DOI: 10.1038/NNANO.2015 - Nature · Oxygen-Activated Growth and Bandgap Tunability of Large Single-Crystal Bilayer ... 10.1038/NNANO.2015.322 ULEENTARY ... Dual Beam235) was then

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NNANO.2015.322

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1

Supplementary Information

Oxygen-Activated Growth and Bandgap Tunability of Large Single-Crystal Bilayer

Graphene

Yufeng Hao, Lei Wang, Yuanyue Liu, Hua Chen, Xiaohan Wang, Cheng Tan, Shu Nie, Ji

Won Suk, Tengfei Jiang, Tengfei Liang, Junfeng Xiao, WenjingYe, Cory R. Dean, Boris I.

Yakobson, Kevin F. McCarty, Philip Kim, James Hone, Luigi Colombo, Rodney S. Ruoff

SUPPLEMENTARY METHODS

Cu foil pretreatment, BLG growth, and transfer.

Similar to our previous studies19, two types of commercially available Cu foils were used in

this work: (1) OR-Cu (Alfa-Aesar stock#46365, #13382, etc.) and (2) OF-Cu (Alfa-Aesar

stock#46986, #42972, etc.). The O concentrations in (1) are ~10−2 atomic %; while in (2), they

are below 10−6 atomic %, which is the detection limit of time-of-flight secondary ion mass

spectrometry (TOF-SIMS).

Both types of Cu foils were placed in acetic acid (CH3COOH) for 8 hours followed by

blow-drying with nitrogen gas. Electrochemical polishing also cleans the Cu surface and has

similar growth results. After cleaning, the Cu foils were made into a semi-sealed pocket (Fig. S1)

and then loaded into the quartz tube of a low pressure CVD (LPCVD) system. The pockets were

“sitting” directly in a quartz tube (lower panel of Fig. S1). The typical width of the pocket is

~18mm and the inner diameter of the quartz tube is ~22mm. In this way, when the pocket sits

inside the tube, the distance between the bottom surface and the quartz tube wall is ~7 mm,

Oxygen-activated growth and bandgap tunabilityof large single-crystal bilayer graphene

© 2016 Macmillan Publishers Limited. All rights reserved.

http://dx.doi.org/10.1038/nnano.2015.322

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SUPPLEMENTARY INFORMATION DOI: 10.1038/NNANO.2015.322

2

which is slightly smaller than that between the top surface and the wall, ~14 mm. In the LPCVD

process, the growth environments of the top and bottom surfaces are similar. Also, the substrate

configuration in this work is different from the sandwich structure (flat quartz plate/Cu

foil/quartz plate) or Cu tubes with both of their two ends open32.

Figure S1 | Upper panel: Illustration of Cu pocket fabrication process flow. Lower panel:

Placement of a Cu pocket in a quartz tube.

The growth system was heated to 1035°C under a H2 flow of 10 cm3 per min (sccm),

corresponding to 0.1 Torr, and annealed for 30 min; CH4 was then introduced into the system for

graphene growth. The typical PCH4 range is ~1×10-1 - 1×10-3 Torr, and the growth time varied

3

from 10 to 500 min. Note that for "O2-treated OF-Cu", pure O2 was used for different exposure

time right before introducing CH4 and the corresponding PO2 is 1×10-3 Torr. After growth, the

system was cooled down to room temperature while still under the H2 and CH4 flow. The bilayer

and few-layer graphene films formed on the exterior surface of the Cu pockets were

characterized and analyzed.

The graphene domains/films were transferred onto dielectric surfaces, Si and h-BN, using a

poly(methyl methacrylate) (PMMA)-assisted method33 for Raman characterization and electrical

device fabrication. Prior to transfer, the graphene surface was spin-coated with a layer of PMMA

to provide mechanical support throughout the transfer process. The PMMA/graphene/Cu stack

was then floated over an ammonium persulfate ((NH4)2S2O8, 0.5 M, Sigma Aldrich) aqueous

solution to etch the Cu. The resulting graphene/PMMA membranes are thoroughly rinsed with

deionized water, and then transferred onto the target substrates. The PMMA was removed with

acetone, then rinsed in isopropanol, and finally blow-dried with nitrogen gas.

SEM images were taken with an FEI Quanta-600 FEG Environmental SEM with the

accelerating voltage of 30 KV, and spot size of 5. Raman spectra and mapping images were

taken from a WiTec Alpha 300 micro-Raman imaging system. A 488 nm excitation laser with a

50× or 100 × objective lens were used for the acquisition of Raman spectra and images. The spot

size is 200-500 nm, and the mapping step size is ~300nm.

SUPPLEMENTARY NOTES

A. Gas-flow dynamics of Cu pocket and its effects on graphene growth





2

which is slightly smaller than that between the top surface and the wall, ~14 mm. In the LPCVD

process, the growth environments of the top and bottom surfaces are similar. Also, the substrate

configuration in this work is different from the sandwich structure (flat quartz plate/Cu

foil/quartz plate) or Cu tubes with both of their two ends open32.

Figure S1 | Upper panel: Illustration of Cu pocket fabrication process flow. Lower panel:

Placement of a Cu pocket in a quartz tube.

The growth system was heated to 1035°C under a H2 flow of 10 cm3 per min (sccm),

corresponding to 0.1 Torr, and annealed for 30 min; CH4 was then introduced into the system for

graphene growth. The typical PCH4 range is ~1×10-1 - 1×10-3 Torr, and the growth time varied

3

from 10 to 500 min. Note that for "O2-treated OF-Cu", pure O2 was used for different exposure

time right before introducing CH4 and the corresponding PO2 is 1×10-3 Torr. After growth, the

system was cooled down to room temperature while still under the H2 and CH4 flow. The bilayer

and few-layer graphene films formed on the exterior surface of the Cu pockets were

characterized and analyzed.

The graphene domains/films were transferred onto dielectric surfaces, Si and h-BN, using a

poly(methyl methacrylate) (PMMA)-assisted method33 for Raman characterization and electrical

device fabrication. Prior to transfer, the graphene surface was spin-coated with a layer of PMMA

to provide mechanical support throughout the transfer process. The PMMA/graphene/Cu stack

was then floated over an ammonium persulfate ((NH4)2S2O8, 0.5 M, Sigma Aldrich) aqueous

solution to etch the Cu. The resulting graphene/PMMA membranes are thoroughly rinsed with

deionized water, and then transferred onto the target substrates. The PMMA was removed with

acetone, then rinsed in isopropanol, and finally blow-dried with nitrogen gas.

SEM images were taken with an FEI Quanta-600 FEG Environmental SEM with the

accelerating voltage of 30 KV, and spot size of 5. Raman spectra and mapping images were

taken from a WiTec Alpha 300 micro-Raman imaging system. A 488 nm excitation laser with a

50× or 100 × objective lens were used for the acquisition of Raman spectra and images. The spot

size is 200-500 nm, and the mapping step size is ~300nm.

SUPPLEMENTARY NOTES

A. Gas-flow dynamics of Cu pocket and its effects on graphene growth





4

(1) Cu pocket fabrication and gap size along the edges

As shown in Fig. S1, a Cu pocket was made by first bending a Cu foil and then crimping &

pressing the three open edges carefully by using metal tweezers. During the fabrication, no

special mechanical machine was used to seal the edges. We first measured the gap size along the

folded edges by cutting the pocket with scissors, which turns out to be undesirable since the

folded edges were always smeared during the cutting, and thus no accurate gap size can be

obtained. A focused ion beam (FIB, FEI Strata, Dual Beam235) was then used to cut, so that the

real gap size at the edge could be revealed. We found that the gap size along the folded edges is

typically in the range of a few μm (Fig. S2c). After annealing (1035 °C, the growth temperature),

the gap size was found to be reduced to 200-400 nm (Fig. S2d) because the mechanical strength

was reduced and the accumulated strain during the pocket fabrication process was released too.

Gas exchange between the interior and exterior of the pocket is through this narrow gap.

5

Figure S2 | The pocket was cut by scissors first a, and then focused ion beams were used to cut

the local region as indicated by the blue-line box in b. The gap sizes before and after annealing

are shown in c and d, respectively.

(2) Gas equilibrium and Knudsen diffusion

In the experimental environment, where the temperature is above 1000°C and the gas

pressure is ~0.1 Torr, the calculated mean free path of CH4 molecules is larger than 1mm34.

Hence the Knudsen number, which is defined as the ratio of the mean free path of CH4 molecules

to the gap size of the Cu pocket, is on the order of 104. Such a high Knudsen number suggests

that the diffusion of CH4 from the exterior environment into the interior through the gap of the

pocket is dominated by the collisions between CH4 molecules and the gap sidewall, and is in the

Knudsen diffusion regime. The diffusivity in the gap channel (indicated in Fig. S3a) is thus much

lower than the diffusivity outside the Cu pocket.

The diffusivity in the Knudsen diffusion regime depends on both the shape and dimensions

of the channel. Monte Carlo simulation35,36 provides a convenient way to calculate the diffusivity

of CH4 molecules inside the channel of the Cu pocket which is modelled as a nano-channel. In

the simulation, the channel connects two infinitely large reservoirs of which the gas

concentrations (or called number densities) are maintained at constant, but different values.

When the system reaches the steady state, a linear density profile along the length of the channel

is established and the number flux of gas molecules is measured. It is found that in the Knudsen

diffusion regime, the number flux, J, follows the Fick’s first law of diffusion,

dnJ Ddx

=− , (1)





4

(1) Cu pocket fabrication and gap size along the edges

As shown in Fig. S1, a Cu pocket was made by first bending a Cu foil and then crimping &

pressing the three open edges carefully by using metal tweezers. During the fabrication, no

special mechanical machine was used to seal the edges. We first measured the gap size along the

folded edges by cutting the pocket with scissors, which turns out to be undesirable since the

folded edges were always smeared during the cutting, and thus no accurate gap size can be

obtained. A focused ion beam (FIB, FEI Strata, Dual Beam235) was then used to cut, so that the

real gap size at the edge could be revealed. We found that the gap size along the folded edges is

typically in the range of a few μm (Fig. S2c). After annealing (1035 °C, the growth temperature),

the gap size was found to be reduced to 200-400 nm (Fig. S2d) because the mechanical strength

was reduced and the accumulated strain during the pocket fabrication process was released too.

Gas exchange between the interior and exterior of the pocket is through this narrow gap.

5

Figure S2 | The pocket was cut by scissors first a, and then focused ion beams were used to cut

the local region as indicated by the blue-line box in b. The gap sizes before and after annealing

are shown in c and d, respectively.

(2) Gas equilibrium and Knudsen diffusion

In the experimental environment, where the temperature is above 1000°C and the gas

pressure is ~0.1 Torr, the calculated mean free path of CH4 molecules is larger than 1mm34.

Hence the Knudsen number, which is defined as the ratio of the mean free path of CH4 molecules

to the gap size of the Cu pocket, is on the order of 104. Such a high Knudsen number suggests

that the diffusion of CH4 from the exterior environment into the interior through the gap of the

pocket is dominated by the collisions between CH4 molecules and the gap sidewall, and is in the

Knudsen diffusion regime. The diffusivity in the gap channel (indicated in Fig. S3a) is thus much

lower than the diffusivity outside the Cu pocket.

The diffusivity in the Knudsen diffusion regime depends on both the shape and dimensions

of the channel. Monte Carlo simulation35,36 provides a convenient way to calculate the diffusivity

of CH4 molecules inside the channel of the Cu pocket which is modelled as a nano-channel. In

the simulation, the channel connects two infinitely large reservoirs of which the gas

concentrations (or called number densities) are maintained at constant, but different values.

When the system reaches the steady state, a linear density profile along the length of the channel

is established and the number flux of gas molecules is measured. It is found that in the Knudsen

diffusion regime, the number flux, J, follows the Fick’s first law of diffusion,

dnJ Ddx

=− , (1)





6

and the diffusivity D can be calculated based on the simulated number flux and the gradient of

number density along the channel, dndx

. Using this method, the diffusivity of CH4 molecules in a

channel with a rectangular cross section of which the dimensions are 400 nm and 8 cm,

respectively, is computed. The result is found to be close to that calculated from the formula for

the diffusivity of gas molecules between two infinitely large parallel plates, which is derived

based on ref. 37,

MTKHD B

p ππ 8

41 Λ= , (2)

where H is the gap size, 400nm, M is the molecular weight, and pΛ a is a pre-factor calculated in

ref. 37.

In our experiments, the channel dimensions are: H = 400 nm, W = 8 cm (the edge length of

a pocket), L = 2 mm (length of gap channel, Fig. S3a), and the volume of the Cu pocket is 2mm3.

