Sub-Nanometre Holes in Hexagonal Boron Nitride

• Sub-nanometre holes in hBN are engineered vacancy defects and nanopores with atomic precision that enable advances in quantum transport and nanoelectronics.
• Advanced fabrication methods such as electron irradiation, focused ion beam milling, and dielectric breakdown allow controlled pore size and modified edge chemistry.
• These nanostructures influence ion transport, quantum interference, and optical sensing, driving innovation in quantum sensing and matter-wave optics.

Sub-nanometre holes in hexagonal boron nitride (hBN) refer to vacancy defects and engineered nanopores with lateral dimensions below 1 nm, fabricated and characterized at atomic precision. These features in hBN have become central to developments in nanoelectronics, nanophotonics, quantum sensing, and matter-wave optics due to the material's wide bandgap, layered structure, and robust physical properties. Their formation, electronic effects, and role in both quantum transport and atomic diffraction span several experimental and theoretical approaches detailed in recent research.

1. Fabrication Approaches for Sub-Nanometre Holes

Atomic-scale hole formation in hBN leverages techniques such as electron irradiation, focused ion beam (FIB) milling, dielectric breakdown, and freeform thermal scanning-probe lithography. In transmission electron microscopy (TEM) at controlled acceleration voltages, boron atoms are ejected preferentially due to their lower threshold energies, leading to the initial formation of boron vacancies and quantized pore growth (Gilbert et al., 2017). Condensed followed by diffuse beam conditions enable atomically precise termination of pore size from sub-nanometre to several nanometres. Focused ion beam processes induce site-specific local amorphization and removal, enabling defect arrays and nanopores whose geometry can be tuned down to the ion beam spot size and dwell time parameters (Glushkov et al., 2021). Freeform profiles with sub-nanometre height resolution are achievable by patterning thermally decomposable resist via a heated scanning probe followed by nearly one-to-one profile transfer through reactive-ion etching (Lassaline et al., 2021).

Dielectric breakdown methods can yield single-atomic-layer holes (~0.6 nm deep) if voltage termination occurs near the onset of breakdown; this process is gradual and proceeds layer-by-layer due to the strong in-plane sp² bonding and weak interlayer van der Waals interactions (Hattori et al., 2015). The controlled formation of boron-terminated tetravacancies using high-dose STEM irradiation provides further atomic-scale control, with characterization by Z-contrast imaging, electron energy-loss spectroscopy (EELS), and electron ptychography revealing precise edge termination and electronic relaxation (Byrne et al., 19 Apr 2025).

2. Atomic Structure and Edge Chemistry

Sub-nanometre holes in hBN frequently manifest as triangular or hexagonal nanopores, determined by the symmetry and atomic termination resulting from fabrication conditions. Triangular pores form with uniform nitrogen or boron-terminated zigzag edges depending on beam type and dose rate. High-dose STEM irradiation predominantly produces boron-terminated tetravacancies, confirmed by the absence of nitrogen contrast in HAADF-STEM and by pre-peaks in the boron K-edge fine structure in EELS (Byrne et al., 19 Apr 2025). Ptychography shows that boron atoms at the vacancy corners relax inward, contracting bond distances to ~1.9 Å compared to 2.5 Å in the pristine lattice, a direct signature of edge reconstruction and new bonding effects.

Edge atoms around the holes acquire modified (screened) polarizabilities compared to bulk due to broken symmetry and reduced coordination. This is quantified via Hirshfeld partitioning and self-consistent screening equations, resulting in "polarizability ripples" with nitrogen edge atoms showing enhancements up to 40% and boron edges ~20% above bulk values (Osestad et al., 24 Jun 2024). The edge chemistry strongly determines ion transport, quantum emission characteristics, and atomic diffraction patterns due to local variations in electronic density and electrostatic potential.

