Atomically Precise Electron Beam Sculpting of Bilayer h-BN: The Role of Crystallographic Orientation and Milling Strategy

TL;DR

This work tackles the challenge of atomic-precision top-down nanofabrication by using a focused electron beam in STEM to sculpt bilayer h-BN, achieving nanoribbons down to $6~\text{Å}$ with atomically smooth edges. It combines HAADF imaging, multislice simulations, and a moiré-lattice formalism to identify stacking configurations and map crystallographic directions to milling trajectories, revealing that edge quality is governed by milling along the moiré armchair direction rather than the twist angle itself. A sequential milling strategy, where the beam box translates during processing, yields substantially better edges than parallel milling, a finding supported by a stochastic milling model that attributes improvement to reduced beam-tail exposure. Overall, the paper provides a general framework linking crystallographic orientation, milling strategy, and edge reconstruction to achieve atomic precision in two-dimensional bilayers, with implications for broader vdW materials processing.

Abstract

Achieving atomic precision in top-down manufacturing remains a fundamental challenge nanofabrication technology. Here, the focused electron beam of a scanning transmission electron microscope is used to demonstrate atomically precise sculpting of hexagonal boron nitride (h-BN) bilayers, achieving nanoribbons as narrow as 6 Å with atomically smooth edges. The key to this precision lies in understanding how the underlying atomic structure, particularly in twisted bilayer systems, influences the milling process. High-angle annular dark-field imaging combined with multislice simulations reveals distinct intensity signatures that allow identification of different stacking arrangements within moiré patterns. Mathematical analysis of moiré lattices provides a predictive framework for determining optimal cutting directions, with cuts along armchair directions yielding superior edge quality compared to zigzag orientations. Surprisingly, a sequential milling approach, where a small electron beam subscan area is translated during the process, produces significantly better results than parallel milling of the entire target region. To understand these differences we implemented a stochastic milling model that reveals that sequential milling minimizes unwanted exposure to surrounding material through beam tail effects. These findings establish a framework for achieving atomic precision in electron beam sculpting of two-dimensional materials and provide fundamental insights applicable to the broader challenge of top-down nanofabrication.

Figures (13)

• Figure 1: Electron beam milling of monolayer h-BN. (a) HAADF image before milling. The boxed region shows the subscan area with the arrow indicating the direction of movement of the subscan box. (b) After milling, the top and bottom edges show irregular atomic structure even though this is the crystallographically preferred milling direction. The unsatisfactory result motivated the investigation of bilayer systems, where interlayer coupling might provide additional structural constraints.
• Figure 2: Analysis of twisted bilayer h-BN image intensity features. (a) HAADF image of twisted bilayer h-BN. The fast Fourier transform is overlaid, from which we can measure the twist angle ($\sim$ 8 deg.). The nodes marked 1-3 are magnified below. (b) Schematic illustration the expected intensity of an AA$'$ stacked region, assuming a Gaussian shape and z2 intensity. B intensity is shown in blue; N intensity is shown in red; the sum of two layers is shown in black. (c) Schematic illustration of the expected intensity of an AA stacked region. Dotted horizontal line is a guide for the eye, illustrating that two B atoms are approximately the same intensity as a single N atom. Note, (b) and (c) are not simulated intensities. They are intended as a schematic representation only. (d) Model of an AA$'$ stacked bilayer with an 8 deg. rotation. One set of nodes maintain AA$'$ stacking, while the other two nodes exhibit AB stacking; B above B in one node, and N above N in the other, highlighted by the blue circles. (e) Model of an AA stacked bilayer with an 8 deg. rotation. One set of nodes maintain AA stacking, while the nodes exhibit AB' stacking; B above N in one anti-node and N above B in the other anti-node, highlighted by the blue circles. (f) Multislice simulation of AA$'$ stacked h-BN with an 8 deg. rotation. Nodes marked 1-3 are shown magnified to the left for comparison with those from the experimental image (a). (g) Multislice simulation of AA stacked h-BN with an 8 deg. rotation. Nodes marked 1-3 are shown to the left.
• Figure 3: Diagram of the substrate, $\vec{R}_i$, and overlayer, $\vec{R}'_i$, basis vectors and the rotation angle, $\alpha$. The resulting moiré lattice vectors, $\vec{R}_{Mi}$, their rotation angles, $\gamma_i$, relative to the basis vectors, and the angle between them, $\delta$.
• Figure 4: Summary of milling results in twisted bilayer h-BN. (a) Diagram illustrating the AC and ZZ directions in the two layers and the moiré. (b) HAADF image of the result of the first cut in the ZZ direction. (c) Additional cut in the AC direction. (d) Further milling produces an atomically sharp h-BN nanoribbon that is 6 Å wide.
• Figure 5: Summary of milling results in AA' stacked bilayer h-BN. (a) Initial cut in the AC direction. Blue box indicates the parallel milling location. (b) Second cut in the ZZ direction. (c) Third cut using a sequential milling strategy. Blue boxes indicate the start and end of the cut. (d) Intensity profile near the edge of the cut, showing a decrease in intensity approaching the edge and then an increase in intensity at the edge. (e) Magnified view of the edge. Beam damage is already evident.