Non-perturbative cathodoluminescence microscopy of beam-sensitive materials

1 Introduction

Color centers and localized excitons in two-dimensional (2D) materials have emerged as a promising resource for quantum networking and quantum sensing in recent years [1], [2], [3], [4] because of the potential for atomic scale control over the defect environment [5], [6], compatibility with integrated photonic circuits [3], [4], [7], [8], and the potential for manipulation of emitter photophysics with engineered strain environments [9], [10], [11], [12], [13] and electrical gating [14], [15], [16]. Unfortunately, many reports in the literature focus on ‘hero’ emitters that are selected after exhaustive searches of many lower quality emitters. Attempts to locate and pattern individual single photon emitters with desirable brightness, purity, and indistinguishability often result in the observation of multiple emitters within a single diffraction-limited spot or in the emergence of coupled electronic transitions with unwanted photochromic effects [17], [18]. The ability to manipulate and measure the quantum states associated with these color centers relies heavily on our understanding of how nanoscale heterogeneities affect their photophysical behavior. Therefore, advanced nanoscale probes that can accurately assess these effects while allowing for in situ modification are crucial to the development of color centers for practical quantum technologies.

Cathodoluminescence (CL) microscopies have emerged as a powerful nanoscale probe of quantum nanophotonic systems [10], [13], [19], [20], [21], [22], [23]. The converged electron-beam probe offers a nanometer-scale excitation, and far-field collection of CL enables high sensitivity measurements of emitter energetics and dynamics across a wide variety of energy- and time-scales. However, the electron-beam probe has also emerged as a resource for beam-induced modification of 2D materials [20], [24], [25], [26]. Indeed, many monolayer transition metal dichalcogenides only exhibit measurable CL signals when they are encapsulated by hBN [21], [22], an effect that may result from beam-induced damage to beam-sensitive materials. While clear examples exist in the literature using the electron beam to either probe or manipulate color centers in 2D materials, the necessary electron-beam dose to measure emitter photophysics is in many cases also sufficient to substantially modify the defect environment in that material. Thus, identifying new minimally-perturbative approaches to CL microscopy capable of probing the color center environment without modifying it – while allowing for intentional in situ modification at higher electron-beam doses – is critical to improved understanding and control of 2D quantum photonic systems.

Pan-sharpening (PS) methods may offer a minimally perturbative approach to CL microscopy by combining separate high-spatial-resolution and high-spectral-resolution images in order to generate a composite image with both high spatial and spectral resolution. First used in satellite imaging [27], [28], PS methods have now emerged as powerful tools for multidimensional imaging in a wide variety of use cases. In nanoscience, PS has been applied to electron energy loss spectroscopy [29], scanning probe microscopy [30], and secondary ion mass spectrometry [31], though PS-CL has not yet been explored despite the substantial benefit associated with minimizing beam-induced damage through undersampling of hyperspectral CL images. Most PS algorithms rely on either (i) the substitution of spectral components from a hyperspectral dataset with a high spatial resolution panchromatic image or (ii) a multiresolution analysis approach based on injection of spatial details from the panchromatic image into resampled hyperspectral bands [32]. Here, we focus on PS-CL performed using the Brovey transform [33], an example of the former class of PS algorithms that uses multiplicative sharpening to spatially modulate spectral pixels [32], and we examine the impact of this approach on CL imaging of color centers in 2D materials.

2 Methods

Hexagonal boron nitride (hBN) is known to be relatively robust to electron-beam exposure, and it has been probed by conventional CL microscopy [13], but there is also a growing literature describing electron-beam induced patterning of color centers in hBN [20], [24], [25], [26]. Thus, hBN offers a valuable platform for examining PS-CL techniques that could be crucial to probes of more environmentally sensitive materials like monolayer transition metal dichalcogenides and some classes of hybrid organic perovskite thin films. All data reported here is based on exfoliated hexagonal boron nitride (hBN) flakes transferred onto a 300 nm silicon dioxide (SiO₂) layer on a silicon substrate.

Cathodoluminescence data was acquired using a Delmic Sparc CL module with an FEI Quattro scanning electron microscope (SEM) operating with a beam energy of 5 kV and a beam current of 110 pA at room temperature and a chamber pressure of 1E-6 Torr. CL spectrum images were acquired with an Andor Kymera spectrograph and an Andor Newton CCD with an acquisition time of 300 ms per spectrum. A pickoff mirror was used to direct the collected CL signal into a photomultiplier tube (PMT) for high-spatial resolution panchromatic CL imaging using a PMT integration time of 10 μs (yielding 300,00x reduced dose per pixel compared with spectrum imaging).

