1978 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 57, NO. 8, AUGUST 2010 Modeling Issues and Performance Analysis of High-Speed Interconnects Based on a Bundle of SWCNT Alessandro Giustiniani, Vincenzo Tucci, Member, IEEE, and Walter Zamboni Abstract—The effects of the uncertainties associated with the transverse pattern of carbon nanotubes (CNTs) of the conducting type in a semiglobal interconnect based on a densely packed CNT bundle are investigated. The effectiveness of the insertion of a vari- able number of repeaters along the interconnect and the influence of the contact resistances between CNTs and external circuitry are also studied. The numerical computations are performed by using a multiconductor transmission line model in which the per-unit length parameters are accurately derived from a macroscopic fluidlike description of the conduction phenomena in CNTs. Index Terms—Carbon nanotubes (CNTs), CNT bundles, high frequency, interconnects, nanotechnology, repeaters, single-walled CNT (SWCNT). I. I NTRODUCTION D URING THE LAST years, carbon nanotube (CNT) outstanding properties (huge current-carrying capability, high thermal conductivity, and high thermal and mechanical stability [1]) motivated the large effort in the performance analysis and future development of CNT-based interconnects [2]–[12]. The CNTs may be single-walled CNTs (SWCNTs, i.e., only one graphene shell) or multiwalled CNTs (MWCNTs, i.e., nested tubes). While MWCNTs always behave as metallic conductors, the SWCNTs can be either conducting (metallic) or semiconducting, depending on their chirality. The most promis- ing interconnect solutions allowing to fulfill the aggressive size shrink for Very Large Scale Integration (VLSI) circuits foreseen by the International Technology Roadmap for Semiconductors [13] are based on bundles of SWCNTs and on MWCNTs. Adequate circuit models, such as transmission line (TL) models, have been proposed in order to analyze the nanoin- terconnect performances in different operating conditions. The development of circuit models is obviously based on a macroscopic description of the electron transport phenomena [14]–[17]. Manuscript received January 13, 2010; revised April 30, 2010; accepted May 3, 2010. Date of publication June 28, 2010; date of current version July 23, 2010. This work was supported in part by the European Union within the project “Carbon nAnotube Technology for High-speed nExt-geneRation nano-InterconNEcts (CATHERINE)” 216215 and in part by the Università degli Studi di Salerno FARB funds. The review of this paper was arranged by Editor M. Reed. The authors are with the Dipartimento dell’Ingegneria dell’Informazione ed Ingegneria Elettrica (DIIIE), Università degli Studi di Salerno, 84084 Fisciano, Italy (e-mail: wzamboni@unisa.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2010.2050836 Fig. 1. Basic structure of the nanointerconnect. A semiclassical and very effective macroscopic description of the electron transport is the “fluid model” approach: the electrons are considered as a 2-D electron gas confined to a plane and neutralized by an inert uniform rigid positive plane background [18], [19]. The study of small perturbations around the equilibrium point allows deriving a macroscopic constitu- tive relationship that is useful to be coupled with Maxwell’s equations [12], [20]. From Maxwell’s equation, TL models are simply derived for SWCNT [21] and SWCNT bundles [22], and the validity limits of the macroscopic models are clearly stated in terms of CNT size and frequency of interest. In this paper, some key aspects, having both theoretical and practical implications, are considered for a nanointerconnect (see Fig. 1) realized with a densely packed bundle of SWCNTs: 1) the influence of the distribution on the nanointerconnect cross section of the CNTs of the conducting type and 2) the effects of the insertion of a variable number of repeaters along the interconnect length. As far as issue 1 is concerned, it seems reasonable to assume that only one-third of the CNTs in the bundle is metallic [4], [8]. Moreover, it is a common practice to assume as fixed their distribution on the cross section (for example, a uniform random distribution) when performing computations. Indeed, the uncertainties introduced by the manufacturing process may lead to patterns of conducting CNTs that are different from those considered, as well as to unknown parasitic contact resis- tance. Moreover, the proximity between adjacent conductors, particularly in densely packed bundles, requires an accurate computation of the capacitive coupling among conducting CNTs, e.g., [2]. This computation is strictly correlated with the conducting CNT pattern. All the aforementioned reasons could compromise the validity of the estimation of the nanoin- terconnect time delay (either derived directly from simplified time-domain simulations or indirectly from the bandwidth, as shown in Section IV-B). In particular, in such interconnects, it is reasonable to expect a 50% time delay of the order of tens of picoseconds. For what concerns issue 2, the investigation of the possible benefits due to the insertion of repeaters along the interconnect 0018-9383/$26.00 © 2010 IEEE