Layer-by-layer growth of bilayer graphene single-crystals enabled by self-transmitting catalytic activity

Direct growth of large-area vertically stacked two-dimensional (2D) van der Waal (vdW) materials is a prerequisite for their high-end applications in integrated electronics, optoelectronics and photovoltaics. Currently, centimetre- to even metre-scale monolayers of single-crystal graphene (MLG) and hexagonal boron nitride (h-BN) have been achieved by epitaxial growth on various single-crystalline substrates. However, in principle, this success in monolayer epitaxy seems extremely difficult to be replicated to bi- or few-layer growth, as the full coverage of the first layer was believed to terminate the reactivity of those adopting catalytic metal surfaces. Here, we report an exceptional layer-by-layer chemical vapour deposition (CVD) growth of large size bi-layer graphene single-crystals, enabled by self-transmitting catalytic activity from platinum (Pt) surfaces to the outermost graphene layers. In-situ growth and real-time surveillance experiments, under well-controlled environments, unambiguously verify that the growth does follow the layer-by-layer mode on open surfaces of MLG/Pt(111). First-principles calculations indicate that the transmittal of catalytic activity is allowed by an appreciable electronic hybridisation between graphene overlayers and Pt surfaces, enabling catalytic dissociation of hydrocarbons and subsequently direct graphitisation of their radicals on the outermost sp2 carbon surface. This self-transmitting catalytic activity is also proven to be robust for tube-furnace CVD in fabricating single-crystalline graphene bi-, tri- and tetra-layers, as well as h-BN few-layers. Our findings offer an exceptional strategy for potential controllable, layer-by-layer and wafer-scale growth of vertically stacked few-layered 2D single crystals.

Direct growth of large-area vertically stacked two-dimensional (2D) van der Waal (vdW) materials is a prerequisite for their high-end applications in integrated electronics, optoelectronics and photovoltaics. Currently, centimetre-to even metre-scale monolayers of single-crystal graphene (MLG) and hexagonal boron nitride (h-BN) have been achieved by epitaxial growth on various single-crystalline substrates. However, in principle, this success in monolayer epitaxy seems extremely difficult to be replicated to bi-or few-layer growth, as the full coverage of the first layer was believed to terminate the reactivity of those adopting catalytic metal surfaces. Here, we report an exceptional layer-by-layer chemical vapour deposition (CVD) growth of large size bi-layer graphene single-crystals, enabled by selftransmitting catalytic activity from platinum (Pt) surfaces to the outermost graphene layers.
In-situ growth and real-time surveillance experiments, under well-controlled environments, unambiguously verify that the growth does follow the layer-by-layer mode on open surfaces of MLG/Pt(111). First-principles calculations indicate that the transmittal of catalytic activity is allowed by an appreciable electronic hybridisation between graphene overlayers and Pt surfaces, enabling catalytic dissociation of hydrocarbons and subsequently direct graphitisation of their radicals on the outermost sp 2 carbon surface. This self-transmitting catalytic activity is also proven to be robust for tube-furnace CVD in fabricating singlecrystalline graphene bi-, tri-and tetra-layers, as well as h-BN few-layers. Our findings offer an exceptional strategy for potential controllable, layer-by-layer and wafer-scale growth of vertically stacked few-layered 2D single crystals.
Controlled growth of AB-stacked bilayer (BLG) or few-layer graphene (FLG) is of fundamental interest because of their predicted physical properties toward potential applications in electronics and photonics [1][2][3][4] . Currently, metal-catalysed chemical vapour deposition (CVD) is one of the most effective methods to fabricate BLG and FLG on various substrates, including Ni 5,6 , Cu 7-10 , Ru [11][12][13] , Ir 14,15 , Pt 16 , Cu-Ni 17,18 , Pt-Si 19 and Cu-Si 20 alloys. In principle, additional graphene layer could be formed either above 21 or inserted below 22,23 an already grown graphene layer, corresponding to two types of the second layer, namely ad-layer (above) and intercalating layer (insert below), respectively. Hydrocarbons in the flowing gas during CVD growth could intercalate into the MLG-metal-catalyst interface through wrinkles, domain edges and grain boundaries and/or defects of MLG and then be dissociated into radicals at the interface 24 . Surface segregation of metal dissolved carbon onto the MLG-metal-catalyst interface provides an alternative carbon source but is limited by the solubility of carbon within the metal catalyst 18 . Regardless of the carbon source, growth at the MLG-metal-catalyst interface suffers from appreciable metal surface adhesion and strong metal-graphene interface confinement, which often leads to discontinuous carbon feeding, point or line defects, and/or unexpected coalescence boundaries of the grown intercalating graphene layers 19 . Recently, direct nucleation of a bilayer and subsequent formation of a large-area BLG on a metal surface was reported 25 . However, it is extremely technically challenging to control the number of graphene layers precisely and to reach a seamless-coalescence growth condition 25 .
Layer-by-layer, namely Frank-van der Merwe (FM) is, in principle, an ideal and one of the most feasible strategies to prepare large-size BLG or FLG single-crystals, which was, during the preparation of this manuscript, realised using Cu foils in a bottom feeding and interface growing manner 26 . Although it is easier to monitor and control, the FM growth of graphene ad-layers on open surfaces (Fig. 1a) is, however, extremely challenging utilising the gas-phase feeding and opensurface growing manner because of a self-limiting growth effect that overwhelmingly favors monolayer formation 27 . Here, we demonstrate an FM growth of large-size single-crystalline graphene ad-layers (BLG and FLG), termed ``ad-layer FM growth'', directly on fully MLG covered Pt(111) by CVD methods. The choice of the Pt(111) surface enables vertically transmitting its catalytic activity onto the outermost graphene surface through graphene-Pt electronic hybridisation.
With the transmitted catalytic activity, the outermost carbon layer dissociates hydrocarbons on it, giving rise to formation of FLG following the FM growth mode, seamless coalescence of adlayers and healing of defective individual layers into continuous single-crystal over a large-scale.
Catalytic performance of metals to dissociate hydrocarbons was usually believed to abruptly drop after being covered with carbon layers 28,29 . This claim is, most likely, true for widely used Cu in growing graphene and h-BN monolayers 30,31 . However, other transition metals that are conventionally used for metal catalysts in molecular reactions could offer much stronger hybridisation with the MLG. It is yet to be explored whether such hybridisation enables transmitting the catalytic activity of metal d-electrons onto the carbon surface through MLG. If the answer is positive, the MLG thus inherits the metal catalytic activity, being capable of dissociating coming hydrocarbons. While Ru, Rh or other active transition metals provide stronger hybridisation with MLG than Cu, the reinforced MLG-metal interaction results in significant surface Moiré corrugation of the MLG on those surfaces, which suppresses the diffusion of radicals and thus hinders the growth of graphene adlayers 32,33 . In addition, the relatively high carbon solubility of those metals usually leads to carbon segregation at the MLG-metal interfaces, which may compete with the growth process on the outermost surface, leading to the growth behaviour being less controllable. The MLG-Pt(111) interface seems unique among those MLG-metal-catalyst interfaces because of nearly flat MLG on Pt(111) 34 , relatively low carbon solubility in Pt and an appreciably strong C-Pt hybridisation 32,35 .
