碳纳米管互连串扰特性研究
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摘要
随着超大规模集成电路的特征尺寸的不断缩小,当前的工艺技术进入纳米(< 100 nm)阶段,微电子技术已经进入了纳米集成电路时代。在之前的深亚微米工艺阶段,互连线问题已经引起人们的广泛关注,成为集成电路设计的关键问题之一。在纳米级电路中,互连线将产生更为严重的问题,比如金属电阻率的增加,热稳定性下降,可靠性问题日益突出等。为此,互连线新工艺、新结构和新材料的研究逐渐成为热点,也越发重要。
     碳纳米管作为碳的第四种形态,于1992年被发现,其具有特殊的电学、热学和机械性能,所以在短短的十几年时间中,就受到了全球研究人员的高度重视。其中碳纳米管具有的电阻率低和电流密度大的特点,使它有可能成为优良的互连线材料。本文通过电磁学和量子电子学的方法,对单壁碳纳米管和双壁碳碳纳米管的等效参数进行提取,并得出了单壁碳纳米管束互连线和双壁碳纳米管束互连线考虑线间串扰的等效电路模型。然后以延时和抖动性能为主要指标,对单壁碳纳米管束互连线、双壁碳纳米管束互连线和铜互连线进行对比研究。为使研究更接近实际,采用ITRS2006作为互连线线宽标准,在相同的互连线环境中计算出延时数据进行对比,结果显示单壁碳纳米管束和双壁碳纳米管束互连线在中间层和全局层能够大大提高电路性能;而对于串扰引起的信号抖动,碳纳米管束互连线与铜互连线性能相当。
     本文工作详细分析了碳纳米管作为未来互连线的电路性能,所提出的电路模型和分析结果对今后碳纳米管互连线的分析和设计有着重要的意义,同时也对今后碳纳米管互连线的制备应用提供了导向。
Due to the feature size of VLSI continues shrinking, the process technology has moved into nanoscale (< 100 nm) region, and microelectronics has been developed into the era of nanoscale integrated circuits (IC). In previous deep sub-micron technology, interconnect issue has arised lots of concern and become one of critical issues of IC design. In nanoscale integrated circuits, interconnect is going to encounter more limitation problems, such as the increasing of metal resistivity, degradation of thermal properties and more serious reliability issue. Hence, the research of new process, new structure and new material for interconnect is becoming more and more active and important.
     CNT (Carbon Nanotube), as the forth form of carbon, was discovered in 1992. Since it has special electrical property, thermal property and mechanical characteristics, researchers have paid much attention on it in the recent decade. CNT has low resistance and high current density, so it may become the next generation interconnect material. In this paper, we extract the equivalent circuit of SWCNT (Single-Walled Carbon Nanotube) and DWCNT (Double-Walled Carbon Nanotube) based on electromagnetism and quantum theory. The equivalent circuit models of SWCNT bundles interconnect and DWCNT bundles interconnect considering crosstalk effect are obtained. Then we compare SWCNT bundle interconnect and DWCNT bundle interconnect with Cu interconnect for the crosstalk-induced delay and glitch performance. In order to make this research useful, we take the line width from ITRS 2006 as the standard, and build the equivalent circuits for Cu, SWCNT and DWCNT respectively. Then we take these equivalent circuits to the same interconnect system, and calculate the delay time and glitch for comparison. We find that SWCNT bundle interconnect and DWCNT bundle interconnect obviously improve the time delay performance in the intermediate level and the global level, but SWCNT bundle interconnect and DWCNT bundle interconnect have the similar crosstalk-induced glitch performance as Cu interconnect.
     This work has discussed comprehensively about the circuit performance of CNT as future interconnect in nanoscale IC. The proposed models and analysis results are important for future analysis and design of CNT interconnect. Also, it provides suggestions and guidelines for fabrication efforts and application of CNT.
引文
[1] G. E. Moore,“Cramming More Components onto Integrated Circuits,”Electronics, vol. 38, no. 8, April 1965.
    [2] International Technology Roadmap for Semiconductors (ITRS), 2006 update, Available online: http://public.itrs.net.
    [3] J. M. Rabaey, A. Chandrakasan, and B. Nikolic, Digital Integrated Circuits: A Design Perspective, 2nd Edition, Prentice Hall, 2003.
    [4] L. Geppent,“Quantum transistors: toward nanoelectronics,”IEEE Spectrum, vol. 37, no. 9, Sep. 2000.
