Abstract
This paper presents an electro-thermal radio frequency (RF) model and performance analysis for multilayer graphene nanoribbon (MLGNR) interconnects. The number of conduction channels is calculated as a function of temperature and Fermi energy. A comprehensive model is developed to calculate the temperature dependent effective mean free path (MFP) considering different scattering mechanisms. The RF model of doped and undoped metallic top-contact (TC), as well as side-contact (SC) MLGNR interconnects is demonstrated using ABCD parameter based multi-conductor transmission line formalism. The RF performance of arsenic pentafluoride (\(\text {AsF}_5\)), lithium (Li) and ferric chloride (\(\text {FeCl}_3\)) intercalation doped TC-MLGNR interconnects is investigated and compared with pristine (undoped) TC and SC-MLGNR interconnects for different temperatures. For the first time, our investigation shows that the electro-thermal RF performance of TC-MLGNR can be improved by intercalation doping. It is found that \(\text {AsF}_5\), Li and \(\text {FeCl}_3\) intercalated top-contact MLGNR can operate up to a few GHz for semi-global interconnects (\(100\,\upmu \)m) and several MHz for global interconnects (\(500\,\upmu \)m). Our analysis also proves that the Li intercalated TC-MLGNR shows the best RF performance as compared to conventional copper, pristine, and other type of intercalation doped TC-MLGNR interconnects over the chip operating temperature range from 233 to 378 K. The performance of Li intercalated TC-MLGNR has been found to be improved further by increasing the specularity during fabrication.
Similar content being viewed by others
References
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Electric field effect in atomically thin carbon films. Science 306(5696), 666–669 (2004)
Avouris, P., Chen, Z., Perebeinos, V.: Carbon based electronics. Nat. Nanotechnol. 2(10), 605–615 (2007)
Xu, C., Li, H., Banerjee, K.: Modeling, analysis, and design of graphene nano-ribbon interconnects. IEEE Trans. Electron Devices 56(8), 1567–1578 (2009)
Cui, J.P., Zhao, W.S., Yin, W.Y., Hu, J.: Signal transmission analysis of multilayer graphene nano-ribbon (MLGNR) interconnects. IEEE Trans. Electromagn. Compat. 54(1), 126–132 (2012)
Zhao, W.S., Yin, W.Y.: Comparative study on multilayer graphene nanoribbon (MLGNR) interconnects. IEEE Trans. Electromagn. Compat. 56(3), 638–645 (2014)
Nishad, A.K., Sharma, R.: Analytical time-domain models for performance optimization of multilayer GNR interconnects. IEEE J. Sel. Top. Quantum Electron. 20(1), 1–8 (2014)
Naeemi, A., Meindl, J.D.: Compact physics-based circuit models for graphene nanoribbon interconnects. IEEE Trans. Electron Devices 56(9), 1822–1833 (2009)
Naeemi, A., Meindl, J.D.: Conductance modeling for graphene nanoribbon (GNR) interconnects. IEEE Electron Device Lett. 28(5), 428–431 (2007)
Nasiri, S.H., Moravvej-Farshi, M.K., Faez, R.: Stability analysis in graphene nanoribbon interconnects. IEEE Electron Device Lett. 31(12), 1458–1460 (2010)
Chen, X., Akinwande, D., Lee, K.-J., Close, G.F., Yasuda, S., Paul, B.C., Fujita, S., Kong, J., Wong, H.-S.P.: Fully integrated graphene and carbon nanotube interconnects for gigahertz high-speed CMOS electronics. IEEE Trans. Electron. Devices 57(11), 3137–3143 (2010)
