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Epitaxial Growth of Two-dimensional Insulator Monolayer Honeycomb BeO

The emergence of two-dimensional (2D) materials launched a fascinating frontier of flatland electronics. Most crystalline atomic layer materials are based on layered van der Waals materials with weak interlayer bonding, which naturally leads to thermodynamically stable monolayers. We report the synthesis of a 2D insulator comprised of a single atomic sheet of honeycomb structure BeO (h-BeO), although its bulk counterpart has a wurtzite structure. The h-BeO is grown by molecular beam epitaxy (MBE) on Ag(111) thin films that are conveniently grown on Si(111) wafers. Using scanning tunneling microscopy and spectroscopy (STM/S), the honeycomb BeO lattice constant is determined to be 2.65 angstrom with an insulating band gap of 6 eV. Our low energy electron diffraction (LEED) measurements indicate that the h-BeO forms a continuous layer with good crystallinity at the millimeter scale. Moir\'e pattern analysis shows the BeO honeycomb structure maintains long range phase coherence in atomic registry even across Ag steps. We find that the interaction between the h-BeO layer and the Ag(111) substrate is weak by using STS and complimentary density functional theory calculations. We not only demonstrate the feasibility of growing h-BeO monolayers by MBE, but also illustrate that the large-scale growth, weak substrate interactions, and long-range crystallinity make h-BeO an attractive candidate for future technological applications. More significantly, the ability to create a stable single crystalline atomic sheet without a bulk layered counterpart is an intriguing approach to tailoring novel 2D electronic materials.

atomic sheet without a bulk layered counterpart is an intriguing approach to tailoring novel 2D electronic materials.

Introduction
The discovery of graphene and its unprecedented properties inspired an extraordinary increase in research progress, launching an era of two-dimensional (2D) electronic materials. [1][2][3][4][5][6][7] One property these emerging materials share is strong in-plane bonding with weak interlayer interactions, leading to the existence of stable crystalline atomic layers. This enables the design of ultrathin 2D devices with different crystalline atomic layers as the building blocks. While many conceptual devices are fabricated by mechanical exfoliation, in order to create a scalable technology platform, it is critical to develop an epitaxial growth of single crystalline 2D materials. Early exploration of 2D materials focused on van der Waals (vdW) crystals, which have a naturally occurring bulk layered structure, and have already demonstrated significant potential for 2D technological applications. Synthesis of epitaxial wafer scale monolayers has been achieved for graphene 8 and hBN, 9 proving that large scale growth is feasible for vdW materials. While the success of vdW crystals is promising, the family of layered bulk solids is limited, constraining the variety of structural and electronic properties available for device design.
Driven by the desire to expand the library of 2D materials, there has been increased exploration into the synthesis of stable atomically thin phases of electronic materials without a bulk layered structure. For example, 2D allotropes of group IV elements silicene, germanene, and stanene have been successfully grown and are predicted to have attractive electronic properties. [10][11][12][13][14] However, unlike graphene, these elements do not favor sp2 hybridization and adopt a mixed sp2-sp3 hybridization, resulting in a buckled honeycomb structure. This lack of a stable planar phase creates challenges such as multi-phase growth, buckled superstructures, and strong substrate interactions. [10][11][12][13][14] By contrast, polar wurtzite structure materials were surprisingly predicted to circumvent the bulk thermodynamic constraint at the few layer limit, resulting in a stable planar sp2 hybridized graphitic phase. 15 In the thin regime of a few atomic layers, polar ionic bonds may turn into the in-plane direction, forming a honeycomb structure to diminish unstable surface polarization (shown schematically in Figure 1a). 15,16 This theory indicates that initial growth forms a graphitic film, and at a critical layer thickness, the crystal becomes unstable and converts to a wurtzite structure. 15 These predictions have stimulated intensive experimental investigations of the graphitic phases of bulk wurtzite structure materials, 17,18 with ZnO grown on (Ag, Au) substrates drawing the most attention. [19][20][21] Motivated by the success of these experimental studies, the question naturally arises as to whether other wurtzite structure materials can be epitaxially grown as a 2D graphitic layer.
