Nanoscale Cathodoluminescence and Conductive Mode Scanning Electron Microscopy of van der Waals Heterostructures

van der Waals heterostructures (vdW-HSs) integrate dissimilar materials to form complex devices. These rely on the manipulation of charges at multiple interfaces. However, at present, submicrometer variations in strain, doping, or electrical breakages may exist undetected within a device, adversely affecting macroscale performance. Here, we use conductive mode and cathodoluminescence scanning electron microscopy (CM-SEM and SEM-CL) to investigate these phenomena. As a model system, we use a monolayer WSe2 (1L-WSe2) encapsulated in hexagonal boron nitride (hBN). CM-SEM allows for quantification of the flow of electrons during the SEM measurements. During electron irradiation at 5 keV, up to 70% of beam electrons are deposited into the vdW-HS and can subsequently migrate to the 1L-WSe2. This accumulation of charge leads to dynamic doping of 1L-WSe2, reducing its CL efficiency by up to 30% over 30 s. By providing a path for excess electrons to leave the sample, near full restoration of the initial CL signal can be achieved. These results indicate that the trapping of charges in vdW-HSs during electron irradiation must be considered, in order to obtain and maintain optimal performance of vdW-HS devices during processes such as e-beam lithography or SEM. Thus, CM-SEM and SEM-CL form a toolkit through which nanoscale characterization of vdW-HS devices can be performed, allowing electrical and optical properties to be correlated.


S1. Role of hBN Encapsulation in Obtaining a Bright CL Signal
In Fig.S1 we compare the CL signal obtained from unencapsulated WSe2 on SiO2. From this we find no CL signal from WSe2 can be detected without encapsulation.

S2. Device Characterisation
The van der Waals heterostructures (vdW-HSs) are characterized by Raman and PL spectroscopy using a Horiba LabRAM Evolution at 514nm with a 100x objective (NA: 0.9), acquired using, respectively, 1800 l/mm and 150 l/mm gratings. The laser power is <1 mW to exclude heating effects. Fig.S2a indicates that 1L-WSe2, exhibits 1 2g and 1 modes 1 as a single peak ~250 cm -1 . Fig.S2b shows the Raman spectra of hBN encapsulated few layer graphene (FLG), both with and without the overlying 1L-WSe2, with the G peak ~1580 cm -1 and structured 2D band, as expected for FLG. 2 The feature seen in Fig.1b~1366 cm -1 corresponds to the 2g mode of hBN. 3 This demonstrates all constituent layers within the vdW-HS are preserved throughout the fabrication process. From Fig. S2a, we estimate the strain variation across the 1L-WSe2 by comparing the position of the degenerate 1 2g + 1 peak and the 2LA(M) overtone peak, as extracted by Lorentzian fitting, at different points. 4 We estimate a tensile strain variation ~0.13% across the hBN encapsulated 1L-WSe2 based upon the shift (Δ ~ 0.07 cm -1 ) of the 2LA (M) Raman mode. 4
PL measurements on 1L-WSe2 within the vdW-HS in the absence of FLG confirm that the flake is 1L-WSe2, Fig.S2c. The peak~750 nm is ascribed to the neutral exciton, X 0 . 1 The relative intensity and full width at half maximum (FWHM) of both hBN/1L-WSe2/FLG/hBN and hBN/1L-WSe2/ hBN on 285 nm SiO2/Si are extracted via Lorentzian fitting: FWHM~14.8 nm (0.016 eV) and 16.5 nm (0.018 eV), respectively. The relative emission intensity of 1L-WSe2 in contact with FLG within the vdW-HS significantly decreases due to exciton dissociation induced by interlayer charge transfer. 5 The absolute value varies spatially, with a minimum reduction factor ~1100. Fig.S3 plots the edge response in CL and electrode current along the line indicated in Fig.2c. Comparing the edge response in CL from 1L-WSe2 to the electrode current we can see they do not perfectly overlap. The electrode current signal decays slower. This is because the spatial resolution of CL is high 6 , and is limited by the diffusion of excitons in the hBN 6 , however RCI tracks majority carriers, which are free to travel through the hBN. The decay in signal can be understood by considering what happens as the probe is scanned beyond the edge of the grounded 1L-WSe2. Away from the grounded 1L-WSe2, electrons can either travel horizontally through hBN back to the 1L-WSe2, or vertically down to the substrate. The distance through the hBN to the substrate will remain constant, whereas, as the horizontal distance increases, the resistance of the path through hBN to the electrode also increases, leading to a drop in electrode current.

