# Mini-Review: Modeling and Performance Analysis of Nanocarbon Interconnects
## 5 Cu-Nanocarbon Interconnect
### Cu-CNT Composite Interconnect  
Generally speaking, nanocarbon and conventional metals have their own pros and cons for interconnect applications. For instance, nanocarbon has high ampacity, but their conductivity is still low due to fabrication limits. On the contrary, the fabrication and integration processes of metal interconnects are mature, but the ampacity of metals cannot satisfy the requirements [2]. [PERSON], et al. [111] attempted to advance a possible solution to this problem by co-depositing Cu with CNTs, i.e., Cu-CNT composite interconnect. It was experimentally demonstrated that Cu-CNT composite interconnect can achieve a balance between performance and reliability. This is, such Cu-CNT composite interconnect possesses a 100 times higher ampacity, but comparable conductivity than the Cu counterpart. The presence of CNTs inside Cu wire can also alleviate the electromigration void growth rate by about four times, which is due to large Lorenz number of the CNTs [112; 113]. Figure 18 shows the schematic of a Cu-CNT composite interconnect over a ground plane. In the figure, \(N\) identical CNTs are uniformly distributed inside the Cu wire. The CNTs can be SWCNTs or MWCNTs. Here, we define the CNT filling ratio as \(f_{\text{CNT}}=N\pi(D+0.31\text{ nm})^{2}/(4 WT)\), where 0.31 nm is due to the separation between carbon and Cu atoms. The p.u.l. scattering resistance of the Cu-CNT composite interconnect can be calculated as \(R=1/(\sigma_{\text{eff}}WT)\), where \(\sigma_{\text{eff}}=(1-f_{\text{CNT}})\sigma_{\text{Cu}}+f_{\text{CNT}} \sigma_{\text{CNT}}\)[114; 115]. The effective conductivity of CNTs \(\sigma_{\text{CNT}}\) is given by [116]  
\[\sigma_{\text{CNT}}\approx Fm\times\frac{4L}{\pi(D+0.31\text{ nm})^{2}}\frac{1}{Z_{\text{CNT}}} \tag{10}\]  
where \(Fm\) the metallic fraction, and \(Z_{\text{CNT}}\) is the self-impedance of an isolated CNT. Figure 17: Effective resistivity of Cu and Cu-graphene interconnects versus (**a**) temperature and (**b**) technology node [110]. Figure 18: Schematic of Cu-CNT composite interconnect. Figure 19a compares the effective resistivities of Cu, SWCNT, and Cu-SWCNT composite interconnects. Unlike the ideally packed SWCNTs discussed earlier, it is assumed that the CNT filling ratios are 0.3, 0.45, and 0.6 in the figure. It is evident that the resistivity of such sparsely distributed SWCNTs is much larger than Cu counterpart. However, co-depositing Cu with such sparsely distributed SWCNTs can reduce the resistivity. The predicted values are close to the measured data, which ranges from 2 to 2.27 \(\mu\)G [111]. Further, the time delays of Cu, SWCNT, and Cu-SWCNT composite interconnects are plotted in Figure 19b. The Cu-SWCNT composite interconnect can provide comparable performance with Cu counterpart, while the sparsely distributed SWCNTs show much worse performance due to their large resistivity. As the CNT quality may be degraded due to fabrication limits, the cases of lower value of CNT MFP are also plotted in Figure 19b. It can be seen that the Cu-SWCNT composite interconnects are much less influenced than pure SWCNTs. In summary, this paper reviewed the current status of research on nanocarbon interconnects from the modeling perspective. The electrical performances of GNR, CNT, and Cu-nanocarbon interconnects are analyzed and discussed, with their pros and cons illustrated in Table 1. Although Cu wires have been widely used in modern ICs, their resistivity increases significantly with the scaling of feature size, which is exacerbated by the influence of diffusion barrier layer. In comparison with Cu counterparts, nanocarbon interconnects including GNR and CNT possess long MFP, high ampacity, and high electromigration resistance. However, the electrical properties of horizontal graphene are susceptible to substrate. Moreover, as nanocarbons are anisotropic, both MLGNR and CNT interconnects would hinder the IC heat dissipation. This problem can be resolved by utilizing VGNR interconnects although there is still a long way to go in the fabrication methods.