    [5] C. Hu,“Silicon nanoelectronics for the 21st century,”Nanotechnology, vol. 10, no. 2, June 1999.
    [6] J. A. Davis, R. Venkatesan, A. Kaloyeros, M. Beylansky, S. J. Souri, K. Banerjee, K. C. Saraswat, A. Rahman, R. Reif, and J. D. Meindl,“Interconnect limits on gigascale integration in the 21st century,”Proceedings of the IEEE, vol. 89, no. 3, Mar. 2001.
    [7] K. Hinode, Y. Hanaoka, K. Takeda, and S. Kondo,“Resistivity increase in ultrafine-line copper conductor for ULSIs,”Japanese Journal of Applied Physics, Part 2, 40, L1097, 2001.
    [8] W. Steinhogl, G. Schindler, G. Steinlesberger, and M. Engelhardt,“Size-dependent resistivity of metallic wires in the mesoscopic range,”Physical Review B, 66 (075414), 2002.
    [9] W. Steinhogl, G. Schindler, G. Steinlesberger, M. Traving, and M. Engelhardt,“Comprehensive study of the resistivity of copper wires with lateral dimensions of 100 nm and smaller,”Journal of Applied Physics, 97 (023706), 2005.
    [10] S. P. Murarka,“Advanced materials for future interconnections of the future need and strategy,”Microelectronic Eng., 37(38), 29, 1997.
    [11] S. Im, N. Srivastava, K. Banerjee and K. E. Goodson,“Scaling Analysis of Multilevel Interconnect Temperatures for High Performance ICs,”IEEE Transactions on Electron Devices, Vol. 52, No. 12, pp. 2710-2719, 2005.
    [12] A. V. Vairagar, S. G. Mhaisalkar, and A. Krishnamoorthy,“Electromigration behavior of dual-damascene Cu interconnects-structure, width, and length dependences,”Condens.Matter, vol. 54, no. 24, pp. 17 954–17 961, Dec. 1996.
    [37] R. Van Noorden,“Moving towards a graphene world,”Nature, vol. 442, no. 7100, pp. 228–229, Jul. 2006.
    [38] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov,“Electric field effect in atomically thin carbon films,”Science, vol. 306, no. 5696, pp. 666–669, Oct. 2004.
    [39] C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer,“Electronic confinement and coherence in patterned epitaxial graphene,”Science, vol. 312, no. 5777, pp. 1191–1196, May 2006.
    [40] Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, and S.-S. Pei,“Graphene segregated on Ni surfaces and transferred to insulators,”Appl. Phys. Lett., vol. 93, no. 11, p. 113 103, Nov. 2008.
    [41] P. L. McEuen, M. S. Fuhrer, and H. K. Park,“Single-walled carbon nanotube electronics,”IEEE Trans. Nanotechnology, vol. 1, no. 1, pp. 78-85, 2002.
    [42] L. M. Peng,Z. L. Zhang,and Z. Q. Xue,et al.,“Stability of Carbon Nanotubes: How small They be?”Phys. Rev. Lett., 85(15), 3249-3252, 2000.
    [43] L. C. Qin, X. L. Zhao, K. Hirahara, et al.,“The smallest carbon nanotubes,”Nature, 408, 6808, 2000.
    [44] P. G. Collins, et al.,“Current Saturation and Electrical Breakdown in Multiwalled Carbon Nanotubes,”Phys. Rev. Lett., vol. 86, no. 14, pp 3128-3131, 2001.
    [45] B. Q. Wei, et al.,“Reliability and Current Carrying Capacity of Carbon Nanotubes,”Appl. Phys. Lett., vol. 79, no. 8, pp. 1172-1174, 2001.
    [46] M. Radosavljevic, J. Lefebvre and A. T. Johnson,“High-field Electrical Transport and Breakdown in Bundles of Single-wall Carbon Nanotubes”, Physical Review B, Vol. 64, 241307, 2001.
    [47] International Technology Roadmap for Semiconductors, http://public.itrs.net.
    [48] C. Yu, L. Shi, Z .Yao, D. Li, and A. Majumdar,“Thermal conductance and thermopower of an individual single-wall carbon nanotube,”Nano Letters, vol. 5, no. 9, pp. 1842-1846, 2005.
