Carbon nanotube (CNT) can be considered as an emerging interconnect material in current nanoscale regime. They are more promising than other interconnect materials such as Al or Cu because of their robustness to electromigration. This research paper aims to address the crosstalk-related issues (signal integrity) in interconnect lines. Different analytical models of single- (SWCNT), double- (DWCNT), and multiwalled CNTs (MWCNT) are studied to analyze the crosstalk delay at global interconnect lengths. A capacitively coupled three-line bus architecture employing CMOS driver is used for accurate estimation of crosstalk delay. Each line in bus architecture is represented with the equivalent RLC models of single and bundled SWCNT, DWCNT, and MWCNT interconnects. Crosstalk delay is observed at middle line (victim) when it switches in opposite direction with respect to the other two lines (aggressors). Using the data predicted by ITRS 2012, a comparative analysis on the basis of crosstalk delay is performed for bundled SWCNT/DWCNT and single MWCNT interconnects. It is observed that the overall crosstalk delay is improved by 40.92% and 21.37% for single MWCNT in comparison to bundled SWCNT and bundled DWCNT interconnects, respectively. 1. Introduction Advancement of VLSI technology leads to the development of high-speed complex integrated circuits (ICs) in current nanoscale regime. Due to shrinking feature sizes and increasing clock frequency, interconnect plays an important role in determining the overall circuit performance. Therefore, in recent technology, interconnect delay dominates over the gate delay. The global interconnects are widely employed to distribute data, clock, power supply, and ground throughout the entire area of an IC. At global interconnect, most materials (such as Al or Cu) are susceptible to electromigration due to higher current density. This electromigration problem substantially affects the reliability of high-speed VLSI circuits. To avoid such problems, researchers are forced to find an alternative solution for global VLSI interconnects. Carbon nanotubes (CNTs) can be considered as alternative interconnect material in current nanoscale regime. After discovery in 1991 [1], CNTs have received tremendous research interest for their unique mechanical [2], electrical [3], thermal [4], and chemical properties [5]. The bonding in graphene is even stronger than the bonds in diamond that gives CNTs extremely high mechanical strength [6]. The unique electrical and thermal properties are primarily due to the movement of electrons in
References
[1]
R. Satio, G. Dresselhaus, and S. Desselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, UK, 1998.
[2]
S. Berber, Y.-K. Kwon, and D. Tománek, “Unusually high thermal conductivity of carbon nanotubes,” Physical Review Letters, vol. 84, no. 20, pp. 4613–4616, 2000.
[3]
B. Q. Wei, R. Vajtai, and P. M. Ajayan, “Reliability and current carrying capacity of carbon nanotubes,” Applied Physics Letters, vol. 79, no. 8, pp. 1172–1174, 2001.
[4]
P. G. Collins, M. Hersam, M. Arnold, R. Martel, and P. Avouris, “Current saturation and electrical breakdown in multiwalled carbon nanotubes,” Physical Review Letters, vol. 86, no. 14, pp. 3128–3131, 2001.
[5]
A. Javey and J. Kong, Carbon Nanotube Electronics, Springer, New York, NY, USA, 2009.
[6]
H. Li, C. Xu, N. Srivastava, and K. Banerjee, “Carbon nanomaterials for next-generation interconnects and passives: physics, status, and prospects,” IEEE Transactions on Electron Devices, vol. 56, no. 9, pp. 1799–1821, 2009.
[7]
S.-N. Pu, W.-Y. Yin, J.-F. Mao, and Q. H. Liu, “Crosstalk prediction of single- and double-walled carbon-nanotube (SWCNT/ DWCNT) bundle interconnects,” IEEE Transactions on Electron Devices, vol. 56, no. 4, pp. 560–568, 2009.
[8]
P. Avorious, Z. Chen, and V. Perebeions, “Carbon-based electronics,” Nature Nanotechnology, vol. 2, pp. 605–613, 2007.
[9]
K. Tsukagoshi, B. W. Alphenaar, and H. Ago, “Coherent transport of electron spin in a ferromagnetically contacted carbon nanotube,” Nature, vol. 401, no. 6753, pp. 572–574, 1999.
[10]
J. A. Misewich, R. Martel, P. Avouris, J. C. Tsang, S. Heinze, and J. Tersoff, “Electrically induced optical emission from a carbon nanotube FET,” Science, vol. 300, no. 5620, pp. 783–786, 2003.