We first theoretically consider the MLG-Pt(111) interface using a MLG-(9×9)/Pt(111)-(8×8)-R0° supercell (Extended Data Fig. 1a), which was found to be the most experimentally common configuration for this interface 36,37 . A projected and unfolded electronic band structure illustrates the MLG-Pt hybridisation details (Fig. 1b). While it clearly shows a blue cross representing the Dirac cone sitting at ~0.35 eV above the Fermi level (EF), substantially flatter Pt d bands (light blue lines) that appreciably hybridise with the carbon pz component were identified both near EF and around roughly -1 eV below EF. Visualised wavefunction norm (Fig. 1c)   Here, letters ``P" and ``D" represent ``Pt" and ``Dissociation", respectively and PD1(2) thus denotes the first (second) transition state for C2H4 dissociation on MLG/Pt(111), while, given ``C" for ``Cu", CD1(2) stands for that on MLG/Cu(111). Given ``A" for the first letter of term ``Aggregation", PA2 (3)   Given the overall barrier of 2.93 eV for the most likely pathways on MLG/Pt(111), dehydrogenation and nucleation processes are predicted to occur over 850°C, highly consistent with our experimentally observed initialisation temperature of 900 °C. However, the same processes on Cu(111) requires a temperature of near 1400 °C to initialise, which largely exceeds the melting point of Cu(111). Indeed, the formation of an adlayer is barely observed even on liquid copper surfaces. 38 Chemical potential analysis also supports the difficulty of growing BLG on Cu(111) surface, as shown in Fig. 1f. The chemical potential of the 2 nd layer Gr on Cu(111) is only -0.02 eV, very close to that of graphite, which is taken as a zero reference for the chemical potential. In comparison, the potential level of BLG lowers to -0.05 eV on Pt(111). This appreciably lowered potential level indicates reinforced interlayer interaction of BLG with the Pt surface. Our simulations show that the carbon-platinum hybridisation, the reduced dissociation barrier of hydrocarbons and the lowered chemical potential are not limited to the MLG-(9×9)/Pt(111)-(8×8)-R0° interface. We have observed that these effects are maintained at another MLG-Pt interface, namely MLG-(3×3)/Pt(111)-(√7×√7)-R19° (Extended Data Fig. 2), which could be found under some experimental conditions as well. 34 Additionally, our DFT calculation shows that such strong carbon-platinum hybridisation still exists in BLG/Pt(111) and 3L-Graphene/Pt(111) using the FLG-(3×3)/Pt(111)-(√7×√7)-R19° models which are computationally less demanding (Extended Data Fig. 3). Thus, all these results support the inheritance of the catalytic activity arising from Pt onto the outermost-layer of FLG/Pt(111), suggesting a likely route to the ad-layer FM growth of FLG, as we elucidate later.
Next, the theoretically predicted ad-layer FM growth mode of BLG (Fig. 2a) was verified by our near atmosphere pressure (NAP) experiments as follows. A MLG sample was first prepared using a C2H4 carbon source on a Pt(111) surface in a modified environmental scanning electron microscope (ESEM) 39 (Fig. 2a and 2b). By tuning the C2H4/H2 ratio under ESEM surveillance, we explicitly observed that MLG domains, which are hexagonal in shape and are oriented parallel to each other, nucleate at moment t0 (Fig. 2b), expand and eventually stitch to each other at t0+8s ( It is of crucial importance in distinguishing this work from other growth strategies that whether the growth fronts are on top of the MLG/Pt(111). It was experimentally verified in two ways. An insitu etching experiment was conducted by slightly lifting the chemical potential level of BLG, i.e.
increasing the H2 partial pressure, in which the hexagonal ad-layer (second layer) flake shown in Fig. 2f begins to shrink at time t0' and develops to a smaller and less regular flake at time t0'+43s ( Fig. 2g), while the first layer maintains intact. This observation proves that nucleation of the adlayer graphene occurs on top of MLG/Pt(111) (the first layer) and is thus exposed to the etching atmosphere ( Fig. 2f-g) 40 . This in-situ observation thus compellingly supports the ad-layer FM growth of BLG on Pt(111). Additionally, a cross-sectional view of such growth and etching process is provided using in-situ transmission electron microscopy (TEM) (see Methods for details).  The nucleation and subsequent growth of the second layer are inevitably accompanied by nucleation of third-or thicker-layer islands, because of the comparable (within 0.05 eV) chemical potential levels of those ad-layer islands. Figure 3a-3d shows a formation process of MLG where thicker-layer islands were nucleated, which are, however, undesired. Nevertheless, they are removable by precise keeping the relative chemical potential (μ) of graphene layers and waiting for the sample to approach its dynamic equilibrium, during which defective regions are spontaneously replaced by perfectly oriented lattices driven by the thermal stability of the latter, as shown in Fig. 3e-3h. We further term this process ``vertical healing (VH)".
