On the modeling of resistance in graphene nanoribbon (GNR) for future interconnect applications

ABSTRACT

In this paper, we present a comprehensive model for the resistance in graphene nanoribbon (GNR) interconnects. We use the recent experimental and theoretical results to model the impact of stacking of graphene layers in multi-layer GNR interconnects. We compare the resistance of GNR interconnects with both single-walled carbon nanotube (SWCNT) bundle interconnects and conventional copper interconnects. Our simulation results demonstrate the performance superiority of multi-layer GNR interconnects over conventional copper interconnects at small widths (< 15 nm). Consequently, multi-layer GNR interconnects demonstrate a great potential to replace conventioanl copper interconnects in future technologies.

REFERENCES

• 1: 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, 2004.
• 2: J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, "The structure of suspended graphene sheets," Nature, vol. 446, pp. 60--63, 2007.
• 3: A. K. Geim and K. S. Novoselov, "The rise of graphene," Nature Materials, vol. 6, pp. 183--191, 2007.
• 4: 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, pp. 1191--1196, 2006.
• 5: K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless dirac fermions in graphene," Nature, vol. 438, pp. 197--200, 2005.
• 6: A. Naeemi and J. D. Meindl, "Conductance modeling for graphene nanoribbon (gnr) interconnects," IEEE Electron Device Letters, vol. 28, no. 5, pp. 428--431, 2007.
• 7: J. Guo, Y. Yoon, and Y. Ouyang, "Gate electrostatics and quantum capacitance of graphene nanoribbons," Nano Letters, vol. 7, pp. 1935--1940, 2007.
• 8: G. Liang, N. Neophytou, D. Nikonov, and M. Lundstrom, "Performance projections for ballistic graphene nanoribbon field-effect transistors," IEEE Transactions on Electron Devices, vol. 54, no. 4, pp. 677 -- 682, 2007.
• 9: G. Liang, N. Neophytou, M. Lundstorm, and D. E. Nikonov, "Contact effects in graphene nanoribbon transistors," Nano Letters, 2008.
• 10: F. Munoz-Rojas, J. Fernandez-Rossier, L. Brey, and J. J. Palacios, "Performance limits of graphene-ribbon-based field effect transistors," Physical Review B, vol. 77, 2008.
• 11: G. Fiori and G. Iannaccone, "Simulation of graphene nanoribbon fieldeffect transistors," IEEE Electron Device Letters, vol. 28, no. 8, pp. 760--762, 2007.
• 12: Y. M. Lin and P. Avouris, "Strong suppression of electrical noise in bilayer graphene nanodevices," Nano Letters, 2008.
• 13: S. S. Datta, D. R. Strachan, S. M. Khamis, and A. T. C. Johnson, "Crystallographic etching of few-layer graphene," Nano Letters, vol. 8, pp. 1912--1915, 2008.
• 14: T. Ohta, A. Bostwick, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, "Interlayer interaction and electronic screening in multilayer graphene investigated with angle-resolved photoemission spectroscopy," Physical Review Letters, vol. 98, 2007.
• 15: S. Latil and L. Henrard, "Charge carriers in few-layer graphene films," Physical Review Letters, vol. 97, 2006.
• 16: M. Y. Han, B. Oezyilmaz, Y. Zhang, and P. Kim, "Energy band gap engineering of graphene nanoribbons," Physical Review Letters, vol. 98, 2007.
• 17: P. Burke, "Luttinger Liquid Theory as a Model of the Gigahertz Electrical Properties of Carbon Nanotubes," IEEE Transactions on Nanotechnology, vol. 1, no. 3, pp. 129--144, 2002.
• 18: S. Datta, Electronic Transport in Mesoscopic Systems. Cambridge University Press, 1995.
• 19: J. Fernandez-Rossier, J. J. Palacios, and L. Brey, "Electronic structure of gated graphene and graphene ribbons," Physical Review B, vol. 75, 2007.
• 20: E. H. Hwang, S. Adam, and S. D. Sarma, "Carrier transport in twodimensional graphene layers," Physical Review Letters, vol. 98, 2007.
• 21: J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, "Electric field effect tuning of electron-phonon coupling in graphene," Physical Review Letters, vol. 98, 2007.