The calculated diffusivity inside the channel is: D = 1.05 ×10-3 m2/s, which is about 4 orders of

magnitude lower than that outside the pocket, which is in the continuum gas transport regime.

We then calculate the time it takes for the number density (equivalent to PCH4) of CH4

molecules to equilibrate between the interior and the exterior of the pocket. The exterior

environment is modelled as an infinitely large reservoir at , in which the number density of

CH4 molecules is maintained at a constant value . It is connected to the Cu pocket through the

nano-channel with a length L. Assuming a uniformly distributed number density of CH4

molecules in the interior environment of the pocket, the change of the number density of CH4

7

molecules inside the Cu pocket, �� , is determined by the mass conservation law at the

interface between the channel and the Cu pocket,

( , ) ( , )

x L

n L t n x tV D WHt x =

∂ ∂= −∂ ∂

, (3)

where x is the coordinate along the length of the channel and �� is the number density of

CH4 molecules inside the channel. Since the volume of Cu pocket is much larger than that of the

channel, the number density of CH4 molecules in the pocket changes much slower than the time

needed for the linear profile to be established along the channel. Hence at any time instant, the

number density profile along the channel is nearly linear, and the gradient ( , )n x tx

∂∂

can be

approximated by ( ) 0,n L t n

L−

. Finally, equation (3) can be simplified as

( ) 0,( , ) n L t ndn L tV D WHdt L

−= − . (4)

The solution to Eq. (4) is �� = �� 1 � �� = �� 1 � ��

��, where the

characteristic time �� = �� = 136s.

We plot the ratio of n(CH4) between the interior and exterior as a function of time, as shown

in Fig. S3b. From the calculation, we estimate that it takes about 4-8 min for the number density

inside the pocket to get close to that of the exterior environment (such as 90% of the number

density of CH4 inside the pocket). As a comparison, different gap sizes, such as H = 300 nm, 800

nm, 3 μm, etc. were used to calculate the time. Results show that the time decreases with the





6

and the diffusivity D can be calculated based on the simulated number flux and the gradient of

number density along the channel, dndx

. Using this method, the diffusivity of CH4 molecules in a

channel with a rectangular cross section of which the dimensions are 400 nm and 8 cm,

respectively, is computed. The result is found to be close to that calculated from the formula for

the diffusivity of gas molecules between two infinitely large parallel plates, which is derived

based on ref. 37,

MTKHD B

p ππ 8

41 Λ= , (2)

where H is the gap size, 400nm, M is the molecular weight, and pΛ a is a pre-factor calculated in

ref. 37.

In our experiments, the channel dimensions are: H = 400 nm, W = 8 cm (the edge length of

a pocket), L = 2 mm (length of gap channel, Fig. S3a), and the volume of the Cu pocket is 2mm3.

The calculated diffusivity inside the channel is: D = 1.05 ×10-3 m2/s, which is about 4 orders of

magnitude lower than that outside the pocket, which is in the continuum gas transport regime.

We then calculate the time it takes for the number density (equivalent to PCH4) of CH4

molecules to equilibrate between the interior and the exterior of the pocket. The exterior

environment is modelled as an infinitely large reservoir at , in which the number density of

CH4 molecules is maintained at a constant value . It is connected to the Cu pocket through the

nano-channel with a length L. Assuming a uniformly distributed number density of CH4

molecules in the interior environment of the pocket, the change of the number density of CH4

7

molecules inside the Cu pocket, �� , is determined by the mass conservation law at the

interface between the channel and the Cu pocket,

( , ) ( , )

x L

n L t n x tV D WHt x =

∂ ∂= −∂ ∂

, (3)

where x is the coordinate along the length of the channel and �� is the number density of

CH4 molecules inside the channel. Since the volume of Cu pocket is much larger than that of the

channel, the number density of CH4 molecules in the pocket changes much slower than the time

needed for the linear profile to be established along the channel. Hence at any time instant, the

number density profile along the channel is nearly linear, and the gradient ( , )n x tx

∂∂

can be

approximated by ( ) 0,n L t n

L−

. Finally, equation (3) can be simplified as

( ) 0,( , ) n L t ndn L tV D WHdt L

−= − . (4)

The solution to Eq. (4) is �� = �� 1 � �� = �� 1 � ��

��, where the

characteristic time �� = �� = 136s.

We plot the ratio of n(CH4) between the interior and exterior as a function of time, as shown

in Fig. S3b. From the calculation, we estimate that it takes about 4-8 min for the number density

inside the pocket to get close to that of the exterior environment (such as 90% of the number

density of CH4 inside the pocket). As a comparison, different gap sizes, such as H = 300 nm, 800

nm, 3 μm, etc. were used to calculate the time. Results show that the time decreases with the





8

increased gap size. From the curve in Fig.S3c, the time decreases to a few seconds when the gap

is more than a few μm.

In summary, the narrow gap of a few hundred nm creates a stagnant growth environment in

the interior of the pocket. Significantly low gas exchange rate occurs when the gap size is lower

than about 1 μm. In addition, we are also aware that some CH4 molecules are adsorbed on the Cu

sidewall of the gap channel when diffusing into the pocket, which may further slow-down the

gas exchange.

Figure S3 | a, A schematic drawing of the cross section of Cu pocket shows the CH4 transport

channel into the pocket interior environment. b, CH4 molecule concentration ratio of interior

environment to the exterior as a function of time for different gap size. c, The time needed for 90%

equilibrium in CH4 concentration between the interior and the exterior as a function of pocket

gap size.

9

(3) The growth results from OF-Cu pocket

The graphene domain growth starts from nuclei, the density of which is proportional to the

PCH4 at the beginning of the growth19,21,22. The PCH4 on the exterior surface of the pocket is

immediately established as it is directly exposed to the flowing gases. However, as discussed

above, PCH4 is low in the interior and takes a few minutes to reach equilibrium with the exterior.

Therefore, the graphene nucleation density on the interior surface is lower than that on the

exterior surface. Our experimental observations based on OF-Cu showed that the nucleation

density on the interior surface is lower than that on the exterior surface (Fig. S4c and S4d).

Therefore, the experimental observations are in agreement with the calculation results.

After nucleation, the new C radicals predominantly contribute to the graphene growth

instead of new nuclei formation due to the high barriers of nucleation compared to that of

growth21,24. In this way, the areal growth rate of graphene domains is proportional to the

perimeter length of graphene domains. Therefore, high nucleation density of graphene leads to

high graphene surface coverage rate. As a result, the graphene growth rate on the exterior surface

remains higher than that on the interior surface even after PCH4 equilibrates between the interior

and exterior surfaces. We consistently observed that the exterior surface of the pocket becomes

fully covered with graphene earlier than the interior (Fig. S4). In addition, it is worth noting that

both interior and exterior surfaces of OF-Cu were covered with only SLG, indicating that the

growth is surface-limited.

Note that the grown SLG on both interior and exterior surfaces of OF-Cu was confirmed by

optical contrast and multiple Raman spectroscopy measurements after being transferred onto

SiO2/Si substrates (data not shown). We did not find any BLG or few-layer graphene.





8

increased gap size. From the curve in Fig.S3c, the time decreases to a few seconds when the gap

is more than a few μm.

In summary, the narrow gap of a few hundred nm creates a stagnant growth environment in

the interior of the pocket. Significantly low gas exchange rate occurs when the gap size is lower

than about 1 μm. In addition, we are also aware that some CH4 molecules are adsorbed on the Cu

sidewall of the gap channel when diffusing into the pocket, which may further slow-down the

gas exchange.

Figure S3 | a, A schematic drawing of the cross section of Cu pocket shows the CH4 transport

channel into the pocket interior environment. b, CH4 molecule concentration ratio of interior

environment to the exterior as a function of time for different gap size. c, The time needed for 90%

equilibrium in CH4 concentration between the interior and the exterior as a function of pocket

gap size.

9

(3) The growth results from OF-Cu pocket

The graphene domain growth starts from nuclei, the density of which is proportional to the

PCH4 at the beginning of the growth19,21,22. The PCH4 on the exterior surface of the pocket is

immediately established as it is directly exposed to the flowing gases. However, as discussed

above, PCH4 is low in the interior and takes a few minutes to reach equilibrium with the exterior.

Therefore, the graphene nucleation density on the interior surface is lower than that on the

exterior surface. Our experimental observations based on OF-Cu showed that the nucleation

density on the interior surface is lower than that on the exterior surface (Fig. S4c and S4d).

Therefore, the experimental observations are in agreement with the calculation results.

After nucleation, the new C radicals predominantly contribute to the graphene growth

instead of new nuclei formation due to the high barriers of nucleation compared to that of

growth21,24. In this way, the areal growth rate of graphene domains is proportional to the

perimeter length of graphene domains. Therefore, high nucleation density of graphene leads to

high graphene surface coverage rate. As a result, the graphene growth rate on the exterior surface

remains higher than that on the interior surface even after PCH4 equilibrates between the interior

and exterior surfaces. We consistently observed that the exterior surface of the pocket becomes

fully covered with graphene earlier than the interior (Fig. S4). In addition, it is worth noting that

both interior and exterior surfaces of OF-Cu were covered with only SLG, indicating that the

growth is surface-limited.

Note that the grown SLG on both interior and exterior surfaces of OF-Cu was confirmed by

optical contrast and multiple Raman spectroscopy measurements after being transferred onto

SiO2/Si substrates (data not shown). We did not find any BLG or few-layer graphene.





10

Figure S4 | The parameter effects on the growth results of graphene on both interior and exterior

surfaces of OF-Cu pockets. T=1035°C, growth time varies in different cases.

B. Experimental study of BLG growth mechanism

(1) The comparison of graphene growth between OR-Cu foils and OR-Cu pockets

An OR-Cu foil and an OR-Cu pocket were placed side-by-side in the quartz tube for

graphene growth (PCH4=1×10-2 Torr) so that both were under the same growth conditions. The

results for different growth times are shown in Fig. S5. After 30 min of growth, we find similar

nucleation densities on the Cu foil and on the exterior surface of the OR-Cu pocket. This is

expected since both the exterior surface of pocket and the foil surface are directly exposed to the

growth atmosphere. We also observed that on the Cu foil, the nucleation density and growth

rates of graphene on both top and bottom surfaces are similar. The 2nd layer, up to ~5% of the

whole surface area38, does not grow larger once the surfaces are fully covered. In contrast, for the

11

Cu pocket, the nucleation density on the interior surface is much lower than that on Cu foil and

the exterior surface of the pocket. Also, there is much larger areal coverage of additional layers

growing on the exterior surface compared to the Cu foil. Furthermore, these additional layers

continue to grow larger and thicker with time even after the exterior surface is fully covered with

SLG. We observed that the growth of additional layers on the exterior surface does not stop until

the SLG graphene fully covers the interior surface. This indicates that there is a connection

between the growth on the two surfaces; even though they are separated by a Cu foil of 25 μm

thick.

Figure S5 | An OR-Cu foil and an OR-Cu pocket were placed side-by-side for graphene growth.

The SEM images of graphene growth results as a function of growth time.





10

Figure S4 | The parameter effects on the growth results of graphene on both interior and exterior

surfaces of OF-Cu pockets. T=1035°C, growth time varies in different cases.

B. Experimental study of BLG growth mechanism

(1) The comparison of graphene growth between OR-Cu foils and OR-Cu pockets

An OR-Cu foil and an OR-Cu pocket were placed side-by-side in the quartz tube for

graphene growth (PCH4=1×10-2 Torr) so that both were under the same growth conditions. The

results for different growth times are shown in Fig. S5. After 30 min of growth, we find similar

nucleation densities on the Cu foil and on the exterior surface of the OR-Cu pocket. This is

expected since both the exterior surface of pocket and the foil surface are directly exposed to the

growth atmosphere. We also observed that on the Cu foil, the nucleation density and growth

rates of graphene on both top and bottom surfaces are similar. The 2nd layer, up to ~5% of the

whole surface area38, does not grow larger once the surfaces are fully covered. In contrast, for the

11

Cu pocket, the nucleation density on the interior surface is much lower than that on Cu foil and

the exterior surface of the pocket. Also, there is much larger areal coverage of additional layers

growing on the exterior surface compared to the Cu foil. Furthermore, these additional layers

continue to grow larger and thicker with time even after the exterior surface is fully covered with

SLG. We observed that the growth of additional layers on the exterior surface does not stop until

the SLG graphene fully covers the interior surface. This indicates that there is a connection

between the growth on the two surfaces; even though they are separated by a Cu foil of 25 μm

thick.

Figure S5 | An OR-Cu foil and an OR-Cu pocket were placed side-by-side for graphene growth.

The SEM images of graphene growth results as a function of growth time.





