Suppression of intrinsic roughness in encapsulated graphene

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Suppression of intrinsic roughness in encapsulated graphene

Joachim Dahl Thomsen, Tue Gunst, Søren Schou Gregersen, Lene Gammelgaard, Bjarke Sørensen Jessen, David M. A. Mackenzie, Kenji Watanabe, Takashi Taniguchi, Peter Bøggild, and Timothy J. Booth

Phys. Rev. B 96, 014101 – Published 5 July 2017

Abstract

Roughness in graphene is known to contribute to scattering effects which lower carrier mobility. Encapsulating graphene in hexagonal boron nitride (hBN) leads to a significant reduction in roughness and has become the de facto standard method for producing high-quality graphene devices. We have fabricated graphene samples encapsulated by hBN that are suspended over apertures in a substrate and used noncontact electron diffraction measurements in a transmission electron microscope to measure the roughness of encapsulated graphene inside such structures. We furthermore compare the roughness of these samples to suspended bare graphene and suspended graphene on hBN. The suspended heterostructures display a root mean square (rms) roughness down to 12 pm, considerably less than that previously reported for both suspended graphene and graphene on any substrate and identical within experimental error to the rms vibrational amplitudes of carbon atoms in bulk graphite. Our first-principles calculations of the phonon bands in graphene/hBN heterostructures show that the flexural acoustic phonon mode is localized predominantly in the hBN layer. Consequently, the flexural displacement of the atoms in the graphene layer is strongly suppressed when it is supported by hBN, and this effect increases when graphene is fully encapsulated.

Received 21 March 2017

DOI:https://doi.org/10.1103/PhysRevB.96.014101

Physics Subject Headings (PhySH)

Phonons Roughness

Graphene

Density functional theory Electron diffraction Transmission electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Joachim Dahl Thomsen¹, Tue Gunst¹, Søren Schou Gregersen¹, Lene Gammelgaard¹, Bjarke Sørensen Jessen¹, David M. A. Mackenzie¹, Kenji Watanabe², Takashi Taniguchi², Peter Bøggild¹, and Timothy J. Booth¹

¹Center for Nanostructured Graphene, Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
²National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

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Issue

Vol. 96, Iss. 1 — 1 July 2017

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Images

Figure 1
(a) Schematic of ripples in graphene with normal vectors to the graphene lattice indicated (not to scale). (b) The reciprocal lattice of rippled graphene is a set of cones due to the angular distribution of real-space lattice normal vectors. Also shown are two planes which approximate the surface of the Ewald sphere, indicating the points of intersection with the reciprocal space lattice to form the diffraction pattern. The red plane shows the intersection at zero sample tilt, while the blue plane shows the intersection at a nonzero tilt angle. This leads to two distinctly different diffraction patterns: (c) one for zero tilt and (d) one for a tilted sample where the spots have become diffuse and the pattern has been stretched along an axis perpendicular to the tilt axis.
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Figure 2
(a) Optical image of a hBN flake on a graphene flake and (b) the same heterostructure as shown in (a) transferred to a TEM sample carrier. (c)–(e) TEM images of suspended graphene: (c) As-transferred graphene. (d) TEM image of annealed graphene showing no residual polymer contamination. A rolled graphene edge separates the graphene from vacuum and provides contrast in the absence of visible resist residues. (e) High-resolution image of the sample shown in (b); inset: fast Fourier transform of the main image. Both the first-order 2.1 Å periodicity and a subset of the second-order 1.42 Å periodicity from the graphene lattice are visible.
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Figure 3
(a) Diffraction patterns of graphene and a graphene/hBN heterostructure at $0^{o}, 1 8^{o}$ , and $3 6^{o}$ tilt. (b) Intensity plots of the second-order graphene diffraction spots circled in (a); note that the intensity is 10× for suspended graphene at 36° tilt due to a very diffuse spot. Peaks are normalized to the $0^{o}$ tilt intensity.
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Figure 4
Roughness measurements of a suspended graphene sample (black squares), graphene supported by hBN (red squares), and fully encapsulated graphene (blue triangles). The inset is a close-up of the data points for the graphene supported by hBN and fully encapsulated graphene. The solid lines are linear fits to the data points.
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Figure 5
(a) Phonon dispersion of AB stacking of graphene on monolayer hBN, with a C atom on top of a B atom. (c) ${ABA}^{'}$ stacking of graphene fully encapsulated in monolayer hBN, with a C atom in between B and N atoms. (b) and (d) The labeled phonon modes are illustrated for $q = Γ$ . (e) and (f) The rms displacement versus temperature for the flexural vibrations of (e) graphene on a monolayer of hBN and (f) graphene fully encapsulated in monolayer hBN.
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