S3. Comparison of Spatial Resolution of RCI and CL
is the width of the beam and is the material thermal conductivity. For our samples, we estimate an upper limit on beam induced heating using the values in Table S1. 300 K This estimates the beam heating to result in up to a 53 K increase in sample temperature. Given that the sample is kept at 300 K, this would raise the temperature to 353K. Additionally, previous works have reported that the temperature of the exciton population during cathodoluminescence can be larger than the lattice, in contrast to photoluminescence. 9 S5 Discussion of CL Line-shape The asymmetry of luminescence from WSe2 is often attributed a trion component, found at ~30 meV below the neutral exciton. [10][11][12][13] The intensity and energy of luminescence from trions has been shown to be sensitive to the carrier concentration in WSe2. [11][12][13] Therefore some changes to the CL line-shape under electron beam doping seen in Figure 3e may be expected. At present, studies of emission from trions at room temperature are lacking. To confirm if the carrier concentration can significantly affect the luminescence line-shape under the conditions used in this work, in Fig.S4a, we collect PL spectra whilst using back gating to modulate the carrier concentration. In Fig.S4a, we see that applying a bias of 30 V, the luminescence intensity reduces by 25% -a comparable amount to that seen after 28s of irradiation at 6 keV. In Fig.S4b we see that despite the reduction in luminescence intensity and change in carrier density, the line-shape of the luminescence is unchanged. This is in agreement with the charging dependent CL spectra shown in (Fig.3e).

S6. Assessing Influence of Dielectric Environment on Emission Energy
As described in the main text, a number of potential factors can influence the luminescence energy of 1L-TMDs, including temperature 10,14 , local dielectric environment 15,16 and strain. 17,18 However, in the case of the data in Fig.1e, we attribute the variation observed to strain. We eliminate temperature as the beam parameters are fixed, hence this should result in a uniform temperature over the sample.
To assess the role of dielectric environment we note that sources of dielectric heterogeneities such as bubbles and contaminants have been shown to quench emission. 19 Therefore, were dielectric environment to be the dominant factor determining CL energy, regions with lower intensities would exhibit higher energies. 15,16 To check this, in Fig.S5, we plot a scatter of peak energies versus peak intensity. With this we observe no clear correlation between the peak energy and intensity, suggesting dielectric environment is not a significant factor dictating the emission energy. We believe this may be because fitting can only be performed in regions with sufficient intensity (> 2400 counts), which may eliminate regions with bubbles and contaminants from this analysis.

S8. Monte-Carlo Simulations
The Nebula Monte-Carlo software allows a number of electron cascades to be simulated 24 . Each cascade is independent. 24 Through a compiler switch, the generation of secondary electrons during the cascade can be turned on and off. With secondary electrons off, one only studies the path of primary or beam electrons (denoted with a superscript pri). With secondary electrons on, one also studies the generation of secondary electrons (denoted with superscript all).
A 1000 X 1000 X 10,000 nm (x, y, z) total sample size is used, with a virtual detector placed 10 nm above the sample, allowing any electrons that leave the sample surface to be counted. Ideal mirrors are placed on the sides of the simulation volume and a terminator placed at the bottom surface. The simulation volume was selected to be beyond the interaction volume of all beams simulated to avoid influencing results.
The backscattered electron coefficient is defined as the ratio of backscattered electrons to incident electrons. 25 To estimate this, we count the number of electrons detected whilst secondary electron generation is off and divide by the number of beam electrons , giving = / . The secondary electron coefficient is defined as the ratio of secondary electrons to incident electrons. 25 As, Nebula cannot discriminate between detection events from secondary or primary electrons 24 , to calculate the secondary electron coefficient , we take the number of detection events with secondary electrons turned on and subtract the number of detection events without , To obtain the depth profile of primary electrons we examine a cascade with no secondary electron generation. Some primary electrons will be backscattered and will hit the virtual detector. Therefore we ignore any electron collisions for electrons that are detected and create a histogram of the depths of the final collision event for undetected primary electrons.

S9. Estimation of Net Charge Deposited into vdW-HS through Monte-Carlo Simulations
To understand the deposition of electrons into vdW-HS in further detail, we consider the range of possible electron-sample interactions and how these may give rise to charging in samples. Fig.S7a shows a range of electron-sample interactions 26,27 . Per unit time, the net charge deposited in a sample under electron irradiation can be expressed by ′ = [1 − ( + )] [26][27][28] . The thickness of our vdW-HS is ~245 nm. This is of the same order or lower than the electron penetration. Since we only consider electrons deposited into our vdW-HS, we must account for this. To do so, we introduce the parameter , which represents the fraction of electrons deposited within the vdW-HS thickness. As secondary electron emission only takes place from the top few-nm 27

S11. CL Signal from hBN
CL emission also occurs from hBN. [35][36][37][38] In Fig.S10 a CL spectrum measured in regions with encapsulated WSe2 and encapsulated FLG. In these spectra we see weak luminescence between 300-700 nm which we attribute to defect emission from the hBN [36][37][38][39] . In the spectral range including WSe2 there is no background from the hBN.