First‑Principles Investigation of the Structural Stability and STM Imaging of Borophene on Ag(111)

Abstract

Recent experimental work has demonstrated the successful growth of atomically thin boron sheets—borophene—on Ag(111) by molecular‑beam epitaxy. Two distinct surface phases were observed, yet the precise atomic arrangements and their thermodynamic stability remain debated. In this study we employ density‑functional theory to examine the most plausible borophene polymorphs—buckled triangular, β12, and χ3—when supported on Ag(111). Our calculations reveal that all three freestanding sheets are thermodynamically unstable and metallic, whereas the Ag(111) substrate stabilizes them. Simulated scanning tunneling microscopy (STM) images reproduce the experimentally observed stripe and homogeneous phases and unambiguously identify the underlying lattice structures.

Background

Since the discovery of graphene, two‑dimensional (2D) materials have attracted intense research interest owing to their unique electronic, mechanical, and catalytic properties.1–7 Over the past decade, several theoretical proposals for 2D boron sheets—collectively termed borophene—have been reported, featuring diverse arrangements of hexagonal vacancies and buckling patterns.8–21 Although extensive first‑principles studies have suggested that planar triangular boron lattices with periodic hexagonal holes are energetically favored, the 2D form is still higher in energy than bulk boron, implying a thermodynamic drive toward 3D crystallization.22–24 Consequently, a sufficiently “sticky” substrate is required to suppress 3D nucleation and favor the formation of atomically thin layers.25–27

Recent experimental breakthroughs have realized borophene on metal surfaces. Mannix and co‑workers successfully deposited boron onto Ag(111) and observed two distinct surface phases—a striped phase and a homogeneous phase—using high‑resolution STM.28 Feng et al. reported similar phases and assigned the homogeneous structure to a χ3 lattice, while the striped phase was interpreted as either a buckled triangular lattice or a rectangular β12 lattice.29–31 These divergent interpretations underscore the need for a systematic theoretical investigation of the possible atomic configurations and their stability on Ag(111).

Beyond structural identification, borophene polymorphs exhibit remarkable properties. The buckled triangular sheet is predicted to be a highly anisotropic metal with a Young’s modulus exceeding that of graphene along its armchair direction, and displays strongly anisotropic lattice thermal conductivity.32,33 Superconductivity has also been predicted for β12 and χ3 borophene, potentially rivaling MgB2 thin films.34–36 However, the thermodynamic stability of β12 and χ3 remains controversial, with some studies reporting imaginary phonon frequencies near the Γ point.37,38

Computational Methods

All calculations were performed with the Vienna Ab‑Initio Simulation Package (VASP) using density‑functional theory (DFT).38 The projector‑augmented‑wave method described electron–ion interactions,39 and the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional was employed for exchange–correlation.40 Plane‑wave basis sets were truncated at 500 eV, and the Brillouin zone was sampled with 25 × 15 × 1, 15 × 9 × 1, and 11 × 11 × 1 k‑point meshes for the buckled triangular, β12, and χ3 phases, respectively. A vacuum spacing of at least 20 Å along the z‑direction minimized interactions between periodic images. Geometry optimizations converged to forces below 0.02 eV Å⁻¹, while the bottom two layers of Ag were fixed. Phonon dispersions were obtained using the finite‑displacement method implemented in PHONOPY.41

STM images were simulated within the Tersoff–Hamann framework, which relates the tunneling current to the local density of states (LDOS) of the sample.42 The constant‑current mode was used to generate images at various bias voltages, providing direct comparison with experimental STM data.

