[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
research-article

A Global Routing Method for Graphene Nanoribbons Based Circuits and Interconnects

Published: 22 May 2020 Publication History

Abstract

With extreme miniaturization of traditional CMOS devices in deep sub-micron design levels, the delay of a circuit, as well as power dissipation and area are dominated by interconnections between logic blocks. Interconnect today is causing major problems such as delay, power dissipation, and so on. In an attempt to search for alternative materials, Graphene nanoribbons have been found to be potential for both transistors and interconnects due to its outstanding electrical and thermal properties. Graphene nanoribbons provide better options as materials used for global routing trees in VLSI circuits. However, certain special characteristics of Graphene nanoribbon prohibit direct application of existing VLSI routing tree construction methods. In this article, we address this issue and propose heuristic methods for construction of Graphene nanoribbon--based minimum hybrid cost and minimum-delay Steiner trees. We compute the delays for the trees using Elmore delay approximation. Experimental results demonstrate the effectiveness of our proposed methods, which are quite encouraging.

References

[1]
D. A. Areshkin, D. Gunlycke, and C. T. White. 2007. Ballistic transport in graphene nanostrips in the presence of disorder: Importance of edge effects. Nano Lett. 7, 1 (2007), 204--210.
[2]
Phaedon Avouris, Zhihong Chen, and Vasili Perebeinos. 2010. Carbon-based electronics. In Nanoscience and Technology: A Collection of Reviews from Nature Journals. World Scientific, Singapore, 174--184.
[3]
Claire Berger, Zhimin Song, Xuebin Li, Xiaosong Wu, Nate Brown, Cécile Naud, Didier Mayou, Tianbo Li, Joanna Hass, Alexei N. Marchenkov, et al. 2006. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 5777 (2006), 1191--1196.
[4]
K. D. Boese, A. B. Kahng, B. A. McCoy, and G. Robins. 1993. Fidelity and near-optimality of Elmore-based routing constructions. In Proceedings of the IEEE International Conference on Computer Design (ICCD’93). 81--84.
[5]
K. D. Boese, A. B. Kahng, B. A. McCoy, and G. Robins. 1994. Rectilnear Steiner trees with minimum elmore delay. In Proceedings of the 31st ACM/IEEE Design Automation Conference (DAC’94). 381--386.
[6]
K. D. Boese, A. B. Kahng, B. A. McCoy, and G. Robins. 1995. Near-optimal critical sink routing tree constructions. IEEE Trans. Comput.-Aided Design Integr. Circ. Syst. 14, 12 (Dec. 1995), 1417--1436.
[7]
Ying-Yu Chen, Amit Sangai, Morteza Gholipour, and Deming Chen. 2013. Graphene nano-ribbon field-effect transistors as future low-power devices. In Proceedings of the International Symposium on Low Power Electronics and Design (ISLPED’13). IEEE, 151--156.
[8]
M. Corso, E. Carbonell-Sanrom’a, and D. G. de Oteyza. 2018. Bottom-Up Fabrication of Atomatically Precise Graphene Nanoribbon.
[9]
Debaprasad Das and Hafizur Rahaman. 2017. Carbon Nanotube and Graphene Nanoribbon Interconnects. CRC Press, Boca Raton, FL.
[10]
S. Das and D. K. Das. 2017. A technique to construct global routing trees for graphene nanoribbon (GNR). In Proceedings of the International Symposium on Quality Electronic Design (ISQED’17). 111--118.
[11]
S. Das, S. Das, A. Majumder, P. Dasgupta, and D. K. Das. 2016. Delay estimates for graphene nanoribbons: A novel measure of fidelity and experiments with global routing trees. In Proceedings of the ACM Great Lakes Symposium on VLSI (GLSVLSI’16). 263--268.
