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Appl. Phys. Lett. 100, 153106 (2012); http://dx.doi.org/10.1063/1.3701594 (3 pages)

A graphene electron lens

L. Gerhard1, E. Moyen2, T. Balashov1, I. Ozerov2, M. Portail3, H. Sahaf2, L. Masson2, W. Wulfhekel1, and M. Hanbücken2

1Physikalisches Institut, Karlsruhe Institute of Technology, Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
2CINaM-CNRS, Aix-Marseille University, Campus Luminy - Case 913, 18288 Marseille, France
3CRHEA-CNRS, Parc de Sophia - Antipolis, rue B. Gregory, 06560 Valbonne, France

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(Received 26 November 2011; accepted 20 March 2012; published online 10 April 2012)

An epitaxial layer of graphene was grown on a pre patterned 6H-SiC(0001) crystal. The graphene smoothly covers the hexagonal nano-holes in the substrate without the introduction of small angle grain boundaries or dislocations. This is achieved by an elastic deformation of the graphene by ≈0.3% in accordance to its large elastic strain limit. This elastic stretching of the graphene leads to a modification of the band structure and to a local lowering of the electron group velocity of the graphene. We propose to use this effect to focus two-dimensional electrons in analogy to simple optical lenses.

© 2012 American Institute of Physics

KEYWORDS, PACS, and IPC

PACS

  • 41.85.Ne

    Electrostatic lenses, septa

  • 42.79.-e

    Optical elements, devices, and systems

International Patent Classification (IPC)

  • H01J37/26

    Electron or ion microscopes; Electron- or ion-diffraction tubes

ARTICLE DATA

PUBLICATION DATA

ISSN

0003-6951 (print)  
1077-3118 (online)

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    References

    N. Peres, Rev. Mod. Phys. 82, 2673 (2010).

    M. Mohr, K. Papagelis, J. Maultzsch, and C. Thomsen, Phys. Rev. B 80, 205410 (2009).

    S. Bero, A. Arnold, F. Evers, R. Narayanan, and P. Wölfle, Phys. Rev. B 82, 195445 (2010).


Figures (3)

Figures (click on thumbnails to view enlargements)

FIG.1
(a) Schematics of the patterning process of SiC(0001). Nano-holes are created on the SiC(0001) surface through a porous alumina mask. The wafer is then etched in hydrogen to form regular nano-holes of hexagonal shape. (b) SEM image of the patterned SiC(0001) wafer after hydrogen etching showing regular hexagonal holes with well defined facets.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
(a) Large scale STM image of one nano-hole in the graphenized SiC(0001) wafer. The left inset shows the Fourier transform of the area in the dotted box. It displays a sixfold pattern caused by the mono-domain (1 × 1) structure of the few layer graphene. The right inset shows a low pass filtered image of the structure at the bottom of the hexagonal hole and reveals a (6 × 6) superstructure of the few layer graphene film. (b) Line section of the hole (c-j) show STM images of higher resolution at places indicated in (a). The (1 × 1) structure is clearly visible showing no dislocations or small angle domain boundaries even in the corner of the holes (j).

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
Calculated electron propagation through strained graphene lenses. All three lenses have the same outer diameter of 200 nm with varying depth as indicated in the figure. The side facets are inlined by 5, 6 and 7° for the holes of 2.5, 6, and 10 nm depth, respectively.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint



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