Results and Discussion

Figure 1 displays the optimized geometries of the three borophene polymorphs considered: buckled triangular (a), β12 (b), and χ3 (c). The buckled triangular sheet exhibits a single out‑of‑plane buckling along the b‑axis, whereas β12 and χ3 are planar with distinct arrangements of hexagonal vacancies. The lattice constants—1.613 Å × 2.866 Å for buckled triangular, 2.916 Å × 5.075 Å for β12, and 4.448 Å for χ3—agree well with previous theoretical and experimental reports.23,25,27

Top and side views of buckled triangular (a), β12 (b), and χ3 (c) boron sheets. The green balls represent the boron atoms. The rectangles and rhombus enclosed by solid black lines denote the unit cells. The letters a and b represent the lattice parameter

The vacancy concentration η is 1/6 for β12 and 1/5 for χ3, indicating a higher degree of defect ordering in the latter. The relative stability was assessed by calculating the average binding energy per boron atom, E_FB, defined as E_boron/n. Results (Table 2) show that the freestanding β12 sheet is the most stable, while χ3 is least stable, differing by 0.08 eV per atom. However, phonon dispersion calculations (Figure 2) reveal imaginary frequencies near Γ for all three structures, confirming that they are thermodynamically unstable in isolation.

The phonon dispersion of the a buckled triangular, b β12, and c χ3 boron sheets. The high symmetry points are shown on the left corner

Electronic band structures (Figure 3) confirm that all three polymorphs are metallic. The buckled triangular sheet exhibits strong anisotropy, with band crossings along S–Y and G–X, and sizeable gaps along X–S (9.63 eV) and Y–G (4.32 eV). These features suggest directional conductivity confined to the unbuckled a‑axis.

Calculated band structures for a buckled triangular, b β12, and c χ3 boron sheets. The Fermi energy was set to zero. The high-symmetry points are shown on the left corner

When placed on Ag(111), the lattice mismatch is minimal (~1 %) for β12 and moderate (~3 %) for buckled triangular. The χ3 sheet adopts two distinct registries (χ3 and χ3′) on the substrate, with lattice constants 8.67 Å and 2.89 Å × 25.02 Å, respectively. The vertical separation between the borophene layer and the Ag surface ranges from 2.4 to 3.3 Å, indicating weak physisorption that preserves the planar character of β12, χ3, and χ3′. These interlayer distances are consistent with the experimental thicknesses reported for borophene on Ag(111).23,28

Simulated STM images (Figure 5) reproduce the experimentally observed stripe (Mannix et al.) and homogeneous (Feng et al.) phases. The stripe pattern for buckled triangular appears as spindle‑shaped bright ridges, while β12 yields oval‑shaped protrusions surrounded by bright corners. The χ3 sheet displays a rhombohedral dumbbell pattern matching the S2 phase reported by Feng et al. Bias‑dependent simulations (Figure 6) further distinguish the two stripe configurations: the buckled triangular stripe reverses contrast between positive and negative bias, whereas the β12 stripe retains its oval shape regardless of bias, supporting the assignment of the Mannix stripe to buckled triangular and the Feng stripe to β12.

Simulated STM images of freestanding and epitaxial boron sheets on Ag(111) surface. Freestanding a triangular, b β12, and c χ3 boron sheets. Partial charge density of freestanding d triangular, e β12, and f χ3 boron sheets. g Buckled triangular, h β12, i χ3, and j χ3′ boron sheet on the Ag(111) surface. The bias voltage is 1.0 V. The green balls represent the boron atoms. The rectangles and rhombus enclosed by solid red lines denote the unit cells of freestanding and as‑grown boron sheets on Ag(111) surface. Experimentally observed k stripe phase in Ref. [22], l stripe phase in Ref. [23], and m homogeneous phase in Ref. [23]

In summary, first‑principles calculations demonstrate that freestanding buckled triangular, β12, and χ3 borophene are thermodynamically unstable and metallic. The Ag(111) substrate stabilizes these sheets, lowering their energies by 0.1–0.2 eV per boron atom. The simulated STM images provide a definitive mapping between observed surface phases and underlying lattice structures, resolving the long‑standing debate over the atomic configuration of borophene on silver. These insights lay the groundwork for rational design of borophene‑based devices and for guiding future experimental synthesis on metallic substrates.

Abbreviations

2D

Two‑dimensional

3D

Three‑dimensional

STM

Scanning tunneling microscopy