Beryllium oxide (BeO) is a polar wurtzite structure material with remarkable physical and mechanical properties, such as a high thermal conductivity, hardness, and a large insulating bandgap of 10.7 eV. These attractive properties have inspired significant theoretical research interest concerning the existence of other possible structural phases of BeO. In particular, as a member of the isoelectronic series of first row elements like graphene and hBN, studies predicted BeO might also exist in a sp 2 hybridized atomic layer with a honeycomb structure (h-BeO). 22,23 Later, monolayer graphitic h-BeO was predicted to be energetically stable in free space, and that it could be synthesized from BeO molecules. 24 Further, not only was h-BeO predicted to have the most stable graphitic phase of wurtzite materials, 15 but theoretical surveys of possible monolayer honeycomb structures of II-VI semiconductors predicted h-BeO has the lowest formation energy corresponding to the bulk phase, 25 and was deemed the most experimentally achievable. 16 Though h-BeO is predicted to exist at the ultra-thin limit, synthesis of this intriguing material has remained elusive until recently. The only experimental evidence of planar h-BeO to date was achieved by a wet chemistry approach in a graphene liquid cell, but the growth was ~20 layers thick and polycrystalline on the order of tens of nanometers. 26 Nevertheless, these promising theoretical and experimental results strongly suggest that the epitaxial growth of crystalline, monolayer h-BeO is experimentally achievable.
In this work, we report the realization of the epitaxial growth of a single atomic sheet of h-BeO grown on Ag(111) substrates using molecular beam epitaxy (MBE). Here, we employ scanning tunneling microscopy (STM) to directly characterize the atomic and electronic structure of the BeO, and further show that the monolayers maintain high crystallinity across the Ag terraces.  reconstruction, a 150 nm Ag film is epitaxially grown, and honeycomb BeO is grown epitaxially on top. To the right is a top and side view of the heterostructure.

Results and Discussion
Honeycomb structure BeO was epitaxially grown on Ag(111) substrates using the growth process shown schematically in Figure 1b (111) surface ( Figure 3c). We note that the contrast of the moiré pattern is curiously reversed from the pattern shown in Figure 2a, which will be clarified later. The hexagonal moiré pattern has a periodicity of 3.2 ± 0.1 nm and is rotationally aligned with the Ag substrate step along the ⟨110⟩ direction, which indicates that the Ag(111) and h-BeO lattices are also rotationally aligned. 27 Briefly, moiré pattern periodicity depends on the rotational misalignment and/or difference in lattice periodicity of the overlayer with respect to the substrate. 27 With this knowledge, we can exploit the moiré pattern to determine the h-BeO lattice constant with greater accuracy: with a moiré periodicity of 3.2 nm, and the known lattice constant of 2.89 Å for Ag (111), one can deduce a lattice constant of 2.65 ± 0.01 Å for the h-BeO. This calculated lattice constant is consistent with the atomic resolution measurements, displaying a reduction in BeO bond length compared to bulk wurtzite structure, as theoretically predicted. 16,22,24,[28][29][30][31][32] The decrease in lattice constant was previously theorized to stem from the graphitic Be-O bond having an increased covalent character, and as a result the atoms move closer to increase the orbital overlap of nearest neighbors. 16,23,28  The Be/Ag atomic fraction ratio is determined to be 1:4.23.
In Figure 3d-j we utilize LEED to further examine the structure of the h-BeO film. Figure 3d shows the sharp hexagonal LEED pattern of the bare Ag(111) substrate, and after the growth of a BeO monolayer, additional spots appear in the pattern. In order to establish that the h-BeO forms a continuous layer, LEED patterns were obtained at different locations along the sample surface, indicated by the red dots in Figure 3e. Figures 3h-j show the LEED patterns of the full coverage h-BeO growth, providing additional evidence that the monolayer has a hexagonal structure rotationally aligned with the Ag(111) surface. A zoom in of the LEED pattern shows the formation of the moiré pattern (see Figure 3f). Each LEED measurement was obtained at a location more than one millimeter apart, reinforcing our assertion that the formation of the h-BeO is uniform across the wafer, similar to the wafer scale growth of graphene 8 and hBN. 9 As additional verification that the surface is BeO, we carried out ex-situ XPS (x-ray photoelectron spectroscopy) measurements of the Ag and Be core levels (Figure 4l, m), from which we determine a Be/Ag atomic ratio consistent with a single monolayer of honeycomb BeO on Ag(111).
Interestingly, not only do we find that the single atomic sheet can be extended across the whole wafer, but the phase of the atomic registry is also well maintained even across the Ag step. This conclusion is based on analysis of the moiré pattern; small changes in the lattice constants due to defects and strain are greatly magnified by the moiré pattern, making it an excellent tool to gauge the crystallinity of materials. 33 Shown in Figure 4a   Combined with the above analysis, one can conclude that after nucleation in the middle of terraces, the 2D islands grow laterally over the Ag steps, creating a uniform sheet. Amazingly, as these 2D atomic layer islands merge, the boundary self-heals, maintaining the long-range phase coherence in atomic registry (> 120 nm, as shown in Figure 3c). We next utilize scanning tunneling spectroscopy to study the electronic structure of the h-BeO for the first time. The differential conductance (dI/dV) spectroscopy, representing the local density of states (LDOS), is shown in Figure 5a  Interestingly, the Ag surface state is preserved in the BeO region except for an upward shift of 0.12 ± 0.03 eV. This behavior closely resembles that of systems that are weakly interacting via vdW forces, for example hBN and Xe on Cu(111), which shift the Cu(111) surface state upward by ~ 0.1 eV. 34,35 The preservation of the Ag (111) surface states is strong evidence that similarly, the h-BeO layer is weakly interacting with the Ag substrate. As mentioned before, the observed h-BeO/Ag(111) moiré pattern displays a peculiar bias dependent contrast reversal, as shown in Figures 2a and 3c. This implies that the moiré patterns not only introduce a change in height corrugation, but also a spatial modulation of the electronic character. Here we adopt the terminology used in this field and call different regions in the moiré pattern "hole" and "wire" regions, as labeled in the inset of Figure 6a. Figure 6b is an STM image that illustrates the contrast reversal of the h-BeO that shows the hole region (white dashed line) changing from a protrusion to a depression when the bias was changed from Vs = 3.7 V (top) to 4.5 V (bottom). To investigate the contrast mechanism, we use Z-V spectroscopy to examine the field emission resonance (FER), as the sample bias of the first FER is a good approximation for the local work function. In this spectroscopic technique, the tunneling current is held constant while the tip-sample distance (Z) versus bias sweep is recorded. When the bias reaches the tunneling barrier resonance, a steep increase in Z occurs, therefore peaks in the derivative ( ¶Z/ ¶V) I denote the locations of the FER. Figure 6a shows the Z-V (top) spectra and their derivatives ( ¶Z/ ¶V) I (bottom) acquired at the hole region (red curve) and wire region (blue curve). We find that energy locations of FER in the hole region are consistently lower than those in the wire regions by about 0.08 eV, suggesting that the local work function is modulated across the moiré pattern.
