Abstract-For nanoscale interconnection, the scattering effect will soon become prominent due to scaling. It will increase the effective resistivity and thus interconnection delay significantly. Existing works on scattering effect are mostly performed using very complicated physics-based models, while the scattering impact on nanoscale VLSI interconnect and optimization have not been studied. In this paper, we first present a simple, closed-form scattering effect resistivity model based on extensive empirical studies on measurement data. Then we apply the proposed scattering model to revisit several classic wire sizing/shaping problems. Our experimental results show that if the scattering effect is ignored or characterized inaccurately beyond 65nm, the resulting interconnect optimization might be way off from the real optimal solution, e.g., up to 70% underestimation of the delay, or 20x oversizing. We also obtain the new closed-form wiresizing functions with consideration of scattering effects. I INTRODUCTIONS the feature size continues to shrink, the lateral dimension of conductors will be approaching the mesoscopic regime in which the diameter of the wire is in the range of or smaller than the mean free path of the electrons ( , about 40nm for copper at room temperature), and the electrical resistivity of metallic conductors is increased compared to the resistivity of bulky metal. The earliest work on this dates back to 1938, when an expression for the resistivity of metal thin films (1-dimensional) was derived by Fuchs [1]. Later on it was extended to 2-dimensional by the FS model [2] for thin/narrow wires. Basically, the FS model accounts for the surface scattering. Later on, the MS model [3] was developed to incorporate the grain boundary scattering, which also increases the wire resistivity. For both surface and grain boundary scattering effects, very complicated quantum mechanical effects can be applied to obtain the empirical parameters in FS or MS model [4,5].While MS and FS models have been tested with measurement data for polycrystalline nanowires [6][7][8], very few experimental results on copper (Cu) film or interconnect have been reported until recently, e.g., the size effect of copper thin film was studied in [9], and the resistivity of copper wires with widths under 50nm was reported in [10][11][12][13]. The key observation is that the resistivity of copper wires will increase significantly as the wires width decreases [9][10][11][12][13][14]. While exploratory structures such as carbon nanotubes are being studied as possible replacement of copper interconnect [15][16][17], at least by 22nm technology, it is not likely that copper will be replaced by carbon nanotube or other materials [15]. There are also efforts in manufacturing improvement to partially reduce the scattering effect of copper wires [18,19], but even so the scattering effect can no longer be ignored as the technology continues to scale down.A popular method to reduce the interconnection delay is wire sizing. In fact, there have be...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.