Corrugation of Graphene - Nanotechnology - Lecture Slides, Slides of Nanotechnology

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 Introduction

 Purpose and impact

 Structure of graphene

 Suspended

 Over Ru

 Over SiO 2

 Electrical transport

 Future research

 Conclusion

 According to the Mermin-Wagner theorem crystalline membranes like graphene can exist but they should be rippled.

 These ripples were observed in graphene and it is believed that they play an important role in its electronic properties.

 Intrinsic rippling has been proposed as one of the possible mechanisms for electron scattering to explain the variation in the resistivity with the number of charge carriers experimentally seen in graphene.

 The corrugation and electronic properties of graphene can also be influenced by the substrate where the experiments is carried out.

 The fabrication method can also influence the corrugation of graphene especially if the method introduce oxygen addends.

http://www.thp.uni-koeln.de/graphene08/wavy-graphene.jpeg

 According to the Mermin-Wagner theorem crystalline membranes like graphene can exist but they should be rippled.

 Introduction

 Purpose and impact

 Structure of graphene

 Suspended

 Over Ru

 Over SiO 2

 Electrical transport

 Future research

 Conclusion

 Introduction

 Purpose and impact

 Structure of graphene

 Suspended

 Over Ru

 Over SiO 2

 Electrical transport

 Future research

 Conclusion

 The central part of the suspended graphene normally appear on TEM images as homogeneous and featureless regions (arrows).

 The folds provide a clear TEM signature for the number of graphene layers.

 Monolayer graphene fold exhibits only one dark line (a).

 Bilayer graphene fold exhibits two dark lines (b).

 The edges tend to scroll. Also folded regions are observed.

 Folded graphene is locally parallel to the electron beam.

500nm 2nm^ 2nm

Meyer, JC Geim, AK Katsnelson, MI Novoselov, KS Booth, TJ Roth. “The structure of suspended graphene sheets” NATURE March 2007, 446,7131, 60-

 The full 3D Fourier transform of a flat graphene crystal (a) consists of a set of rods perpendicular to the plane of the reciprocal hexagonal lattice (c).

 In particular, this picture suggests that the intensity of diffraction peaks monotonically change with tilt angle.

 The observed broadening explicitly reveals that graphene sheets are not flat.

 The increasing broadening of diffraction peaks without changes in their total intensity implies that the rods wander around their average direction (d). This corresponds to a slightly uneven sheet (b).

 Such roughness results in sharp diffraction peaks for normal incidence, but that the peaks rapidly become wider with increasing tilt angle (e). Meyer, JC Geim, AK Katsnelson, MI Novoselov, KS Booth, TJ Roth. “The structure of suspended graphene sheets” NATURE March 2007, 446-7131, 60-

 Figures f and g show the detailed evolution of the broadening of the diffraction peaks with changing incidence angle.

 The peak widths increase linearly with tilt and also proportionally to the peaks' position in reciprocal space, in quantitative agreement with the simulations for corrugated graphene.

 The width of the cones in f and g provide a direct measure of the membrane's roughness. For different monolayers the cone angles were between 8° and 11°. For bilayer membranes, this value was found to be about 2° (g).

 The corrugations are less than or equal to 25 nm with a height about 1 nm. Importantly, atomic-resolution images show that the corrugations are static, because otherwise, changes during the exposure would lead to blurring and disappearance of the additional contrast.

Meyer, JC Geim, AK Katsnelson, MI Novoselov, KS Booth, TJ Roth. “The structure of suspended graphene sheets” NATURE March 2007, 446-7131, 60-

 Monolayer graphene is epitaxialy growth on Ru (0001).

 Figure a shows that monoatomic steps and dislocations of the substrate are reproduced by the graphene layer.

 Figure b shows a STM topographic image of graphene showing the formation of ripples. The inset is a Fourier transformation of the image.

 The ripples height are approximately 0.02nm (d).

 Figure c shows the structure model.

Vazquez de Parga, A. L. and Calleja, F. and Borca, B. and Passeggi, M. C. G. and Hinarejos, J. J. and Guinea, F. and Miranda, R. “Periodically Rippled Graphene: Growth and Spatially Resolved Electronic Structure “. Phys. Rev. Lett. 100, 056807,

 Figure a shows spatially resolved dI/dV tunneling spectra, which are roughly proportional to the local density of states (LDOS), recorded on top of the ‘‘high’’ and ‘‘low’’ regions of the corrugated graphene layer. Figure b shows the corresponding calculation.

 The left and right images in the upper panel are maps of dI/dV at 100 meV and 200 meV and reflects the spatial distribution of the LDOS below and above the Fermi level, respectively.

 The central image shows the topographic image recorded simultaneously. The lower panel shows the corresponding calculations for the spatially resolved LDOS for a periodically corrugated graphene layer.

Vazquez de Parga, A. L. and Calleja, F. and Borca, B. and Passeggi, M. C. G. and Hinarejos, J. J. and Guinea, F. and Miranda, R. “Periodically Rippled Graphene: Growth and Spatially Resolved Electronic Structure “. Phys. Rev. Lett. 100, 056807,

 Introduction

 Purpose and impact

 Structure of graphene

 Suspended

 Over Ru

 Over SiO 2

 Electrical transport

 Future research

 Conclusion

 Figure a shows the topography of graphene deposited on SiO2. The square indicates the region shown in c. The wide white line is an electrical contact.

 Figure c shows the graphene sheet. The standard deviation of the height variation in a square of side 600 nm is approximately 3 Å.

500nm

300nm

Masa Ishigami, J. H. Chen, W. G. Cullen, M. S. Fuhrer, and E. D. Williams. “Atomic Structure of Graphene on SiO 2 “. Nano Lett. Vol7, 1643-1648,

 Figure a shows an AFM image of the boundary between the graphene sheet and SiO 2 substrate.

 An histogram acquired across the boundary shown in figure b shows that the film thickness is 4.2 Å, comparable to the layer- to-layer spacing in bulk graphite of 3.4 Å. Therefore, the imaged graphene device area is a monolayer.

 Figure c shows histograms of the heights over graphene and SiO 2. The graphene sheet is approximately 60% smoother than the oxide surface.

Masa Ishigami, J. H. Chen, W. G. Cullen, M. S. Fuhrer, and E. D. Williams. “Atomic Structure of Graphene on SiO 2 “. Nano Lett. Vol7, 1643-1648,

 The observed 2H value demonstrates that the observed graphene morphology is not representative of the intrinsic structure.

 Interpolating the intersection of the power law and saturated regimes yields values of the correlation length, which are ξ=32nm for graphene and ξ=23nm for SiO 2.

 The larger correlation length and smaller roughness of the graphene surface would arise naturally due to an energy cost for graphene to closely follow sharp orientation changes on the substrate.

 The height-height correlation function g(x)=(z(x 0 + x) - z(x 0 )) 2 , is shown in figure d.

 Both correlation functions rapidly increase as g~x 2H^ at short distances 2H=1.11 for graphene and 2H=1.17 for SiO 2. A value of the exponent 2H~1 indicates a domain structure with short range correlations among neighboring domains.

Masa Ishigami, J. H. Chen, W. G. Cullen, M. S. Fuhrer, and E. D. Williams. “Atomic Structure of Graphene on SiO 2 “. Nano Lett. Vol7, 1643-1648,