Three-dimensional (3D) distributions of photoinduced fields at or beyond the nanometer scale are essential for understanding the full dimensional symmetry of molecular excited states governing internal phenomena in specially functionalized quantum dots (QDs) or molecules and complex molecular substances. The gradients of these 3D distributions, in the form of vector maps, are also crucial for analyzing and designing approach paths for optical trapping. Therefore, direct visualization of these photoinduced electric fields in individual materials is crucial for creating optical functions at the single-nanometer scale, surpassing the limitations of theoretical speculation or ensemble measurements. This is challenging due to sensitivity bottlenecks in current visualization technologies. This research demonstrates the visualization of photoinduced electric field distributions on composite QDs—designed as photocatalysts with special electronic and optical structures—at the single-nanometer scale using photoinduced force microscopy (PiFM). This is achieved through 3D mapping using PiFM, which observes the optical gradient force proportional to the gradient of the electric field intensity (Fgrad ∝ ∇|E|²). The 3D mapping reveals spatially inhomogeneous photoinduced interaction potential and force field vectors related to electric field intensity and field variations, respectively. The single-nanometer-scale visualization is made possible by conducting PiFM measurements under ultra-high vacuum (UHV).

Previous research has explored various techniques for high-resolution scanning near-field optical microscopy, including optical stethoscopy achieving λ/20 resolution, scanning interferometric apertureless microscopy reaching 10 angstrom resolution, and other methods described in Principles of Nano-optics. These studies provide a foundation for understanding the challenges and potential of nanoscale optical imaging. The development of plasmon-enhanced Raman scattering has allowed for chemical mapping of single molecules, and visualization of vibrational normal modes of single molecules with atomically confined light. Studies have also shown selection-rule breakdown in plasmon-induced electronic excitation of isolated single-walled carbon nanotubes and single-molecule strong coupling at room temperature in plasmonic nanocavities. Optical trapping of quantum dots based on gap-mode excitation of localized surface plasmons has also been demonstrated. Previous photoinduced force microscopy (PiFM) work has shown its potential for molecular resonance imaging. However, these techniques often suffer from limitations in sensitivity and resolution, particularly at the single-nanometer scale, motivating the need for the advancement presented in this paper.

The researchers employed a custom-built PiFM apparatus operating under ultra-high vacuum (<5.0 × 10⁻⁷ Pa) at room temperature. They used the frequency modulation atomic force microscopy (FM-AFM) mode, controlling tip-sample distance by monitoring cantilever resonance frequency shifts (Δf). A gold-coated silicon cantilever (OPUS 240AC-GG, Micromash) with a spring constant of ~2 N/m and a first resonance frequency of ~44.849 kHz was used. The driven amplitude (A₁) in FM-AFM was maintained at 10 nm. Imaging was performed in constant frequency feedback mode (Δf = 20 Hz) for Figures 1 and 2, and 3D mapping acquired a force curve at each pixel with feedback controlling the closest distance (z₀) at Δf = -28 Hz. Differences in z₀ were compensated to obtain images at the bottom plane (Figures 3d and 4e, f). The key innovation is the use of a heterodyne frequency modulation (heterodyne-FM) technique to address artifacts in PiFM signals stemming from laser modulation-induced photothermal vibrations of the cantilever and resonance frequency shifts. In this technique, laser intensity is modulated at 2f₁ + fm, where f₁ is the cantilever's resonance frequency and fm is selected from the phase-locked loop circuit's bandwidth for detecting resonance frequency shifts (Δf). Δf is also used for tip-sample distance control. The modulated signal (Δf(fm)) is measured using a lock-in amplifier, with the non-delayed lock-in X (LIX) component (Δf(fm)X) used for analysis. The high modulation frequency (2f₁ + fm) significantly different from f₁ avoids interference from photothermal vibrations, while the heterodyne-FM signal (f₁ + fm) shifts with the cantilever's resonance frequency, allowing accurate photoinduced force detection. Simultaneous imaging at multiple wavelengths (520 nm, 660 nm, and 785 nm) was achieved by selecting different modulation frequencies (fm) for each wavelength. Zn-Ag-In-S (ZAIS) quantum dots (QDs) with a dumbbell structure (nanoellipsoids at both ends of a nanorod) were used as samples. These QDs, synthesized using state-of-the-art chemical synthesis technology, exhibited enhanced photocatalytic activity due to their designed electronic level scheme (1.97 eV at the ends, 2.92 eV in the middle). Side illumination at a 70° incidence angle was used, with PiFM images normalized against Δf(fm)X on a thin gold film (~100 nm thick) to account for laser spot accuracy. The discrete dipole approximation (DDA) method was used for theoretical calculations to compare with experimental results. 3D photoinduced force mapping was performed by acquiring force curves (Δf(fm)Xz) in feedback mode, adjusting QD height based on simultaneous AFM images.

