Single photon emitters in hBN: Limitations of atomic resolution imaging and potential sources of error

Abstract

There is a growing interest in identifying the origin of single-photon emission in hexagonal boron nitride (hBN), with proposed candidates including boron and nitrogen vacancies as well as carbon substitutional dopants. Because photon emission intensity often increases with sample thickness, hBN flakes used in these studies commonly exceed 30 atomic layers. To identify potential emitters at the atomic scale, annular dark-field scanning transmission electron microscopy (ADF-STEM) is frequently employed. However, due to the intrinsic AA' stacking of hBN with vertically alternating boron and nitrogen atoms, this approach is complicated even in few-layer systems. Here, we demonstrate using STEM image simulations and experiments that, even under idealized conditions, the intensity differences between boron- and nitrogen-dominated columns and carbon substitutions become indistinguishable at thicknesses beyond 17 atomic layers (ca. 6 nm). While vacancy-type defects can remain detectable at somewhat larger thicknesses, also their detection becomes unreliable at thicknesses typically used in photonic studies. We further show that common residual aberrations, particularly threefold astigmatism, can lead to artificial contrast differences between columns, which may result in misidentification of atomic defects. We systematically study the effects of non-radially symmetric aberrations on multilayer hBN and demonstrate that even small residual threefold astigmatism can significantly distort the STEM contrast, leading to misleading interpretations.

Figures (14)

• Figure 1: Thickness-dependent visibility of atomic features in HAADF-STEM images in hBN. a) Simulated images of hBN with different layer numbers and line profiles. The labels N and B refer to the atoms in the bottom layer in the respective atomic column. b) Average intensity ratio of columns with a boron ("B") and nitrogen ("N") in the bottom layer as a function of layer number, for even layer numbers (solid line) and odd layer numbers (dotted line); the error bars (mostly within the markers) represent the 90 % confidence interval of the ratio. c) Simulated images of hBN with different layer numbers with a carbon atom replacing one boron atom, as well as line profiles over substituted and pristine atomic column pairs. d) Intensity ratio between a pristine "B" column and a carbon implanted "B" column. The dark blue error bars represent the 90 % confidence interval of the ratio, the light blue error bars represent the standard deviation of the "B" columns relative to the ratio. e) Simulated images of hBN with different layer numbers with a boron vacancy in the "B" column as well as line profiles over defective and pristine atomic column pairs. f) Intensity ratio between a defective and pristine "B" column as a function of layer number. The error bars represent the 90 % confidence interval of the ratio.
• Figure 2: Detection of carbon substitutions using HAADF-STEM and EELS. a) Raw and double Gaussian filtered images of different carbon features found in monolayer hBN. b) Experimental MAADF-STEM image of bilayer hBN with clusters of carbon substitutions. Green arrows mark clusters with corresponding EELS carbon K-edge intensity peaks, purple and red arrows mark single defects and clusters without such an intensity peak. c) Corresponding EELS map integrated around the carbon K-edge energy loss region (290-310 eV energy loss). To increase the visibility of the carbon edge the highest and lowest 5 percentile of integrated intensity values have been clipped. The white arrow indicates the approximate direction of drift during EELS acquisition. d) Equivalent experimental MAADF-STEM image of a six-layer hBN sample with clusters of substitutional carbon. Green arrows mark clusters with corresponding EELS carbon K-edge intensity peaks, red arrows mark clusters without such an intensity peak. e) Corresponding EELS map integrated around the carbon K-edge energy loss region (290-310 eV energy loss). To increase the visibility of the carbon edge the highest and lowest 5 percentile of integrated intensity values have been clipped. The white arrow indicates the approximate direction of drift during EELS acquisition.
• Figure 3: Effects of non-centrosymmetrical aberrations on B/N intensity ratios. a) Simulated images of bilayer hBN showcasing the typical effect of astigmatism, coma and threefold astigmatism for different relative angles between crystal direction and aberration phase. b) Intensity ratios of neighboring columns as a function of layer number for aberration-free settings, with 50 nm A23 aberration in phase with the crystal direction and with 50 nm A23 in counter-phase with the crystal direction. c) Intensity ratios of 10-layer hBN for aberration-free and 50 nm in-phase A23 aberration settings as a function of defocus. d) Intensity ratio as a function of A23 amplitude ($C_{23}$) for the in-phase condition. Inset: Simulation showing the artificial "AB-stacking" effect at higher amplitudes. e) Intensity ratio as a function of A23 phase ($\phi_{23}$) at a fixed A23 amplitude of 50 nm. f) Simulated images showcasing the effect of strong threefold astigmatism at different amplitudes and phases.
• Figure 4: Experimental validation for A23-related effects. a) Light microscope image of the exfoliated hBN flake on a 280 nm SiO$_2$/Si substrate. The red, purple and blue stars denote the locations in the near-bulk where the images in Fig. \ref{['Fig 5']}d-g have been obtained. Inset: Overview bright field electron microscopy image of the flake after transfer to the TEM grid obtained with the CCD camera. b) Raw, Gaussian-filtered (G) ($\sigma$ = 3 px) and double Gaussian-filtered (DG) (bandpass around first order FFT peaks, inner/outer radius 3.0/6.0 nm$^{-1}$) ADF-STEM images of a bilayer-monolayer step region without additional A23 aberration as well as a line profile over the bilayer-monolayer step in the double Gaussian-filtered image. The scale bar in the first image is valid for all images. c) Equivalent images from the same region, but with additional ($C_{23}$ = 132 nm, $\phi_{23}$ = -80°) corrector detuning. d) Equivalent images from the same region but with ($C_{23}$ = 132 nm, $\phi_{23}$ = +80°) corrector detuning.
• Figure 5: A23-related effects in multilayer hBN. a) Raw, Gaussian-filtered (G) ($\sigma$ = 3 px) and double Gaussian-filtered (DG) (bandpass around first order FFT peaks, inner/outer radius 2.0/10.0 nm$^{-1}$) ADF-STEM images of a 6-layer hBN region without additional A23 aberration as well as a line profile over the double Gaussian-filtered image. The scale bar in the first image is valid for all images. b) Equivalent images from the same region but with additional corrector detuning ($R_{23}$ = 132 nm, $\phi_{23}$ = -80°). c) Equivalent images from the same region but with different corrector detuning($R_{23}$ = 132 nm, $\phi_{23}$ = +80°). d), e), f) ADF-STEM images of the approximately 15 nm thick regions marked by red (f), blue (e) and green (f) stars in Fig. \ref{['Fig 4']}a. g) Magnified ADF-STEM image of the interference pattern in panel f.