12

(2) Control experiments show that the 2nd layer growth is supported by C diffusion through

Cu

To elucidate how the growth of the 2nd graphene layer on the exterior OR-Cu surface is

influenced by the interior surface, we designed a two-step growth control experiment as

schematically shown in Fig. S6. An OR-Cu foil was first fully covered on both surfaces with 12C

graphene using CVD. The graphene was then partially etched on one surface, and the foil

wrapped into a pocket with the partially etched surface in the interior. A second growth was then

carried out with 13CH4 (1×10-2 Torr) for 30 min. In the etched area region, dendritic graphene

domains formed on the interior surface (Fig. S6b) and hexagonal 2nd layer domains appeared on

the corresponding exterior surface regions (Fig. S6c). Raman mapping (insets of Fig. S6b and

S6c) shows that these new domains on both surfaces are composed of 13C, while the remaining

graphene films are 12C. In contrast, on the part of foil where both surfaces were covered by

original 12C-graphene, no new graphene domains were found on either surface. This control

experiment unambiguously proves and demonstrates that the C source forming the 2nd layer

graphene is the C that dissolves from the exposed interior Cu surface and then diffuses through

the Cu bulk to the exterior surface. It also reveals that graphene is an impermeable barrier to C

atoms and hydrocarbon molecules, which prevents C diffusion through Cu while passivating the

catalytic Cu surface, thus the 2nd layer graphene cannot nucleate and grow on top of the 1st layer,

contrary to previous reports14,17,18.

Superficially, the exposed Cu area on the interior surface allows C to dissolve and diffuse in

the Cu bulk to yield the 2nd layer growth. However, further investigation suggests that the 2nd

layer growth is affected by oxygen (O) impurities present on the Cu surface. For example, when

we intentionally increase the PCH4 in the growth system for the case of OR-Cu pocket, the

13

nucleation density and growth rate on the interior surface was found to be similar to that for the

OF-Cu. However, as shown in Fig. S7, the 2nd layer is formed only on the exterior surface of

OR-Cu, suggesting that O is playing a critical role in the formation of dissolved C, versus none

for the OF-Cu.

Figure S6 | a, Schematic of the control experiment. b and c, SEM images of the areas indicated

in a. Insets in b and c are the corresponding 13C Raman mapping, corresponding to peak intensity

in the range of 1450-1550cm-1. The corresponding Raman spectra at different points were shown

in Fig. S14. d, Schematic drawing of C diffusion processes for the BLG growth in the form of

Cu pocket. Graphene domain edges (C sinks) were highlighted with dash-line boxes.





12

(2) Control experiments show that the 2nd layer growth is supported by C diffusion through

Cu

To elucidate how the growth of the 2nd graphene layer on the exterior OR-Cu surface is

influenced by the interior surface, we designed a two-step growth control experiment as

schematically shown in Fig. S6. An OR-Cu foil was first fully covered on both surfaces with 12C

graphene using CVD. The graphene was then partially etched on one surface, and the foil

wrapped into a pocket with the partially etched surface in the interior. A second growth was then

carried out with 13CH4 (1×10-2 Torr) for 30 min. In the etched area region, dendritic graphene

domains formed on the interior surface (Fig. S6b) and hexagonal 2nd layer domains appeared on

the corresponding exterior surface regions (Fig. S6c). Raman mapping (insets of Fig. S6b and

S6c) shows that these new domains on both surfaces are composed of 13C, while the remaining

graphene films are 12C. In contrast, on the part of foil where both surfaces were covered by

original 12C-graphene, no new graphene domains were found on either surface. This control

experiment unambiguously proves and demonstrates that the C source forming the 2nd layer

graphene is the C that dissolves from the exposed interior Cu surface and then diffuses through

the Cu bulk to the exterior surface. It also reveals that graphene is an impermeable barrier to C

atoms and hydrocarbon molecules, which prevents C diffusion through Cu while passivating the

catalytic Cu surface, thus the 2nd layer graphene cannot nucleate and grow on top of the 1st layer,

contrary to previous reports14,17,18.

Superficially, the exposed Cu area on the interior surface allows C to dissolve and diffuse in

the Cu bulk to yield the 2nd layer growth. However, further investigation suggests that the 2nd

layer growth is affected by oxygen (O) impurities present on the Cu surface. For example, when

we intentionally increase the PCH4 in the growth system for the case of OR-Cu pocket, the

13

nucleation density and growth rate on the interior surface was found to be similar to that for the

OF-Cu. However, as shown in Fig. S7, the 2nd layer is formed only on the exterior surface of

OR-Cu, suggesting that O is playing a critical role in the formation of dissolved C, versus none

for the OF-Cu.

Figure S6 | a, Schematic of the control experiment. b and c, SEM images of the areas indicated

in a. Insets in b and c are the corresponding 13C Raman mapping, corresponding to peak intensity

in the range of 1450-1550cm-1. The corresponding Raman spectra at different points were shown

in Fig. S14. d, Schematic drawing of C diffusion processes for the BLG growth in the form of

Cu pocket. Graphene domain edges (C sinks) were highlighted with dash-line boxes.





14

Figure S7 | Control experiments. PCH4 for OF-Cu is 1 × 10-3Torr, while it is 8 × 10-2 Torr for

OR-Cu. The surface coverage is similar on both interior surfaces, but only on the exterior surface

of OR-Cu, BLG domains were observed. The growth time is 60 minutes for OF-Cu, and 30

minutes for OR-Cu.

(3) The driving force of C diffusion through the Cu bulk to the exterior surface.

The whole growth process of graphene (both SLG and BLG) is a non-equilibrium process

driven by the much lower energy of C in the graphene phase than that of the C radicals on the Cu

surface, which is independent of the local graphene coverage.

We point out that the driving force for C to diffuse through Cu bulk to the exterior surface

to grow the 2nd graphene layer is the higher C atom (or C radical) concentration on the interior

surface than that on the exterior surface, which is the consequence of higher nucleation density

of 2nd layer on the exterior surface than that of SLG on the interior surface. A schematic drawing

15

(not to scale) regarding the process is shown in Fig. S6d. In our previous work19 on the effect of

oxygen on the nucleation density of graphene on Cu, we showed that the interior surface of the

Cu pocket can be exposed to methane for many hours without nucleating new graphene domains,

but becomes covered with a significant amount of C radicals. Therefore when the exterior

surface is fully covered by 1st layer graphene, the C atoms on the largely exposed interior Cu

surface can diffuse either on the interior surface to the sparse graphene domain edges for their

enlargement, or through the Cu bulk to the exterior surface to grow 2nd layer graphene, with

comparable diffusion energy barriers thanks to the help of oxygen (0.92eV vs. 1eV, Table S1).

The nucleation density of 2nd layer on the exterior surface is higher than that of SLG on the

interior surface (this is a general characteristic, and can be seen in Figure 1b and 1c; Figure S5,

S7, and S11, etc). Correspondingly, on the exterior surface there are more 2nd layer domain edges,

which are sinks for C incorporation into graphene lattice and thus keep the C radical

concentration low. Consequently, more C is driven to diffuse through the Cu bulk to the exterior

surface. Further, because the thickness of the Cu is only 25 μm, much smaller than the separation

between graphene islands on the interior surface (~ mm), one can readily see that a significant

fraction of C atoms will diffuse through the foil to the exterior surface to form the 2nd layer

graphene rather than diffusing to the growing domains on the interior surface.

(4) The C bulk diffusion at the beginning of the growth.

To provide a complete picture of the whole growth process, we comment here on the C

diffusion at the beginning of the growth process. Nucleation and growth of 1st layer graphene

islands on the exterior surface of the OR-Cu pocket quickly proceeds through the well-

established surface-mediated mechanism, similar to the case of Cu foil. It is also possible for the





14

Figure S7 | Control experiments. PCH4 for OF-Cu is 1 × 10-3Torr, while it is 8 × 10-2 Torr for

OR-Cu. The surface coverage is similar on both interior surfaces, but only on the exterior surface

of OR-Cu, BLG domains were observed. The growth time is 60 minutes for OF-Cu, and 30

minutes for OR-Cu.

(3) The driving force of C diffusion through the Cu bulk to the exterior surface.

The whole growth process of graphene (both SLG and BLG) is a non-equilibrium process

driven by the much lower energy of C in the graphene phase than that of the C radicals on the Cu

surface, which is independent of the local graphene coverage.

We point out that the driving force for C to diffuse through Cu bulk to the exterior surface

to grow the 2nd graphene layer is the higher C atom (or C radical) concentration on the interior

surface than that on the exterior surface, which is the consequence of higher nucleation density

of 2nd layer on the exterior surface than that of SLG on the interior surface. A schematic drawing

15

(not to scale) regarding the process is shown in Fig. S6d. In our previous work19 on the effect of

oxygen on the nucleation density of graphene on Cu, we showed that the interior surface of the

Cu pocket can be exposed to methane for many hours without nucleating new graphene domains,

but becomes covered with a significant amount of C radicals. Therefore when the exterior

surface is fully covered by 1st layer graphene, the C atoms on the largely exposed interior Cu

surface can diffuse either on the interior surface to the sparse graphene domain edges for their

enlargement, or through the Cu bulk to the exterior surface to grow 2nd layer graphene, with

comparable diffusion energy barriers thanks to the help of oxygen (0.92eV vs. 1eV, Table S1).

The nucleation density of 2nd layer on the exterior surface is higher than that of SLG on the

interior surface (this is a general characteristic, and can be seen in Figure 1b and 1c; Figure S5,

S7, and S11, etc). Correspondingly, on the exterior surface there are more 2nd layer domain edges,

which are sinks for C incorporation into graphene lattice and thus keep the C radical

concentration low. Consequently, more C is driven to diffuse through the Cu bulk to the exterior

surface. Further, because the thickness of the Cu is only 25 μm, much smaller than the separation

between graphene islands on the interior surface (~ mm), one can readily see that a significant

fraction of C atoms will diffuse through the foil to the exterior surface to form the 2nd layer

graphene rather than diffusing to the growing domains on the interior surface.

(4) The C bulk diffusion at the beginning of the growth.

To provide a complete picture of the whole growth process, we comment here on the C

diffusion at the beginning of the growth process. Nucleation and growth of 1st layer graphene

islands on the exterior surface of the OR-Cu pocket quickly proceeds through the well-

established surface-mediated mechanism, similar to the case of Cu foil. It is also possible for the





16

CHx on the exterior surface of the OR-Cu pocket to completely dissociate and dissolve into the

Cu bulk, followed by C diffusion to the interior surface. But such processes will unavoidably

stop after the exterior surface being fully covered by graphene, which grows much faster than on

the interior surface because of the asymmetric growth environment of the Cu pocket.

We note that the bulk diffusion from the interior surface to the exterior surface is a critical

pathway for the large 2nd layer graphene growth, which is one of the main points in this work;

while the diffusion in the reversed direction occurs only at the beginning of growth when the

exterior surface is not fully covered with SLG, and is unimportant for the main claim of this

paper.

(5) The possibility of C diffusion through grain boundaries in polycrystalline Cu

Multiple experimental and theoretical works presented in this work have clearly

demonstrated that the 2nd layer growth is closely associated with O, not Cu grain boundaries

(GBs): oxygen can promote dissolution of C atoms into Cu, and then these C atoms diffuse

through the Cu bulk for 2nd layer growth. Furthermore, we did not find that the 2nd layer domains

preferentially grow along the Cu GBs: as shown in Figs.S8a and S9b, both high density and low

density 2nd layer domain growth are found to be independent of the Cu GBs; in a low

magnification SEM image (Fig. S8c), the 2nd layer domains can grow in regions more than one

millimeter away from the Cu GBs, which demonstrates that the GB is not the dominant C

diffusion pathway. These observations are in contrast to those in Ref. 39.

17

Figure S8 | The relationship between Cu grain boundaries and 2nd layer growth sites. Note that

in (c) the brightness contrast is due to the non-flatness of Cu surface at large-scale.

(6) Domain shapes: Dendritic versus compact

Different graphene domain shapes are the results of different growth kinetics. In the

previous work 19, we have clearly confirmed that Cu surface O impurities play a critical role in

determining the growth kinetics and hence the domain shapes. So the explanation is as follows:

As grown on the OR-Cu, the 1st layer domains were always dendritic, indicating diffusion-

limited growth. During the growth of the 1st layer, the surface oxygen species were depleted

through the reactions: CHx + O CHx-1 + OH (x=4, 3, 2, 1). Thus the 2nd layer domains were

grown in an oxygen-free environment. The compact domain shapes are a direct consequence of

the edge-attachment-limited growth kinetics in such an environment. This is consistent with our

previous work.

