Abstract
This chapter reviews the Cu-based on-chip interconnect modeling. The unique atomic structure and properties of carbon nanotube (CNT) and graphene nanoribbon (GNR) are discussed. The characteristics and semiconducting/metallic properties of graphene-based on-chip interconnects are presented. Depending on the physical configuration, equivalent electrical models of MWCNT and MLGNR interconnect lines are also introduced. An extensive review on performance analysis of on-chip interconnects is presented.
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Livshits P, Sofer S (2012) Aggravated electromigration of copper interconnection lines in ULSI devices due to crosstalk noise. IEEE Trans Device Mater Reliab 12(2):341–346
Moll F, Roca M, Rubio A (1998) Inductance in VLSI interconnection modeling. IEEE Proc Circuits Devices Syst 145(3):175–179
Sakurai T, Newton R (1990) Alpha-power law MOSFET model and its applications to CMOS inverter delay and other formulas. IEEE J Solid-State Circuits 25(2):584–594
Bowman KA, Austin BL, Eble JC, Xingha T, Meindl JD (1999) A physical alpha-power law MOSFET model. IEEE J Solid State Circuits 34(10):1410–1414
Dutta S, Shetti SSM, Lusky SL (1995) A comprehensive delay model for CMOS inverters. IEEE J Solid-State Circuits 30(8):864–871
Bisdounis L, Nikolaidis S, Koufopavlou O (1998) Analytical transient response and propagation delay evaluation of the CMOS inverter for short-channel devices. IEEE J Solid-State Circuits 33(2):302–306
Qian J, Pullela S, Pillage L (1994) Modeling the effective capacitance for the RC interconnect of CMOS gates. IEEE Trans Comput Aided Des 13(12):1526–1535
Hafed M, Oulmane M, Rumin NC (2001) Delay and current estimation in a CMOS inverter with an RC load. IEEE Trans Comput Aided Des 20(1):80–89
Chatzigeorgiou A, Nikolaidis S, Tsoukalas I (2001) Modeling CMOS gates driving RC interconnect loads. IEEE Trans Circuits Syst II Analog Digital Signal Process 48(4):413–418
Adler V, Friedman EG (1998) Repeater design to reduce delay and power in resistive interconnect. IEEE Tran Circuits Syst II Analog Digital Signal Process 45(5):607–616
Bakoglu HB, Meindl JD (1985) Optimal interconnection circuits for VLSI. IEEE Trans Electron Devices 32(5):903–909
Rubinstein J, Penfield P, Horowitz MA (1983) Signal delay in RC tree networks. IEEE Trans Comput Aided Des 2(3):202–211
Kahng A, Muddu S (1997) An analytical delay model for RLC interconnects. IEEE Trans Comput Aided Des 16(2):1507–1514
Ismail YI, Friedman EG, Neves JL (2000) Equivalent elmore delay for RLC trees. IEEE Trans Comput Aided Des 19(1):83–97
Bai X, Chandra R, Dey S, Srinivas PV (2004) Interconnect couplingaware driver modeling in static noise analysis for nanometer circuits. IEEE Trans Comput Aided Des 23(8):1256–1263
Davis JA, Meindl JD (2000) Compact distributed RLC models, part I: single line transient, time delay, and overshoot expressions. IEEE Trans Electron Devices 47(11):2068–2077
Davis JA, Meindl JD (2000) Compact distributed RLC models, part II: coupled line transient expressions and peak crosstalk in multilevel networks. IEEE Trans Electron Devices 47(11):2078–2087
Agarwal K, Sylvester D, Blaauw D (2006) Modeling and analysis of crosstalk noise in coupled RLC interconnects. IEEE Trans Comput Aided Des Integr Circuits Syst 25(5):892–901
Liu T, Kuo J, Zhang S (2012) A closed-form analytical transient response model for on-chip distortion less interconnect. IEEE Trans Electron Devices 59(12):3186–3192
Kaushik BK, Sarkar S (2008) Crosstalk analysis for a CMOS gate driven inductively and capacitively coupled interconnects. Microelectron J 39(12):1834–1842
Kaushik BK, Sarkar S, Agarwal RP, Joshi RC (2010) An analytical approach to dynamic crosstalk in coupled interconnects. Microelectron J 41(2):85–92