[12]
P. Dasgupta. 2008. On some selected issues in VLSI interconnect layouts in the nanometer range. In Indian Institute of Management-Working Paper.
[13]
W. C. Elmore. 1948. The transient response of damped linear network with particular regard to wideband amplifiers. J. Appl. Phys. 19 (Jan. 1948), 55--63.
[14]
Gianluca Fiori and Giuseppe Iannaccone. 2007. Simulation of graphene nanoribbon field-effect transistors. IEEE Electron. Device Lett. 28, 8 (2007), 760--762.
[15]
M. Gholipour and N. Masoumi. 2014. Graphene nanoribbon crossbar architecture for low power and dense circuit implementations. Microelectron. J. (Nov. 2014), 1533--1541.
[16]
A. Y. Goharrizi, M. Pourfath, M. Fathipour, H. Kosina, and S. Selberherr. 2011. An analytical model for line-edge roughness limited mobility of graphene nanoribbons. IEEE Trans. Electron. Devices 58, 1 (Nov. 2011), 3725--3735.
[17]
D. Gunlycke, D. A. Areshkin, and C. T. White. 2007. Semiconducting graphene nanostrips with edge disorder. Appl. Phys. Lett. 90, 14 (Apr. 2007), 142104.
[18]
M. Y. Han, B. Ozyilmaz, Y. Zhang, and P. Kim. 2007. Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett. 98 (May 2007), 206805.
[19]
M. Hanan. 1966. On Steiner’s problem with rectilinear distance. SIAM J. Appl. Math. 14, 2 (March 1966), 255--265.
[20]
Ayako Hashimoto, Kazu Suenaga, Alexandre Gloter, Koki Urita, and Sumio Iijima. 2004. Direct evidence for atomic defects in graphene layers. Nature 430, 7002 (2004), 870.
[21]
Justin Haskins, Alper Kınacı, Cem Sevik, Hâldun Sevinçli, Gianaurelio Cuniberti, and Tahir Cagin. 2011. Control of thermal and electronic transport in defect-engineered graphene nanoribbons. ACS Nano 5, 5 (2011), 3779--3787.
[22]
A. Hazra and S. Basu. 2018. Graphene nanoribbon as potential on-chip interconnect material—A review. Appl. Phys. Lett. 4, 3 (Sept. 2018).
[23]
ITRS Report. 2015. http://www.itrs2.net/itrs-reports.html.
[24]
R. M. Jacobberger, M. Fortin-Deschenes B. Kiraly, P. L. Levesque, K. M. McElhinny, G. J. Brady, R. R. Delgado, S. S. Roy, A. Mannix, M. G. Lagally, P. G. Evans, P. Desjardins, R. Martel, M. C. Hersam, N. P. Guisinger, and M. S. Arnold. 2015. Alignment of semiconducting graphene nanoribbons on Vicinal Ge(001). Nat. Commun. 6, 11, 8006.
[25]
Paul Penfield Jr. and Jorge Rubinstein. 1981. Signal delay in RC tree networks. In Proceedings of the ACM/IEEE Design Automation Conference (DAC’81). 613--617.
[26]
A. B. Kahng and B. Liu. 2003. Q-tree: A new iterative improvement approach for buffered interconnect optimization. In Proceedings of the IEEE Computer Society Annual Symposium on VLSI (ISVLSI’03). 183--188.
[27]
M. I. Katsnelson and A. K. Geim. 2007. Electron scattering on microscopic corrugations in graphene. Philos. Trans. Roy. Soc. A: Math. Phys. Eng. Sci. 366, 1863 (2007), 195--204.
[28]
Eun-Ah Kim and AH Castro Neto. 2008. Graphene as an electronic membrane. Europhys. Lett. 84, 5 (2008), 57007.
[29]
M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz. 2007. A graphene field-effect device. IEEE Electron. Device Lett. 28, 4 (Apr. 2007), 282--284.
[30]
H. Li, C. Xu, and K. Banerjee. 2010b. Carbon nanomaterials: The ideal interconnect technology for next-generation ICS. IEEE Design Test Comput. 27, 4 (2010), 20--31.
[31]
Xuesong Li, Carl W. Magnuson, Archana Venugopal, Jinho An, Ji Won Suk, Boyang Han, Mark Borysiak, Weiwei Cai, Aruna Velamakanni, Yanwu Zhu, et al. 2010a. Graphene films with large domain size by a two-step chemical vapor deposition process. Nano Lett. 10, 11 (2010), 4328--4334.