In the meantime, another healing type, i.e. ``lateral healing (LH)'', occurs within layers, which could both remove point defects and eliminate line defects formed in domain coalescence, as examined by etching the samples under H2 atmosphere. Figure 3i shows a fast-grown MLG sample where the MLG nucleates from hundreds of domains (Fig. 3b) and expands into monolayer before other layers start to nucleate. Massive and irregular holes (Fig. 3j) are observable under direct etching of the sample, and it eventually fragments ( Fig. 3k and 3l), suggesting its quality is inferior.
However, the MLG shown in Fig. 3h was treated with both VH and LH processes, which was replotted in Fig. 3m. There are only three pin-holes found in this sample after 10 s direct etching.
They subsequently merge into two larger holes and eventually into a single hole after 2640 s etching, suggesting large quality improvement. Panel e shows an image of an as-grown MLG with multi-layer islands, shrinking of those FLG islands (f and g) and their final disappearance(h). During this period MLG is also laterally healed. Panels i to l show an etching process of a fast-grown MLG , without both VH and LH. Panel i depicts the MLG sample while panels j-l show the subsequent etching process. Panel h was replotted in panel m, which represents a thermodynamically stable structure after both the VH and LH processes, while the subsequent etching process, with the same etching condition, is shown in panel n-p.
In terms of BLG samples, Extended Data Fig. 5, remarkably, shows in-situ observations of etching before and after healing. The line etched between two hexagonal pin-holes is indicative of line defect presence in the sample before LH (Extended Data Fig. 5a and 5b). After LH, the absence of the etched line defects (within an inspected area of 500 μm 2 ) indicates the sample is, most likely, free of line defects (Extended Data Fig. 5c-5e). Additionally, aligned shapes of those hexagonal pinholes suggest that the BLG film is a single-crystal. 41 Supplementary Movie 3 illustrates all those processes, i.e. nucleation, expansion, etching and healing, of FLG at NAP.
To further validate the above discussion and generalise the layer-by-layer mechanism from NAP to UHV (Ultra-High Vacuum), we performed additional in-situ SEM observation, reproducing the BLG growth, healing and etching processes in a one-round continuous experiment utilising the temperature variation strategy in UHV. Extended Data Fig. 6 illustrates the growth and etching processes of the first and second layers using totally 12 snapshots from a complete movie (Supplementary Movie 4) recording the experimental procedure, in which the third healing type, i.e.
``regrowth healing (RH)'' is clearly depicted for MLG. The RH is an accelerated process of VH and/or LH that the defective region is locally etched, promoting subsequent regrowth at near equilibrium. The local etching could be realised by either increasing the H2 partial pressure at NAP or heating the substrate for reducing the concertation of CnHn radicals on the surface in UHV. The latter strategy utilises the adsorption-desorption balance of C2H4 molecules and hydrocarbon radicals, which was employed in the process shown in Supplementary Movie 4.
We magnified those parameters obtained from our in-situ observations to fit the size of our tube furnace systems for further verifying the generality of our strategy; this allows the ad-layer FM growth of BLG (FLG) to be accessed by the conventional CVD method (see Methods for more details). Figure 4a and Extended Data Fig. 7 show SEM and optical images of as-grown BLG domains, respectively, which are in a hexagonal shape with aligned edges. These domains coalesce and eventually form a uniformly continuous BLG film after a prolonged growth time (Fig. 4b).  Fig. 9) further prove the desired AB-stacked 42 , single-crystalline and defect-free BLG. The high quality and uniformity of BLG were also examined using optical measurements. We used a previously reported electrochemical bubbling method to transfer our tube-furnace grown BLG onto a SiO2/Si substrate. 43 Figure 4f shows the characteristic 2D peak of a representative Raman spectrum of the transferred BLG sample. This peak is asymmetric and is fitted using four Lorentzian peaks at different frequencies. A full-widthat-half-maximum (FWHM) mapping of the 2D peak is displayed in Fig. 4g, offering a uniform FWHM of about 50 cm -1 across tens of microns, again, verifying the AB-stacking of our BLG sample.
In addition, an optical transmittance of ~ 95.2% at 500 nm was achieved in a BLG film being transferred onto a quartz substrate; conforming its bilayer nature 44 (Fig. 4h). All those experimental results represented above demonstrate that the catalytic activities of Pt could indeed penetrate through MLG and enable the FM growth of BLG as our theory predicted.
Meanwhile, our calculations also identified the catalytic activity on the outermost carbon layer of BLG/Pt(111) and 3L-Graphene/Pt(111), which was experimentally realised by increasing the C2H4 partial pressure. As shown in Fig. 5a-5d, 3L-and 4L-graphene were successfully prepared. Raman characterisations verified the numbers of layers and the AB stacking order. Bilayer h-BN thin-films can also be grown in the ad-layer FM mode on Pt(111), suggesting the transmitting catalytic activity on monolayer h-BN inheriting from Pt(111) (Fig. 5e). Figure 5f highlights the FWHM, i.e. 11.2 cm -1 , of a specific Raman peak of the h-BN bilayer, which is even smaller than those usually measured in few-layer CVD h-BN (14-20 cm -1 ) 45,46 , suggesting, most likely, higher quality of the ad-layer FM grown bilayer h-BN than other CVD prepared samples.
In summary, we theoretically predicted the ad-layer FM-mode growth of AB-stacked singlecrystal BLG on Pt(111), as well as FLG and bilayer h-BN, which were experimentally verified using in-situ CVD under NAP and UHV, respectively, and tube-furnace CVD.

Methods
Density functional theory calculation. Our first-principles density functional theory (DFT) calculations were carried out using the projector-augmented wave (PAW) potential approach 48  In electronic structure calculations, denser k-meshes of 3×3×1 and 9×9×1 were adopted. The shape and volume of the supercells were kept fixed during relaxation, and all atoms except the two bottom layers of Pt were allowed to fully relax until the residual force on each atom is less than 0.01 eV/Å. Chemical potentials were derived by comparing the formation enthalpy of each species while those of graphite, hydrogen gas and platinum surface were set to reference zero. We used the KPROJ program 54 based on a k-projection method to unfold those highly folded supercell bands into unit cell ones. A k-point route from Γ(0,0,0) to K(3,3,0) was used for the electronic band unfolding.
Reaction barriers were revealed using the nudged elastic band theory calculations 55  Tube-furnace CVD growth of graphene on Pt(111). A single-crystal Pt(111) substrate was specifically pretreated to remove its dissolved carbon atoms before the FM growth of graphene adlayers. Then the Pt(111) substrate was first annealed at 1000 °C for 40 min under reducing atmosphere. Subsequent growth of BLG was conducted in two steps: CH4 was first fed into the system to grow the first graphene layer. With the full coverage of the first layer, CH4 was cut off and C2H4 was introduced to activate the growth of the second graphene layer. The whole growth process was conducted at atmospheric pressure.
In-situ TEM characterisation. Pt nanoparticles (Adamas-beta) were dispersed in pure ethanol. The mixture was subsequently drop-casted on a 2mm × 2mm microelectromechanical system (MEMS) chip with heating membrane provided by Protochips Inc (Morrisville, NC, USA) followed by drying in air. The as-prepared chip is paired with another 4.5 mm × 6 mm chip with e-beam transparent SiNx window to compose the in situ environmental reaction cell. An electrical current is applied through the gold contacts to the SiC heating membrane of the bottom chip, which contains six holes of 8 μm diameter layered with a thin SiNx film to facilitate sample observation in TEM 56 . Due to the small size of the heating area, a homogeneous temperature distribution is obtained within the analysed areas. Thereby, it is feasible of heating the sample up to 1000 °C with a temperature rate up to 10 °C/s. The chips were then loaded with gaskets onto an in situ TEM holder provided by Protochips to ensure hermetic sealing from the TEM vacuum. A 5μm spacer bridges the top and bottom chips for the cell. A flowing gas was applied to the cell from an external gas feeding system.
An integrated residual gas analyser (RGA) was used to verify the gas mixture applied to the cell 57 .
An aberration-corrected JEM GrandARM 300F transmission electron microscope (operated at 300 kV) was used to carry out in situ graphene growth experiments. The Pt nanoparticles were treated at 700 °C in 10%H2/90%Ar gas (1 bar, 0.1 sccm) for one hour. In situ observations of graphene growth under CVD conditions were made at 950°C with a gas mixture of 0.5%C2H4/9.95%H2/89.55%Ar gas (1 bar, 0.1 sccm). Observations of graphene etching under 0.5%C2H4/9.95%H2/89.55%Ar gas (1 bar, 0.1 sccm) were carried out at 900°C. Sequential bright field TEM images were recorded in situ by Gatan OneView IS Camera at acquisition rates of 4-25 frames per second at 2K × 2K frame resolution.
Ex-situ characterisations. SEM and STEM: SEM images were obtained using Thermal Fisher Quattro S system. STEM and TEM experiments were performed in FEI Titan Themis G2 300 operated at 80 kV.
STM/STS: The BLG/Pt(111) sample was heated at ~300 °C for 3 hrs after loading into the UHV chamber (base pressure 2 × 10 −10 mbar) for degassing, and then the sample was transferred into the STM head (Createc) to perform the measurements. STM imaging was performed using mechanically cut PtIr tips at the liquid helium temperature (4.2 K). The dI/dV tunnelling spectra were acquired using lock-in detection by applying an AC modulation of 20 mV (r.m.s.) at 973 Hz to the bias voltage.
Raman: Raman spectra and mappings were collected with a homemade optical system using a 532 nm laser excitation. The transmittance was measured using a Varian Cary 5000 UV-Vis-NIR spectrophotometer.
LEED: low-energy electron diffraction was conducted in a SPECS low-energy electron microscopy system, which is connected to the Vacuum Interconnected Nanotech Workstation (NANO-X) of Suzhou Institute of Nano-Tech and Nano-Bionics, the Chinese Academy of Sciences, which is installed with a preparation chamber and the main chamber. LEED was performed to investigate surface structure after graphene growth. The incident electron beam energies are always kept at 50 eV during LEED measurements. The Dirac point (DP) and C-Pt hybridised states (HS) were highlighted by the triangles and arrows, respectively. c, Projected band structures of the supercell with orbital decomposition of Pt dz2 (blue) and C pz (red). Those C-Pt hybridised bands show a mixture of red and blue colours. d, Visualised wavefunction norm square of a hybridised state residing at -0.05 eV and the Gamma point. The isosurface value of the contours is 2 × 10 -4 e/Bohr 3 . e, Three potential pathways and their corresponding barrier heights for the C2H4 dissociation reaction and subsequent radical nucleation on the MLG/Pt(111) surface. Each step is denoted in the same scheme as Extended Data Fig. 1 Extended Data Fig. 6 | One-round continuous in-situ SEM image sequence showing a comprehensive picture of the dynamics of the FM mode growth, healing and etching processes of BLG in UHV. The image sequence was cut from Supplementary Movie 4 recorded in a UHV-SEM. For growth, the temperature was slightly decreased to allow nucleation of the 1 st and 2 nd layers, while slightly increased for etching.