Li XC, Ma JF, Swaminathan M (2011) Transient analysis of CMOS gate driven RLGC interconnects based on FDTD. IEEE Trans Comput Aided Des Integr Circuits Syst 30(4):574–583
Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1985) C60: buckminsterfullerene. Nature 318:162–163
Scarselli M, Castrucci P, Crescenzi M (2012) Electronic and optoelectronic nano-devices based on carbon nanotubes. J Phys Condens Matter 24(31):313202-1–313202-36
Xu T, Wang Z, Miao J, Chen X, Tan CM (2007) Aligned carbon nanotubes for through-wafer interconnects. Appl Phys Letts 91(4):042108-1–042108-3
Monthioux M, Serp P, Flahaut E (2010) Introduction to carbon nanotubes. In: Bhushan B (ed) Handbook of nano-technology. Springer, New York
Wang N, Tang ZK, Li GD, Chen JS (2000) Single-walled 4 Å carbon nanotube arrays. Nature 408:50–51
Javey A, Kong J (2009) Carbon nanotube electronics. Springer
Hamada N, Sawada SI, Oshiyama A (1992) New one-dimensional conductors, graphite microtubules. Phys Rev Lett 68:1579–1581
Li HJ, Lu WG, Li JJ, Bai XD, Gu CZ (2005) Multichannel ballistic transport in multiwall carbon nanotubes. Phys Rev Lett 95(8):86601
Nihei M, Kondo D, Kawabata A (2005) Low-resistance multi-walled carbon nanotube vias with parallel channel conduction of inner shells. In: Proceedings of the IEEE international interconnect technology conference, pp 234–36
Forró L, Schönenberger C (2000) Physical properties of multi-wall nanotubes in topics in applied physics, carbon nanotubes: synthesis, structure, properties and applications. In: Dresselhaus MS, Dresselhaus G, Avouris P (eds) Springer-Verlag, Berlin, Germany
Wei BQ, Vajtai R, Ajayan PM (2001) Reliability and current carrying capacity of carbon nanotubes. Appl Phys Lett 79(8):1172–1174
Close GF, Wong HSP (2008) Assembly and electrical characterization of multiwall carbon nanotube interconnects. IEEE Trans Nanotechnol 7(5):596–600
Shah TK, Pietras BW, Adcock DJ, Malecki HC, Alberding MR (2013) Composites comprising carbon nanotubes on fiber. US Patent, US8585934 B2
Dresselhaus M, Dresselhaus G, Avouris Ph (2001) Carbon nanotubes: synthesis, structure, properties and applications. Top Appl Res 80
Hsieh JYL, Huang JM, Hwang CC (2006) Theoretical variations in the young’s modulus of single-walled carbon nanotubes with tube radius and temperature: a molecular dynamics study. Nanotechnology 17:3920–3924
Forro L, Salvetat JP, Bonard J (2002) Electronic and mechanical properties of carbon nanotubes. In: Tománek D, Enbody RJ (eds) Science and application of nanotubes. Plenum Publishers, New York, pp 297–320
Wei C, Srivastava D, Cho K (2002) Thermal expansion and diffusion coefficients of carbon nanotube-polymer composites. Nano Lett 2(6):647–650
Wang Z, Zhao GL (2013) Microwave absorption properties of carbon nanotubes-epoxy composites in a frequency range of 2-20 GHz. Open J Compos Mater 3(2):17–23
Ifeanyi HN, John IE, Zhou W, Diola B, Guang-Lin Z (2015) Microwave absorption properties of multi-walled carbon nanotube (outer diameter 20–30 nm)–epoxy composites from 1 to 26.5 GHz. Diam Relat Mater 52:66–71
Srivastava A, Xu Y, Sharma AK (2010) Carbon nanotubes for next generation very large scale integration interconnects. J Nanophotonics 4(1):1–26
Li H, Yin WY, Banerjee K, Mao JF (2008) Circuit modeling and performance analysis of multi-walled carbon nanotube interconnects. IEEE Trans Electron Devices 55(6):1328–1337
Naeemi A, Meindl JD (2006) Compact physical models for multiwall carbon-nanotube interconnects. IEEE Electron Device Lett 27(5):338–340
Naeemi A, Sarvari R, Meindl JD (2005) Performance comparison between carbon nanotube and copper interconnects for gigascale integration (GSI). IEEE Electron Device Lett 26(2):84–86
Burke PJ (2002) Lüttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes. IEEE Trans Nanotechnol 1(3):129–144
