${\mathrm{Ni}}_{2}\mathrm{C}$ surface carbide to catalyze low-temperature graphene growth

${Ni}_{2} C$ surface carbide to catalyze low-temperature graphene growth

Rafael Martinez-Gordillo, Céline Varvenne, Hakim Amara, and Christophe Bichara

Phys. Rev. B 97, 205431 – Published 18 May 2018

Abstract

The possibility to grow a graphene layer using the chemical-vapor-deposition technique over a ${Ni}_{2} C / Ni (111)$ substrate has been identified experimentally, with the advantage of having a lower processing temperature ( $T < 500^{\circ} C$ ), compared to standard growth over a $Ni (111)$ surface. To understand the role of the metal carbide/metal catalyst, we first perform a static study of the ${Ni}_{2} C / Ni (111)$ structure and of the binding and removal of a carbon atom at the surface, using both a tight-binding (TB) energetic model and ab initio calculations. Grand-canonical Monte Carlo TB simulations then allow us (i) to determine the thermodynamic conditions to grow graphene and (ii) to separate key reaction steps in the growth mechanism explaining how the ${Ni}_{2} C / Ni (111)$ substrate catalyzes graphene formation at low temperature.

Received 16 October 2017
Revised 22 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.205431

Physics Subject Headings (PhySH)

Adhesion Chemical bonding Growth Interface & surface thermodynamics Semiconductors Surface reconstruction

Carbon-based materials Graphene Nanostructures

Metropolis algorithm Monte Carlo methods Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rafael Martinez-Gordillo¹, Céline Varvenne¹, Hakim Amara^2,*, and Christophe Bichara¹

¹Aix Marseille Université–CNRS, CINaM, Campus de Luminy, 13288, Marseille, France
²Laboratoire d'Etudes des Microstructures, ONERA-CNRS, Boîte Postale 72, 92322 Châtillon Cedex, France

^*Corresponding author: hakim.amara@onera.fr

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Vol. 97, Iss. 20 — 15 May 2018

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Figure 1
Atomic structure of the ${Ni}_{2} C$ /Ni(111) system. (a) Supercell view in the (111) plane, with the carbide layer before and after the clock reconstruction. The thin lines indicate the underlying fcc Ni lattice in the (111) plane. The supercell periodicity vectors are given in units of the in-plane fcc Ni basis vectors $a_{0} / 2 [\bar{1} 01]$ and $a_{0} / 2 [\bar{1} 10]$ . The shaded zone highlights the in-plane unit cell of the ${Ni}_{2} C$ carbide. (b) Side view of the system showing the carbide layer and the three (111) planes of fcc Ni. (c) Scheme representing the shift vector $\vec{F}$ of the ${Ni}_{2} C$ layer with respect to the $Ni (111)$ substrate which is applied to study the stability of the system (see text).
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Figure 2
Relative stability of the ${Ni}_{2} C$ layer on the $Ni (111)$ substrate, with the TB model. (a) Map of adhesion energies, as computed with Eq. (1), for all possible shift vectors $\vec{F}$ and with atomic relaxations performed only along the Ni [111] direction. (b) Scheme showing the $\vec{F}$ vectors of the specific configurations of the ${Ni}_{2} C / Ni (111)$ that are then fully relaxed. The arrows indicate the in-plane displacement experienced by the ${Ni}_{2} C$ layer relative to the $Ni (111)$ substrate during a subsequent annealing of the structures (see text). The inset illustrates the aspect of the energy landscape along the $[\bar{2} 11]$ direction for TB and DFT. (c) Fully relaxed adhesion energies for these selected configurations.
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Figure 3
Maps representing (a) the interaction energies [Eq. (2)] of a single C atom forming a C dimer with the ${Ni}_{2} C / Ni (111)$ system and (b) the energy cost to remove a C atom from the carbide layer [Eq. (2)]. Energies are computed for all C atom positions in the ${Ni}_{2} C$ layer within the supercell, adopting the following representation: big dots correspond to C atoms from ${Ni}_{2} C$ and are colored according to the appropriate energy value, and open circles represent two successive (111) layers of fcc Ni. Atomic positions are from the relaxed initial group-A configuration before adding or removing carbon. The Ni atoms from the carbide are omitted for clarity.
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Figure 4
Identification of the thermodynamic conditions $(T, μ_{c})$ to stabilize a graphene layer over the ${Ni}_{2} C / Ni (111)$ system. When going to the top right corner of the graphene zone, i.e., close to the domain of amorphous carbon, the obtained graphene layer contains more defects.
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Figure 5
Snapshots of atomic configurations during the growth of graphene on a ${Ni}_{2} C$ /Ni(111) interface at 500 K and $μ_{C} = - 4.75$ eV/atom. Ni atoms are orange, C atoms of ${Ni}_{2} C$ are gray, and outer C atoms on the surface to form graphene are black. The Ni atoms from Ni(111) are omitted for clarity. (a) Atoms adsorbed on top of C atoms of ${Ni}_{2} C$ . (b) C atoms of the interface (in red) integrated into the graphene network. (c) Chains forming and crossing to form hexagons. (d) Equilibrium structures at 500 K.
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Figure 6
Equilibrium structures at 700 K, obtained from GCMC simulations performed on a ${Ni}_{2} C / Ni (111)$ interface for $μ_{C} = - 5.15$ eV/atom. Ni atoms are orange, C atoms of ${Ni}_{2} C$ are gray, and outer C atoms on the surface to form graphene are black. The Ni atoms from $Ni (111)$ are omitted for clarity. (a) Top view, where many hexagons can be seen. (b) Side view, where C-C bonds between graphene and the interface (C atoms are in red) are clearly present.
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Physical Review B

covering condensed matter and materials physics

${Ni}_{2} C$ surface carbide to catalyze low-temperature graphene growth

Rafael Martinez-Gordillo, Céline Varvenne, Hakim Amara, and Christophe Bichara

Phys. Rev. B 97, 205431 – Published 18 May 2018

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Physical Review B

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Ni2C surface carbide to catalyze low-temperature graphene growth

Rafael Martinez-Gordillo, Céline Varvenne, Hakim Amara, and Christophe Bichara

Phys. Rev. B 97, 205431 – Published 18 May 2018

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${Ni}_{2} C$ surface carbide to catalyze low-temperature graphene growth