In addition, comparison of the h-BeO ( ¶Z/ ¶V)I spectra with spectra obtained on an Ag (111) surface (black curve) shows the h-BeO layer significantly reduces the work function, explaining the darker contrast of the h-BeO regions at low bias as discussed previously (Figure 2b,c). A closer look at the work function modulation explains the variation of the moiré pattern contrast observed by STM (Figure 6b). In Figure 6c, we plot the tip height difference between the hole and wire regions directly deduced from the Z-V curves in Figure 6a and find that the positive values indicate the bias range where the hole regions appear as a protrusion, while at negative values it becomes a hole. We note that this work function behavior closely mirrors the trends observed for hBN on transitions metals, [35][36][37][38][39][40] providing further evidence that the interaction of the h-BeO and Ag(111) is similar to a vdW interface.  and exhibit multilayer, polycrystalline growth at higher coverage. [19][20][21] In contrast, our LEED and STM measurements suggest the astonishing formation of wafer scale coverage of a single atomic sheet of honeycomb BeO that maintains long-range phase of the atomic lattice. In our case, the growth appears to be self-terminated at one atomic layer, implying a catalytic role played by the underlying Ag (111) substrate. Yet another similarity to vdW materials is the preservation of the pristine Ag (111) surface electronic structure, indicating a weak interaction with the h-BeO atomic sheet, an assertion that is supported by our complimentary DFT calculations. We note that the size of our Si substrates is constrained by our sample holders, which are limited by the STM sample stage. Considering the h-BeO is directly grown on epitaxial Ag films on Si wafers, such a method may be translated to a larger growth format, providing a powerful scalable technology platform.
The large insulating band gap of 6 eV and weak substrate interactions of the h-BeO make it an attractive candidate for multilayer heterostructures and as a template to support other 2D materials.
We expect that our work demonstrates that insulating h-BeO is an outstanding addition to the library of 2D materials and will create future possibilities for bottom-up fabrication of 2D devices.

Methods
Sample growth and STM Characterization. Our experiments were performed in a UHV system that combines a homebuilt STM with two homebuilt MBE systems, one for growth of the Ag thin films, and one for BeO growth and LEED measurements. All of the chambers have base pressures below 1 x 10 -10 Torr. The growth of the Ag(111) thin film substrate begins with preparing Si(111) wafers with 0.5 mm thickness by cutting them into 10 x 4 mm2 pieces, compatible with the STM sample holders. The sample is prepared following the standard procedure of flashing (1400 °C) and annealing (950 °C) in UHV to prepare an atomically clean surface with a well-defined 7x7 reconstruction. Growth of the Ag(111) thin films was carried out at room temperature with a deposition rate of 3 nm/min. The average thickness of the Ag films used in this study is 150 nm.
The as-grown Ag film already has a well-defined (111) orientation, however, the surface is relatively rough. Annealing the film at 500 °C for one hour yields a much smoother surface with well-defined triangular terraces whose step edges are parallel to the <110> directions. See Ref. 41 for details. Next, a monolayer sheet of BeO was grown epitaxially on the epitaxial Ag(111) thin films. A Knudsen-cell with a BeO crucible purchased from Fermi Instruments (> 99% purity) was used as the evaporation source with a source temperature of 1200 °C. The Ag(111) substrate was maintained at 500 °C during the growth. Under these conditions, the growth rate is roughly ~ 0.07 ML per minute. After the desired coverage was reached, the shutter to the BeO source was closed, and the BeO sample was annealed at the growth temperature for 15 minutes. The chamber pressure during the growth reached 8 x 10 -10 Torr.
STM measurements were performed at 77 K with a tungsten tip. The bias voltages were defined as the sample bias, and the topographic images were taken using constant current mode. The STM topography images were processed using Gwyddion software, and the STS was processed using the Origin software.
DFT Calculations. Our first-principles calculations were performed using the Vienna ab-initio simulation package (VASP) 42,43 with the projector augmented wave method. 44,45 The slab contains three layers of Ag atoms with the bottom two layers fixed and a vacuum region of about 16 Å. A plane-wave cut-off energy of 500 eV was used, and only the Gamma point was sampled for this large supercell. The optB86b functional including the van der Waals correction 46 was adopted for the structural relaxation. A dipole correction scheme was used to eliminate the long-range effect arising from the surface dipole between monolayer BeO and the Ag substrate. The atomic positions were fully relaxed until the force on each atom was smaller than 0.01 eV Å-1. For the local work function calculation, we took the difference between the Fermi level and the electrostatic potential at the center of the vacuum above a specific region.