Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Controlled ripple texturing of suspended graphene and ultrathin graphite membranes

Abstract

Graphene is nature's thinnest elastic material and displays exceptional mechanical1,2 and electronic properties3,4,5. Ripples are an intrinsic feature of graphene sheets6 and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials7,8,9,10,11,12. The ability to control ripple structure in graphene could allow device design based on local strain13 and selective bandgap engineering14. Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions and making use of graphene's negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices15,16, a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Images, morphology and strain of suspended graphene sheets.
Figure 2: Dependence of ripple morphology on temperature.
Figure 3: Thermomechanical manipulation of the amplitude and orientation of the ripples.
Figure 4: TEC measurement of suspended graphene membranes.

References

  1. Bunch, J. S. et al. Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007).

    Article  CAS  Google Scholar 

  2. Lee, C., Wei, X. D., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005).

    Article  CAS  Google Scholar 

  5. Miao, F. et al. Phase coherent transport in graphene quantum billiards. Science 317, 1530–1533 (2007).

    Article  CAS  Google Scholar 

  6. Meyer, J. C. et al. The structure of suspended graphene sheets. Nature 446, 60–63 (2007).

    Article  CAS  Google Scholar 

  7. Guinea, F., Horovitz, B. & Le Doussal, P. Gauge field induced by ripples in graphene. Phys. Rev. B 77, 205421 (2008).

    Article  Google Scholar 

  8. Guinea, F., Katsnelson, M. I. & Vozmediano, M. A. H. Midgap states and charge inhomogeneities in corrugated graphene. Phys. Rev. B 77, 075422 (2008).

    Article  Google Scholar 

  9. de Parga, A. L. V. et al. Periodically rippled graphene: growth and spatially resolved electronic structure. Phys. Rev. Lett. 100, 056807 (2008).

    Article  Google Scholar 

  10. Kim, E.-A. & Castro Neto, A. H. Graphene as an electronic membrane. Europhys. Lett. 84, 057007 (2008).

    Article  Google Scholar 

  11. Katsnelson, M. I. & Geim, A. K. Electron scattering on microscopic corrugations in graphene. Phil. Trans. Roy. Soc. A 366, 195–204 (2008).

    Article  CAS  Google Scholar 

  12. Morozov, S. V. et al. Giant intrinsic carrier mobilities in graphene and its bilayer. Phys. Rev. Lett. 100, 016602 (2008).

    Article  CAS  Google Scholar 

  13. Pereira, V. M. & Castro Neto, A. H. All-graphene integrated circuits via strain engineering. Preprint at <http://arXiv.org/abs/0810.4539v1> (2008).

  14. Elias, D. C. et al. Control of graphene's properties by reversible hydrogenation. Science 323, 610–613 (2009).

    Article  CAS  Google Scholar 

  15. Du, X., Skachko, I., Barker, A. & Andrei, E. Y. Approaching ballistic transport in suspended graphene. Nature Nanotech. 3, 491–495 (2008).

    Article  CAS  Google Scholar 

  16. Bolotin, K. I., Sikes, K. J., Hone, J., Stormer, H. L. & Kim, P. Temperature-dependent transport in suspended graphene. Phys. Rev. Lett. 101, 096802 (2008).

    Article  CAS  Google Scholar 

  17. Cerda, E. & Mahadevan, L. Geometry and physics of wrinkling. Phys. Rev. Lett. 90, 074302 (2003).

    Article  CAS  Google Scholar 

  18. Lifshitz, E. M. & Landau, L. D. Theory of Elasticity 3rd edn, Vol. 7 (Butterworth-Heinemann, 1986).

  19. Zakharchenko, K. V., Katsnelson, M. I. & Fasolino, A. Finite temperature lattice properties of graphene beyond the quasiharmonic approximation. Phys. Rev. Lett. 102, 046808 (2009).

    Article  CAS  Google Scholar 

  20. Scarpa, F., Adhikari, S. & Phani, A. S. Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology 20, 065709 (2009).

    Article  CAS  Google Scholar 

  21. Wong, Y. W. & Pellegrino, S. Wrinkled membranes. Part II: analytical models. J. Mech. Mater. Struct. 1, 25–29 (2006).