Lee, K.J., Qazi, M., Kong, J., Chandrakasan, A.P.: Low-swing signalling on monolithically integrated global grapheme interconnects. IEEE Trans. Electron. Devices 57(12), 3418–3425 (2010)
Sarkar, D., Xu, C., Li, H., Banerjee, K.: High-frequency behavior of graphene-based interconnects—part I: impedance modeling. IEEE Trans. Electron Devices 58(3), 843–852 (2011)
Kumar, V., Rakheja, S., Naeemi, A.: Modeling and optimization for multi-layer graphene nanoribbon conductors. In: IEEE IITC/MAM, pp. 1–3 (2011)
Kumar, V., Rakheja, S., Naeemi, A.: Performance and energy-per-bit modeling of multilayer graphene nanoribbon conductors. IEEE Trans. Electron Devices 59(10), 2753–2761 (2012)
Bao, W., Wan, J., Han, X., Cai, X., Zhu, H., Kim, D., Ma, D., Xu, Y., Munday, J.N., Dennis Drew, H., Fuhrer, M.S., Hu, L.: Approaching the limits of transparency and conductivity in graphitic materials through lithium intercalation. Nat. Commun. 5, 4224 (2014)
Jiang, J., Kang, J., Cao, W., Xie, X., Zhang, H., Chu, J., Liu, W., Banerjee, K.: Intercalation doped multilayer-graphene-nanoribbons for next-generation interconnects. Nano Lett. 17(3), 1482–1488 (2017)
ITRS International Technology Working Groups, International Technology Roadmap for Semiconductors (2013)
Jiang, J., Kang, J., Banerjee, K.: Characterization of self-heating and current-carrying capacity of intercalation doped graphene-nanoribbon interconnects. In: IEEE International Reliability Physics Symposium (IRPS) (2017)
Bhattacharya, S., Das, D., Rahaman, H.: Analysis of temperature dependent power supply voltage drop in graphene nanoribbon and Cu based power interconnects. AIMS Mater. Sci. 3(4), 1493–1506 (2016)
Chen, J.H., Jang, C., Xiao, S., Ishigami, M., Fuhrer, M.S.: Intrinsic and extrinsic performance limits of graphene devices on SiO\(_2\). Nat. Nanotechnol. 3, 206–209 (2008)
Fratini, S., Guinea, F.: Substrate-limited electron dynamics in graphene. Phys. Rev. B 77, 195415 (2008)
Nishad, A.K., Sharma, R.: Lithium-intercalated graphene interconnects: prospects for on-chip applications. IEEE J. Electron Devices Soc. 4(6), 485–489 (2016)
Kumar, V.R., Majumder, M.K., Kukkam, N.R., Kaushik, B.K.: Time and frequency domain analysis of MLGNR interconnects. IEEE Trans. Nanotechnol. 14(3), 484–492 (2015)
Kumar, V.R., Majumder, M.K., Alam, A., Kukkam, N.R., Kaushik, B.K.: Stability and delay analysis of multi-layered GNR and multi-walled CNT interconnects. J. Comput. Electron. 14(2), 611–618 (2015)
Reddy, K.N., Majumder, M.K., Kaushik, B.K.: Delay uncertainty in MLGNR interconnects under process induced variations of width, doping, dielectric thickness and mean free path. J. Comput. Electron. 13(3), 639–646 (2014)
Rai, M.K., Sarkar, S., Kaushik, B.K.: Performance analysis of multilayer graphene nanoribbon (MLGNR) interconnects. J. Comput. Electron. 15(2), 358–366 (2016)
Rai, M.K., Arora, S., Kaushik, B.K.: Temperature dependent modeling and performance analysis of coupled MLGNR interconnects. Int. J. Circuit Theory Appl. 46, 299–312 (2018)
Clayton, P.R.: Analysis of Multiconductor Transmission Lines. Wiley, New York (1994)
Dresselhaus, M.S., Dresselhaus, G.: Intercalation compounds of graphite. Adv. Phys. 51(1), 1–186 (2002)
Enoki, T., Suzuki, M., Endo, M.: Graphite Intercalation Compounds and Applications. Oxford University Press, New York (2003)