C. Optimization of growth parameters towards larger BLG domains





16

CHx on the exterior surface of the OR-Cu pocket to completely dissociate and dissolve into the

Cu bulk, followed by C diffusion to the interior surface. But such processes will unavoidably

stop after the exterior surface being fully covered by graphene, which grows much faster than on

the interior surface because of the asymmetric growth environment of the Cu pocket.

We note that the bulk diffusion from the interior surface to the exterior surface is a critical

pathway for the large 2nd layer graphene growth, which is one of the main points in this work;

while the diffusion in the reversed direction occurs only at the beginning of growth when the

exterior surface is not fully covered with SLG, and is unimportant for the main claim of this

paper.

(5) The possibility of C diffusion through grain boundaries in polycrystalline Cu

Multiple experimental and theoretical works presented in this work have clearly

demonstrated that the 2nd layer growth is closely associated with O, not Cu grain boundaries

(GBs): oxygen can promote dissolution of C atoms into Cu, and then these C atoms diffuse

through the Cu bulk for 2nd layer growth. Furthermore, we did not find that the 2nd layer domains

preferentially grow along the Cu GBs: as shown in Figs.S8a and S9b, both high density and low

density 2nd layer domain growth are found to be independent of the Cu GBs; in a low

magnification SEM image (Fig. S8c), the 2nd layer domains can grow in regions more than one

millimeter away from the Cu GBs, which demonstrates that the GB is not the dominant C

diffusion pathway. These observations are in contrast to those in Ref. 39.

17

Figure S8 | The relationship between Cu grain boundaries and 2nd layer growth sites. Note that

in (c) the brightness contrast is due to the non-flatness of Cu surface at large-scale.

(6) Domain shapes: Dendritic versus compact

Different graphene domain shapes are the results of different growth kinetics. In the

previous work 19, we have clearly confirmed that Cu surface O impurities play a critical role in

determining the growth kinetics and hence the domain shapes. So the explanation is as follows:

As grown on the OR-Cu, the 1st layer domains were always dendritic, indicating diffusion-

limited growth. During the growth of the 1st layer, the surface oxygen species were depleted

through the reactions: CHx + O CHx-1 + OH (x=4, 3, 2, 1). Thus the 2nd layer domains were

grown in an oxygen-free environment. The compact domain shapes are a direct consequence of

the edge-attachment-limited growth kinetics in such an environment. This is consistent with our

previous work.

C. Optimization of growth parameters towards larger BLG domains





18

Since the BLG growth mechanism is established, further efforts were devoted to understand

the effects of various growth parameters so as to achieve larger and more uniform 2nd layer

graphene, while suppressing thicker layer nucleation & growth. In this work, we investigate the

effects of methane partial pressures and O2 pretreatments on BLG growth, and to explore the

optimal growth conditions of large BLG domains, as detailed below.

Figure S9 | Raman images show isotope-labeled BLG domains at different growth conditions.

Lower inset is the growth rate plot at different PCH4.

(1) 2nd layer domain growth rates

We measured the 2nd layer domain growth rates. Using isotope-labeled growth at different

conditions and Raman mapping (details can be found in Note E), we are able to visualize the

time-resolved growth progress of the BLG (Fig. S9), and thus to extract the radial growth rates.

We plotted the growth rates as a function of methane partial pressure (lower inset of Fig. S9),

showing that the growth rates of individual 2nd layer domains increase with PCH4.

19

(2) Effects of PCH4

As shown in Fig. S10, by adjusting PCH4, we found that the exposed interior Cu surface area,

low PCH4, and proper growth time are critical for the formation of large and uniform BLG

domains.

At high PCH4 (~0.1Torr), due to the relatively high graphene nucleation density and growth

rate on the interior surface, it is almost fully covered with graphene in ~15min. In this case, only

small and sparse 2nd layer domains (~10 μm in lateral size) are formed on the exterior surface,

and these domains cannot grow larger because the graphene-covered interior surface prevents

further C dissolution and diffusion.

At medium PCH4 (~0.01Torr), the relatively low nucleation density and low growth rate on

the interior surface leaves a relatively large area of exposed Cu. In this case, the 2nd layer

graphene domains are dominant and can grow to more than 50 μm in about 40 min. However,

with time, more and more C atoms diffuse through the Cu. As a result, the 3rd, 4th, and even more

layer also starts to grow.

At low PCH4 (~0.001-0.002 Torr), the nucleation density on the interior surface is very low,

only about 0.5 mm-2 and the corresponding C that diffuses through the bulk and segregates onto

the exterior surface is also low. In this case, the low C concentration leads to a film that is

predominantly BLG and after 200min of growth, individual 2nd layer domains can grow to ~200-

400 μm.





18

Since the BLG growth mechanism is established, further efforts were devoted to understand

the effects of various growth parameters so as to achieve larger and more uniform 2nd layer

graphene, while suppressing thicker layer nucleation & growth. In this work, we investigate the

effects of methane partial pressures and O2 pretreatments on BLG growth, and to explore the

optimal growth conditions of large BLG domains, as detailed below.

Figure S9 | Raman images show isotope-labeled BLG domains at different growth conditions.

Lower inset is the growth rate plot at different PCH4.

(1) 2nd layer domain growth rates

We measured the 2nd layer domain growth rates. Using isotope-labeled growth at different

conditions and Raman mapping (details can be found in Note E), we are able to visualize the

time-resolved growth progress of the BLG (Fig. S9), and thus to extract the radial growth rates.

We plotted the growth rates as a function of methane partial pressure (lower inset of Fig. S9),

showing that the growth rates of individual 2nd layer domains increase with PCH4.

19

(2) Effects of PCH4

As shown in Fig. S10, by adjusting PCH4, we found that the exposed interior Cu surface area,

low PCH4, and proper growth time are critical for the formation of large and uniform BLG

domains.

At high PCH4 (~0.1Torr), due to the relatively high graphene nucleation density and growth

rate on the interior surface, it is almost fully covered with graphene in ~15min. In this case, only

small and sparse 2nd layer domains (~10 μm in lateral size) are formed on the exterior surface,

and these domains cannot grow larger because the graphene-covered interior surface prevents

further C dissolution and diffusion.

At medium PCH4 (~0.01Torr), the relatively low nucleation density and low growth rate on

the interior surface leaves a relatively large area of exposed Cu. In this case, the 2nd layer

graphene domains are dominant and can grow to more than 50 μm in about 40 min. However,

with time, more and more C atoms diffuse through the Cu. As a result, the 3rd, 4th, and even more

layer also starts to grow.

At low PCH4 (~0.001-0.002 Torr), the nucleation density on the interior surface is very low,

only about 0.5 mm-2 and the corresponding C that diffuses through the bulk and segregates onto

the exterior surface is also low. In this case, the low C concentration leads to a film that is

predominantly BLG and after 200min of growth, individual 2nd layer domains can grow to ~200-

400 μm.





20

Figure S10 | SEM images of graphene or BLG grown on surfaces of Cu pockets, showing the

effects of methane partial pressure.

21

Figure S11 | Optical images of large BLG domains and continuous films on SiO2/Si substrates.

We demonstrate that at low PCH4 and after appropriate growth time, large area BLG and trilayer

graphene can be achieved.

Fig. S11 shows the optical images of individual domains and continuous films of large BLG

and trilayer graphene (TLG) after being transferred onto Si substrates, which were grown at

PCH4=0.001Torr and different growth time.

(3) Effects of O2 pretreatments

In this experimental comparison, we treat the OF-Cu substrates with O2 at PO2 = 1×10-3 Torr

for different exposure time ranging from 20 s to 5 min. During growth the PCH4 was fixed at

2×10-3 Torr in each case. The results are shown in Fig. S12.

On the exterior surface of OF-Cu pockets, we do not observe any BLG growth for a wide

range of growth parameters. However, once small amount of O2 are introduced, say ~20 s before

feeding CH4, we immediately note a change in the growth behavior: on the interior surface, the

graphene domain shape becomes fractal, distinct from the compact domains on pristine OF-Cu,

in agreement with our previous work on SLG. On the exterior surface, we observed low density

2nd layer domains with average size of about 10 μm. Obviously, this is the effect of oxygen

activating the BLG growth as reported in this work. We also note that with the short O2 exposure,

the 2nd layer domains do not grow larger than about 10 μm since the interior surface becomes

fully covered with graphene in about 20 min.

When the O2 exposure time increases, i.e., the surface oxygen concentration increases prior

to growth, the nucleation density of graphene domains on the interior surface decreases as





20


effects of methane partial pressure.

21

Figure S11 | Optical images of large BLG domains and continuous films on SiO2/Si substrates.

We demonstrate that at low PCH4 and after appropriate growth time, large area BLG and trilayer

graphene can be achieved.

Fig. S11 shows the optical images of individual domains and continuous films of large BLG

and trilayer graphene (TLG) after being transferred onto Si substrates, which were grown at

PCH4=0.001Torr and different growth time.

(3) Effects of O2 pretreatments

In this experimental comparison, we treat the OF-Cu substrates with O2 at PO2 = 1×10-3 Torr

for different exposure time ranging from 20 s to 5 min. During growth the PCH4 was fixed at

2×10-3 Torr in each case. The results are shown in Fig. S12.

On the exterior surface of OF-Cu pockets, we do not observe any BLG growth for a wide

range of growth parameters. However, once small amount of O2 are introduced, say ~20 s before

feeding CH4, we immediately note a change in the growth behavior: on the interior surface, the

graphene domain shape becomes fractal, distinct from the compact domains on pristine OF-Cu,

in agreement with our previous work on SLG. On the exterior surface, we observed low density

2nd layer domains with average size of about 10 μm. Obviously, this is the effect of oxygen

activating the BLG growth as reported in this work. We also note that with the short O2 exposure,

the 2nd layer domains do not grow larger than about 10 μm since the interior surface becomes

fully covered with graphene in about 20 min.

When the O2 exposure time increases, i.e., the surface oxygen concentration increases prior

to growth, the nucleation density of graphene domains on the interior surface decreases as





22

expected, the nucleation density of the 2nd layer domains on the exterior surface decreased too,

and thus the 2nd layer domain size increases. Therefore O2 treatment not only makes 2nd layer

growth possible, but also helps to improve the 2nd layer domain growth by suppressing

nucleation of graphene islands on both surfaces of the pocket. We plot the 2nd layer domain size

as a function of O2 exposure time, as shown in the lower inset of Fig. S12. We find that after 180

s exposure, the 2nd layer domain size can be up to about 660 μm, indicating that experimental

conditions could be designed for further enlargement of the 2nd layer domain size.


effects of O2 pretreatments. In each case, PCH4=0.002 Torr. Lower inset is the 2nd layer domain

size as a function of O2 exposure time.

23

We are aware that other growth parameters, such as PH2, Cu foil thickness, growth time,

growth temperature, etc., may also affect the 2nd layer growth. By tuning the combination of

different parameters, we expect that further improvement in the growth of BLG can be achieved.

D. Low-energy electron microscopy and low-energy electron diffraction

Low-energy electron microscopy (LEEM) and low-energy electron diffraction (LEED)

were utilized to investigate the crystallinity of BLG on the exterior surface of OR-Cu (Fig. S13).

LEEM & LEED are also reliable and well-established tool to test the stacking sequence 40 (the

2nd layer graphene above or below the 1st layer): the LEED spot intensity from the under-layer is

always weaker than that from the top-layer, which is a consequence of the strong attenuation of

the incident electrons during transmission through the top-layer. The measurements were

performed using an Elmitec LEEM III instrument. As-grown BLG-Cu samples were transferred

through air into the instrument and then degassed at ~250 °C overnight in ultra-high vacuum

(base pressure < 2×10-10 Torr). The analysis was performed at room temperature.

Fig. S13a1 is a LEEM image of a region that contains a hexagonal island of BLG. The

LEED patterns in a2 are from the whole 50 μm-sized view-field of a1, and thus the diffraction

patterns can be associated with different domains of the 1st layer. We can then obtain the dark

field images, b1, b2, and b3, and re-build the color-coded 1st layer (b4) with respect to crystal

orientations and domain morphology. With this detailed but necessary background, we now turn

to the key mechanistic issue of whether the 2nd layer is next to the substrate or on top of the 1st

layer.





22

expected, the nucleation density of the 2nd layer domains on the exterior surface decreased too,

and thus the 2nd layer domain size increases. Therefore O2 treatment not only makes 2nd layer

growth possible, but also helps to improve the 2nd layer domain growth by suppressing

nucleation of graphene islands on both surfaces of the pocket. We plot the 2nd layer domain size

as a function of O2 exposure time, as shown in the lower inset of Fig. S12. We find that after 180

s exposure, the 2nd layer domain size can be up to about 660 μm, indicating that experimental

conditions could be designed for further enlargement of the 2nd layer domain size.


effects of O2 pretreatments. In each case, PCH4=0.002 Torr. Lower inset is the 2nd layer domain

size as a function of O2 exposure time.

23

We are aware that other growth parameters, such as PH2, Cu foil thickness, growth time,

growth temperature, etc., may also affect the 2nd layer growth. By tuning the combination of

different parameters, we expect that further improvement in the growth of BLG can be achieved.

D. Low-energy electron microscopy and low-energy electron diffraction

Low-energy electron microscopy (LEEM) and low-energy electron diffraction (LEED)

were utilized to investigate the crystallinity of BLG on the exterior surface of OR-Cu (Fig. S13).

LEEM & LEED are also reliable and well-established tool to test the stacking sequence 40 (the

2nd layer graphene above or below the 1st layer): the LEED spot intensity from the under-layer is

always weaker than that from the top-layer, which is a consequence of the strong attenuation of

the incident electrons during transmission through the top-layer. The measurements were

performed using an Elmitec LEEM III instrument. As-grown BLG-Cu samples were transferred

through air into the instrument and then degassed at ~250 °C overnight in ultra-high vacuum

(base pressure < 2×10-10 Torr). The analysis was performed at room temperature.

Fig. S13a1 is a LEEM image of a region that contains a hexagonal island of BLG. The

LEED patterns in a2 are from the whole 50 μm-sized view-field of a1, and thus the diffraction

patterns can be associated with different domains of the 1st layer. We can then obtain the dark

field images, b1, b2, and b3, and re-build the color-coded 1st layer (b4) with respect to crystal

orientations and domain morphology. With this detailed but necessary background, we now turn

to the key mechanistic issue of whether the 2nd layer is next to the substrate or on top of the 1st

layer.





24

Figure S13 | a, LEEM image and the corresponding LEED patterns of a BLG region. The

electron energy is 3.2eV and 50eV for a1 and a2, respectively. b, Dark-field images obtained

from the three sets of diffraction spots in a2, as indicated by red, green, and blue rings. b4, Map

of the 1st layer domains. The three colors represent domains with three different in-plane

rotational orientations of the 1st layer, as revealed by the dark-field LEEM images. The electron

energy is 50eV for b1 to b3. Un-colored 1st layer domains have a different, uncharacterized in-

plane rotation. c, Select-area LEED patterns taken from different regions (2 μm size) in a1, and

the electron energy is 50 eV for each pattern in c. Note that the additional diffraction spots in

each diffraction pattern result from the faceted Cu substrate. The Lower inset schematically

shows the cross-section of this region, where different colors refer to different orientations of

each domain.

25

Distinct from a2, the patterns in c1-c4 are from 2 μm regions, as indicated in a1 and the

schematic drawing in the lower inset. From single-layer regions, c1 and c4 show one set of

strong patterns, while c2 and c3 show two sets of patterns, respectively, since they are taken

from bilayer regions. After comparison with domain morphology (b4) and diffraction pattern

orientations (red spots in c1 and c2; blue spots in c3 and c4), we are able to confirm the red- and

blue-coded spots are from 1st layer and the green-coded spots from the 2nd layer. The consistent

and clear comparisons in each pattern can exclude any artifacts. We then compare the diffraction

spot intensities between the 1st and the 2nd layers and thus conclude the 2nd layer (with weaker

intensity spots) is below the 1st layer.

In addition, we note that the (weak) diffraction spots of the 2nd layer graphene had the same

rotational alignment at all points examined in the hexagonal domain. This indicates that the

hexagonal 2nd layer is a single crystal, a general result found in our analysis of discrete 2nd layer

domains. In addition, by comparing the 2nd layer domain shape with the corresponding

diffraction pattern orientations, the 2nd layer domains were found to be zigzag-edge-terminated,

in accord with previous reports of hexagonal SLG domains on Cu4,19.

E. BLG characterizations using Raman spectroscopy and TEM

(1) Raman spectroscopy characterizations

Raman spectroscopy was used to study the characteristics of BLG and isotope-labeled BLG

6, 20, 23, 26, 41. Two well-established criteria were used to judge the characteristics of the BLG:

(a) G band positions were used to determine the C isotope-labeling of the graphene regions.

The peak at ~1580 cm-1 indicates 12C graphene, and ~1525cm-1 indicates 13C. If the peak is

between 1525 and 1580cm-1, such as at ~1550cm-1, the film being mixed with both 12C and 13C;





24

Figure S13 | a, LEEM image and the corresponding LEED patterns of a BLG region. The

electron energy is 3.2eV and 50eV for a1 and a2, respectively. b, Dark-field images obtained

from the three sets of diffraction spots in a2, as indicated by red, green, and blue rings. b4, Map

of the 1st layer domains. The three colors represent domains with three different in-plane

rotational orientations of the 1st layer, as revealed by the dark-field LEEM images. The electron

energy is 50eV for b1 to b3. Un-colored 1st layer domains have a different, uncharacterized in-

plane rotation. c, Select-area LEED patterns taken from different regions (2 μm size) in a1, and

the electron energy is 50 eV for each pattern in c. Note that the additional diffraction spots in

each diffraction pattern result from the faceted Cu substrate. The Lower inset schematically

shows the cross-section of this region, where different colors refer to different orientations of

each domain.

25

Distinct from a2, the patterns in c1-c4 are from 2 μm regions, as indicated in a1 and the

schematic drawing in the lower inset. From single-layer regions, c1 and c4 show one set of

strong patterns, while c2 and c3 show two sets of patterns, respectively, since they are taken

from bilayer regions. After comparison with domain morphology (b4) and diffraction pattern

orientations (red spots in c1 and c2; blue spots in c3 and c4), we are able to confirm the red- and

blue-coded spots are from 1st layer and the green-coded spots from the 2nd layer. The consistent

and clear comparisons in each pattern can exclude any artifacts. We then compare the diffraction

spot intensities between the 1st and the 2nd layers and thus conclude the 2nd layer (with weaker

intensity spots) is below the 1st layer.

In addition, we note that the (weak) diffraction spots of the 2nd layer graphene had the same

rotational alignment at all points examined in the hexagonal domain. This indicates that the

hexagonal 2nd layer is a single crystal, a general result found in our analysis of discrete 2nd layer

domains. In addition, by comparing the 2nd layer domain shape with the corresponding

diffraction pattern orientations, the 2nd layer domains were found to be zigzag-edge-terminated,

in accord with previous reports of hexagonal SLG domains on Cu4,19.

E. BLG characterizations using Raman spectroscopy and TEM

(1) Raman spectroscopy characterizations

Raman spectroscopy was used to study the characteristics of BLG and isotope-labeled BLG

6, 20, 23, 26, 41. Two well-established criteria were used to judge the characteristics of the BLG:

(a) G band positions were used to determine the C isotope-labeling of the graphene regions.

The peak at ~1580 cm-1 indicates 12C graphene, and ~1525cm-1 indicates 13C. If the peak is

between 1525 and 1580cm-1, such as at ~1550cm-1, the film being mixed with both 12C and 13C;





26

in this work, no such regions were found. The co-existence of the two peaks (1525 and 1580cm-1)

in bilayer regions indicates two possibilities: (i) one layer is formed by 12C and the other is

formed by 13C graphene; (ii) the laser spot illuminates both 12C and 13C graphene regions

bordering each other, which could be easily distinguished by Raman mapping in this work.

(b) FWHM of 2D (G’) band was used to check the stacking orders of the BLG. When the

FWHM was between 20-40cm-1, the region was considered as twisted BLG. If the FWHM is 50-

55cm-1(either 12C or 13C BLG) or 100-110cm-1 (one layer is 12C and the other layer is 13C), the

region is considered as Bernal-stacking.

Raman image is able to further visualize the spatial distributions of the layer number,

stacking order, isotope distribution, domain size, domain shape, domain growth rate, domain

boundary, etc, as shown in Fig. 1, Fig. 2, Fig. S6 and Fig. S9. Corresponding Raman spectra

from Raman images are shown in Fig. S14.

Figure S14 | Raman spectra for the figure panels in the paper. “AB” in the panels refers to

Bernal-stacking.

27

(2) Further explanations of isotope-labeled Raman images

In order to highlight the 2nd layer growth, we presented the “zoom-in” image in Fig. 2f,

which shows only part of the 1st layer domain. Here, we added the “zoom-out” image (Fig. S15),

in which one complete 1st layer domain is shown, and its adjacent 1st layer domains are shown

too. We also note that in Fig. 2f and 2j, the Raman images were taken according to the “center of

mass” of the 2D peak in the range of 2500 cm-1-2850 cm-1. The brighter regions in the maps

indicate that the “center of mass” of the peaks approach higher wavenumbers (lower panel in Fig.

S15). We choose this Raman characteristic because it can clearly distinguish both layers of the

isotope-labeled BLG. From the isotope-labeled Raman images, we are able to achieve more

information regarding the growth mechanism, as follows:

(a) The high 12C surface coverage at the central region of the 1st layer simply means that the

first 12C cycle grows faster in this selected area. Similarly, the nearly 1-to-1 ratio of C isotopes in

the 2nd layer domain suggests that this domain grows at a constant radial rate. The higher growth

rate of the central part of 1st layer domain during the 1st 12C cycle is mainly due to the fact that

the separation between it and the neighboring domains in the early stage of growth is larger than

the C diffusion length, so that the growth of different domains are relatively independent of each

other. As the domains keep growing and the distance between edges of neighboring domains

becomes smaller than the C diffusion length, the surface concentration of C species between the

two domains will be insufficient for each of them to maintain the same growth rate as before,

hence the narrower isotopic rings in the subsequent cycles. Finally, all the domains merge

together into a continuous graphene film. Detailed study of this phenomenon was reported in one

of our previous works on SLG 42. In contrast, because the relatively small sizes of the 2nd layer

domains and the fact that they are typically well separated (edges of 2nd layer domains are far





26

in this work, no such regions were found. The co-existence of the two peaks (1525 and 1580cm-1)

in bilayer regions indicates two possibilities: (i) one layer is formed by 12C and the other is

formed by 13C graphene; (ii) the laser spot illuminates both 12C and 13C graphene regions

bordering each other, which could be easily distinguished by Raman mapping in this work.

(b) FWHM of 2D (G’) band was used to check the stacking orders of the BLG. When the

FWHM was between 20-40cm-1, the region was considered as twisted BLG. If the FWHM is 50-

55cm-1(either 12C or 13C BLG) or 100-110cm-1 (one layer is 12C and the other layer is 13C), the

region is considered as Bernal-stacking.

Raman image is able to further visualize the spatial distributions of the layer number,

stacking order, isotope distribution, domain size, domain shape, domain growth rate, domain

boundary, etc, as shown in Fig. 1, Fig. 2, Fig. S6 and Fig. S9. Corresponding Raman spectra

from Raman images are shown in Fig. S14.

Figure S14 | Raman spectra for the figure panels in the paper. “AB” in the panels refers to

Bernal-stacking.

27

(2) Further explanations of isotope-labeled Raman images

In order to highlight the 2nd layer growth, we presented the “zoom-in” image in Fig. 2f,

which shows only part of the 1st layer domain. Here, we added the “zoom-out” image (Fig. S15),

in which one complete 1st layer domain is shown, and its adjacent 1st layer domains are shown

too. We also note that in Fig. 2f and 2j, the Raman images were taken according to the “center of

mass” of the 2D peak in the range of 2500 cm-1-2850 cm-1. The brighter regions in the maps

indicate that the “center of mass” of the peaks approach higher wavenumbers (lower panel in Fig.

S15). We choose this Raman characteristic because it can clearly distinguish both layers of the

isotope-labeled BLG. From the isotope-labeled Raman images, we are able to achieve more

information regarding the growth mechanism, as follows:

(a) The high 12C surface coverage at the central region of the 1st layer simply means that the

first 12C cycle grows faster in this selected area. Similarly, the nearly 1-to-1 ratio of C isotopes in

the 2nd layer domain suggests that this domain grows at a constant radial rate. The higher growth

rate of the central part of 1st layer domain during the 1st 12C cycle is mainly due to the fact that

the separation between it and the neighboring domains in the early stage of growth is larger than

the C diffusion length, so that the growth of different domains are relatively independent of each

other. As the domains keep growing and the distance between edges of neighboring domains

becomes smaller than the C diffusion length, the surface concentration of C species between the

two domains will be insufficient for each of them to maintain the same growth rate as before,

hence the narrower isotopic rings in the subsequent cycles. Finally, all the domains merge

together into a continuous graphene film. Detailed study of this phenomenon was reported in one

of our previous works on SLG 42. In contrast, because the relatively small sizes of the 2nd layer

domains and the fact that they are typically well separated (edges of 2nd layer domains are far





28

from edges of other 2nd layer domains), they maintain a constant radial growth rate as indicated

by the equal widths of the isotopic rings.

