Sub-diffraction-resolved spatial distribution of emitting excitons in STM-induced luminescence of 2D semiconductors via Richardson-Lucy deconvolution

TL;DR

This work tackles the diffraction-limited nature of STM-induced luminescence mappings by applying Richardson-Lucy deconvolution to real-space optical images, using a physics-based PSF derived from in-plane spin-bright exciton emission in monolayer TMDs. The method yields sub-diffraction spatial distributions of radiatively recombining excitons in WSe_2 and WS_2, revealing that emitter width broadens with tunnel current ($\sim$ $0.05$–$0.06~\mu$m per nA) and that distant hotspots arise from defect-assisted recombination rather than simple diffusion, with hotspots correlating to nanofolds. Convergence-aware RL deconvolution on upsampled data provides robust, high-resolution emitter maps that surpass the diffraction limit ($0.25~\mu$m at $\lambda_0=748$ nm, NA=1.49), offering a valuable tool to study exciton drift, diffusion, and defect interactions in 2D semiconductors and guiding the design of nanoscale optoelectronic devices. The approach is generalizable to other STM-enabled optical systems and can be used to probe field- and strain-induced modulation of exciton transport.

Abstract

Using scanning tunneling microscopy-induced luminescence (STML), the optical properties of two-dimensional (2D) semiconductors may be investigated at the nanoscale. This is possible because the tunneling current under the tip is an extremely localized electrical excitation source. However, in most STML applications, the spatial distribution of the emission relative to the excitation point is unresolved. Yet this distribution contains key information about how the interaction of excitons with injected charge carriers affects the luminescence of these materials, and about exciton transport. Resolving this spatial distribution at the nanoscale is relevant both for a fundamental understanding of exciton physics and for device applications; yet it remains a significant challenge. In this work, we resolve the spatial distribution of the emission beyond the diffraction limit of light by deconvolving real-space optical microscopy images of the STML using an iterative algorithm, i.e., Richardson-Lucy (RL) deconvolution. To showcase this technique, we apply it to the STML of monolayer tungsten diselenide ($\mathrm{WSe_2}$) and tungsten disulfide ($\mathrm{WS_2}$). Thus, we highlight hitherto ignored or misunderstood aspects of STML on 2D semiconductors related to exciton and charge carrier transport, namely the dependence of the spatial distribution of emission on the tunnel current setpoint and the origin of the emission from hot spots located micrometers from the excitation source.

Figures (4)

• Figure 1: (a) Schematic of the experiment: the sample is a WSe_2 flake on an ITO-coated glass coverslip, placed between the tungsten tip of an STM and a high-NA microscope objective. (b) Schematic of the local electrical excitation of excitons in monolayer WSe_2 using the tunneling current from the STM tip, and the diffusion of these excitons before they radiatively decay. (c) White-light transmission optical microscopy of the sample: a flake of monolayer (1L) WSe_2. (d) Optical microscopy image of the STM-induced luminescence (STML) of the same area as in (c): the STM tip is located at a fixed lateral position, i.e., where the bright spot is observed, and is in the tunneling regime (sample bias $V_\mathrm{s}=3.0$ V, current setpoint $I_\mathrm{t}=0.5$ nA). (e) Intensity profiles obtained from the image shown in (d) (black curve), a numerical simulation of the point spread function (PSF) (blue curve), the image deconvolved using the Richardson-Lucy algorithm (red curve) and fitted using a Gaussian function (dashed orange curve), and the 2D convolution of the deconvolved image with the PSF (dashed magenta curve) along the $\mathbf{x}$ axis. Inset: zoomed image of the area delineated by a dotted line in (d). (f) Same as in (e) along the $\mathbf{y}$ axis. (g) Zoomed images of (from left to right) the STML data, the simulated PSF, the deconvolved image, and the 2D convolution of the latter with the PSF, using two different versions of the Richardson-Lucy algorithm (see Methods). In (g), the native pixel sampling of the STML image is used. (h) Same as (g), where a $10\times$ upsampled version of the STML image is used.
• Figure 2: Effect of the tunneling current on the spatial distribution of emitters in STML experiments on monolayer WSe_2. The full width at half maximum (FWHM) of this distribution is determined by fitting Gaussian intensity profiles to deconvolved optical microscopy images of STML measured for various current setpoints on the same sample area. The obtained FWHM is plotted as a function of the current setpoint. Intensity profiles obtained from the same deconvolved images along the $\mathbf{x}$ and $\mathbf{y}$ axes are considered in (a) and (b), respectively. Two different versions of the Richardson-Lucy deconvolution algorithm are compared. In the first script (black squares) 2D convolution between object and PSF is computed at each iteration, while in the second script (red dots) this operation is replaced by the product of object and PSF Fourier transforms (see Methods). The dashed lines are linear fits of the data. Sample bias is $2.8$ V for all data.
• Figure 3: (a) White-light transmission and (b) wide-field PL microscopy images of the sample: a flake of WS_2 exhibiting monolayer (1L) and multilayer areas. (c) to (e) Raw-data optical microscopy images of the STML measured on the same area as in (a) and (b). The lateral position of the STM tip is the same in (c) to (e). STM parameters: (c) $V_\mathrm{s}=2.0$ V, $I_\mathrm{t}=1$ nA; (d) $V_\mathrm{s}=4.0$ V, $I_\mathrm{t}=2$ nA. Acquisition time is $150$ s for both (c) and (d). For comparison purposes, the data is plotted on the same intensity scale in (c) and (d), yielding a saturated image in (d). The unsaturated image shown in (e) is the same data as in (d), plotted on a ($24$ times) larger intensity scale. (f) Overlay of the (grayscale) PL image shown in (b) and the STML data shown in (e). (g) Schematic of the local injection of electrons in monolayer WS_2 from the STM tip and their diffusion before they radiatively recombine with defect-trapped holes at flake folds or edges. (h) to (k) Images based on the same data as (c) to (f), respectively, except that the data are deconvolved using the Richardson-Lucy algorithm (script 2) on $10\times$ upsampled data. Moreover, a smaller area is considered in (h) to (k) as compared to (c) to (f), corresponding to the area delineated by a dotted square in images (c) to (f). In (h), a zoom of the STML spot is shown.
• Figure 4: (a) Optical microscopy image of STML measured on monolayer WS_2, deconvolved using Richardson-Lucy algorithm on $10\times$ upsampled data [same data as in Fig. \ref{['FIG-3']}(j)]. (b) to (d) Intensity profiles obtained along the dotted lines in the deconvolved image shown in (a) (red lines) and in the corresponding raw (not deconvolved, not upsampled) image shown in Fig. \ref{['FIG-3']}(e) (black lines). The FWHM values shown in (b) to (d) are obtained from a 1D Gaussian fit of the presented profiles and are given to an accuracy of $0.005~\mu$m.