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Measurement of the quantum capacitance of graphene

Nature Nanotechnology volume 4, pages 505–509 (2009)Cite this article

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Abstract

Graphene has received widespread attention due to its unique electronic properties1,2,3,4,5. Much of the research conducted so far has focused on electron mobility, which is determined by scattering from charged impurities and other inhomogeneities6,7. However, another important quantity, the quantum capacitance, has been largely overlooked. Here, we report a direct measurement of the quantum capacitance of graphene as a function of gate potential using a three-electrode electrochemical configuration. The quantum capacitance has a non-zero minimum at the Dirac point and a linear increase on both sides of the minimum with relatively small slopes. Our findings—which are not predicted by theory for ideal graphene—suggest that charged impurities also influences the quantum capacitance. We also measured the capacitance in aqueous solutions at different ionic concentrations, and our results strongly indicate that the long-standing puzzle about the interfacial capacitance in carbon-based electrodes has a quantum origin.

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Figure 1: Single-layer graphene device.
Figure 2: Capacitance of graphene as a function of gate potential.
Figure 3: Dependence of quantum capacitance on graphene.
Figure 4: Capacitance of graphene in aqueous solution.

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Change history

  • 15 July 2009

    In the version of this Letter initially published online, Fig. 2b was incorrect. This error has been corrected for all versions.

References

  1. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  CAS  Google Scholar 

  2. Chen, J. H., Jang, C., Xiao, S. D., Ishigami, M. & Fuhrer, M. S. Intrinsic and extrinsic performance limits of graphene devices on SiO2 . Nature Nanotech. 3, 206–209 (2008).

    Article  CAS  Google Scholar 

  3. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007).

    Article  CAS  Google Scholar 

  4. Meric, I. et al. Current saturation in zero-bandgap, top-gated graphene field-effect transistors. Nature Nanotech. 3, 654–659 (2008).

    Article  CAS  Google Scholar 

  5. Schedin, F. et al. Detection of individual gas molecules adsorbed on graphene. Nature Mater. 6, 652–655 (2007).

    Article  CAS  Google Scholar 

  6. Martin, J. et al. Observation of electron–hole puddles in graphene using a scanning single-electron transistor. Nature Phys. 4, 144–148 (2008).

    Article  CAS  Google Scholar 

  7. Das, A. et al. Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor. Nature Nanotech. 3, 210–215 (2008).

    Article  CAS  Google Scholar 

  8. Tan, Y. W. et al. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 99, 246803 (2007).

    Article  Google Scholar 

  9. Trushin, M. & Schliemann, J. Minimum electrical and thermal conductivity of graphene: a quasiclassical approach. Phys. Rev. Lett. 99, 216602 (2007).

    Article  Google Scholar 

  10. Chen, Z. & Appenzeller, J. Mobility extraction and quantum capacitance impact in high performance graphene field-effect transistor devices. IEEE IEDM Tech. Digest 21.1, 509–512 (2008).

    Google Scholar 

  11. John, D. L., Castro, L. C. & Pulfrey, D. L. Quantum capacitance in nanoscale device modeling. J. Appl. Phys. 96, 5180–5184 (2004).

    Article  CAS  Google Scholar 

  12. Fang, T., Konar, A., Xing, H. L. & Jena, D. Carrier statistics and quantum capacitance of graphene sheets and ribbons. Appl. Phys. Lett. 91, 092109 (2007).

    Article  Google Scholar 

  13. Giannazzo, F., Sonde, S., Raineri, V. & Rimini, E. Screening length and quantum capacitance in graphene by scanning probe microscopy. Nano Lett. 9, 23–29 (2009).

    Article  CAS  Google Scholar 

  14. Ishigami, M., Chen, J. H., Cullen, W. G., Fuhrer, M. S. & Williams, E. D. Atomic structure of graphene on SiO2 . Nano Lett. 7, 1643–1648 (2007).

    Article  CAS  Google Scholar 

  15. Stolyarova, E. et al. High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface. Proc. Natl Acad. Sci. USA 104, 9209–9212 (2007).