(b) Further, we observe that after the first 6-7 isotope cycles (105 minutes of growth time),

the 1st layer domains on the exterior surface merge with adjacent domains and fully cover the Cu

surface. However, because of a lower growth rate, the 2nd layer domains continue to grow up to

12 cycles (180 minutes growth). The difference in growth kinetics for the two layers clearly

shows that the enlargement of the 2nd layer domains is not restricted by the full coverage of the

1st layer graphene on the exterior Cu surface. This further suggests that the 2nd layer growth is

supported by the C bulk diffusion from the interior surface.

29

Figure S15 | “Zoom-out” Raman image of Figure 2f. The growth progress of the whole domains

of both layers was shown, and the grain boundary of the 1st layer film is shown too. Note that

this image was taken according to the “center of mass” of 2D peaks, and the corresponding

Raman spectra at different regions were shown in the lower-right panel.

(c) “Sharp isotope labeled 2nd layer graphene”. In our previous work 23, the contrasting

features between the isotope-labeled graphene films on Ni and on Cu strongly suggest that the

extremely low C solubility in Cu restricts the whole growth processes, such as nucleation and

diffusion, to happening only at surface. We emphasize that those samples were grown in the

conventional geometry (i.e. same conditions on both sides of the Cu foil, such that there is no net

flux of C through the foil). In contrast, in current work we intentionally utilize the asymmetric

growth environment with a Cu pocket to promote the isothermal growth of the 2nd layer. Multiple

control experiments confirmed that small amounts of C can diffuse through the Cu bulk and

segregate onto the exterior surface for the 2nd layer growth. Interestingly, we found the similar

isotopic rings. This appears to be different from the previous case. Here we revisit the scenario,

and found that the occurrence of isotope rings are the results of extremely low C solubility,

efficient diffusion both in bulk and along the interface between Cu and the 1st graphene layer.

We note that significant isotope mixing requires that there is a C reservoir in the bulk of the

metal substrate, i.e. the number of C atoms in the substrate bulk exceeds that in the graphene

grown on it.23 However, the C solubility in Cu is extremely low, so that even if there is mixing

between 12C and 13C dissolved in the Cu foil, the amount is too small to give an obvious isotope-

mixing contrast from that of pure 12C or 13C regions. In other words, the total number of C atoms

passing through the Cu foil and forming graphene on the exterior surface during one isotope





28

from edges of other 2nd layer domains), they maintain a constant radial growth rate as indicated

by the equal widths of the isotopic rings.

(b) Further, we observe that after the first 6-7 isotope cycles (105 minutes of growth time),

the 1st layer domains on the exterior surface merge with adjacent domains and fully cover the Cu

surface. However, because of a lower growth rate, the 2nd layer domains continue to grow up to

12 cycles (180 minutes growth). The difference in growth kinetics for the two layers clearly

shows that the enlargement of the 2nd layer domains is not restricted by the full coverage of the

1st layer graphene on the exterior Cu surface. This further suggests that the 2nd layer growth is

supported by the C bulk diffusion from the interior surface.

29

Figure S15 | “Zoom-out” Raman image of Figure 2f. The growth progress of the whole domains

of both layers was shown, and the grain boundary of the 1st layer film is shown too. Note that

this image was taken according to the “center of mass” of 2D peaks, and the corresponding

Raman spectra at different regions were shown in the lower-right panel.

(c) “Sharp isotope labeled 2nd layer graphene”. In our previous work 23, the contrasting

features between the isotope-labeled graphene films on Ni and on Cu strongly suggest that the

extremely low C solubility in Cu restricts the whole growth processes, such as nucleation and

diffusion, to happening only at surface. We emphasize that those samples were grown in the

conventional geometry (i.e. same conditions on both sides of the Cu foil, such that there is no net

flux of C through the foil). In contrast, in current work we intentionally utilize the asymmetric

growth environment with a Cu pocket to promote the isothermal growth of the 2nd layer. Multiple

control experiments confirmed that small amounts of C can diffuse through the Cu bulk and

segregate onto the exterior surface for the 2nd layer growth. Interestingly, we found the similar

isotopic rings. This appears to be different from the previous case. Here we revisit the scenario,

and found that the occurrence of isotope rings are the results of extremely low C solubility,

efficient diffusion both in bulk and along the interface between Cu and the 1st graphene layer.

We note that significant isotope mixing requires that there is a C reservoir in the bulk of the

metal substrate, i.e. the number of C atoms in the substrate bulk exceeds that in the graphene

grown on it.23 However, the C solubility in Cu is extremely low, so that even if there is mixing

between 12C and 13C dissolved in the Cu foil, the amount is too small to give an obvious isotope-

mixing contrast from that of pure 12C or 13C regions. In other words, the total number of C atoms

passing through the Cu foil and forming graphene on the exterior surface during one isotope





30

feeding cycle far exceeds that of saturating C atoms inside the Cu bulk. Therefore the minimal

isotope mixing also indicates efficient C bulk diffusion at the elevated temperature. In addition,

minor isotope mixing near the isotope ring boundaries cannot be completely excluded since the

spatial resolution of the Raman mapping is ~300 nm. Last, the interface diffusion has been

confirmed by the first-principles calculations, as detailed in Fig.3 of the main text and Note G.

(3) TEM characterization

Transmission electron microscopy and selected area electron diffraction (SAED) were used

to further confirm the Bernal-stacking order. As shown in Fig. S16, only one set of six-fold

diffraction pattern was exhibited from the area with 2D FWHM of 53 cm-1. Furthermore, the spot

intensity of {2−1

−10} is consistently higher than those of {01

−10}, in agreement with previous

characterization of Bernal-stacked BLG11,43.

Figure S16 | a, SAED pattern of bilayer area with Raman 2D band FWHM ~53 cm-1. b, Profile

plots of diffraction spot peak intensities along arrows in a. c, TEM image of folded edge,

indicating that it is a BLG.

31

F. Estimation of C solubility and diffusivity in Cu bulk.

(1) C solubility

It is well known that the C solubility in Cu is extremely low, but our experimental

observations have convinced that appreciable amounts of C can diffuse through the bulk for the

2nd layer growth on the exterior surface of a pocket. In this way, it would be more informative if

there is knowledge of C solubility in Cu at the growth temperature. However, C solubility is lack

of consistent value in literature. In one of the most recent works, Lopez and Mittemeijer25

measured the C solubility in Cu: 7.4 ± 0.5 at. ppm at 1020°C.

One attempt to estimate the C solubility based on our own data is from the amount of 2nd

layer domains grown underneath a full-coverage SLG during the cooling down stage, which are

from the segregation of the dissolved C in the Cu bulk (presumably saturated before the surfaces

being fully passivated by SLG). Obviously we cannot use our Cu pockets for such estimates,

since even though the Cu bulk is saturated with C, C atoms can continuously diffuse through Cu

bulk to the exterior surface as long as the interior surface is not passivated with graphene.

However, in our previous work38 and the result of the control experiment in Fig. S5 of this work,

we observed that there are always ~5% areas of BLG on SLG-covered Cu foil surface. These

BLG domains should be formed by the segregated C from the saturated Cu foil. By using this

data we may estimate the C solubility through the calculations as follows:

Given the standard atomic weight of Cu (63.546 g/mol) and the Cu density (8.96 g/cm3), we

obtain that in a Cu foil of 25 μm thick and 1cm2 area, the number of Cu atoms is NCu = 2.15 ×

1020. The C sp2 bond distance is 0.142 nm, and there are two C atoms in one graphene unit cell.

So, in the area of 1 cm2, there are 3.8 × 1015 C atoms in graphene if assuming full coverage.

Considering the top and bottom surfaces of a Cu foil of 1cm2 area and 5% coverage, we can get





30

feeding cycle far exceeds that of saturating C atoms inside the Cu bulk. Therefore the minimal

isotope mixing also indicates efficient C bulk diffusion at the elevated temperature. In addition,

minor isotope mixing near the isotope ring boundaries cannot be completely excluded since the

spatial resolution of the Raman mapping is ~300 nm. Last, the interface diffusion has been

confirmed by the first-principles calculations, as detailed in Fig.3 of the main text and Note G.

(3) TEM characterization

Transmission electron microscopy and selected area electron diffraction (SAED) were used

to further confirm the Bernal-stacking order. As shown in Fig. S16, only one set of six-fold

diffraction pattern was exhibited from the area with 2D FWHM of 53 cm-1. Furthermore, the spot

intensity of {2−1

−10} is consistently higher than those of {01

−10}, in agreement with previous

characterization of Bernal-stacked BLG11,43.

Figure S16 | a, SAED pattern of bilayer area with Raman 2D band FWHM ~53 cm-1. b, Profile

plots of diffraction spot peak intensities along arrows in a. c, TEM image of folded edge,

indicating that it is a BLG.

31

F. Estimation of C solubility and diffusivity in Cu bulk.

(1) C solubility

It is well known that the C solubility in Cu is extremely low, but our experimental

observations have convinced that appreciable amounts of C can diffuse through the bulk for the

2nd layer growth on the exterior surface of a pocket. In this way, it would be more informative if

there is knowledge of C solubility in Cu at the growth temperature. However, C solubility is lack

of consistent value in literature. In one of the most recent works, Lopez and Mittemeijer25

measured the C solubility in Cu: 7.4 ± 0.5 at. ppm at 1020°C.

One attempt to estimate the C solubility based on our own data is from the amount of 2nd

layer domains grown underneath a full-coverage SLG during the cooling down stage, which are

from the segregation of the dissolved C in the Cu bulk (presumably saturated before the surfaces

being fully passivated by SLG). Obviously we cannot use our Cu pockets for such estimates,

since even though the Cu bulk is saturated with C, C atoms can continuously diffuse through Cu

bulk to the exterior surface as long as the interior surface is not passivated with graphene.

However, in our previous work38 and the result of the control experiment in Fig. S5 of this work,

we observed that there are always ~5% areas of BLG on SLG-covered Cu foil surface. These

BLG domains should be formed by the segregated C from the saturated Cu foil. By using this

data we may estimate the C solubility through the calculations as follows:

Given the standard atomic weight of Cu (63.546 g/mol) and the Cu density (8.96 g/cm3), we

obtain that in a Cu foil of 25 μm thick and 1cm2 area, the number of Cu atoms is NCu = 2.15 ×

1020. The C sp2 bond distance is 0.142 nm, and there are two C atoms in one graphene unit cell.

So, in the area of 1 cm2, there are 3.8 × 1015 C atoms in graphene if assuming full coverage.

Considering the top and bottom surfaces of a Cu foil of 1cm2 area and 5% coverage, we can get





32

that the number of C atoms in the 2nd layer graphene on the Cu foil surface is NC = 3.8 × 1014.

The solubility of C in Cu is therefore NC / NCu = 1.8 at. ppm. This value is in the same order of

magnitude as the value measured by Lopez and Mittemeijer25.

We nevertheless note that our number may be an underestimate since the Cu foil is not

necessarily saturated with C during the growth, nor is it necessary that all C segregated from the

bulk Cu to form the 2nd layer graphene upon cooling. It is also safe to say, by following this

estimation procedure, that the C dissolved in the bulk of our Cu pocket cannot lead to the

significant growth of BLG that we observed.

(2) C diffusivity

The diffusivity for solid state diffusion is described by the Arrhenius formula:

kTeDDΔ

−= 0 ,

where Δ is the microscopic kinetic energy barrier for a C atom to hop between adjacent lowest

energy sites in bulk Cu. 0D is given by

ν6

2

0

aD = ,

where a is the length of a hopping step and is equal to the Cu nearest neighbor distance 2.5 Å,

6

2a is from the assumption of 3D random walk, and ν is the attempt frequency, which is

basically the atomic vibration frequency ~ 1013 Hz. With these numbers the C diffusivity is

kTeDΔ

−−= 310 cm2s-1.

33

When T=1300 K, Δ=1 eV (DFT calculation result in this work, Fig. 3d), the diffusivity of C in

bulk Cu is found to be about 1.3×10-7 cm2s-1. This value is comparable with the C diffusivity in

γ-Fe (fcc Fe), ~5 ×10-7 cm2s-1 at ~1100 °C (Ref. 44), indicating that C can efficiently diffuse

inside Cu bulk. It is remarkable that although the C solubility of Fe is orders of magnitude larger

than that of Cu, the diffusivity values of C in these two materials are comparable. This again

points out that the diffusivity as a kinetic property is not necessarily strongly correlated with the

solubility, which is a thermal equilibrium property.

