The princess and the pea at the nanoscale: Wrinkling and delamination of graphene on nanoparticles

Physical Review X

Volumn 2, Issue 4, 2012, Pages

  Yamamoto, Mahito ^a   Pierre Louis, Olivier ^b   Huang, Jia ^a   Fuhrer, Michael S ^a   Einstein, Theodore L ^a   Cullen, William G ^a  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

Condensed matter Physics; Graphene

Indexed keywords

COMPLEX RESPONSE; ELECTRONIC PROPERTIES OF GRAPHENE; EXTERNAL FORCE; GEOMETRICAL CONSTRAINTS; NANOPARTICLE DENSITY; PERCOLATING NETWORKS; SILICA NANOPARTICLES; SILICA SUBSTRATE;

CONDENSED MATTER PHYSICS; DELAMINATION; ELECTRONIC PROPERTIES; GRAPHENE; PLANTS (BOTANY);

NANOPARTICLES;

EID: 84880896251     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.2.041018     Document Type: Article

References (47)

1. N. Bowden, S. Brittain, A. G. Evans, J.W. Hutchinson, and G. M. Whitesides, Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer, Nature (London) 393, 146 (1998).
2. J. Huang, M. Juszkiewicz, W. H. de Jeu, E. Cerda, T. Emrick, N. Menon, and T. P. Russell, Capillary Wrinkling of Floating Thin Polymer Films, Science 317, 650 (2007).
3. E. Cerda, L. Mahadevan, and J. M. Pasini, The Elements of Draping, Proc. Natl. Acad. Sci. U.S.A. 101, 1806 (2004).
4. E. Cerda and L. Mahadevan, Geometry and Physics of Wrinkling, Phys. Rev. Lett. 90, 074302 (2003).
5. T. A. Witten, Stress Focusing in Elastic Sheets, Rev. Mod. Phys. 79, 643 (2007).
6. D.-Y. Khang, H. Jiang, Y. Huang, and J. A. Rogers, A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates, Science 311, 208 (2006).
7. Y. Sun, W. M. Choi, H. Jiang, Y.Y. Huang, and J. A. Rogers, Controlled Buckling of Semiconductor Nanoribbons for Stretchable Electronics, Nat. Nanotechnol. 1, 201 (2006).
8. Y. Huang, J. Wu, and K. C. Hwang, Thickness of Graphene and Single-Wall Carbon Nanotubes, Phys. Rev. B 74, 245413 (2006).
9. A. Fasolino, J. H. Los, and M. I. Katsnelson, Intrinsic Ripples in Graphene, Nat. Mater. 6, 858 (2007).
10. C. Lee, X. Wei, J.W. Kysar, and J. Hone, Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene, Science 321, 385 (2008).
11. O. Pierre-Louis, Adhesion of Membranes and Filaments on Rippled Surfaces, Phys. Rev. E 78, 021603 (2008).
12. C.Y. Wang, K. Mylvaganam, and L. C. Zhang, Wrinkling of Monolayer Graphene: A Study by Molecular Dynamics and Continuum Plate Theory, Phys. Rev. B 80, 155445 (2009).
13. T. Li and Z. Zhang, Snap-Through Instability of Graphene on Substrates, Nanoscale Res. Lett. 5, 169 (2009).
14. Z. H. Aitken and R. Huang, Effects of Mismatch Strain and Substrate Surface Corrugation on Morphology of Supported Monolayer Graphene, J. Appl. Phys. 107, 123531 (2010).
15. S. Viola Kusminskiy, D.K. Campbell, A. H. Castro Neto, and F. Guinea, Pinning of a Two-Dimensional Membrane on Top of a Patterned Substrate: The Case of Graphene, Phys. Rev. B 83, 165405 (2011).
16. T. J.W. Wagner and D. Vella, The Sensitivity of Graphene "Snap-Through"to Substrate Geometry, Appl. Phys. Lett. 100, 233111 (2012).
17. W. G. Cullen, M. Yamamoto, K. M. Burson, J. H. Chen, C. Jang, L. Li, M. S. Fuhrer, and E. D. Williams, High-Fidelity Conformation of Graphene to SiO2 Topographic Features, Phys. Rev. Lett. 105, 215504 (2010).
18. W. Bao, F. Miao, Z. Chen, H. Zhang, W. Jang, C. Dames, and C. N. Lau, Controlled Ripple Texturing of Suspended Graphene and Ultrathin Graphite Membranes, Nat. Nanotechnol. 4, 562 (2009).
19. Z. Li, Z. Cheng, R. Wang, Q. Li, and Y. Fang, Spontaneous Formation of Nanostructures in Graphene, Nano Lett. 9, 3599 (2009).
20. S. Scharfenberg, D. Z. Rocklin, C. Chialvo, R. L. Weaver, P. M. Goldbart, and N. Mason, Probing the Mechanical Properties of Graphene Using Corrugated Elastic Substrate, Appl. Phys. Lett. 98, 091908 (2011).
21. S. Scharfenberg, N. Mansukhani, C. Chialvo, R. L. Weaver, and N. Mason, Observation of Snap-Through Instability in Graphene, Appl. Phys. Lett. 100, 021910 (2012).