    Article  CAS  Google Scholar 

  16. Baldelli, S. Surface structure at the ionic liquid-electrified metal interface. Acc. Chem. Res. 41, 421–431 (2008).

    Article  CAS  Google Scholar 

  17. Chen, J. H. et al. Charged-impurity scattering in graphene. Nature Phys. 4, 377–381 (2008).

    Article  CAS  Google Scholar 

  18. Adam, S., Hwang, E. H., Galitski, V. M. & Das Sarma, S. A self-consistent theory for graphene transport. Proc. Natl Acad. Sci. USA 104, 18392–18397 (2007).

    Article  CAS  Google Scholar 

  19. Victor, M. G., Shaffique, A. & Sarma, S. D. Statistics of random voltage fluctuations and the low-density residual conductivity of graphene. Phys. Rev. B 76, 245405 (2007).

    Article  Google Scholar 

  20. Ando, T. Screening effect and impurity scattering in monolayer graphene. J. Phys. Soc. Jpn 75, 074716 (2006).

    Article  Google Scholar 

  21. Jang, C. et al. Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering. Phys. Rev. Lett. 101, 146805 (2008).

    Article  CAS  Google Scholar 

  22. Cho, S. & Fuhrer, M. S. Charge transport and inhomogeneity near the minimum conductivity point in graphene. Phys. Rev. B 77, 081402 (2008).

    Article  Google Scholar 

  23. Randin, J. P. & Yeager, E. Differential capacitance study of stress/annealed pyrolytic graphite electrodes. J. Electrochem. Soc. 118, 711–714 (1971).

    Article  CAS  Google Scholar 

  24. Bockris, J. O. M. Modern Electrochemistry: An Introduction to an Interdisciplinary Area 1st edn (Plenum Press, 1970).

    Book  Google Scholar 

  25. Randin, J. P. & Yeager, E. Differential capacitance study on basal plane of stress-annealed pyrolytic-graphite. J. Electroanal. Chem. 36, 257–276 (1972).

    Article  CAS  Google Scholar 

  26. Chen, F., Xia, J. L. & Tao, N. J. Ionic screening of charged-impurity scattering in graphene. Nano Lett. 9, 1621–1625 (2009).

    Article  CAS  Google Scholar 

  27. Zhou, S. Y. et al. First direct observation of Dirac fermions in graphite. Nature Phys. 2, 595–599 (2006).

    Article  CAS  Google Scholar 

  28. http://www.semicorp.com.

  29. Blake, P. et al. Making graphene visible. Appl. Phys. Lett. 91, 063124 (2007).

    Article  Google Scholar 

  30. Gao, L. B., Ren, W. C., Li, F. & Cheng, H. M. Total color difference for rapid and accurate identification of graphene. ACS Nano 2, 1625–1633 (2008).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank the Department of Energy (DE-FG03-01ER45943; J.L.X.) and the National Science Foundation (CHE-0554786; F.C.) for financial support.

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Authors and Affiliations

  1. Department of Electrical Engineering, Center for Bioelectronics and Biosensors, Biodesign Institute, Arizona State University, Tempe, 85287, Arizona, USA

    Jilin Xia, Fang Chen & Nongjian Tao

  2. Department of Chemistry, Tsinghua University, Beijing, 100084, China

    Jinghong Li

Authors
  1. Jilin Xia
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  2. Fang Chen
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  3. Jinghong Li
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  4. Nongjian Tao
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Contributions

J.L.X. carried out the experiments and data analysis. F.C. assisted with the experiments. J.H.L. provided critical sample preparation. N.J.T. conceived the experiment and wrote the manuscript.

Corresponding authors

Correspondence to Jinghong Li or Nongjian Tao.

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Xia, J., Chen, F., Li, J. et al. Measurement of the quantum capacitance of graphene. Nature Nanotech 4, 505–509 (2009). https://doi.org/10.1038/nnano.2009.177

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