[32]
J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth. 2007. The structure of suspended graphene sheets. Nature 446 (2007), 60--63.
[33]
A. Naeemi and J. D. Meindl. 2009. Compact physics-based circuit models for graphene nanoribbon interconnects. IEEE Trans. Electron. Devices 56, 9 (2009), 1822--1833.
[34]
A. Naeemi and J. D. Meindl. 2008. Performance benchmarking for graphene nano-ribbon, carbon nanotube, and Cu interconnects. In Proceedings of the IEEE International Interconnect Technology Conference. 183--185.
[35]
Mehdi Neek-Amal and F. M. Peeters. 2012. Effect of grain boundary on the buckling of graphene nanoribbons. Appl. Phys. Lett. 100, 10 (2012), 101905.
[36]
A. H. Castro Neto, Francisco Guinea, Nuno M. R. Peres, Kostya S. Novoselov, and Andre K. Geim. 2009. The electronic properties of graphene. Rev. Modern Phys. 81, 1 (2009), 109.
[37]
J. M. Rabey, A. Chandrakasan, and B. Nikolic. 2009. Digital Integrated Circuit- A Design Perspective (2nd. ed.). Prentice-Hall of India Pvt. Ltd., India.
[38]
T. Ragheb and Y. Massoud. 2008. On the modeling of resistance in graphene nanoribbon (GNR) for future interconnect applications. In Proceedings of the IEEE/ACM International Conference on Computer-Aided Design. 593--597.
[39]
T. Samanta, P. Ghosal, H. Rahaman, and P. Dasguptata. 2006. A heuristic method for constructing hexagonal Steiner minimal trees for routing in VLSI. In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’06). 1788--1791.
[40]
T. Samanta, P. Ghosal, H. Rahaman, and P. Dasguptata. 2008. Revisiting fidelity: A case of Elmore-based y-routing trees. In Proceedings of the International Workshop on System Level Interconnect Prediction (SLIP’08). 27--34.
[41]
Q. Shao, G. Liu, D. Teweldebrhan, and A. A. Balandin. 2008. High temperature quenching of electrical resistance in graphene interconnects. Appl. Phys. Lett. 92, 20 (May 2008), 202108.
[42]
K. Wakabayashi and S. Dutta. 2012. Nanoscale and edge effect on electronic properties of graphene. Solid State Commun. 152, 15 (2012), 1420–1430.
[43]
C. Xu, H. Li, and K. Banerjee. 2009. Modeling, analysis, and design of graphene nanoribbon interconnects. IEEE Trans. Electron. Devices 56, 8 (Aug. 2009), 1567--1578.
[44]
W. Xu and Tae-Woo Lee. 2016. Recent progress in fabrication techniques of graphene nanoribbons. Mater. Horiz. Roy. Soc. Chem. 3 (2016), 186--207.
[45]
Tan Yan, Qiang Ma, Scott Chilstedt, Martin D. F. Wong, and Deming Chen. 2011. Routing with graphene nanoribbons. In Proceedings of the 16th Asia and South Pacific Design Automation Conference (ASP-DAC’11). IEEE, 323--329.
[46]
Tan Yan, Q. Ma, S. Chilstedt, M. D. F. Wong, and D. Chen. 2013. A routing algorithm for graphene nanoribbon circuit. ACM Trans. Design Autom. Electron. Syst. 18, 4 (Oct. 2013).
[47]
Gao Yang, Lihua Li, Wing Bun Lee, and Man Cheung Ng. 2018. Structure of graphene and its disorders: A review. Sci. Technol. Adv. Mater. 19, 1 (2018), 613--648.
[48]
Y. Yang and R. Murali. 2010. Impact of size effect on graphene nanoribbon transport. IEEE Electron. Device Lett. 31, 3 (Mar. 2010), 237--239.
[49]
Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, and S.-S. Pei. 2008. Graphene segregated on Ni surfaces and transferred to insulators. Appl. Phys. Lett. 93, 11 (Nov. 2008), 111 103.
[50]
Z. Z. Zhang, Z. H. Wu, Kai Chang, and F. M. Peeters. 2009. Resonant tunneling through S- and U-shaped graphene nanoribbons. Nanotechnology 20, 41 (2009), 415203.