3 Results

An SEM image of a prototypical hBN flake is illustrated in Figure 1a. While we were able to acquire moderately coarse spatial resolution CL spectrum images of hBN flakes with minimal apparent degradation (with pixel sizes of order 100 nm), improving spatial resolution while maintaining the beam energy and current along with a constant dwell time per pixel resulted in growing evidence of beam-induced modification of the hBN flake. Increasing the beam energy also resulted in substantially faster beam-induced modification, as highlighted by Fig. S2 in the Supporting Information. This dose-dependent beam-induced modification is most easily visualized through time-series spectra acquired while the electron beam rapidly scanned 768 × 512 pixels across a 500 nm spot with a 100 ns/pixel electron dwell time. Note that acquiring time-series spectra with the electron beam focused on a single spot resulted in immeasurably fast changes in the CL spectra, so averaging across a 500 nm spot allowed us to reduce the effective dose/pixel during time-series CL spectrum acquisition as discussed in the Supporting Information. A reduced CL spectrum acquisition time of 50 ms (approximately equal to the time required to scan 768 × 512 pixels) was used in order to monitor the time-dependent changes in CL spectra as a function of electron-beam dose.

Figure 1:

Combined SEM-CL analysis of a prototypical hBN flake. (a) SEM image of an hBN flake with horizontal width of 10.5 μm. (b) Time-series CL spectra acquired at a single point on the hBN flake highlighting the beam-induced changes in the hBN CL spectrum as a function of increasing dose. (c) Spectral components and (d) intensity maps generated by non-negative matrix factorization of CL spectrum image acquired in conventional rastered CL spectrum imaging modality.

Figure 2:

Benchmark PS-CL results generated from a single CL hyperspectral image of an hBN flake with dimensions of 100 × 100 × 1024 (horizontal, vertical, wavelength) pixels with a horizontal field of view of 30 μm. A panchromatic image was generated from the spectrum image by summing along the wavelength axis while spectrum images with reduced spatial resolution were generated by binning spatial pixels together. The Brovey pan-sharpening algorithm was used to reconstruct a hyperspectral CL image from these datasets. NMF reconstructions of the pan-sharpened CL images are shown for data generated from the panchromatic image and (a) the complete 100 × 100 × 1024 spectrum image, (b) a 50 × 50 × 1024 spectrum image, (c) a 25 × 25 × 1024 spectrum image, (d) a 12 × 12 × 1024 spectrum image, (e) a 6 × 6 × 1024 spectrum image, and (f) a 1 × 1 × 1024 spectrum image.

Several features are immediately apparent in the time-series spectra shown in Figure 1b: A prominent CL band centered at a wavelength of 647 nm exhibits minimal change with increasing dose (though this band exhibits increased beam sensitivity at higher energies, as shown in the Supporting Information). On the other hand, a blue CL band near 417 nm grows monotonically with increasing dose, and the CL from a narrow linewidth color center near 533 nm is quickly bleached with increasing dose. These results highlight the importance of alternative SEM-CL acquisition modalities, especially for smaller pixel sizes where the increased electron-beam dose can result in rapid modification of the hBN color center photophysics. Additionally, it is difficult to interpret CL spectra acquired at a single point, as we expect some CL contribution from defect bands in the SiO₂ substrate.

Figure 1c and d illustrate a non-negative matrix factorization (NMF) decomposition of a CL spectrum image acquired across this flake using conventional raster scanning with a pixel size of 100 nm. For all NMF decompositions shown in this manuscript, reconstructions were attempted with varying numbers of components, and it was determined that three components were sufficient to provide a reasonable reconstruction of the raw data based on (1) an analysis of the explained variance as a function of number of components and (2) a qualitative physical understanding of the defect bands observed in the NMF components, as discussed in the Supporting Information. The NMF decomposition shown in Figure 1 immediately aids in the interpretation of the single point CL spectra shown in Figure 1b: Component 3 is solely a result of the hBN flake, while Component 2 appears to be primarily a result of the SiO₂ substrate luminescence. Component 1, which features the narrow transition at 548 nm, appears to be primarily due to the hBN flake, though it includes some convolution with substrate luminescence. The NMF decomposition doesn’t perfectly recover this narrowband transition from the raw data, so additional point spectra are included in the Supporting Information for reference. The narrow band color centers seen in Component 1 are reasonably densely distributed across the hBN flake. Unfortunately, it is hard to image these color centers with improved spatial resolution using conventional CL raster scanning because reducing pixel sizes while maintaining the field of view yields a combination of beam-induced damage and unacceptably long measurement times. However, PS-CL techniques offer a promising pathway to address this challenge.

The Brovey transform was identified as a PS algorithm well suited to our data, and it was benchmarked by generating high spatial resolution and high spectral resolution datasets from a single 100 × 100 × 1,024 (horizontal × vertical × wavelength) pixel hyperspectral CL image of a hBN flake (by separately binning all wavelengths together to create a 100 × 100 pixel panchromatic image and binning adjacent spatial pixels to create spectrum images with 1,024 spectral pixels and between 1 × 1 and 50 × 50 spatial pixels). We then up-sampled the hyperspectral dataset to match its spatial resolution with that of the panchromatic image using the resize function in skimage.transform with linear splines. Each spatial pixel’s spectrum in this new dataset is scaled to match the net intensity of the corresponding normalized panchromatic pixel’s intensity. The pan-sharpened CL spectrum image then had dimensions of 100 × 100 × 1,024 and could be easily compared with the original spectrum image.