    [49] S. Berber, et al.,“Unusually High Thermal Conductivity of Carbon Nanotubes,”Phys. Rev. Lett., vol. 84, no. 20, pp. 4613-4616, 2000.
    [50] J. Hone, M. Whitney, C. Piskoti and A. Zettl,“Thermal Conductivity of Single-walled Carbon Nanotubes”, Physical Review B, Vol. 59, No. 4, R2514, 1999.
    [51] K. M. Liew, et al.,“Thermal Stability of Single and Multi-walled Carbon Nanotubes”, Physical Review B, vol. 71, 075424, 2005.
    [52] P. Kim, L. Shi, A. Majumdar and P. L. McEuen,“Thermal Transport Measurements of Individual Multiwalled Nanotubes”, Physical Review Letters, Vol. 87, No. 21, 215502, 2001.
    [53] A.P. Graham, G.S. Duesberg, W. Hoenlein, F. Kreupl, M. Liebau, R. Martin, B. Rajasekharan, W. Pamler, R. Seidel, W. Steinhoegl, and E. Unger,“How Do Carbon Nanotubes Fit Into the Semiconductor Roadmap?,”Applied Physics A, Vol. 80, No. 6, pp. 1141-1151, 2005.
    [54] J. Robertson,“Growth of Nanotubes for Electronics,”Materials Today, Vol. 10, Issues 1-2, pp. 36-43, 2007.
    [55] A.-C. Dupuis,“The Catalyst in the CCVD of Carbon Nanotubes - A Review,”Progress in Materials Science, Vol. 50, Issue 8, pp. 929-961, 2005.
    [56] R. Seidel, G. S. Duesberg, E. Unger, A. P. Graham, M. Liebau and F. Kreupl,“Chemical Vapor Deposition Growth of Single-Walled Carbon Nanotubes at 600°C and a Simple Growth Model,”Journal of Physical Chemistry B, Vol. 108, Issue 6, pp. 1888-1893, 2004.
    [57] Y. M. Choi, S. Lee, H. S. Yoon, M. S. Lee, H. Kim , I. Han, Y. Son, I. S. Yeo, U.-I. Chung and J. T. Moon,“Integration and Electrical Properties of Carbon Nanotube Array for Interconnect Applications,”Proc. of the IEEE Conference on Nanotechnology, 2006.
    [58] J. Li, et al.,“Bottom-up Approach for Carbon Nanotube Interconnects,”Applied Physics Letters, vol. 82, no. 15, pp. 2491-2493, April 2003.
    [59] F. Kreupl, A. P. Graham, G. S. Duesberg, W. Steinhogl, M. Liebau, E. Unger and W. Honlein,“Carbon Nanotubes in Interconnect Applications,”Microelectronic Engineering, 64 (2002), pp. 399-408.
    [60] M. Nihei, D. Kondo, A. Kawabata, S. Sato, H. Shioya, M. Sakaue, T. Iwai, M. Ohfuti, and Y. Awano,“Low-resistance multi-walled carbon nanotube vias with parallel channel conduction of inner shells,”Interconnect Technology Conference, 2005, pp.234-236.
    [61] B. Q. Wei, R. Vajtai, Y. Jung, J. Ward, Y. Zhang, G. Ramanath and P. M. Ajayan,“Organized assembly of carbon nanotubes,”Nature, 416, 495, 2002.
    [62] S. Huang, X. Cai, and J. Liu,“Growth of Millimeter-Long and Horizontally Aligned Single-Walled Carbon Nanotubes on Flat Substrates,”J. Am. Chem. Soc., Vol. 125, pp. 5636-5637, 2003.
    [63] X. Huijun and A. T. Woolley,“Directional orientation of carbon nanotubes on surfaces using a gas flow cell,”Nano Letters, Vol. 4, N.8, pp. 1481-1484, 2004.
    [64] Nojeh, A. Ural, R. F. Pease, and H. Dai," Electric-field-directed growth of carbon nanotubes in two dimensions," J. Vac. Sci. Technol. B, 22, 3421-3425, 2004.
    [65] Y. H. Yan, S. Li, L. Q. Chen, M. B. Chan-Park and Qing Zhang,“Large-scale submicron horizontally aligned single-walled carbon nanotube surface arrays on various substrates produced by a fluidic assembly method,”Nanotechnology 17, pp. 5696-5701, 2006.
    [66] M. Meyyappan, L. Delzeit, A. Cassell, D. Hash,“Carbon nanotube growth by PECVD: a review”, Plasma Sources Sci. Technol., 12, pp. 205–216, 2003.