22. V. M. Pereira, A. H. Castro Neto, H.Y. Liang, and L. Mahadevan, Geometry, Mechanics, and Electronics of Singular Structures and Wrinkles in Graphene, Phys. Rev. Lett. 105, 156603 (2010).
23. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009).
24. N. Levy, S.A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. Castro Neto, and M. F. Crommie, Strain-Induced Pseudo-Magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles, Science 329, 544 (2010).
25. F. Guinea, M. I. Katsnelson, and A. K. Geim, Energy Gaps and a Zero-Field Quantum Hall Effect in Graphene by Strain Engineering, Nat. Phys. 6, 30 (2010).
26. V. M. Pereira and A. H. Castro Neto, Strain Engineering of Graphene's Electronic Structure, Phys. Rev. Lett. 103, 046801 (2009).
27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevX.2.041018 for the distribution of nanoparticle heights, the distribution of wrinkle lengths, the distribution of opening angles produced by the neighboring wrinkles, the orientations of wrinkles, the distribution of the number of wrinkles propagating form single protrusions, and the particle-particle correlation functions.
28. M. Ishigami, J. H. Chen, W. G. Cullen, M. S. Fuhrer, and E. D. Williams, Atomic Structure of Graphene on SiO2, Nano Lett. 7, 1643 (2007).
29. C. H. Lui, L. Lui, K. F. Mak, G.W. Flynn, and T. F. Heinz, Ultraflat Graphene, Nature (London) 462, 339 (2009).
30. J. Xue, J. Sanchez-Yamagishi, D. Bulmash, P. Jacquod, A. Deshpande, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, and B. J. LeRoy, Scanning Tunneling Microscopy and Spectroscopy of Ultra-Flat Graphene on Hexagonal Boron Nitride, Nat. Mater. 10, 282 (2011).
31. A. Lobkovsky, S. Gentges, H. Li, D. Morse, and T. A. Witten, Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet, Science 270, 1482 (1995).
32. S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. Scott Bunch, Ultrastrong Adhesion of Graphene Membranes, Nat. Nanotechnol. 6, 543 (2011).
33. D. L. González and T. L. Einstein, Voronoi Cell Patterns: Theoretical Model and Applications, Phys. Rev. E 84, 051135 (2011).
34. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, Washington, DC, 1992).
35. E. T. Gawlinski and H. E. Stanley, Continuum Percolation in Two Dimensions: Monte Carlo Tests of Scaling and Universality for Non-Interacting Discs, J. Phys. A 14, L291 (1981).
36. S. N. Magonov, V. Elings, and M.-H. Whangbo, Phase Imaging and Stiffness in Tapping-Mode Atomic Force Microscopy, Surf. Sci. 375, L385 (1997).
37. J. Nicolle, D. Machon, P. Poncharal, O. Pierre-Louis, and A. San-Miguel, Pressure-Mediated Doping in Graphene, Nano Lett. 11, 3564 (2011).
38. M. Poot and H. S. J. van der Zant, Nanomechanical Properties of Few-Layer Graphene Membranes, Appl. Phys. Lett. 92, 063111 (2008).
39. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon Press, New York, 1970).
40. E. Schwerin, Ü ber Spannungen und Formänderungen Kreisringförmiger Membranen, Z. Angew. Math. Mech. 9, 482 (1929).
41. Z. Zong, C.-L. Chen, M. R. Dokmeci, and K.-T. Wan, Direct Measurement of Graphene Adhesion on Silicon Surface by Intercalation of Nanoparticles, J. Appl. Phys. 107, 026104 (2010).
42. U. Komaragiri, M. R. Begley, and J. G. Simmonds, The Mechanical Response of Freestanding Circular Elastic Films under Point and Pressure Loads, J. Appl. Mech. 72, 203 (2005).
43. H. Suzuura and T. Ando, Phonons and Electron-Phonon Scattering in Carbon Nanotubes, Phys. Rev. B 65, 235412 (2002).
44. N. N. Klimov, S. Jung, S. Zhu, T. Li, C. A. Wright, S. D. Solares, D. B. Newell, N. B. Zhitenev, and J. A. Stroscio, Electromechanical Properties of Graphene Drumheads, Science 336, 1557 (2012).
45. M. Neek-Amal, L. Covaci, and F. M. Peeters, Nanoengineered Nonuniform Strain in Graphene Using Nanopillars, Phys. Rev. B 86, 041405(R) (2012).
46. H. Tomori, A. Kanda, H. Goto, Y. Ootsuka, K. Tsukagoshi, S. Moriyama, E. Watanabe, and D. Tsuya, Introducing Nonuniform Strain to Graphene Using Dielectric Nanopillars, Appl. Phys. Express 4, 075102 (2011).
47. U. Seifert and R. Lipowski, Adhesion of Vesicles, Phys. Rev. A 42, 4768 (1990).