G. 2nd Layer Growth Mechanism studied by First-Principles Calculations

Besides the O-activated hydrocarbon dissociation on Cu, large 2nd layer growth requires fast

kinetics for (i) C diffusion in Cu bulk; (ii) C diffusion near the Cu-graphene interface. Overall,

the Cu(111) surfaces with and without graphene top layer are adopted as an example to do the

calculations.

Since the Cu lattice cannot accommodate large C clusters [C-C dimer, CHx (x=1-4), etc.];

At the Cu-graphene interface, these species are also found energetically unfavorable28,45.

Therefore, in this work, only individual C atoms are calculated in various processes.

We perform density functional theory (DFT) calculations using Projector Augmented

Wave (PAW) pseudopotentials 46,47 and the VDW-DF functional,48 as implemented in VASP.49,50

The energy cutoff for the plane wave functions is 400 eV. All structures are relaxed until the

force on each atom is < 0.01 eV/Å. The Cu-graphene interface is modeled by a 4×4 Cu(111)

surface cell with 4 layers, as shown in Fig. S17a. The bottom layer is fixed in the direction

perpendicular to the surface. 5×5×1 Monkhorst-Pack (MP) k-points51 are used (5×5 points in the

surface plane and 1 along the surface normal direction) to sample the Brillouin zone. C atom in





32

that the number of C atoms in the 2nd layer graphene on the Cu foil surface is NC = 3.8 × 1014.

The solubility of C in Cu is therefore NC / NCu = 1.8 at. ppm. This value is in the same order of

magnitude as the value measured by Lopez and Mittemeijer25.

We nevertheless note that our number may be an underestimate since the Cu foil is not

necessarily saturated with C during the growth, nor is it necessary that all C segregated from the

bulk Cu to form the 2nd layer graphene upon cooling. It is also safe to say, by following this

estimation procedure, that the C dissolved in the bulk of our Cu pocket cannot lead to the

significant growth of BLG that we observed.

(2) C diffusivity

The diffusivity for solid state diffusion is described by the Arrhenius formula:

kTeDDΔ

−= 0 ,

where Δ is the microscopic kinetic energy barrier for a C atom to hop between adjacent lowest

energy sites in bulk Cu. 0D is given by

ν6

2

0

aD = ,

where a is the length of a hopping step and is equal to the Cu nearest neighbor distance 2.5 Å,

6

2a is from the assumption of 3D random walk, and ν is the attempt frequency, which is

basically the atomic vibration frequency ~ 1013 Hz. With these numbers the C diffusivity is

kTeDΔ

−−= 310 cm2s-1.

33

When T=1300 K, Δ=1 eV (DFT calculation result in this work, Fig. 3d), the diffusivity of C in

bulk Cu is found to be about 1.3×10-7 cm2s-1. This value is comparable with the C diffusivity in

γ-Fe (fcc Fe), ~5 ×10-7 cm2s-1 at ~1100 °C (Ref. 44), indicating that C can efficiently diffuse

inside Cu bulk. It is remarkable that although the C solubility of Fe is orders of magnitude larger

than that of Cu, the diffusivity values of C in these two materials are comparable. This again

points out that the diffusivity as a kinetic property is not necessarily strongly correlated with the

solubility, which is a thermal equilibrium property.

G. 2nd Layer Growth Mechanism studied by First-Principles Calculations

Besides the O-activated hydrocarbon dissociation on Cu, large 2nd layer growth requires fast

kinetics for (i) C diffusion in Cu bulk; (ii) C diffusion near the Cu-graphene interface. Overall,

the Cu(111) surfaces with and without graphene top layer are adopted as an example to do the

calculations.

Since the Cu lattice cannot accommodate large C clusters [C-C dimer, CHx (x=1-4), etc.];

At the Cu-graphene interface, these species are also found energetically unfavorable28,45.

Therefore, in this work, only individual C atoms are calculated in various processes.

We perform density functional theory (DFT) calculations using Projector Augmented

Wave (PAW) pseudopotentials 46,47 and the VDW-DF functional,48 as implemented in VASP.49,50

The energy cutoff for the plane wave functions is 400 eV. All structures are relaxed until the

force on each atom is < 0.01 eV/Å. The Cu-graphene interface is modeled by a 4×4 Cu(111)

surface cell with 4 layers, as shown in Fig. S17a. The bottom layer is fixed in the direction

perpendicular to the surface. 5×5×1 Monkhorst-Pack (MP) k-points51 are used (5×5 points in the

surface plane and 1 along the surface normal direction) to sample the Brillouin zone. C atom in





34

Cu bulk is modeled by a 4×4 Cu(111) surface cell with 6 layers. 5×5×3 k-points are used.

Vacuum spacing is kept larger than 15 Å in the direction perpendicular to the Cu or graphene

surface.

Figure S17 | a, Model of Cu-graphene interface. C: black; Cu: orange. Blue-line arrows indicate

the supercell. b-d, top-view and corresponding side-view of C monomer at FCC, HCP, and

subsurface sites of graphene-Cu interface, respectively. Note that the C monomer at Cu bridge

sites of graphene-Cu interface is unstable, and automatically fallen into subsurface, so no images

shown here.

The binding energy of C, shown in Table S1, is calculated as:

Eb = E(C+Cu) – E(Cu) – E(C), where E(C+Cu) is the total energy of the system which contains

both C and Cu, E(Cu) is the energy of Cu substrate, and E(C) is the energy of an isolated C atom.

The calculated binding energy values (Eb) of C monomer at various sites of Cu are listed in

Table S1. The corresponding atomic-scale views are shown in Fig. S17b-d. Near the Cu-

graphene interface, C prefers to stay at the subsurface site (beneath one atomic layer of Cu

35

surface). This is consistent with previous reports28,45,52 and indicates that after bulk diffusion,

most C atoms should sit on the Cu subsurface.

The energy of CHx for the without-O case, shown in Fig. 3, is calculated as: E = E(CHx+Cu)

– E(CH4+Cu) + x[E(Cu+H)-E(Cu)]; and for the with-O case: E = E(CHx+Cu) – E(CH4+Cu) +

x[E(Cu+OH)-E(Cu+O)].

Table S1 | The calculated energetics and diffusion barriers of C atoms during various processes.

The unit is eV/atom.

Since Cu surface is not atomically smooth in real experiments, it is necessary to consider

whether the surface defects would take effects on the dehydrogenation processes. Step edges

have been found to be the most popular defects on Cu surface at elevated temperature. We

calculated the dehydrogenation barriers from CH4 to C monomers. The Cu step is modeled by

cutting the Cu (111) surface along the <011> direction, with a spacing of 3*a*sqrt(3)/2 between

the step edges (where a is the lattice parameter of Cu). The results are shown in Fig. S18a and

compared with the results shown in Fig. 3c. We can clearly see that the step edge can only





34

Cu bulk is modeled by a 4×4 Cu(111) surface cell with 6 layers. 5×5×3 k-points are used.

Vacuum spacing is kept larger than 15 Å in the direction perpendicular to the Cu or graphene

surface.

Figure S17 | a, Model of Cu-graphene interface. C: black; Cu: orange. Blue-line arrows indicate

the supercell. b-d, top-view and corresponding side-view of C monomer at FCC, HCP, and

subsurface sites of graphene-Cu interface, respectively. Note that the C monomer at Cu bridge

sites of graphene-Cu interface is unstable, and automatically fallen into subsurface, so no images

shown here.

The binding energy of C, shown in Table S1, is calculated as:

Eb = E(C+Cu) – E(Cu) – E(C), where E(C+Cu) is the total energy of the system which contains

both C and Cu, E(Cu) is the energy of Cu substrate, and E(C) is the energy of an isolated C atom.

The calculated binding energy values (Eb) of C monomer at various sites of Cu are listed in

Table S1. The corresponding atomic-scale views are shown in Fig. S17b-d. Near the Cu-

graphene interface, C prefers to stay at the subsurface site (beneath one atomic layer of Cu

35

surface). This is consistent with previous reports28,45,52 and indicates that after bulk diffusion,

most C atoms should sit on the Cu subsurface.

The energy of CHx for the without-O case, shown in Fig. 3, is calculated as: E = E(CHx+Cu)

– E(CH4+Cu) + x[E(Cu+H)-E(Cu)]; and for the with-O case: E = E(CHx+Cu) – E(CH4+Cu) +

x[E(Cu+OH)-E(Cu+O)].

Table S1 | The calculated energetics and diffusion barriers of C atoms during various processes.

The unit is eV/atom.

Since Cu surface is not atomically smooth in real experiments, it is necessary to consider

whether the surface defects would take effects on the dehydrogenation processes. Step edges

have been found to be the most popular defects on Cu surface at elevated temperature. We

calculated the dehydrogenation barriers from CH4 to C monomers. The Cu step is modeled by

cutting the Cu (111) surface along the <011> direction, with a spacing of 3*a*sqrt(3)/2 between

the step edges (where a is the lattice parameter of Cu). The results are shown in Fig. S18a and

compared with the results shown in Fig. 3c. We can clearly see that the step edge can only





36

slightly decrease the overall barrier from 4.3eV to 3.7eV, which is still significantly higher than

the case with ‘O assistance’ (1.4eV). It is therefore reasonable to conclude that Cu surface

defects cannot efficiently catalyze methane dissociations either, while surface O is critical for

this process.

The binding energy of C atoms in Cu bulk was obtained based on the Cu interstitial

positions, such as the C staying at the center of octahedral Cu atom cages. The value is slightly

higher than that on Cu subsurface. So, this is in agreement with the low solubility of C in Cu

bulk. The C monomer diffusion barrier in the bulk is ~1eV by hopping between adjacent

octahedra (Fig. S18b). This value is lower than the graphene growth activation energy, which is

up to 1.7eV 19. The bulk diffusion is thus not rate-limiting step for the 2nd layer growth. It is

worth noting that this relatively low kinetic barrier is not necessarily contradictory to the low C

solubility in Cu, while the latter is a thermal equilibrium property. The reasonably low diffusion

barriers allow for the massive C transport to underneath the 1st graphene layer, finally leading to

the formation of large 2nd layer.

Our calculation shows that on bare Cu, the C atom diffusion barrier along the subsurface

is ～0.92eV. During the diffusion, one Cu atom is found to be slightly lifted up, as shown in

Fig.3. In contrast, for graphene layer covered Cu, when the hopping of a C atom occurs along the

subsurface, the distance between graphene over-layer and the lifted Cu atom is found to be ~2.1

Å. The charge density distribution also indicates the formation of weak chemical bond between

the lifted Cu atom and graphene, which help to reduce the barrier to 0.45eV (Fig. 3d). The low

barrier facilitated the C diffusion along the subsurface.

In Fig. 3d, the charge density difference of the “lifted” Cu atom is defined as:

37

ρ(Cu+substrate+graphene) - ρ(substrate+graphene) - ρ(Cu atom), where the first term is

the total charge density of the whole system, the second term is the charge density of the system

without the “lifted” Cu atom (other atoms are in fixed positions), and the last term is the charge

density of the isolated Cu atom.”

From the calculations, we established that at atomic-scale the C diffusion through Cu bulk

and interface diffusion along the Cu subsurface are reasonable and can be incorporated into the

graphene growth steps for the large 2nd graphene layer.

Figure S18 | a, Cu (111) step edge dehydrogenation processes and the associated barriers. Inset

shows the equilibrium positions of each CHx radical at Cu step edges. The red and black lines are

for the ideal Cu and for the OR-Cu, respectively, as shown in Fig. 3c of the main text. b, C atom

diffusion inside the Cu bulk. The three panels show the initial, transition, and final states of the

hopping process. The Cu octahedron is found to be slightly distorted at the transition state.

H. Device fabrication and transport measurements

The fabrication process of the BLG devices was schematically shown in Fig. S19. First, the

BLG domains were transferred onto h-BN/SiO2/Si substrates (Step 1) by the PMMA-assisted

method. Then, electron-beam lithography (EBL), reactive ion etching, and physical vapor





36

slightly decrease the overall barrier from 4.3eV to 3.7eV, which is still significantly higher than

the case with ‘O assistance’ (1.4eV). It is therefore reasonable to conclude that Cu surface

defects cannot efficiently catalyze methane dissociations either, while surface O is critical for

this process.

