Epitaxial growth mechanisms of graphene and effects of substrates

The growth process of single layer graphene with and without substrate is investigated using ab initio, finite temperature molecular dynamic calculations within density functional theory. An understanding of the epitaxial graphene growth mechanisms in the atomic level is provided by exploring the transient stages which occur at the growing edges of graphene. These stages are formation and collapse of large carbon rings together with the formation and healing of Stone-Wales like pentagon-heptagon defects. The activation barriers for the healing of these growth induced defects on various substrates are calculated using the climbing image nudge elastic band method and compared with that of the Stone-Wales defect. It is found that the healing of pentagon-heptagon defects occurring near the edge in the course of growth is much easier than that of Stone-Wales defect. The role of the substrate in the epitaxial growth and in the healing of defects are also investigated in detail, along with the effects of using carbon dimers as the building blocks of graphene growth.

Figure 1

Snapshots from ab initio MD simulations of planar graphene growth at $T=1300$ K without a template substrate. An initial flake was placed and in each 1 ps MD calculation two carbon atoms were sent from the left hand side to monitor the growth in the indicated direction. Each snapshot includes two periodic supercells. (a) Change of the armchair edge to zigzag edge and vice versa is shown. (b) Structures obtained when simulation of growth presented in (a) is proceeded. Formation of big rings and chains were observed, and the resulting structures were far away from being a perfect graphene layer. Note that defects formed in part (a) are still present in part (b).

Figure 2

Snapshots from ab initio MD simulation of epitaxial growth of graphene on a BN substrate. In the ball and stick model B, N, and C atoms are represented by green, blue, and brown balls while only bonds between carbon atoms having a distance less than 2 Å are shown. Each snapshot includes two periodic supercells in the horizontal direction. (a) General trends are presented by including final configurations of MD calculations involving 30, 35, 40, and 42 carbon atoms. Some of the critical configurations in the evolution of ring collapse and defect healing mechanisms are highlighted by solid and dashed lines respectively. (b) Snapshots from the MD simulation of the structure having 42 carbon atoms taken after 1, 7, 14, and 20 MD steps. Carbon atom migration causing the growth of rings and defect healing can be traced in dotted and dashed circles, respectively. (c) Snapshots from the same MD simulation taken after 40, 83, 222, and 290 MD steps. Three subsequent hexagon formations are indicated by solid, dashed, and dotted circles.

Figure 3

Snapshots from ab initio MD simulation of epitaxial growth of graphene on BN when carbon dimers are used as building blocks. B, N, and C atoms are represented by green, blue, and brown balls. (a) The final configurations of MD simulations involving 26, 30, 32, and 34 carbon atoms. Graphene growth is less defected as compared to growth with monomers, but ring formation and PH defects still occur as seen in columns iii and iv. (b) Migration of a carbon dimer on a graphene surface. The side view snapshots are from an MD simulation having 34 carbon atoms. The dimer moves to its final position each time by binding and detaching from a different carbon atom of graphene.

Figure 4

(a) Energetics of the healing path of SW and PH defects in graphene for three cases: without template, graphene on BN, and graphene on Ni(111) substrates. The solid red, green, and blue lines show the healing path of SW defect and associated energy barriers for graphene without template, graphene on BN, and graphene on Ni(111) surfaces, respectively. Energies of the defected states are set to zero. The PH healing barriers are also shown with dashed lines. The healing barrier of PH defect of graphene on Ni(111) with the lattice constant increased by 1$\%$ is shown by a dotted blue line. The inset shows the healing of PH defect of graphene on BN substrate. In the PH defect one of the carbon atoms forming the middle bond is missing the third $s{p}^2$-like bond. (b) Top and side views of SW defect healing on Ni substrate. The Ni atoms forming the top, middle, and bottom atomic layers of the substrate are indicated by numerals 1, 2, and 3, respectively. The lateral positions of atoms in these layers are indicated by sites 1, 2, and 3. The interaction between graphene and Ni(111) is manifested in the side view of the fifth NEB image, where carbon atoms forming the C-C bond between two heptagon are pulled down when they are passing over site-2 and site-3 of the Ni substrate.