Crosstalk analysis of carbon nanotube bundle interconnects
 Kailiang Zhang^{1}Email author,
 Bo Tian^{1},
 Xiaosong Zhu^{1},
 Fang Wang^{1}Email author and
 Jun Wei^{1, 2}
DOI: 10.1186/1556276X7138
© Zhang et al; licensee Springer. 2012
Received: 28 November 2011
Accepted: 17 February 2012
Published: 17 February 2012
Abstract
Carbon nanotube (CNT) has been considered as an ideal interconnect material for replacing copper for future nanoscale IC technology due to its outstanding current carrying capability, thermal conductivity, and mechanical robustness. In this paper, crosstalk problems for singlewalled carbon nanotube (SWCNT) bundle interconnects are investigated; the interconnect parameters for SWCNT bundle are calculated first, and then the equivalent circuit has been developed to perform the crosstalk analysis. Based on the simulation results using SPICE simulator, the voltage of the crosstalkinduced glitch can be reduced by decreasing the line length, increasing the spacing between adjacent lines, or increasing the diameter of SWCNT.
Keywords
interconnects carbon nanotube bundles simulation crosstalkIntroduction
Due to electron scattering on copper wire surface and grain boundary, the resistivity of a copper wire will increase rapidly when the interconnect feature size becomes smaller than 45 nm [1]. As a result, the time delay of the transmission signal will increase dramatically, which will restrict the circuit performance. Besides, as the integration density of interconnects increases, crosstalk issues will be the concerns. The crosstalk issue directly affects the circuit performance. To address the issues, carbon nanotube (CNT) interconnects have recently been proposed as ideal substitutes in future interconnect designs [2]. CNT can be metallic or semiconducting [3], depending on their chiralities, and metallic CNTs are the preferred candidates for interconnect applications [4–6].
Although a few studies on the crosstalk noise of CNTbased interconnections have been reported [7, 8], the influencing factors are not fully understood. Crosstalk is the unexpected voltage noise interference due to the electromagnetic coupling of adjacent transmission lines when the signal propagates in the transmission lines. It is well known that crosstalk between interconnects may cause signal delay and glitch that may be propagated to the output of a receiver, which can cause a logic error at the output of the receiving device [9]. Therefore, to understand the influencing factors which affect the crosstalk voltage of singlewalled carbon nanotube (SWCNT) interconnects and how to decrease them are particularly important.
In this paper, the main factors affecting the crosstalk of SWCNT bundle interconnects were studied, including the influence of the SWCNTs position when their length is fixed, which was proposed for the first time. Firstly, we considered three coupled SWCNT interconnects to form a standard parallel wire architecture over a ground plane by calculating the coupling capacitances between adjacent interconnects; this model was then extended to the SWCNT bundle by calculating the corresponding parameters.
Methodology
RLC equivalent circuit parameters of SWCNT
The resistance of a SWCNT contains imperfect contact resistance (R_{C}) which is in the range of 0 to 120 KΩ, quantum resistance (R_{Q}) (R_{Q} = h/4e^{2}, and scattering resistance (R_{S}) per unit length (R_{S} = h/(4e^{2}·λ_{CNT})), where h is Planck's constant, e is the charge of an electron, and λ_{CNT} is the mean free path length.
where D is the diameter, y is the distance away from a ground plane treating the CNT as a thin wire, and v_{F} is the Fermi velocity.
For D = 1 nm and y = 1 μm, L_{M} ≈ 1.5 pH/μm. Clearly, the magnetic inductance can be neglected.
Crosstalk modeling for CNT bundle interconnects
In practice, CNT bundles are closer to actual application than individual CNT. Here, the crosstalk modeling is being established.
where N_{H} is the number of rows in the interconnect bundle, N_{W} is the number of columns, and N_{CNT} is the total number of CNTs. Since a SWCNT bundle consists of several individual SWCNT in parallel, the formulas of the resistance, inductance, and capacitance of a SWCNT bundle have been listed in previous papers [12].
Results and discussion
The crosstalk voltage in a SWCNT bundle depends on several factors, such as line length, the position when the length is fixed, spacing between SWCNTs, etc., which will be discussed using the RLC model, respectively. Simulations are performed using SPICE simulator.