    Google Scholar 

  22. Blakslee, O. L., Proctor, D. G., Seldin, E. J., Spence, G. B. & Weng, T. Elastic constants of compression-annealed pyrolytic graphite. J. Appl. Phys. 41, 3373–3382 (1970).

    Article  CAS  Google Scholar 

  23. Peyla, P. Buckling of a compressed elastic membrane: a simple model. Eur. Phys. J. B 48, 379–383 (2005).

    Article  CAS  Google Scholar 

  24. Simon, M. E. & Varma, C. M. Dynamics of some constrained lattices. Phys. Rev. Lett. 86, 1781–1784 (2001).

    Article  CAS  Google Scholar 

  25. Bowden, N., Brittain, S., Evans, A., Hutchinson, J. W. & Whitesides, G. M. Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature 393, 146–149 (1998).

    Article  CAS  Google Scholar 

  26. Isacsson, A., Jonsson, L. M., Kinaret, J. M. & Jonson, M. Electronic superlattices in corrugated graphene. Phys. Rev. B 77, 035423 (2008).

    Article  Google Scholar 

  27. Park, C. H., Son, Y. W., Yang, L., Cohen, M. L. & Louie, S. G. Electron beam supercollimation in graphene superlattices. Nano Lett. 8, 2920–2924 (2008).

    Article  CAS  Google Scholar 

  28. Mounet, N. & Marzari, N. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite and derivatives. Phys. Rev. B 71, 205214 (2005).

    Article  Google Scholar 

  29. Kwon, Y. K., Berber, S. & Tomanek, D. Thermal contraction of carbon fullerenes and nanotubes. Phys. Rev. Lett. 92, 015901 (2004).

    Article  Google Scholar 

  30. Schelling, P. K. & Keblinski, R. Thermal expansion of carbon structures. Phys. Rev. B 68, 035425 (2003).

    Article  Google Scholar 

  31. Watanabe, H., Yamada, N. & Okaji, M. Linear thermal expansion coefficient of silicon from 293 to 1,000 K. Int. J. Thermophys. 25, 221–236 (2004).

    Article  CAS  Google Scholar 

  32. Wehling, T. O., Balatsky, A. V., Tsvelik, A. M., Katnelson, M. I. & Lichtenstein, A. I. Midgap states in corrugated graphene: ab-initio calculations and effective field theory. Europhys. Lett. 84, 017003 (2008).

    Article  Google Scholar 

  33. Herbut, I. F., Juricic, V. & Vafek, O. Coulomb interaction, ripples and the minimal conductivity of graphene. Phys. Rev. Lett. 100, 046403 (2008).

    Article  Google Scholar 

  34. Brey, L. & Palacios, J. J. Exchange-induced charge inhomogeneities in rippled neutral graphene. Phys. Rev. B 77, 041403 (2008).

    Article  Google Scholar 

  35. de Juan, F., Cortijo, A. & Vozmediano, M. A. H. Charge inhomogeneities due to smooth ripples in graphene sheets. Phys. Rev. B 76, 165409 (2007).

    Article  Google Scholar 

Download references

Acknowledgements

We thank M. Bockrath and G. Xu for discussions, and B. Chim, D. Yan and Z. Zhao for assistance with SEM imaging. This research is supported in part by NSF/CAREER DMR/0748910, NSF/CBET 0756359, ONR N00014-09-1-0724 and ONR/DMEA H94003-09-2-0901. The trenches were fabricated at the UCSB nanofabrication facility.

Author information

Authors and Affiliations

Authors

Contributions

C.N.L. and W.B. conceived the experiments. C.N.L., C.D. and W.B. designed the experiments and interpreted the data. C.N.L., W.B., F.M. and H.Z. analysed the data. W.B., F.M., Z.C. and W.J. performed the experiments. Z.C. performed numerical simulations. C.N.L. and C.D. co-wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Chun Ning Lau.

Supplementary information

Supplementary information

Supplementary information (PDF 1603 kb)

Supplementary information

Supplementary movie (MOV 8439 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bao, W., Miao, F., Chen, Z. et al. Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nature Nanotech 4, 562–566 (2009). https://doi.org/10.1038/nnano.2009.191

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2009.191

This article is cited by

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research