Avouris P, Appenzeller J, Martel R, Wind SJ (2003) Carbon nanotube electronics. Proc IEEE 91(11):1772–1784
Li J, Ye Q, Cassell A, Ng HT, Stevens R, Han J, Meyyappan M (2003) Bottom-up approach for carbon nanotube interconnects. Appl Phys Lett 82(15):2491–2493
Ngo Q, Petranovic D, Krishnan S, Cassell AM, Ye Q, Li J, Meyyappan M, Yang CY (2004) Electron transport through metal–multiwall carbon nanotube interfaces. IEEE Trans Nanotechnol 3(2):311–317
Miano G, Villone F (2005) An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model. IEEE Trans Antennas Propag 54(10):2713–2724
Xu Y, Srivastava A (2009) A model for carbon nanotube interconnects. Int J Circuit Theory Appl 38(6):559–575
Sarto MS, Tamburrano A (2010) Single conductor transmission-line model of multiwall carbon nanotubes. IEEE Trans Nanotechnol 9(1):82–92
Tang M, Lu J, Mao J (2012) Study on equivalent single conductor model of multi-walled carbon nanotube interconnects. In: Proceedings of the IEEE Asia Pacific microwave conference, Taiwan, pp 1247–1249
D’Amore M, Sarto MS, Tamburrano A (2010) Fast transient analysis of next-generation interconnects based on carbon nanotubes. IEEE Trans Electromagn Compat 52(2):496–503
Lamberti P, Tucci V (2012) Impact of variability of the process parameters on CNT-based nanointerconnects performances: a comparison between SWCNTs bundles and MWCNT. IEEE Trans Nanotechnol 11(5):924–933
Liang F, Lin H, Wang G (2010) Prediction of crosstalk effects in future multiwall carbon nanotube (MWCNT) interconnects. In: Proceedings of the IEEE symposium on antennas propagation and EM theory (ISAPE), Guangzhou, pp 1031–1034
Das D, Rahaman H (2011) Analysis of crosstalk in single- and multiwall carbon nanotube interconnects and its impact on gate oxide reliability. IEEE Trans Nanotechnol 10(6):1362–1370
Das D, Rahaman H (2011) IR drop analysis in single- and multi-wall carbon nanotube power interconnects in sub-nanometer designs. In: Proceedings of the IEEE Asia symposium on quality electronic design (ASQED), pp 174–183
Liang F, Wang G, Lin H (2012) Modeling of crosstalk effects in multiwall carbon nanotube interconnects. IEEE Trans Electromagn Compat 54(1):133–139
Sahoo M, Rahaman H (2013) Performance analysis of multiwalled carbon nanotube bundles. In: Electronics and Nanotechnology (ELNANO), IEEE XXXIII international scientific conference, pp 200–204
Tang M, Mao J (2015) Modeling and fast simulation of multiwalled carbon nanotube interconnects. IEEE Trans Electromagn Compat 57(2):232–240
Fujita M, Wakabayashi K, Nakada K, Kusakabe K (1996) Peculiar localized state at zigzag graphite edge. J Phys Soc Jpn 65(7):1920–1923
Nakada K, Fujita M, Dresselhaus G, Dresselhaus MS (1996) Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys Rev 54(24):17954–17961
Echtermeyer TJ, Lemme MC, Baus M, Szafranek BN, Geim AK, Kurz H (2008) Nonvolatile switching in graphene field-effect devices. IEEE Electron Device Lett 29(8):952–954
Lemme MC, Echtermeyer TJ, Baus M, Kurz H (2007) A graphene field-effect device. IEEE Electron Device Lett 28(4):282–284
Rawat B, Paily R (2015) Analysis of graphene tunnel field-effect transistors for analog/RF applications. IEEE Trans Electron Devices 62(8):2663–2669
Naeemi A, Meindl JD (2007) Conductance modeling for graphene nanoribbon (GNR) interconnects. IEEE Electron Device Lett 28(5):428–431
Li H, Xu C, Srivastava N, Banerjee K (2009) Carbon nanomaterials for next-generation interconnects and passives: physics, status and prospects. IEEE Trans Electron Devices 56(9):1799–1821
Kan, E.; Li, Z.; Yang. J. “Graphene nanoribbons: geometric electronic and magnetic properties,” In Physics and Applications of Graphene—Theory, INTECH, ed. S. Mikhailov, Chapter 16, 2011.
