This document summarizes simulations of graphene growth on a copper substrate. Monte Carlo simulations were performed on a honeycomb lattice with various levels of static and dynamic substrate disorder. For static disorder, carbon atoms reside on favorable substrate sites, reducing mobility and resulting in smaller islands. For dynamic disorder, the changing substrate allows islands to move and reform, enhancing island size at optimal temperatures. The substrate itself shows no ordering without carbon islands at high dynamic disorder temperatures.

1. SIMULATIONS OF GRAPHENE GROWTH
G. Enstone1, D. Quigley2, G.R. Bell3, P. Brommer4
1Centre for Complexity Science, 2Department of Physics and Centre for Scientific Computing, 3Department of Physics, 4Warwick Centre for
Predictive Modelling, School of Engineering and Centre for Scientific Computing. All University of Warwick, Coventry, CV4 7AL.
ENHANCEMENT OF ISLAND SIZE BY DYNAMIC SUBSTRATE DISORDER IN
DOI: 10.1039/C6CP00788KPhys. Chem. Chem. Phys., 2016,18, 15102-15109
SUBSTRATE DISORDER
HAS A PROFOUND EFFECT ON
ISLAND GROWTH
LATTICE AND MC MOVES
Effective bond energies of ECC=-1.0, ECH=-0.1 and
EHH=0.0 are used, such that all energies scale to the
effective CC energy, and hydrogen is in excess. We use
typical growth temperatures of around 1000K.
Simulations have a growth and an annealing stage.
During growth, insertion moves are allowed until the
lattice reaches coverage , and during annealing carbon
atoms can only diffuse.
SUBSTRATE DISORDER
Snapshot of an island on
a rough surface. Colored
voronoi cells around
each site denote
strength of disorder;
darker shades are more
negative (favorable).
Simulations take the form of simple Monte Carlo moves
on a honeycomb lattice. Hydrogen is assumed to be in
excess, so an empty site corresponds to a hydrogen site.
Carbon is introduced by trialing insertion moves, and
atoms can diffuse to empty sites in near hexagons
Graphic showing
possible sites
accessible to carbon
atoms. There are a
total of 12 possible
targets.
Each site on the honeycomb lattice is assigned a
roughness energy drawn from a top hat distribution
symmetric about 0, . Carbon atoms can effectively bond
to these sites, gaining or losing the energy of the site.
This surface can be either static, sites retain their energy
for the duration of the simulation, or dynamic, sites can
exchange their energies to neighbors, with the same rules
and frequency as carbon atoms. A decoupled temperature
TS is assigned to the substrate to vary substrate mobility.
METHODS
WHAT HAPPENS TO
THE SUBSTRATE?
For static disorder, carbon atoms reside on favorable sites on the substrate, with increasing
preference as increases (points C,D). This reduces carbon atom mobility, and results in
smaller clusters with shape dictated by the substrate.
For dynamic disorder the constantly changing surface allows islands to move and reform,
reducing the stability of regular terminating islands. This leads to an enhancement of island
size at optimal (TS) (point A). At high values of the dynamic disorder prevents any
stable island formation (point B). This suggests an optimal disorder level for growth.
In chemical vapour deposition (CVD) of graphene on
copper, hydrocarbon gas is passed over a hot
copper chip. Carbon atoms adhere to the surface,
forming islands and – eventually – full graphene
layers. Understanding the mechanisms involved in
this process will allow for more consistent material
production.
Image of copper
deposits on tube
from CVD setup:
experiments occur
at temperatures
sufficient to
sublimate copper
from the substrate.
SURFACES AREN’T
SMOOTH!
ISDs for islands formed on smooth surfaces. The
left panel shows the un-scaled distributions at three
different distributions and the right scaled
distributions.
Snapshot at the
end of annealing
for a surface
without disorder
showing regular,
smoothly
terminating
islands.
In the absence of disorder, regular clusters form on
the surface. When a cluster with no dangling carbon
atoms is formed, it is stable and does not move or
reform.
NS =
ϑeff
s
2
f (s / s ).
Island size distributions (ISDs) formed at different
coverages on smooth surfaces obey a widely
observed scaling relation [2]:
SMOOTH SURFACE
SIMULATIONS
Whilst the dynamic roughness allows the carbon atoms to
form larger islands, what happens to the substrate itself?
For static roughness, there is a strong dependence of
energy on , whilst for dynamic roughness the
dependence decreases with increasing TS.
Average energy under carbon atoms against
Snapshots with and without carbon islands, after
annealing in a dynamic roughness simulation ( =1.2,
TS=∞). Note there is no clear clustering or ordering in the
substrate.
This research was supported by EPSRC grants EP/
H00341X/1, EP/I01358X/1 and used computing resources
provided by the Centre for Scientific Computing at the
University of Warwick.
1. Wilson, Neil R., et al. “Weak mismatch epitaxy and
structural Feedback in graphene growth on copper
foil.” Nano Research 6.2 (2013): 99-112
2. Krzyzewski, T. J., et al. "Scaling behavior in InAs/GaAs
(001) quantum-dot formation." Physical Review B
66.20 (2002): 201302.
REFERENCES
300 K
1360 K
EAM MD simulations of a copper surface at different
temperatures. At high temperature the surface starts
to become rough.
increasingly active and the substrate becomes rough.
Observed copper faceting [1], and difficulties
associated with in situ imaging, make CVD of
graphene on copper a strong candidate for
simulation. This work aims to adapt surface disorder
into a lattice model, and explore the effects and
implications on graphene growth.
As temperature increases the copper becomes
Dynamic TS=∞
Dynamic TS=1.0
Dynamic TS=0.5
Static TS=0
0
–0.1
–0.2
–0.3
–0.4
Energy
–0.4–0.5
0 0.5 1 1.5 2
1
0
0 1
0.8
0.6
0.4
0.2
P(S)*S2/θ
2 3 4
S/S
0.05
0
0 50
0.04
0.03
0.02
0.01
P(S)
100 150 200
S
θ=0.1
θ=0.2
θ=0.3
Theory
θ=0.1
θ=0.2
θ=0.3
Dynamic TS=∞
Dynamic TS=1.0
Dynamic TS=0.5
Static TS=0
ξ (DISORDER STRENGTH)
150
S
100
50
0
0 0.5 1 1.5 2
200
250
300
A B
C D