    [67] S. Sato, M. Nihei, A. Mimura, A. Kawabata, D. Kondo, H. Shioya, T. Iwai, M. Mishma, M. Ohfuti and Y. Awano,“Novel approach to fabricating carbon nanotube via interconnects using size-controlled catalyst nanoparticles,”Interconnect Technology Conference, 2006, pp. 230-232.
    [68] P. L. McEuen, M. S. Fuhrer, and H. K. Park,“Single-walled carbon nanotube electronics,”IEEE Trans. Nanotechnology, vol. 1, no. 1, pp. 78-85, 2002.
    [69] P. Avouris, J. Appenzeller, R. Martel, and S. J. Wind,“Carbon nanotube electronics,”Proceedings of The IEEE, vol. 91, no. 11, pp. 1772-1784, 2003.
    [70] D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie and G. A. C. Jones,“One-dimensional Transport and the Quantisation of the Ballistic Resistance,”J. Phys. C: Solid State Phys., Vol. 21, pp. L209-214, 1988.
    [71] J. Kong, E. Yenilmez, T. W. Tombler, W. Kim, H. Dai, R. B. Laughlin, L. Liu, C. S. Jayanthi and S. Y. Wu,“Quantum Interference and Ballistic Transmission in Nanotube Electron Waveguides”, Physical Review Letters, Vol. 87, No. 10, 106801, 2001.
    [72] J.-Y. Park, S. Rosenblatt, Y. Yaish, V. Sazonova, H. Ustunel, S. Braig, T. A. Arias, P. W. Brouwer and P. L. McEuen,“Electron-Phonon Scattering in Metallic Single-Walled Carbon Nanotubes”, Nano Letters, Vol. 4, No. 3, pp. 517-520, 2004.
    [73] Z. Yao, C. L. Kane, and C. Dekker,“High Field Electrical Transport in Single-Wall Carbon Nanotubes,”Physical Review Letters, Vol. 84, No. 13, pp. 2941-2944, 2000.
    [74] A. Naeemi, R. Sarvari, and J. D. Meindl,“Performance comparison between carbon nanotube and copper interconnects for gigascale integration (GSI),”IEEE Electron Device Letters, vol. 26, no. 2, pp. 84-86, 2005.
    [75] A. Naeemi and J. D. Meindl,“Impact of electron-phonon scattering on the performance of carbon nanotube interconnects for GSI,”IEEE Electron Device Letters, Vol. 26, Issue 7, pp. 476-478, 2005.
    [76] S. Heinze, J. Tersoff, R. Martel, V. Derycke, J. Appenzeller and Ph. Avouris,“Carbon Nanotubes as Schottky Barrier Transistors,”Physical Review Letters, 89, 106801, 2002.
    [77] Y. Yaish, J.-Y Park, S. Rosenblatt, V. Sazonova, M. Brink and P. L. McEuen,“Electrical Nanoprobing of Semiconducting Carbon Nanotubes Using an Atomic Force Microscope,”Physical Review Letters, 92, 046401, 2004.
    [78] A. Javey, J. Guo, M. Paulsson, Q. Wang, D. Mann, M. Lundstrom and H. Dai,“High-field, Quasiballistic Transport in Short Carbon Nanotubes,”Physical Review Letters, Vol. 92, No. 10, 106804, 2004.
    [79] A. Javey, J. Guo, Q. Wang, M. Lundstrom and H. Dai,“Ballistic Carbon Nanotube Field-Effect Transistors,”Nature, Vol. 424, pp. 654, 2003.
    [80] W. Kim, A. Javey, R. Tu, J. Cao, Q. Wang and H. Dai,“Electrical Contacts to Carbon Nanotubes Down to 1 nm in Diameter,”Applied Physics Letters, 87, 173101, 2005.
    [81] F. Leonard and A. A. Talin,“Electrical Contacts to Nanotubes and Nanowires: Why Size Matters,”Cond-mat/0602003, 2006.
    [82] Th. Hunger, B. Lengeler and J. Appenzeller,“Transport in Ropes of Carbon Nanotubes: Contact Barriers and Luttinger Liquid Theory”, Physical Review B, Vol. 69, 195406, 2004.
    [83] P. J. Burke,“Luttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes,”IEEE Trans. Nanotechnology, vol. 1, no. 3, pp. 129-144, 2002.