Avouris P (2010) Graphene: electronic and photonic properties and devices. Nano Lett 10(11):4285–4294
Murali KH, Brenner K, Yang Y, Beck T, Meindl JD (2009) Resistivity of graphene nanoribbon interconnects. IEEE Electron Device Lett 30(6):611–613
Dresselhaus MS, Dresselhaus G (2002) Intercalation compounds of graphite. Adv Phys 51(1):1–186
Naeemi A, Meindl JD (2009) Compact physics-based circuit models for graphene nanoribbon interconnects. IEEE Trans Electron Devices 56(9):1822–1833
Stan MR, Unluer D, Ghosh A, Tseng F (2009) Graphene devices, interconnect and circuits—challenges and opportunities. In: Proceedings of the IEEE international symposium on circuits and systems (ISCAS), Taipei, pp 69–72
Berger C, Song Z, Li X, Wu X, Brown N, Naud C, Mayou D, Li T, Hass J, Marchenkov AN, Conrad EH, First PN, Heer WA (2006) Electronic confinement and coherence in patterned epitaxial graphene. Science 312(5777):1191–1196
Benedict LX, Crespi VH, Louie SG, Cohen ML (1995) Static conductivity and superconductivity of carbon nanotubes—Relations between tubes and sheets. Phys Rev B Condens Matter 52(20):14935–14940
Xu C, Li H, Banerjee K (2009) Modeling, analysis, and design of graphene nanoribbon interconnects. IEEE Trans Electron Devices 56(8):1567–1578
Hanlon LR, Falardeau ER, Fischer JE (1977) Metallic reflectance of AsF5-graphite intercalation compounds. Solid State Commun 24(5):377–381
Wen-Sheng Zhao; Wen-Yan Yin (2014) Comparative study on multilayer graphene nanoribbon (MLGNR) interconnects. IEEE Trans Electromagn Compat 56(3):638–645
Nasiri SH, Faez R, Moravvej-Farshi MK (2012) Compact formulae for number of conduction channels in various types of grapheme nanoribbons at various temperatures. Mod Phys Lett B 26(1):1150004-1–115004-5
Cui J, Zhao W, Yin W, Hu J (2012) Signal transmission analysis of multilayer graphene nano-ribbon (MLGNR) interconnects. IEEE Trans Electromagn Compat 54(1):126–132
Areshkin DA, Gunlycke D, White CT (2007) Ballistic transport in graphene nanostrips in the presence of disorder: importance of edge effects. Nano Lett 7(1):204–210
Hwang EH, Adam S, Sarma SD (2007) Carrier transport in two-dimensional graphene layers. Phys Rev Lett 98(18):186806-1–186806-4
Yan J, Zhang Y, Kim P, Pinczuk A (2007) Electric field effect tuning of electron-phonon coupling in graphene. Phys Rev Lett 98(16):166802-1–166802-4
Plombon JJ (2007) High-frequency electrical properties of individual and bundled carbon nanotubes. Appl Phys Lett 90(6):063106-1–063106-3
Sarto MS, Tamburrano A (2010) Comparative analysis of TL models for multilayer graphene nanoribbon and multiwall carbon nanotube interconnects. In: Proceedings of the IEEE international symposium on electromagnetic compatibility, Fort Lauderdale, FL, USA, pp 212–217
Nishad AK, Sharma R (2014) Analytical time-domain models for performance optimization of multilayer GNR interconnects. IEEE J Sel Top Quantum Electron 20(1):3700108-1–3700108-8
Sahoo M, Rahaman H (2014) Impact of line resistance variations on crosstalk delay and noise in multilayer graphene nano ribbon interconnects. In: Proceedings of the international symposium on electronic system Design (ISED), pp 94–98
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Kaushik, B.K., Kumar, V.R., Patnaik, A. (2016). Interconnect Modeling, CNT and GNR Structures, Properties, and Characteristics. In: Crosstalk in Modern On-Chip Interconnects. SpringerBriefs in Applied Sciences and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-0800-9_2
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DOI: https://doi.org/10.1007/978-981-10-0800-9_2
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