Real-Time Multiscale Monitoring and Tailoring of Graphene Growth on Liquid Copper

The synthesis of large, defect-free two-dimensional materials (2DMs) such as graphene is a major challenge toward industrial applications. Chemical vapor deposition (CVD) on liquid metal catalysts (LMCats) is a recently developed process for the fast synthesis of high-quality single crystals of 2DMs. However, up to now, the lack of in situ techniques enabling direct feedback on the growth has limited our understanding of the process dynamics and primarily led to empirical growth recipes. Thus, an in situ multiscale monitoring of the 2DMs structure, coupled with a real-time control of the growth parameters, is necessary for efficient synthesis. Here we report real-time monitoring of graphene growth on liquid copper (at 1370 K under atmospheric pressure CVD conditions) via four complementary in situ methods: synchrotron X-ray diffraction and reflectivity, Raman spectroscopy, and radiation-mode optical microscopy. This has allowed us to control graphene growth parameters such as shape, dispersion, and the hexagonal supra-organization with very high accuracy. Furthermore, the switch from continuous polycrystalline film to the growth of millimeter-sized defect-free single crystals could also be accomplished. The presented results have far-reaching consequences for studying and tailoring 2D material formation processes on LMCats under CVD growth conditions. Finally, the experimental observations are supported by multiscale modeling that has thrown light into the underlying mechanisms of graphene growth.


Supplementary Note 1: Concept of continuous 2DM production on LMCats
The hypothetical concept of continuous 2DM production on LMCats (e.g. graphene on molten copper) via direct separation relies on the idea of pulling or sliding graphene from the liquid substrate. 1 The experimentally measured ultimate tensile strength of CVD grown single-layer graphene (SLG) is 30-33 [ m −1 ] at room temperature. 2 At the liquid copper temperature of 1370 K, this value is predicted to be reduced by ~30%. 3 To the best of our knowledge, the adhesion energy between SLG and liquid copper (caused by van der Waals interactions) has not been reported, but it is measured to be 0.3 [ m −2 ] between graphite and liquid copper. 4 The adhesion energy of SLG on liquid copper is expected to be slightly less than the one of graphite, as the weak van der Waals contributions of subsurface layers in graphite are absent in the case of SLG. Hence, the average force per unit width needed to separate the SLG off the molten copper directly is predicted to be about or less than 0.3 [ m −1 ], which is about two orders of magnitude less than its tensile strength. However, one should note that the strength of graphene is a sensitive function of its defects (e.g., vacancies, domain boundaries, cracks). 2,5,6 Therefore, in situ monitoring of graphene's structural quality during its growth (from atomic to macroscopic scale) is of outmost importance for a successful direct separation process.

Supplementary Note 2: Growth conditions
We have grown graphene on a liquid copper surface using a continuous flow of an H2/Ar/CH4 gas mixture. The total pressure in the CVD reactor was usually set at 200 mbar, and the flow of gases at 200 sccm of Ar and 20 sccm of H2. Under these conditions, the power of the sample heater was slowly raised until the melting of copper, observed by optical microscopy. The new copper samples were annealed for a few hours in a mixture of H2 and Ar in order to remove impurities segregating at the surface, visible as bright features slowly moving to the edges of the liquid copper pool. Subsequently, a gas mixture of 2% methane in argon was introduced to the reactor chamber at a flow of 7 sccm, which corresponds to a methane flow of 0.14 sccm.
The initiation of the growth by a so-called "pulsed growth" was done by accumulating the methane-argon gas mixture for 40 s in the gas line and its sudden release to the mainstream of gas by opening the electromagnetic valve. The profile of the pulse is presented in Supplementary Fig. 1. The temporary increase of methane pressure was 22.5 times higher with respect to continuous flow. The gas composition in the main line connected to the reactor was measured using a residual gas analyzer (RGA) separated from the main line with an ultra-high vacuum (UHV) leak valve.

Supplementary Note 3: Radiation-mode optical microscopy
Radiation-mode optical microscopy is an experimental method allowing to monitor the growth of thin layers on surfaces at high temperatures. This method employs an optical microscope measuring the light radiated by the sample. The recorded microscopy images show areas with different intensities (see Supplementary Fig. 2). This contrast originates from sample regions exhibiting different emissivity 7 . The contrast between liquid copper and graphene layer(s) is caused by the interplay between the different emissivities of liquid copper and graphene (0.143 and 0.016, respectively) and the light absorption by the graphene layer (2.5% per layer). 8,9 One monolayer of graphene absorbs the light emitted by the liquid copper that supports it, but also emits light itself. The overall balance results in a theoretically 8% higher luminous emittance for SLG-covered rather than bare liquid copper above its melting temperature. Moreover, the emissivity of multilayer graphene scales linearly with the number of layers.  11 , which is confirmed by microscopy images presented in Supplementary Fig. 3. It has been proposed that the decomposition of the methane on the hot copper leads to the formation of graphitic carbon, in our case, multilayer carbon stacks.
The growth rate of each layer in these stacks depends on the distance to the exposed LMCat surface, acting as a source of carbon atoms. The layers which are closest to the LMCat surface grow at the highest rate. As the bottom carbon layer grows, the distance between top layers and the source of carbon atoms increases, their growth slows down, to finally stop when the first layer is sufficiently large (see Supplementary Fig. 3b). The top layers are continuously attacked by the hydrogen present in the flown gas mixture during the whole growth. When the distance that needs to be travel by carbon atoms is too high, the layer's etching prevails over the growth, and finally, the multilayer-stacks gradually disappear (see Supplementary Fig. 3c and d). Also, this observation supports the idea of the initial growth of graphene from multilayer carbon seeds.