    [84] J. J. Plombon, K. P. O’Brien, F. Gstrein and V. M Dubin,“High-frequency electricalproperties of individual and bundled carbon nanotubes,”Applied Physics Letters, Vol. 90, 063106, 2007.
    [85] A. Naeemi, and J. D. Meindl,“Compact physical models for multiwall carbon-nanotube interconnects,”IEEE Electron Device Letters, vol. 27, no.5, pp338-340, 2006.
    [86] B. Bourlon, C. Miko, L. Forro, D. C. Glattli, and A. Bachtold,“Determination of the intershell conductance in multiwalled carbon nanotubes,”Physical Rev. Lett., pp. 176806-1-176806-4, 2004.
    [87] D. Rossi, J. M. Cazeaux, C. Metra, and F. Lombardi,“Modeling crosstalk effects in CNT bus architectures,”IEEE Trans. Nanotechnology, vol. 6, no. 2, pp. 133-145, 2005.
    [88] H. Stahl, J. Appenzeller, R. Martel, Ph. Avouris and B. Lengeler,“Intertube Coupling in Ropes of Single-Wall Carbon Nanotubes”, Physical Review Letters, Vol. 85, No. 24, pp. 5186-5189, 2000.
    [89] 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 Trans. Electron Device, vol. 54, no. 1, pp. 26–36, Jan. 2007.
    [90] Topics in Applied Physics, Carbon Nanotubes: Synthesis, Structure, Properties and Applications, M. S. Dresselhaus, G. Dresselhaus, and P. Avouris, Eds. New York: Springer-Verlag, 2000.
    [91] N. Srivastava and K. Banerjee,“Performance analysis of carbon nanotube interconnects for VLSI applications,”IEEE/ACM Intl. Conf. on ICCAD, 2005, pp. 383-390.
    [92] A. Nieuwoudt and Y. Massoud,“Understanding the Impact of Inductance in Carbon Nanotube Bundles for VLSI Interconnect Using Scalable Modeling Techniques,”IEEE Transactions on Nanotechnology, Vol. 5, No. 6, pp. 758-765, 2006.
    [93] W. Y. Yin, J. Y. Xie, K. Kang, J. L. Shi, J. F. Mao, and X. W. Sun,“Vertical topologies of miniature multi-spiral stacked inductors,”IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp. 475–486, Feb. 2008.
    [94] Maxwell SV, http://www.ansoft.com/maxwellsv/. Ansoft Corp., 2005.
    [95] Nieuwoudt and Y. Massoud,“Performance Implications of Inductive Effects forCarbon-Nanotube Bundle Interconnect,”IEEE Electron Device Letters, Vol. 28, No. 4, pp. 305-307, 2007.
    [96] A. Deutsch, G. V. Kopcsay, P. J. Restle, et al.,“When are Transmission Line Effects Important for On-Chip Interconnections?”, IEEE Transactions on Microwave Theory and Techniques, Vol. 45, Issue 10, pp. 1836-1846, 1997.
    [97] W. Steinhogl, G. Schindler, G. Steinlesberger, M. Traving, and M. Engelhardt,“Comprehensive study of the resistivity of copper wires with lateral dimensions of 100 nm and smaller,”Journal of Applied Physics, 97 (023706), 2005.
    [98] International Technology Roadmap for Semiconductors, 2006. [Online]. Available: http://public.itrs.net/.
    [99] K. Banerjee and A. Mehrotra,“A Power-Optimal Repeater Insertion Methodology for Global Interconnects in Nanometer Designs,”IEEE Trans. Electron Devices, vol. 49, no. 11, pp. 2001-2007, 2002.
    [100] A. Naeemi, R. Sarvari, and J. D. Meindl,“Performance comparison between carbon nanotube and copper interconnects for gigascale integration (GSI),”IEEE Electron Device Letters, vol. 26, no. 2, pp. 84-86, 2005.
    [101] Naeemi and J. D. Meindl,“Impact of electron-phonon scattering on the performance of carbon nanotube interconnects for GSI,”IEEE Electron Device Letters, Vol. 26, Issue 7, pp. 476-478, 2005.
    [102] N. Srivastava, R. V. Joshi and K. Banerjee,“Carbon nanotube interconnect: implications for performance, power dissipation and thermal management,”IEDM Tech. Dig., 2005, pp. 257-260.

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