• 22: Y. W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. D. Sarma, H. L. Stormer, and P. Kim, "Measurement of scattering rate and minimum conductivity in graphene," Physical Review Letters, vol. 99, 2007.
• 23: J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, "Charged-impurity scattering in graphene," Nature Physics, vol. 4, pp. 377--381, 2008.
• 24: S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, "Giant intrinsic carrier mobilities in graphene and its bilayer," Physical Review Letters, vol. 100, 2008.
• 25: D. Gunlycke, H. M. Lawler, and C. T. White, "Room-temperature ballistic transport in narrow graphene strips," Physical Review B, vol. 75, 2007.
• 26: T. Stauber, N. M. R. Peres, and F. Guinea, "Electronic transport in graphene: A semiclassical approach including midgap states," Physical Review B, vol. 76, 2007.
• 27: D. A. Areshkin, D. Gunlycke, and C. T. White, "Ballistic transport in graphene nanostrips in the presence of disorder: Importance of edge effects," Nano Letters, vol. 7, pp. 204--210, 2007.
• 28: Y.-W. Tan, Y. Zhang, H. L. Stormer, and P. Kim, "Temperature dependent electron transport in graphene," The European Physical Journal - Special Topics, vol. 148, no. 1, pp. 15--18, 2007.
• 29: F. T. Vasko and V. Ryzhii, "Voltage and temperature dependencies of conductivity in gated graphene," Physical Review B, vol. 76, 2007.
• 30: B. Partoens and F. Peeters, "From graphene to graphite: Electronic structure around the k point," Physical Review B, vol. 74, 2006.
• 31: D. Finkenstadt, G. Pennington, and M. J. Mehl, "From graphene to graphite: A general tight-binding approach for nanoribbon carrier transport," Physical Review B, vol. 76, 2007.
• 32: J. Nilsson, A. H. C. Neto, F. Guinea, and N. M. R. Peres, "Electronic properties of graphene multilayers," Physical Review Letters, vol. 97, 2006.
• 33: F. Varchon, R. Feng, J. Hass, X. Li, B. N. Nguyen, C. Naud, P. Mallet, J.-Y. Veuillen, C. Berger, E. H. Conrad, and L. Magaud, "Electronic structure of epitaxial graphene layers on sic:effect of the substrate," Physical Review Letters, vol. 99, 2007.
• 34: H. Min and A. H. MacDonald, "Chiral decomposition in the electronic structure of graphene multilayers," Physical Review B, vol. 77, 2008.
• 35: J. Hass, F. Varchon, J. E. Millan-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, "Why multilayer graphene on 4h-sic(0001) behaves like a single sheet of graphene," Physical Review Letters, vol. 100, 2008.
• 36: International Technology Roadmap for Semiconductors (ITRS), 2007.
• 37: Yehia Massoud , Arthur Nieuwoudt, Modeling and design challenges and solutions for carbon nanotube-based interconnect in future high performance integrated circuits, ACM Journal on Emerging Technologies in Computing Systems (JETC), v.2 n.3, p.155-196, July 2006 [doi>10.1145/1167943.1167944]
• 38: A. Nieuwoudt and Y. Massoud, "On the optimal design, performance, and reliability of future carbon nanotube-based interconnect solutions," IEEE Transactions on Electron Devices, vol. 55, no. 8, pp. 2097--2110, 2008.
• 39: 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.
• 40: A. Nieuwoudt and Y. Massoud, "On the impact of process variations for carbon nanotube bundles for vlsi interconnect," IEEE Transactions on Electron Devices, vol. 54, no. 3, pp. 446--455, 2007.
• 41: Arthur Nieuwoudt , Yehia Massoud, Assessing the Implications of Process Variations on Future Carbon Nanotube Bundle Interconnect Solutions, Proceedings of the 8th International Symposium on Quality Electronic Design, p.119-126, March 26-28, 2007 [doi>10.1109/ISQED.2007.39]
• 42: A. Nieuwoudt and Y. Massoud, "Predicting the performance of low loss on-chip inductors realized using carbon nanotube bundles," IEEE Transactions on Electron Devices, vol. 55, no. 1, pp. 298--312, 2008.