Neto, A.H.C., Guinea, F., Peres, N., Novoselov, K., Geim, A.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)
Rakheja, S., Kumar, V., Naeemi, A.: Evaluation of the potential performance of graphene nano-ribbons as on chip interconnects. Proc. IEEE 101(7), 1740–1765 (2013)
Morozov, S., Novoselov, K., Katsnelson, M.: Giant intrinsic carrier mobilities in graphene and its bilayer. Phys. Rev. Lett. 100, 016602 (2008)
Perebeinos, V., Avouris, P.: Inelastic scattering and current saturation in graphene. Phys. Rev. B 81(19), 195442 (2010)
Nishad, A.K., Sharma, R.: Self-consistent capacitance model for multilayer graphene nanoribbon interconnects. Micro Nano Lett. 10(8), 404–407 (2015)
Nishad, A.K., Sharma, R.: Performance improvement in SC-MLGNRs interconnects using interlayer dielectric insertion. IEEE Trans. Emerg. Top. Comput. 3(4), 470–482 (2015)
Stellari, F., Lacaita, A.L.: New formulas of interconnect capacitances based on results of conformal mapping method. IEEE Trans. Electron Devices 47(1), 222–231 (2000)
Banerjee, K., Mehrotra, A.: Analysis of on-chip inductance effects for distributed RLC interconnects. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 21(8), 904–915 (2002)
Kumar, M.G., Chandel, R., Agrawal, Y.: Timing and stability analysis of carbon nanotube interconnects. In: IEEE International Symposium on Nanoelectronic and Information Systems, pp. 308–313 (2015)
Bointon, T.H., Khrapach, I., Yakimova, R., Shytov, A.V., Craciun, M.F., Russo, S.: Approaching magnetic ordering in graphene materials by FeCl\(_3\) intercalation. Nano Lett. 14(4), 1751–1755 (2014)
Khrapach, I., Withers, F., Bointon, T.H., Polyushkin, D.K., Barnes, W.L., Russo, S., Craciun, M.F.: Novel highly conductive and transparent graphene based conductors. Adv. Mater. 24, 2844–2849 (2012)
Voiry, D., Yamaguchi, H., Li, J.W., Silva, R., Alves, D.C.B., Fujita, T., Chen, M.W., Asefa, T., Shenoy, V.B., Eda, G., Chhowalla, M.: Enhanced catalytic activity in strained chemically exfoliated WS\(_2\) nanosheets for hydrogen evolution. Nat. Mater. 12, 850–855 (2013)
Seeland, J.A., Dahn, J.R.: Abstract 100, The Electrochemical Society Meeting Abstracts, Vol. 2000-2, Phoenix, AZ, Oct 22–27 (2000)
Wan, J., Lacey, S.D., Dai, J., Bao, W., Fuhrer, M.S., Hu, L.: Tuning two-dimensional nanomaterials by intercalation: materials, properties and applications. Chem. Soc. Rev. 45, 6742–6765 (2016)
Whittingham, M.S., Jacobson, A.J.: Intercalation Chemistry. Academic, New York (1982)
Kahng, A.B., Muddu, S.: An analytical delay model for RLC interconnects. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 16(12), 1507–1514 (1997)
Li, X.C., Mao, J.F., Huang, H.F., Liu, Y.: Global interconnect width and spacing optimization for latency, bandwidth and power dissipation. IEEE Trans. Electron Devices 52(10), 2272–2279 (2005)
Acknowledgements
This work has been partially supported by SMDP-C2SD, DeitY, MCIT, India. The authors would like to thank Dr. P. S. Gupta and Dr. S. Kanungo for their valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Das, S., Das, D. & Rahaman, H. Electro-thermal RF modeling and performance analysis of graphene nanoribbon interconnects. J Comput Electron 17, 1695–1708 (2018). https://doi.org/10.1007/s10825-018-1245-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-018-1245-2