3. Quantum Transport and Electron Interference

Sub-nanometre hBN holes or gaps influence quantum electron transport in associated nanodevices. In graphene nanojunctions electroburnt on hBN substrates, quantum interference effects dominate at the moment before gap formation: a single carbon filament spanning a sub-nanometre gap supports higher current than two parallel filaments due to destructive wavefunction interference, as described by the Landauer–Büttiker formula (Sadeghi et al., 2015). The hBN substrate weakly perturbs transmission probability T(E) near the Fermi energy at low biases, but additional carbon–boron/nitrogen resonances appear at higher energies. Positioned as an insulating substrate, hBN also enables highly reproducible gap formation and strong gating efficiency in nanoelectronic devices.

4. Optical and Quantum Sensing Applications

Nanopores with controlled size and edge chemistry are integral to molecular sensing, DNA sequencing, and selective ion transport due to their ability to sieve molecules or ions with high precision. Nitrogen-terminated edges, prevalent in triangular pores, offer chemical stability and resistance to oxidation, while boron-terminated edges can be functionalized for tailored selectivity (Gilbert et al., 2017). Controlled defect arrays using FIB provide quantum emitters with deterministic spatial positioning, crucial for integrated photonic circuits and quantum sensing. These engineered defects demonstrate optical transitions (610 nm for central, 830 nm for ring emission), short fluorescence lifetimes (~1.1 ns), and high saturation power (~2.5 kW/cm²), supporting applications in quantum communication and optically addressable sensing (Glushkov et al., 2021).

5. Atomic Diffraction and Matter-Wave Optics

Sub-nanometre holes in monolayer hBN serve as diffraction masks for atomic beams, as exemplified by helium matter-wave propagation studies. Atomic transmission and diffraction are constrained by strong dispersion interactions at the edge—described by frequency-dependent Casimir–Polder potentials and locally enhanced van der Waals coefficients C₆,i due to screened polarizabilities (Osestad et al., 24 Jun 2024). Quantum mechanical simulations using the time-dependent Schrödinger equation reveal higher transmission rates through sub-nanometre holes than semi-classical models predict, with distinct diffraction patterns and effective transmission areas that depend on atom velocity and edge termination (Osestad et al., 10 Sep 2025). For the smallest holes (radius ~6 Å), the attractive dispersion forces can lead to effective closure at low velocities, setting the resolution limit for matter-wave lithography or atom holography. The quantum description thus calls for nanohole fabrication with atomic-level edge precision to fully realize the predicted transmission increase and mask performance.

6. Diagnostic Techniques and Internal Structure Probing

Advanced diagnostic methodologies leverage the unique optical properties of hBN to probe sub-surface and internal nanostructures below the diffraction limit. Hyperbolic phonon polaritons in hBN propagate with deeply subwavelength confinement and can be excited and imaged using scattering-type near-field optical microscopy (s-SNOM). When these polaritons interact with sub-nanometre defects (e.g., air gaps, vacancies), they experience reflection and form standing-wave interference fringes at λ_p/2 periodicity, providing a tomographic map of defect location, geometry, and thickness with nanometre resolution (Dai et al., 2018). The normalization of reflection amplitude R(ω) allows quantitative extraction of defect properties from multiple frequency images. This non-destructive technique is extendable to biomedical imaging, molecular sensing, and material diagnostics.

7. Future Directions and Technological Implications

Research in sub-nanometre hBN holes is currently driving advancements in several interconnected domains: atom interferometry sensing, atomic holography, molecular sieving, quantum optics, nanofluidics, and neuromorphic computing. Enhanced process control is suggested through automated beam shuttering and feedback from real-time imaging (Gilbert et al., 2017), with further attention to chemical modifications for edge functionalization and integration into device architectures. Patterned hBN superlattices (“Fourier surfaces”) are now being explored to engineer strain and band alignment in adjacent two-dimensional layers (Lassaline et al., 2021). Highly resolved fabrication techniques are required to fully exploit quantum model benefits for diffractive masks (Osestad et al., 10 Sep 2025).

The ability to engineer atomic-scale holes, with controlled composition and geometry, opens pathways to programmable quantum and electronic materials, nano-optoelectronic devices, and platforms for fundamental studies of many-body and wave phenomena in two-dimensional lattices. Advancements in diagnostic imaging and matter-wave propagation modeling continue to refine understanding of atomic-scale interactions, edge chemistry, and the ultimate resolution limits in nanotechnology.