[11]
N. Wang, Z. K. Tang, G. D. Li, and J. S. Chen, “Materials science: single-walled 4？ carbon nanotube arrays,” Nature, vol. 408, no. 6808, pp. 50–51, 2000.
[12]
M.-F. Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F. Kelly, and R. S. Ruoff, “Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load,” Science, vol. 287, no. 5453, pp. 637–640, 2000.
[13]
F. Lu, L. Gu, M. J. Meziani et al., “Advances in bioapplications of carbon nanotubes,” Advanced Materials, vol. 21, no. 2, pp. 139–152, 2009.
[14]
D. Rossi, J. M. Cazeaux, C. Metra, and F. Lombardi, “Modeling crosstalk effects in CNT bus architectures,” IEEE Transactions on Nanotechnology, vol. 6, no. 2, pp. 133–145, 2007.
[15]
A. Naeemi and J. D. Meindl, “Compact physical models for multiwall carbon-nanotube interconnects,” IEEE Electron Device Letters, vol. 27, no. 5, pp. 338–340, 2006.
[16]
A. Nieuwoudt and Y. Massoud, “Evaluating the impact of resistance in carbon nanotube bundles for VLSI interconnect using diameter-dependent modeling techniques,” IEEE Transactions on Electron Devices, vol. 53, no. 10, pp. 2460–2466, 2006.
[17]
S. Haruehanroengra and W. Wang, “Analyzing conductance of mixed carbon-nanotube bundles for interconnect applications,” IEEE Electron Device Letters, vol. 28, no. 8, pp. 756–759, 2007.
[18]
K.-H. Koo, H. Cho, P. Kapur, and K. C. Saraswat, “Performance comparisons between carbon nanotubes, optical, and Cu for future high-performance on-chip interconnect applications,” IEEE Transactions on Electron Devices, vol. 54, no. 12, pp. 3206–3215, 2007.
[19]
B. K. Kaushik, S. Sarkar, R. P. Agarwal, and R. C. Joshi, “An analytical approach to dynamic crosstalk in coupled interconnects,” Microelectronics Journal, vol. 41, no. 2-3, pp. 85–92, 2010.
[20]
M. K. Majumder, N. D. Pandya, B. K. Kaushik, and S. K. Manhas, “Dynamic crosstalk effect in mixed CNT bundle interconnects,” IET Electronics Letters, vol. 48, pp. 384–385, 2012.
[21]
J. M. Rabaey, Digital Integrated Circuits, A Design Perspective, Prentice Hall, Englewood Cliffs, NJ, USA, 1996.
[22]
W. C. Chen, W.-Y. Yin, L. Jia, and Q. H. Liu, “Electrothermal characterization of single-walled carbon nanotube (SWCNT) interconnect arrays,” IEEE Transactions on Nanotechnology, vol. 8, no. 6, pp. 718–728, 2009.
[23]
“2012 International Technology Roadmap for Semiconductors,” http://public.itrs.net/.
[24]
M. K. Majumder, N. D. Pandya, B. K. Kaushik, and S. K. Manhas, “Analysis of MWCNT and bundled SWCNT interconnects: impact on crosstalk and area,” Electron Device Letters, vol. 33, pp. 1180–1182, 2012.
[25]
P. J. Burke, “Luttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes,” IEEE Transactions on Nanotechnology, vol. 1, pp. 129–144, 2002.
[26]
B. Bourlon, C. Miko, L. Forró, D. C. Glattli, and A. Bachtold, “Determination of the intershell conductance in multiwalled carbon nanotubes,” Physical Review Letters, vol. 93, no. 17, Article ID 176806, 4 pages, 2004.
[27]
A. Naeemi and J. D. Meindl, “Design and performance modeling for single-walled carbon nanotubes as local, semiglobal, and global interconnects in gigascale integrated systems,” IEEE Transactions on Electron Devices, vol. 54, no. 1, pp. 26–37, 2007.
[28]
M. K. Majumder, N. D. Pandya, B. K. Kaushik, and S. K. Manhas, “Analysis of crosstalk delay and area for MWNT and bundled SWNT for global VLSI Interconnects,” in Proceedings of the 13th IEEE International Symposium on Quality Electronic Design (ISQED '12), pp. 291–297, Santa Clara, Calif, USA, 2012.
