Probing the Out-of-Plane Distortion of Single Point Defects in Atomically Thin Hexagonal Boron Nitride at the Picometer Scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride ($h$-BN) accompanied by first-principles calculations reveals a characteristic charge-induced $pm$ symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer $h$-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the $h$-BN membrane.

Figure 1

Reconstructed phase of a bilayer $h$-BN imaged by the TEAM I microscope. The magnified inset images show broken symmetry at the defect sites. Color bar shows the relative phase in radians.

Figure 2

Atomic structure models and phase of distorted boron monovacancies in bilayer $h$-BN with one and two interlayer bonds. (a),(d) The top and cross-sectional view of stable defect configurations predicted from first principles showing in-plane and out-of-plane asymmetric distortions at the boron monovacancy with one and two B-N interlayer bonds. (b),(e) A reconstructed phase, simulated from the models shown in (a) and (d), respectively. (c),(f) Reconstructed phase of two monovacancies in a bilayer $h$-BN recorded on the TEAM I microscope. Color gradient represents the relative phase of the atoms (yellow indicates individual atoms; black corresponds to the centers of hexagons in the honeycomb lattice). The atoms are numbered for the ease of identification. The single mirror plane across the monovacancies is shown by white dashed lines. The scale bar is 2.5 Å. Color bar shows the relative phase in radians.

Figure 3

Normalized phase of the exit wave as a function of out-of-plane interatomic distance for each individual atom column at the vacancy perimeter for the simulated and the TEAM I images in bilayer $h$-BN. The phase in the defect-free region of bilayer $h$-BN is normalized to unity. The two solid and dashed curves show the normalized phase versus the out-of-plane distance for a simulated B-N pair with no in-plane (solid line) and 35 pm in-plane (dashed line) distortion. Normalized phase for each individual atom column at the perimeter of the simulated boron (▵) and simulated nitrogen (▿) monovacancies is projected on the solid and dashed lines. The data points projected on the dashed line correspond to the vacancy edge atoms with in-plane distortion. TEAM I atom columns at the perimeter of the monovacancies (•) are projected on both the solid and dashed lines, while TEAM I atom columns at the defect-free region (▪) are projected on the solid line. The error bar corresponds to 13% variation in the magnitude of the phase shift in the defect-free region of the film.

Figure 4

(a) Phase of a monovacancy and (b) residual phase around the vacancy after the phase from the defect-free region is subtracted. (c) Distribution of residual phase showing a phase shift at the vicinity of the vacancy compared to the background. (d) Residual phase line profile across the vacancy previously shown in (b).