The binding energy of C atoms in Cu bulk was obtained based on the Cu interstitial

positions, such as the C staying at the center of octahedral Cu atom cages. The value is slightly

higher than that on Cu subsurface. So, this is in agreement with the low solubility of C in Cu

bulk. The C monomer diffusion barrier in the bulk is ~1eV by hopping between adjacent

octahedra (Fig. S18b). This value is lower than the graphene growth activation energy, which is

up to 1.7eV 19. The bulk diffusion is thus not rate-limiting step for the 2nd layer growth. It is

worth noting that this relatively low kinetic barrier is not necessarily contradictory to the low C

solubility in Cu, while the latter is a thermal equilibrium property. The reasonably low diffusion

barriers allow for the massive C transport to underneath the 1st graphene layer, finally leading to

the formation of large 2nd layer.

Our calculation shows that on bare Cu, the C atom diffusion barrier along the subsurface

is ～0.92eV. During the diffusion, one Cu atom is found to be slightly lifted up, as shown in

Fig.3. In contrast, for graphene layer covered Cu, when the hopping of a C atom occurs along the

subsurface, the distance between graphene over-layer and the lifted Cu atom is found to be ~2.1

Å. The charge density distribution also indicates the formation of weak chemical bond between

the lifted Cu atom and graphene, which help to reduce the barrier to 0.45eV (Fig. 3d). The low

barrier facilitated the C diffusion along the subsurface.

In Fig. 3d, the charge density difference of the “lifted” Cu atom is defined as:

37

ρ(Cu+substrate+graphene) - ρ(substrate+graphene) - ρ(Cu atom), where the first term is

the total charge density of the whole system, the second term is the charge density of the system

without the “lifted” Cu atom (other atoms are in fixed positions), and the last term is the charge

density of the isolated Cu atom.”

From the calculations, we established that at atomic-scale the C diffusion through Cu bulk

and interface diffusion along the Cu subsurface are reasonable and can be incorporated into the

graphene growth steps for the large 2nd graphene layer.

Figure S18 | a, Cu (111) step edge dehydrogenation processes and the associated barriers. Inset

shows the equilibrium positions of each CHx radical at Cu step edges. The red and black lines are

for the ideal Cu and for the OR-Cu, respectively, as shown in Fig. 3c of the main text. b, C atom

diffusion inside the Cu bulk. The three panels show the initial, transition, and final states of the

hopping process. The Cu octahedron is found to be slightly distorted at the transition state.

H. Device fabrication and transport measurements

The fabrication process of the BLG devices was schematically shown in Fig. S19. First, the

BLG domains were transferred onto h-BN/SiO2/Si substrates (Step 1) by the PMMA-assisted

method. Then, electron-beam lithography (EBL), reactive ion etching, and physical vapor





38

deposition processes were used to pattern the bubble-free area of the BLG into Hall bar geometry

with Cr/Pd/Au electrodes (step 2 and 3). After that, another h-BN flake was transferred by the

polymer transfer method on the top of the device (Step 4 and 5) as top-gate dielectrics, as

described in Ref. 53. Finally the top-gate electrode (Cr/Pd/Au) was defined with EBL again

(Step 6). Note that before top h-BN deposition, Raman spectroscopy was used to confirm that the

device area is composed of Bernal-stacked BLG, where the FWHM of 2D peak is ~53cm-1 (Fig.

S20), and the 2D peak shows the “asymmetric” characteristics and can be well fitted with four

Lorentz components 20.

Figure S19 | Schematic drawing of the device fabrication process.

The completed dual-gated Hall bar device was optically imaged with low- and high-

magnifications, as shown in Fig. S20a and S20b. The atomic force microscopy (AFM) image

before top h-BN layer deposition was shown in Fig. S20d. Samples were cooled in a variable

temperature (1.7K–300K) liquid 4He flow cryostat with samples in He vapor. Transport

39

measurements were acquired in a four-terminal geometry using a standard lock-in technique at

17Hz.

Figure S20 | a, b, The low- and high-magnification optical images of two devices encapsulated

between two h-BN flakes. c, The schematic picture of the device cross section. d, AFM image of

the device before top-gate dielectric deposition, as circled by the green dash-line in c. e, The

Raman spectrum of the device area of the BLG. f, The Lorentz fitting of 2D band of the Bernal-

stacked BLG. On h-BN, we can clearly see the “asymmetry” of the 2D band.

From the electrical transport measurement (Fig. S21), the extracted mobility is ~20,000

cm2V-1S-1 at room temperature. At liquid He temperature, we can clearly observe the quantum

Hall states at a magnetic field of 6 T with filling factors ν=±4, ±8, and ±12, in agreement with





38

deposition processes were used to pattern the bubble-free area of the BLG into Hall bar geometry

with Cr/Pd/Au electrodes (step 2 and 3). After that, another h-BN flake was transferred by the

polymer transfer method on the top of the device (Step 4 and 5) as top-gate dielectrics, as

described in Ref. 53. Finally the top-gate electrode (Cr/Pd/Au) was defined with EBL again

(Step 6). Note that before top h-BN deposition, Raman spectroscopy was used to confirm that the

device area is composed of Bernal-stacked BLG, where the FWHM of 2D peak is ~53cm-1 (Fig.

S20), and the 2D peak shows the “asymmetric” characteristics and can be well fitted with four

Lorentz components 20.

Figure S19 | Schematic drawing of the device fabrication process.

The completed dual-gated Hall bar device was optically imaged with low- and high-

magnifications, as shown in Fig. S20a and S20b. The atomic force microscopy (AFM) image

before top h-BN layer deposition was shown in Fig. S20d. Samples were cooled in a variable

temperature (1.7K–300K) liquid 4He flow cryostat with samples in He vapor. Transport

39

measurements were acquired in a four-terminal geometry using a standard lock-in technique at

17Hz.

Figure S20 | a, b, The low- and high-magnification optical images of two devices encapsulated

between two h-BN flakes. c, The schematic picture of the device cross section. d, AFM image of

the device before top-gate dielectric deposition, as circled by the green dash-line in c. e, The

Raman spectrum of the device area of the BLG. f, The Lorentz fitting of 2D band of the Bernal-

stacked BLG. On h-BN, we can clearly see the “asymmetry” of the 2D band.

From the electrical transport measurement (Fig. S21), the extracted mobility is ~20,000

cm2V-1S-1 at room temperature. At liquid He temperature, we can clearly observe the quantum

Hall states at a magnetic field of 6 T with filling factors ν=±4, ±8, and ±12, in agreement with





40

the σxy=±(4e2/h)N for N ≥1 (Ref. 54,55). This result further indicates that the sample is Bernal-

stacked high-quality BLG.

Figure S21 | a, The resistivity and conductivity as a function of back-gate voltage, Vbg, at room

temperature. b, Longitudinal resistivity, Rxx, measured on left axis (black) and Hall resistance,

Rxy, measured on right axis (red) as a function of Vbg.

Reference:

32. S. Chen et al., Millimeter-Size Single-Crystal Graphene by Suppressing Evaporative Loss of

Cu During Low Pressure Chemical Vapor Deposition. Adv. Mater. 25, 2062-2065 (2013).

33. Suk, J. W. et al. Transfer of CVD-grown monolayer graphene onto arbitrary substrates. ACS

Nano 5, 6916-6924 (2011).

34. Bird, G. A. Molecular gas dynamics and the direct simulation of gas flows. (Oxford Univ.

Press, Oxford. UK, 1994), Chap. 4.

41

35. Malek, K. & Coppens, M. O. Knudsen self- and Fickian diffusion in rough nanoporous

media. J. Chem. Phys.119, 2801-2811 (2003).

36. Gang, H. & Ye, W. A Macro Model for Squeeze-film Air Damping in the Free-Molecule

Regime. Phys. Fluids 22, 012001 (2010).

37. Naris, S., Valougeorgis, D., Kalempa, D. & Sharipov, F. Gaseous mixture flow between two

parallel plates in the whole range of the gas rarefaction. Physica A: Statistical Mechanics

and its Applications 336, 294-318 (2004).

38. Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils.

Science 324, 1312-1314 (2009).

39. Su, C. Y. et al. Direct formation of wafer scale graphene thin layers on insulating substrates

by chemical vapor deposition, Nano Lett. 11, 3612-3616 (2011).

40. Nie, S. et al. Growth from below: bilayer graphene on copper by chemical vapor deposition,

New J. Phys. 14, 093028 (2012).

41. Cai, W. et al. Synthesis and solid-state NMR structural characterization of 13C-labeled

graphite oxide. Science 321, 1815-1817 (2008).

42. Li, X. et al. Graphene films with large domain size by a two-step chemical vapor deposition

process. Nano Lett. 10, 4328-4334 (2010).

43. Meyer, J. C. et al. On the roughness of single- and bi-layer graphene membranes. Solid State

Commun. 143, 101-109 (2007).

44. Edited by Brandes E. A. & Brook, G. B. Smithells Metals Reference Book, 7th Edition.

(Butterworth-Heinemann, March 30, 1998).

45. Zhang, X., Wang, L., Xin, J., Yakobson, B. I. & Ding, F. Role of hydrogen in graphene

chemical vapor deposition growth on a copper surface, J. Am. Chem. Soc. 136, 3040-3047

(2014).

46. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave

method. Phys. Rev. B 59, 1758 (1999).

47. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).

48. Klimeš, J. Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to

solids. Phys. Rev. B 83, 195131 (2011).

49. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558

(1993).





40

the σxy=±(4e2/h)N for N ≥1 (Ref. 54,55). This result further indicates that the sample is Bernal-

stacked high-quality BLG.

Figure S21 | a, The resistivity and conductivity as a function of back-gate voltage, Vbg, at room

temperature. b, Longitudinal resistivity, Rxx, measured on left axis (black) and Hall resistance,

Rxy, measured on right axis (red) as a function of Vbg.

Reference:

32. S. Chen et al., Millimeter-Size Single-Crystal Graphene by Suppressing Evaporative Loss of

Cu During Low Pressure Chemical Vapor Deposition. Adv. Mater. 25, 2062-2065 (2013).

33. Suk, J. W. et al. Transfer of CVD-grown monolayer graphene onto arbitrary substrates. ACS

Nano 5, 6916-6924 (2011).

34. Bird, G. A. Molecular gas dynamics and the direct simulation of gas flows. (Oxford Univ.

Press, Oxford. UK, 1994), Chap. 4.

41

35. Malek, K. & Coppens, M. O. Knudsen self- and Fickian diffusion in rough nanoporous

media. J. Chem. Phys.119, 2801-2811 (2003).

36. Gang, H. & Ye, W. A Macro Model for Squeeze-film Air Damping in the Free-Molecule

Regime. Phys. Fluids 22, 012001 (2010).

37. Naris, S., Valougeorgis, D., Kalempa, D. & Sharipov, F. Gaseous mixture flow between two

parallel plates in the whole range of the gas rarefaction. Physica A: Statistical Mechanics

and its Applications 336, 294-318 (2004).

38. Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils.

Science 324, 1312-1314 (2009).

39. Su, C. Y. et al. Direct formation of wafer scale graphene thin layers on insulating substrates

by chemical vapor deposition, Nano Lett. 11, 3612-3616 (2011).

40. Nie, S. et al. Growth from below: bilayer graphene on copper by chemical vapor deposition,

New J. Phys. 14, 093028 (2012).

41. Cai, W. et al. Synthesis and solid-state NMR structural characterization of 13C-labeled

graphite oxide. Science 321, 1815-1817 (2008).

42. Li, X. et al. Graphene films with large domain size by a two-step chemical vapor deposition

process. Nano Lett. 10, 4328-4334 (2010).

43. Meyer, J. C. et al. On the roughness of single- and bi-layer graphene membranes. Solid State

Commun. 143, 101-109 (2007).

44. Edited by Brandes E. A. & Brook, G. B. Smithells Metals Reference Book, 7th Edition.

(Butterworth-Heinemann, March 30, 1998).

45. Zhang, X., Wang, L., Xin, J., Yakobson, B. I. & Ding, F. Role of hydrogen in graphene

chemical vapor deposition growth on a copper surface, J. Am. Chem. Soc. 136, 3040-3047

(2014).

46. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave

method. Phys. Rev. B 59, 1758 (1999).

47. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).

48. Klimeš, J. Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to

solids. Phys. Rev. B 83, 195131 (2011).

49. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558

(1993).





42

50. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy

calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

51. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B

13, 5188 (1976).

52. Yazyev, O. V. & Pasquarello, A. Effect of metal element in catalytic growth of carbon

nanotubes, Phys. Rev. Lett. 100, 156102 (2008)

53. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat.

Nanotechnol., 5, 722-726 (2010).

54. Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry’s phase of 2π in

bilayer graphene. Nat. Phys. 2, 177-180 (2006).

55. Fallahazad, B. et al. Quantum Hall effect in Bernal stacked and twisted bilayer graphene

grown on Cu by chemical vapor deposition. Phys. Rev. B 85, 201408(2012).



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