Conclusions
The crosstalk problems of using SWCNT bundle as an interconnect candidate in the future design of integrated circuits have been explored in this paper. Equivalent distributed circuit parameter models of SWCNT bundle are obtained firstly, and then crosstalk issues about parallel SWCNT bundle interconnects are analyzed based on ITRS. The simulations show that significant reduction in crosstalk noise can be achieved by decreasing line length, setting the appropriate position when the length is fixed, increasing spacing between adjacent lines, increasing the diameter of SWCNT as well as selecting the appropriate frequency.
Abbreviations
 CNT:

carbon nanotube
 SWCNT:

singlewalled carbon nanotube.
Declarations
Acknowledgements
This work is supported by the National Natural Science Foundation of China (grant no. 60806030), the Tianjin Natural Science Foundation (grant nos. 08JCYBJC14600 and 10SYSYJC27700), and the Tianjin Science and Technology Developmental Funds of Universities and Colleges (grant nos. ZD200709 and 20100703).
Authors’ Affiliations
References
 Naeemi A, Meindl JD: Design and performance modeling for singlewalled carbon nanotube as local, semiglobal and global interconnects in gigascale integrated systems. IEEE Trans Electron Devices 2007, 54: 26–37.View ArticleGoogle Scholar
 Li H, Xu C, Srivastava N, Banerjee K: Carbon nanomaterials for nextgeneration interconnects and passives: physics, status, and prospects. IEEE Trans Electron Devices 2009, 56: 1799–1821.View ArticleGoogle Scholar
 Maffucci A, Miano G, Villone F: Performance comparison between metallic carbon nanotube and copper nanointerconnects. IEEE Trans Advanced Packaging 2008, 31: 692–699.View ArticleGoogle Scholar
 Ngo Q, Petranovic D, Krishnan S, Cassel AM, Ye Q, Meyyappan JLM, Yang CY: Electron transport through metalmultiwall carbon nanotube interfaces. IEEE Trans Nanotechnol 2004, 3: 311–317. 10.1109/TNANO.2004.828553View ArticleGoogle Scholar
 Li HJ, Lu WG, Li JJ, Bai XD, Gu CZ: Multichannel ballistic transport in multiwall carbon nanotubes. Physical Rev Lett 2005, 95: 1–4.Google Scholar
 Choi WB, Bae E, Kang D, Chae S, Cheong B, Ko J, Lee E, Park W: Aligned carbon nanotubes for nanoelectronics. IoP J Nanotechnol 2004, 15: 512–516.View ArticleGoogle Scholar
 Naeemi A, Meindl JD: Performance modeling for single and multiwall carbon nanotubes as signal and power interconnects in gigascale systems. IEEE Trans Electron Devices 2008, 55: 2574–2582.View ArticleGoogle Scholar
 Li H, Yin WY, Banerjee K, Mao JF: Circuit modeling and performance analysis of multiwalled carbon nanotube interconnects. IEEE Trans Electron Devices 2008, 55: 1328–1337.View ArticleGoogle Scholar
 Pu SN, Yin WY, Mao JF, Liu QH: Crosstalk prediction of single and doublewalled carbonnanotube (SWCNT/DWCNT) bundle interconnects. IEEE Trans Electron Devices 2009, 56: 560–568.View ArticleGoogle Scholar
 Rossi D, Cazeaux JM, Metra C, Lombardi F: Modeling crosstalk effects in CNT bus architectures. IEEE Trans Nanotechnol 2007, 6: 133–145.View ArticleGoogle Scholar
 Burke PJ: Luttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes. IEEE Trans Nanotechnol 2002, 1: 129–144. 10.1109/TNANO.2002.806823View ArticleGoogle Scholar
 Das D, Rahaman H: Crosstalk analysis in carbon nanotube interconnects and its impact on gate oxide reliability. 2nd Asia Symp Quality Electronic Design, Penang 2010, 272–280.View ArticleGoogle Scholar
 ITRS2007. [http://www.itrs.net/Links/2007ITRS/2007_Chapters/2007_PIDS.pdf]
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