Three component NMF reconstructions of the PS-CL image with reduced dimensionalities are shown in Figure 2. At first glance, very little information is lost in the PS-CL image as the hyperspectral image is collapsed from a 100 × 100 × 1,024 spectrum image (Figure 2a) to a 6 × 6 × 1,024 image (Figure 2e), though unsurprisingly, all three components of the PS-CL image generated from a 1 × 1 × 1,024 spectrum image (Figure 2f) look nearly identical to one another. The quality of the pan-sharpening algorithm can be calculated here with a structural similarity index (SSI) comparing the pan-sharpened image with the original 100 × 100 × 1,024 spectrum image. The SSI of each pan-sharpened image here was calculated using the scikit-image library. As shown in Figure 3, applying the Brovey transform to the original 100 × 100 × 1,024 spectrum image results in a SSI of 1.0, and a SSI > 0.9 for compression ratios as high as 90 %.

Figure 3:

Calculated structural similarity index as a function of compression ratio for the PS-CL data shown in Figure 2. The compression ratio is calculated based on the compression of the hyperspectral data prior to pan sharpening.

This baseline PS-CL data suggests that CL spectrum images can be acquired with substantially reduced electron-beam exposure by combining short-dwell-time panchromatic CL images acquired on a PMT with very low spatial resolution spectrum images. Further, rastering the electron-beam over each spectrum-image pixel during the comparably-slow spectrum acquisition time will distribute the electron-beam dose over a large area and minimize the risk of beam-induced damage.

With this understanding in hand, PS-CL images were reconstructed from raw hyperspectral and panchromatic CL datasets. Figure 4 illustrates three-component NMF reconstructions of PS-CL images of an hBN flake generated from an 1,168 × 1,034 panchromatic CL image (using 10 μs dwell time per pixel) and a 39 × 35 pixel spectrum image (Figure 4a) and a 117 × 105 pixel spectrum image (Figure 4b) (each using a 300 ms spectrum acquisition time per pixel). Both exhibit very similar spectral components, though the latter does exhibit higher-spatial-resolution intensity maps. Nonetheless, these results show the potential impact of pan-sharpening for CL microscopy with minimal beam-induced damage.

Figure 4:

Three component NMF reconstructions of hBN PS-CL images generated from (a) an 1,168 × 1,034 pixel panchromatic image and a 39 × 35 pixel hyperspectral image and (b) an 1,168 × 1,034 panchromatic image and a 117 × 105 pixel hyperspectral image. The horizontal field of view is 10.5 μm.

Alternative approaches to non-perturbative CL microscopy might include singular value decomposition (SVD) techniques and compressive sensing (CS) schemes. SVD denoising is widely used to improve the signal-to-noise ratio in noisy multi-dimensional datasets, and it has seen limited use for CL microscopy [34], but it has limited benefit for CL microscopy because the spectrometer acquisition time can often not be substantially reduced before running into fundamental noise floors. On the other hand, CS schemes rely on an appropriate selection of sampling matrices and reconstruction algorithms in order to allow for accurate image reconstruction with many fewer measurements than are required by the Shannon-Nyquist sampling theorem [35], [36]. CS schemes have been used to enable new imaging modalities in astronomy [37], for new types of quantum imaging and quantum process tomography [38], [39], [40], and for scanning probe and scanning tunneling microscopies [41], [42], but they have not yet been used for CL microscopy. Additional work is still required to adapt these schemes for CL microscopy, but there is reason to expect that such approaches could complement pan sharpening techniques and allow further reduction in the necessary electron-beam dose to achieve a given CL signal-to-noise ratio.

4 Conclusions

The PS-CL results shown here suggest that hyperspectral CL measurements can be undersampled by 90 % while maintaining at least 90 % fidelity to the ground truth. Because hyperspectral and panchromatic datasets can be easily acquired concurrently (using a beamsplitter) or consecutively (using a pickoff mirror) with no change to the experimental alignment, the approach described here is easily adapted for a wide variety of CL microscopies of beam-sensitive materials. This approach is particularly critical for minimizing beam-induced damage in beam-sensitive materials like monolayer 2D materials and hybrid organic perovskite thin films, and for applications that require high spatial resolution and long spectrum acquisition times. The successful demonstration of PS-CL also unlocks new opportunities for high-dose electron-beam patterning of single photon emitters with low dose PS-CL used for in situ characterization.

Supporting Information: Supporting Information is available from the Wiley Online Library or from the author.