Cited By

View all
  • (2023)Layer-Minimization-Oriented GNR Area Routing2023 30th IEEE International Conference on Electronics, Circuits and Systems (ICECS)10.1109/ICECS58634.2023.10382834(1-4)Online publication date: 4-Dec-2023
  • (2023)A novel routing algorithm for GNR based interconnect considering area optimization, interconnect-reliability and timing issuesAnalog Integrated Circuits and Signal Processing10.1007/s10470-023-02170-y116:1-2(49-67)Online publication date: 1-Aug-2023
  • (2023)Reduction of Interconnect Delay and Resistance While Minimizing Grid Area in GNR-Based VLSI Routing ProblemEmerging Electronic Devices, Circuits and Systems10.1007/978-981-99-0055-8_8(85-97)Online publication date: 1-May-2023
  • Show More Cited By

Index Terms

  1. A Global Routing Method for Graphene Nanoribbons Based Circuits and Interconnects

    Recommendations

    Comments

    Please enable JavaScript to view thecomments powered by Disqus.

    Information & Contributors

    Information

    Published In

    cover image ACM Journal on Emerging Technologies in Computing Systems
    ACM Journal on Emerging Technologies in Computing Systems  Volume 16, Issue 3
    Special Issue on Nanoelectronic Device, Circuit, and Architecture Design, Part 1 and Regular Papers
    July 2020
    214 pages
    ISSN:1550-4832
    EISSN:1550-4840
    DOI:10.1145/3399633
    • Editor:
    • Ramesh Karri
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Journal Family

    Publication History

    Published: 22 May 2020
    Online AM: 07 May 2020
    Accepted: 01 February 2020
    Revised: 01 December 2019
    Received: 01 August 2018
    Published in JETC Volume 16, Issue 3

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Carbon nanomaterial
    2. global routing
    3. graphene nanoribbon
    4. hexagonal steiner tree

    Qualifiers

    • Research-article
    • Research
    • Refereed

    Funding Sources

    • MeitY Government of India for supporting the research work carried out

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)5
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 12 Dec 2024

    Other Metrics

    Citations

    Cited By

    View all
    • (2023)Layer-Minimization-Oriented GNR Area Routing2023 30th IEEE International Conference on Electronics, Circuits and Systems (ICECS)10.1109/ICECS58634.2023.10382834(1-4)Online publication date: 4-Dec-2023
    • (2023)A novel routing algorithm for GNR based interconnect considering area optimization, interconnect-reliability and timing issuesAnalog Integrated Circuits and Signal Processing10.1007/s10470-023-02170-y116:1-2(49-67)Online publication date: 1-Aug-2023
    • (2023)Reduction of Interconnect Delay and Resistance While Minimizing Grid Area in GNR-Based VLSI Routing ProblemEmerging Electronic Devices, Circuits and Systems10.1007/978-981-99-0055-8_8(85-97)Online publication date: 1-May-2023
    • (2022)Reliability Aware Global Routing of Graphene Nanoribbon Based InterconnectVLSI Design and Test10.1007/978-3-031-21514-8_31(373-386)Online publication date: 17-Dec-2022

    View Options

    Login options

    Full Access

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    HTML Format

    View this article in HTML Format.

    HTML Format

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media