ Estimated \(h_{opt}\) & 8 & 12 & 11 & 7 \\ \(T_{\text{min}}\) (ns) & 2.473 & 1.303 & 1.865 & 1.890 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the simulated and estimated optimal number of repeaters, repeater size, and minimum time delay in 1000 μm-long intermediate-level Cu and MWCNT interconnects at the 14 nm and 7 nm technology nodes. Figure 6: Propagation delays versus number of repeaters for 1000-μm-long intermediate-level Cu and MWCNT interconnects. (**a**) Cu; (**b**) MWCNT 1; (**c**) MWCNT 2; and (**d**) MWCNT 3.  
process to reduce the contact resistance. Figure 8 compares the estimated and simulated values of the optimal repeater number and minimum propagation delay for the global interconnects at the 14 nm technology node. It is shown that the optimal repeater number increases linearly with increasing interconnect length. Based on the proposed fitting expressions, the minimum propagation delays of the intermediate and global interconnects are obtained as shown in Figure 9. It can be seen that the minimum propagation delay increases linearly with the length. With the minimum contact resistance, MWCNT interconnects can always provide a smaller delay than their Cu counterparts. However, as the contact resistance increases to 10 k\(\Omega\), MWCNT interconnects would lose their edge at the 14 nm technology node, but still show superior performance over Cu at the 7 nm technology node. This can be explained \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**14 nm Node** & **Cu** & **MWCNT 1** & **MWCNT 2** & **MWCNT 3** \\ \hline Simulated \(n_{opt}\) & 53 & 22 & 11 & 10 \\ Estimated \(n_{opt}\) & 51 & 19 & 12 & 9 \\ Estimated \(h_{opt}\) & 18 & 25 & 14 & 14 \\ \(T_{\text{min}}\) (ns) & 1.172 & 0.678 & 2.067 & 2.038 \\ \hline
**7 nm Node** & **Cu** & **MWCNT 1** & **MWCNT 2** & **MWCNT 3** \\ \hline Simulated \(n_{opt}\) & 95 & 41 & 25 & 23 \\ Estimated \(n_{opt}\) & 91 & 37 & 25 & 20 \\ Estimated \(h_{opt}\) & 14 & 22 & 17 & 15 \\ \(T_{\text{min}}\) (ns) & 2.828 & 1.562 & 2.776 & 2.758 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the simulated and estimated optimal number of repeaters, repeater size, and minimum time delay in 2000-\(\upmu\)m-long global-level Cu and MWCNT interconnects at the 14 nm and 7 nm technology nodes. Figure 7: Propagation delays versus number of repeaters for 2000-\(\upmu\)m-long global-level Cu and MWCNT interconnects. (**a**) Cu; (**b**) MWCNT 1; (**c**) MWCNT 2; and (**d**) MWCNT 3.  
as follows. As shown in Figure 10, at the 14 nm node, an MWCNT interconnect outperforms its Cu counterpart when the contact resistance is smaller than 3.3 k\(\Omega\). With the technology scaling to 7 nm, the maximum tolerable contact resistance of the MWCNT interconnect is increased to 10.5 k\(\Omega\). Figure 8: Optimal number of repeaters (Inset: minimum propagation delay) versus length for global-level Cu and MWCNT interconnects at the 14 nm technology node. Figure 10: Minimum propagation delay versus contact resistance for 2000-\(\upmu\)m-long global-level Cu and MWCNT interconnects. Figure 9: Minimum propagation delays versus length for (**a**) intermediate- and (**b**) global-level Cu and MWCNT interconnects. However, it is worth noting that even without the size effect and fabrication challenges at smaller nodes, the contact resistance of 3.3 k\(\Omega\) will be scaled up by 4 times from the 14 nm node to the 7 nm node.