Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams

Abstract

Imaging charge, spin, and energy flow in materials is a current grand challenge that is relevant to a host of nanoenhanced systems, including thermoelectric, photovoltaic, electronic, and spin devices. Ultrafast coherent x-ray sources enable functional imaging on nanometer length and femtosecond timescales particularly when combined with advances in coherent imaging techniques. Here, we combine ptychographic coherent diffractive imaging with an extreme ultraviolet high harmonic light source to directly visualize the complex thermal and acoustic response of an individual nanoscale antenna after impulsive heating by a femtosecond laser. We directly image the deformations induced in both the nickel tapered nanoantenna and the silicon substrate and see the lowest-order generalized Lamb wave that is partially confined to a uniform nanoantenna. The resolution achieved-sub-100 nm transverse and 0.5-Å axial spatial resolution, combined with ≈10-fs temporal resolution-represents a significant advance in full-field dynamic imaging capabilities. The tapered nanoantenna is sufficiently complex that a full simulation of the dynamic response would require enormous computational power. We therefore use our data to benchmark approximate models and achieve excellent agreement between theory and experiment. In the future, this work will enable three-dimensional functional imaging of opaque materials and nanostructures that are sufficiently complex that their functional properties cannot be predicted.

Fig. 1. Stroboscopic CDI microscope illuminated by 28.9-nm light from HHG.

(A) Experimental layout. Dynamics are launched in a nickel tapered nanoantenna by an IR pump beam and are measured by an EUV probe beam. EUV light scattered from the sample is collected on an EUV-sensitive CCD. (B) Reconstructed, quantitative amplitude image. Scale bar, 5 μm. (C) Height map of the sample, obtained from the reconstructed phase image. Scale bars, 5 μm × 5 μm × 0.5 nm. The circular feature on the right in (B) and (C) is another nanostructure that is not investigated here.

Fig. 2. Dynamic imaging of acoustic waves in an individual nanostructure.

(A) Complex histogram analysis of the reconstructed image at t = −35 ps plotted on a nonlinear scale. Features can be masked to selectively probe dynamics of the nickel feature and of the silicon substrate. (B) Feature mask. (C) Substrate mask: Note that the substrate mask excludes the circular nanostructure shown in Fig. 1 (B and C). (D to I) Reconstructed snapshots of the nickel nanostructure thermal expansion and subsequent propagation of acoustic waves in the substrate. All 2D+1 reconstructions are plotted on the same color scale. The scale bars indicated in (D) are 5 μm × 5 μm × 0.5 nm and are common to (D) to (I). An offset of 1 nm has been added to the nanostructure feature only, for visualization purposes. Insets: Dynamic histogram analysis. All histograms are plotted on the same color scale. Transient changes in the complex histogram are available in a stroboscopic movie in the Supplementary Materials. a.u., arbitrary units.

Fig. 3. Time-resolved EUV diffraction from an individual nanostructure compared to simulations.

(A) Amplitude reconstruction of the nickel tapered nanoantenna on the silicon substrate multiplied by the reconstructed EUV beam (28.9 nm) at the sample. (B) Experimental diffraction pattern. (C) Simulation of the nickel nanoantenna on the silicon substrate, including the EUV illumination beam, which reflects more strongly from nickel than silicon. (D) Simulated diffraction pattern from the cross section of the nanostructure marked with the red dashed line in (C). (E) Transient diffraction efficiency into the marked diffracted orders (white dashed circles), relative to the undiffracted light (zero order) as a function of time, compared to the light diffracted from the unexcited sample. The experimental signal (red solid line) was smoothed over 11 time steps for clarity and is compared to the results obtained from the simulation (gray solid line). Error bars are derived from the standard deviation of the unsmoothed experimental data. (F to I) Snapshots of the simulation at four time delays (50, 200, 400, and 600 ps after laser-driven excitation), showing the thermal response and subsequent propagation of acoustic waves on the nickel nanostructure and also in the silicon substrate. These snapshots of the lineout correspond to the planes indicated in Fig. 4D, and they have been exaggerated by a factor of 250 in the vertical direction for clarity.

Fig. 4. Acoustic wave dispersion in an individual uniform nanoantenna.

(A) Reconstructed amplitude image of the uniform nickel nanoantenna multiplied by the reconstructed probe. The red dashed line indicates the 2.2-μm cross section considered for the nanoline simulation. (B) Experimental diffraction pattern from the uniform nanoantenna indicating the undiffracted light (0) and the diffracted orders (1 to 5). (C) Simulation of a 2.2-μm cross section of the nickel nanoline as a function of time. Lineouts of the simulation at various time delays are shown in Fig. 3 (F to I). (D) The dispersion of the acoustic waves can be calculated from the time-dependent simulation by Fourier transforming—in both time and space—the vertical surface displacement over the nanoline. The dispersion of the lowest-order generalized Lamb wave was also calculated via modal analysis of the nanoline (black dashed curve) and is in agreement with the experimental dispersion relation from the uniform nanoantenna (blue dots), which has a slope of 2790 ± 240 m/s. (E and F) Transient diffraction efficiencies relative to the light diffracted from the unexcited sample (E) and corresponding Fourier components (F) for each diffraction order obtained from the analysis of the uniform nanoantenna diffraction pattern.