The study's key findings include: 1. **Successful 3D Visualization:** The researchers successfully visualized the 3D photoinduced interaction potential distribution and force field vectors around a single ZAIS QD for the first time. This visualization provides quantitative evaluation of localized optical phenomena related to photocatalyst activities and luminescence. 2. **High Spatial Resolution:** An unprecedented spatial resolution of approximately 0.7 nm was achieved, representing the highest spatial resolution for linear optical observations to date. This high resolution enabled the observation of fine structures within the ZAIS QDs, such as variations on the edges of the nanoellipsoids, potentially related to defects or crystal material formed during growth. 3. **Heterodyne-FM Technique Effectiveness:** The heterodyne-FM technique proved highly effective in eliminating photothermal effects, enhancing force sensitivity, resolution, and thermal stability. This technique's applicability extends beyond UHV to ambient and liquid conditions, opening opportunities in biology and chemistry. 4. **Validation through Theoretical Calculations:** The experimental results are well-supported by theoretical calculations using the discrete dipole approximation (DDA) method. The agreement between the experimental 3D maps and theoretical calculations strongly supports the successful synthesis of the QDs and the accuracy of the PiFM technique. 5. **Wavelength-dependent Forces:** Simultaneous PiFM imaging at multiple wavelengths (520 nm, 660 nm, and 785 nm) revealed wavelength-dependent photoinduced forces, further emphasizing the technique's ability to resolve nanoscale optical responses. The variations observed using different wavelengths highlight the distinct optical properties of the different parts of the dumbbell-shaped QD, validating the design of the electronic level scheme. 6. **Force Field Mapping:** 3D force field mapping revealed that the magnitudes of the photoinduced forces increase as the tip approaches the QD surface (Δz approaches 0 nm), with different attenuation lengths observed at different locations on the QD. The interaction potential (20-40 meV) is also mapped, reflecting the intensity of the electric field. 7. **Sub-Nanometer Resolution:** The achieved resolution of ~0.7 nm suggests the potential for visualizing the internal components of a single molecule using PiFM in the future.

The achievement of single-nanometer-scale 3D photoinduced force field visualization using PiFM represents a significant advancement in nanophotonics and related fields. The high spatial resolution achieved (0.7 nm) surpasses previous techniques and opens new avenues for understanding and manipulating light-matter interactions at the molecular level. The successful visualization of the 3D photoinduced interaction potential and force field vectors directly validates the designed electronic structure and targeted catalytic activity of the ZAIS QDs. The method's robustness, demonstrated by the agreement between experimental and theoretical results, establishes its reliability for studying localized optical phenomena. The applicability of the heterodyne-FM technique in various environments (UHV, ambient, liquid) broadens the scope of PiFM applications to include biological and chemical systems. The high sensitivity and resolution achieved pave the way for future studies involving the observation of optical responses within single molecules.

This study successfully demonstrated single-nanometer-scale 3D photoinduced force field visualization using a novel heterodyne-FM PiFM technique under UHV conditions. The achieved resolution of ~0.7 nm is the highest reported for linear optical near-field observations. The findings provide valuable insights into nanoscale light-matter interactions, advancing our understanding of photocatalytic processes and other nanoscale optical phenomena. Future research directions could focus on applying this technique at lower temperatures and using sharper tips to further enhance resolution and enable the observation of optical responses inside individual molecules. Exploring the application of the heterodyne-FM technique to biological and chemical systems would also be highly valuable.

While the study achieved remarkable resolution, several limitations should be noted. The ultra-high vacuum condition might limit the direct applicability to biological or liquid-phase systems, although the heterodyne-FM technique is potentially adaptable to such environments. The analysis relies on the discrete dipole approximation (DDA), which might have limitations in accurately modeling complex nanoscale systems. The current study focuses on a specific type of quantum dot; further studies would be needed to assess the generalizability of the findings to other nanoscale materials and systems. The computational resources required for the DDA method may also present a limitation for very large scale simulations.