Supplementary Note 5: Revealing graphene domain boundaries and defects by hydrogen etching
Etching by the Hydrogen can reveal some defects of a fully-grown graphene layer during one single experiment. After the coalescence of growing graphene flakes, it is possible to determine if the grown layer is continuous, without extended grain boundaries and defects. The flow of the precursor gas, methane, is turned off, and the sample is exposed only to the mixture of Argon and Hydrogen, with the same flows used for the growth. The etching of graphene leads to the appearance of linear voids at the place of domain boundaries 12 and compact voids where other defects are expected 13 . The effects of the initial etching are presented in Supplementary   Fig. 5. From the presence and geometry of voids, it is possible to deduce information about the graphene layer's homogeneity.

Supplementary Note 6: Theoretical framework
Complementing the experiments, we provide a theoretical framework analyzing the interactions between growing graphene flakes. These interactions consist of attractive capillary interactions and repulsive electrostatic interactions. Interactions between particles on a fluidfluid interface have previously been rationalized in terms of the deformation of the fluid surface around the particles as originating from the three-phase contact angle. [14][15][16] In this work, we specifically model such interactions within the general framework of capillary multipoles as formulated by Danov et al., 17 where the formula for the force among two capillary charges is derived assuming a small meniscus slope between the particles. This leads to the following equation for the energy change, Δ ( ), when two particles are brought together to a distance L from infinity: where and are the capillary charges of particles A and B, 0 is the modified Bessel function of second kind and order zero, is the so-called capillary length and is the surface tension of the liquid. The capillary length is given by = √γ/(Δρ ), where Δ is the difference in density between the two fluid phases and is the gravitational acceleration. is calculated to be ~4 mm for Cu at 1370 K using this formula, the density from Assael et al. 18 and the surface tension from Matsumoto et al., 19 The capillary charge can be related to the three-phase contact angle for spherical particles: 20 where is the radius of particle X, its contact angle, and relates the densities of the different phases, here taken as the ratio of the particle and liquid densities. We here model the flakes as spherical particles with a radius of 70 μm, where the radius is chosen to match half of the diagonal of the flake sizes typically observed in the experiment. In turn, the contact angle is related to the liquid-particle interface energy graphene−Cu by Young's equation: where the double integral runs over the interior region of the i-th element and is its surface area. For hexagonal elements the self-interaction term is: where is the radius of the circumscribed circle. A system of equations is then built to find the charge distribution that make all elements equipotential: To account for the conductor surface which lies beneath the flake at a distance , elements Eq. 12 The intercept of such a linear model corresponds to the asymptotic value for very large flakes, which is the one used in our model.

Supplementary Note 8: Purity of the produced graphene
We present Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) spectra recorded from the solid copper covered by graphene. The sample was cooled down to room temperature, removed from the CVD reactor, and quickly transferred to a UHV system equipped with a hemispherical electron analyzer, an X-ray gun, and an electron gun. Before measurements, the sample was degassed at 250 °C for a few hours in UHV. The characteristic peaks of copper are visible in the recorded AES spectrum, shown in Supplementary Fig. 7. The three KLL carbon peaks at ~270 eV confirm the presence of the graphene layer. The peak at 152 eV (S L3M23M23) indicates the presence of residual traces of sulfur, which is an intrinsic impurity of copper or might be adsorbed on the sample surface during transport between the reactor and UHV system. The XPS spectrum ( Supplementary Fig. 8) shows the presence of the carbon (C 1s peak) but not sulfur, which peak position (S 2p) corresponds to 164 eV. This peak absence indicates the presence of sulfur only in the surface region as AES has much higher surface sensitivity. For higher concentrations in bulk, we should be able to detect sulfur using XPS. In summary, the presented spectra show high chemical purity of the samples.

Supplementary Note 9: Van-der-Pauw method
Electrical properties of produced graphene samples were measured through the van der Pauw method which is a common way to measure resistivity. The main advantage of this method is the ability to measure the properties of a sample of any given shape if it is approximately twodimensional. It uses a four-point probe positioned on the sample and provide the average resistivity of the sample under the examined area. A scheme of the van der Pauw configuration is presented in Supplementary Fig. 10 with a probe spacing of around 2 mm.
Once all the voltage measurements are performed, two values of resistivity ρΑ and ρB are derived as follows:  Once ρΑ and ρB are calculated, the average resistivity was determined by: