Atomic mechanism of strong interactions at the graphene/sapphire interface

For atomically thin two-dimensional materials, interfacial effects may dominate the entire response of devices, because most of the atoms are in the interface/surface. Graphene/sapphire has great application in electronic devices and semiconductor thin-film growth, but the nature of this interface is largely unknown. Here we find that the sapphire surface has a strong interaction with some of the carbon atoms in graphene to form a C-O-Al configuration, indicating that the interface interaction is no longer a simple van der Waals interaction. In addition, the structural relaxation of sapphire near the interface is significantly suppressed and very different from that of a bare sapphire surface. Such an interfacial C-O-Al bond is formed during graphene growth at high temperature. Our study provides valuable insights into understanding the electronic structures of graphene on sapphire and remote control of epitaxy growth of thin films by using a graphene–sapphire substrate.

T he interface is the device 1 . At the interface of crystal materials, the broken translation symmetry usually strongly alters the optical, electric, and magnetic properties, resulting in many interesting phenomena such as interfaceinduced superconductivity 2,3 , two-dimensional (2D) electron gas 4 , and magnetoelectric coupling 5,6 . In particular, the interface effects are much more pronounced or dominant in atomically thin 2D materials (e.g., graphene (Gr)), because most of the atoms are part of the interface when supported on a substrate. For instance, in a field-effect transistor system, strong hybridization (orbital overlap) between 2D materials and contact metals can eliminate the van der Waals (vdW) gap, which results in a reduction of the tunnel barrier for carriers 7 . Such an effect is also observed in 2D/2D heterostructures, e.g., the topological current is detected in the Gr/h-BN superlattice 8 and the reconstruction at the Gr/h-BN interface provides a periodic scattering potential for carriers, leading to very unique electrical properties 9 . Moreover, coupling of the Gr/Gr interface via the "magic" angle results in correlated insulating states at half-filling 10 and can be tuned to zero-resistance states upon electrostatic doping 11 .
Recently, Gr/sapphire (α-Al 2 O 3 ) has shown promising applications in electronic devices due to the relatively high dielectric properties of α-Al 2 O 3 as a gate dielectric 12,13 . In addition, Gr/α-Al 2 O 3 is also applied as a platform for remote growth of thirdgeneration semiconductors where Gr acts as a buffer layer to overcome the limitation of lattice mismatch [14][15][16] . The penetration of the electrostatic potential from substrates is governed by the interface nature, which eventually determines the epitaxial crystal quality 17,18 . Therefore, it is vital to reveal the atomic structure and binding nature of the Gr/α-Al 2 O 3 interface 19,20 . Although considerable advances have been achieved in characterization techniques, little is known about the structure and properties of the Gr/α-Al 2 O 3 system because of the lack of effective methods to probe the atomically thin interface of Gr on insulating substrates. For instance, the common scanning tunneling microscopy and low-energy electron diffraction (LEED) methods are usually restricted to conductive substrates, but α-Al 2 O 3 is nonconductive. Therefore, most of the previous knowledge is obtained from computational approaches such as density functional theory (DFT) calculations 21 . Aberration-corrected transmission electron microscopy (Cs-TEM), which enables atomically resolved identification of the structure and chemical composition of materials regardless of their electric conductivity, provides alternative opportunities to study the atomic structure and properties of the interface and surface for insulators 22,23 .
Here, by Cs-TEM, we successfully reveal the atomic arrangement of the Gr/α-Al 2 O 3 interface and accurately measure the gap between Gr and α-Al 2 O 3, which governs the interaction between the substrate and functional layers. We observe that the atomic configuration at the interface is C-O-Al, which is further confirmed by DFT calculations. Such an interfacial bond induces a large adhesion energy of~1.47 J/m 2 , indicating that the interaction of the Gr/α-Al 2 O 3 interface is no longer a simple vdW interaction. In addition, we also precisely obtain the structural relaxation of the surface layers of α-Al 2 O 3 and find that the structure of Al 2 O 3 near the interface is significantly different than either the bulk or bare α-Al 2 O 3 surface. The contraction rate of the first Al layer at the interface is −(35.3 ± 8.2)% with respect to the bulk value compared with −79.4% for a bare α-Al 2 O 3 surface. The pristine surface of α-Al 2 O 3 is further identified to be Al-terminated and the interfacial C-O-Al bond is likely formed during high-temperature growth of Gr. All these findings provide valuable insights into the binding nature between 2D materials on a substrate and would be beneficial to the strategy of remote epitaxial growth by using a Gr buffer layer.

Results
Characterization of the Gr/α-Al 2 O 3 interface. To ensure the cleanness of the interface, we directly grew a Gr film on α-Al 2 O 3 substrates via a chemical vapor deposition (CVD) method (see details in the Methods section). For better protection of the Gr/α-Al 2 O 3 interface, a multilayer Gr film was obtained by prolonging the growth time. Raman mappings of I G and I 2D of the obtained Gr/α-Al 2 O 3 in Supplementary Fig. 1a, b show a high uniform color contrast at the microscale, indicating the uniformity of the grown Gr film. The relatively low value of I 2D /I G (≤0.8) confirms the multilayer feature of Gr ( Supplementary Fig. 1c). Moreover, the G and 2D peaks of CVD-derived Gr/α-Al 2 O 3 are all upshifted with respect to those of transferred Gr on SiO 2 /Si substrates ( Supplementary Fig. 1d), indicating that Gr experiences a compressive strain imposed by α-Al 2 O 3 .
We used the high-angle annular dark-field scanning TEM (HAADF-STEM) imaging mode of Cs-TEM to reveal the atomic structure of the Gr/α-Al 2 O 3 interface. The atomically resolved image of the Gr/α-Al 2 O 3 interface with a viewing direction of [100] is shown in Fig. 1a and the Gr layer can be clearly observed in an image with lower magnification in Supplementary Fig. 2. The corresponding atomic structures of α-Al 2 O 3 and Gr are depicted in Fig. 1b from the [100] direction superimposed on the STEM image and are in good agreement with the simulated result. We observe additional atoms between the Gr layer and the topmost surface Al atoms. These atoms are further identified to be O, which will be explained later in detail. The distance between the topmost surface Al and the additional O is~1.76 Å, whereas the spacing between the O and the Gr is also~1.76 Å, indicating a strong interaction between Gr and the α- The presence of the C-O bond at the interface is further confirmed by the C 1s X-ray photoelectron spectroscopy spectrum ( Supplementary Fig. 3) of Gr/α-Al 2 O 3, which shows an intense sp 2 carbon peak (~284.8 eV), a weak C-H peak (~285.7 eV), and a weak C-O peak (~287.3 eV). Such a C-O peak suggests the existence of a C-O-Al configuration at the interface 24 . additional atoms at the interface is also shown in Supplementary  Fig. 7 for comparison. Figure 2a,b shows the top and side views, respectively, of the geometry of the Gr/α-Al 2 O 3 interface with the additional O atoms obtained from DFT calculations. The additional O atoms directly bond to some of the C atoms of Gr with a bond length of 1.400 Å, as shown in Fig. 2b, whereas the other C atoms are further away from the α-Al 2 O 3 surface. As a result, the average spacing between the additional O atoms and the Gr is 1.762 Å, which is in good agreement with the experimental results.
Effects on the surface structure of α-Al 2 O 3 . Figure 3 shows the quantitative analysis of the surface structure of α-Al 2 O 3 along the [100] orientation based on the image shown in Fig. 1a. We measured the distance between Al atoms from different layers (Al-Al length) and the angle between the Al-Al direction and the normal direction of the interface (Al-Al angle). There are negligible deviations of the Al-Al distance and angle far below the surface compared with bulk α-Al 2 O 3 , whereas a significant difference is observed for the top surface layers, as shown in Fig. 3a,c. In our experiment, the Al-Al distance at the surface is~2.3 Å, which is in sharp contrast to the bulk value of~2.6 Å. Furthermore, a similar trend is observed for the Al-Al angles, i.e., the angle at the surface is 36°, whereas it is~32.5°in the bulk. The DFT calculations also show a large change in surface relaxation for α-Al 2 O 3 , i.e., 2.22 Å for the Al-Al distance at the surface and 2.58 Å inside the bulk and 38.64°for the Al-Al angle at the surface and 32.39°inside the bulk, which is in excellent agreement with the experimental results.
Indeed, the structure relaxation at the surface is an important physical phenomenon in many materials [25][26][27] , including α-Al 2 O 3 . We now compare the structure relaxation of α-Al 2 O 3 near the interface with the bare surface case reported in the literatures in

Discussion
Thus far, we have obtained the atomic structure of the Gr/α-Al 2 O 3 interface and identified the C-O-Al bonding at the interface. It is a prerequisite to determine the pristine structure of the α-Al 2 O 3 surface before growth of Gr to understand the formation of the C-O-Al interfacial structure. In fact, much effort has been made to reveal the surface structure of α-Al 2 O 3 , because it is widely used as a substrate for the growth of thin metals, high-temperature superconductors, 2D materials, and semiconductor films [28][29][30] . Nevertheless, there are controversies regarding the termination layer of α-Al 2 O 3 . Both empirical and theoretical simulations identified only one stable Al-termination stoichiometry for the α-Al 2 O 3 surface, whereas a few studies reported a stable O-termination structure 21 . A recent study of LEED measurements reported that the ratio of Al-to O-terminated domains is 2:1 31 .
We attempt to directly reveal the surface structure of pristine α-Al 2 O 3 using the same Cs-TEM method, however, during the TEM specimen thinning process, the surface amorphization became severe, preventing us from identifying the termination layer of the pristine α-Al 2 O 3 surface. We then transferred Gr onto α-Al 2 O 3 to avoid any high-temperature process before the sample thinning process to protect the α-Al 2 O 3 surface. We find that no bridging O atom is observed at the interface of the transferred Gr/α-Al 2 O 3 , and that the surface of α-Al 2 O 3 is Al-terminated in the ambient environment, as shown in Supplementary Fig. 8a. We also perform DFT calculations, which further confirm that the Al-termination layer is the most stable for the α-Al 2 O 3 surface in Supplementary Fig. 9.
Therefore, it seems that during high-temperature growth of Gr, the O atoms in the α-Al 2 O 3 substrate escape to the interface and are captured by the C atoms to form the C-O-Al configuration. To further verify the role of high temperature, we subsequently annealed the transferred Gr on α-Al 2 O 3 at 1050°C. We find that such an interfacial C-O-Al configuration can also be observed in this case ( Supplementary Fig. 8b), further confirming that the C-O bond is formed at high temperature.
The formation of C-O-Al bonds can significantly change the properties of the interface. The adhesion force/energy of the Gr/α-Al 2 O 3 interface is evaluated using a mechanical nanoscratch method as shown in Supplementary Fig. 10 24 . The interfacial interaction energy of directly grown Gr on α-Al 2 O 3 is~1.47 J m −2 , which is in excellent agreement with our DFT calculations (1.40 J m −2 ). In comparison, the interaction energy of the transferred Gr/α-Al 2 O 3 interface is only~0.66 J m −2 , which is close to the DFT calculation value of 0.46 J m −2 . After high-temperature annealing, the interaction energy of the transferred Gr increases to~1.25 J m −2 , further confirming the formation of a strong interface bond between Gr and α-Al 2 O 3 at high temperature.
Such a strong chemical interaction between Gr and α-Al 2 O 3 completely contrasts with the common assumption of vdW interaction 32,33 . This result provides valuable insight into the remote epitaxy of single-crystalline materials on Gr-coated substrates. The strong interaction between Gr and the substrate (herein, C-O-Al) enables relatively strong atomic interactions from the underlying substrates to penetrate Gr. However, the force between Gr and the epilayer is reduced by nearly two orders of magnitude compared with the covalent bonds formed in the conventional epitaxy approach due to the vdW epitaxy feature 17 . In addition, the strong interaction between Gr/α-Al 2 O 3 would create a modulated potential that breaks the symmetry, changes the on-site energy of atoms, and opens up a small band gap around the K-point 34,35 , which provides promising opportunities for next-generation electronics.
In summary, we obtained the interface structure of Gr/α-Al 2 O 3 by Cs-TEM. We find that the topmost layer is a reconstructed O layer, which directly bonds to Gr to form the C-O-Al interface configuration. In addition, with the presence of Gr and interfacial bonding, the structure relaxation behavior of α-Al 2 O 3 near the interface is suppressed compared with that of the bare surface. All these results are in good agreement with the DFT calculations. Our study suggests that the interface of Gr/α-Al 2 O 3 is not as simple as assumed and the interaction between Gr and substrate is a nonpure vdW interaction. The formation of strong bonding between Gr and α-Al 2 O 3 is expected to significantly change the optical, electrical, and mechanical properties of Gr. In particular, it provides valuable insights into the remote control of the epitaxy growth of thin films by using Gr as a buffer layer.

Methods
Gr synthesis and transfer. Typically, the commercial α-Al 2 O 3 substrate (purchased from Unionlight Technology, Co., Ltd) was loaded into a three-zone hightemperature furnace after the cleaning process. The furnace was heated to 1050°C and was stabilized for~10 min under 100 s.c.c.m. Ar and 100 s.c.c.m. H 2 , and 20 s. c.c.m. CH 4 was introduced into the reaction chamber as a carbon source for the growth of Gr on the α-Al 2 O 3 substrate for~3-5 h.
Transfer of Gr on α-Al 2 O 3 . The CVD grown Gr on copper is also transferred onto α-Al 2 O 3 for comparison, in which process poly (methyl methacrylate) was used as the polymer support 36 .
Annealing of the transferred sample. The transferred sample was loaded into a high-temperature furnace and heated to 1050°C, and then annealed for~10 min under the protection of 500 s.c.c.m. Ar, 100 s.c.c.m. H 2 .
TEM sample preparation. The Gr/α-Al 2 O 3 TEM specimen was prepared by mechanical polishing followed by argon ion milling (Gatan Model 691 system) with a gun voltage of 1.5-4.5 kV (beam angle of~1.5-6°). At the final stage of ion milling, the voltage was set at 1.5 KV for~3 min to remove the surface amorphous layer and minimize the damage.
Adhesion force/energy measurement. The adhesion force/energy of the Gr film on α-Al 2 O 3 was determined using a mechanical nanoscratch method with the aid of an AFM system (Cypher Asylum Research). The radius of the diamond tip used for the measurement was~40 nm and a normal load of 11.9 μN was applied.
Data acquisition and analysis. The atomic scale HAADF-STEM images were acquired using a double aberration-corrected FEI (Titan Cubed Themis G2, spatial resolution up to 60 pm) operated at 300 kV with the convergence semiangle 21.5 mrad and collection semiangle snap 80-379 mrad. We also deliberately minimized the electron dose to avoid specimen damage using a small aperture, small beam current, and short scanning time. The atomistic models were generated by VESTA and XCrysDen software. The plots were created by Origin 2018C. Atom positions were determined by simultaneously fitting 2D Gaussian peaks to an a priori perovskite unit cell using a home-developed code running in MATLAB R2012b. The data mapping was also carried out by MATLAB R2012b.  [21] Theory of ref [21] Theory of ref [21] Experiment of ref [21] Experiment of ref [21]  HAADF-STEM image simulation. The multislice STEM simulation was performed using the software pack developed by Kirkland 37 . We used the single layer Gr/α-Al 2 O 3 interface model shown in Fig. 2. In the simulation, the wave function size, sampling size, and image size were set to 1024 × 1024, 512 × 512, and 512 × 512, respectively. All microscope settings were the same as those in the experiments. The simulated image was then convolved with an 80 pm full width at half maximum Gaussian function considering the incoherent source broadening.

Data availability
All data supporting the findings of this study are available within the paper and its Supplementary Information.