Research ArticlePHYSICS

Tracking ultrafast hot-electron diffusion in space and time by ultrafast thermomodulation microscopy

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Science Advances  10 May 2019:
Vol. 5, no. 5, eaav8965
DOI: 10.1126/sciadv.aav8965
  • Fig. 1 Schematic description of scanning ultrafast thermomodulation microscopy.

    (A) The energy distribution of the conduction band electrons at ambient temperature is perturbed by optical excitation. It quickly evolves to a quasi-thermalized “hot-electron” Fermi-Dirac distribution with high electron temperature (Te), while the lattice temperature (Tl) stays close to the ambient level. Subsequent cooling due to electron-phonon coupling and hot-carrier diffusion leads to thermal equilibrium between the electron and lattice subsystems. (B) An optical pump pulse illuminates a 50-nm thin gold film, thus inducing a local hot-electron distribution. The probe pulse measures the temperature-dependent transient reflectivity (ΔR/R) as a function of both pump-probe time delay and pump-probe spatial offset. (C) We monitor the spatiotemporal evolution of the photoinduced ΔR/R spot size with 20-nm accuracy and 250-fs resolution to visualize and distinguish hot-electron diffusion and thermal (phonon-limited) diffusion.

  • Fig. 2 Hot-electron dynamics.

    (A) Scanning ultrafast thermomodulation images of the gold film recorded by spatially scanning the probe beam (λprobe = 900 nm) relative to a fixed pump beam position (λpump = 450 nm, centered at x = y = 0 in the image) for selected pump-probe delays. (B) Transient reflectivity dynamics for collinear pump and probe pulses, exhibiting two distinct exponential decay contributions with time constants of 1 ps and 0.9 ns, respectively. An offset at Δt < 0 has been subtracted from the data. (C) Spatial profiles (dots) and Gaussian fits (curves) for three selected pump-probe delays, extracted from (A) by cutting horizontal lines through the center of the spots (y = 0).

  • Fig. 3 Two-step diffusion dynamics.

    (A) Spatiotemporal dynamics of the transient reflection signal ΔR/R. We scan the probe beam over the pump beam (1D scan across spot center, vertical axis) as a function of pump-probe delay (horizontal axis) at a pump fluence of 1.0 mJ/cm2. The offset at Δt < 0 has been subtracted from the data. (B) Squared-width evolution of the ΔR/R profile, extracted by Gaussian fitting to the spatial profile at each pump-probe delay (symbols). The error bars show the 68% confidence intervals of the Gaussian fits. We extract the initial and final diffusion coefficients by fitting slopes in the two regions (dashed lines) and comparing to Eq. 1. We find fast diffusion of Dfast = 95 cm2/s within the first few picoseconds, followed by slower diffusion (Dslow = 1.1 cm2/s) after >5 ps. The inset shows the extracted diffusion coefficients for pump fluences in the range of 0.3 to 1.6 mJ/cm2, along with the ratio of electron thermal conductivity ke and electron (lattice) heat capacity Ce (Cl).

  • Fig. 4 Theoretical modeling and identification of different diffusion regimes.

    (A) We simulate the spatiotemporal evolution of the optically excited gold film with a full 3D-space two-temperature model. We obtain the temperature-dependent complex permittivity from the calculated spatiotemporal electron and lattice temperature maps, including the thermal dependence of electron-electron and electron-phonon scattering, as well as thermal expansion of the lattice. We then calculate ΔR/R(x,yt) using the thin-film Fresnel equations and extract its spatial dynamics using the same Gaussian fitting as in the experimental data analysis. (B) Predicted temporal evolution of the electron (top) and lattice (bottom) temperatures at the beam center for the three pump fluences used in the experiment. (C) Theoretical (curves) and experimental (symbols) evolution of the squared width of ΔR/R for different pump fluences F (top). In accordance with Fig. 3B, we identify a fast diffusion regime at high electron temperatures, within the first few picoseconds, followed by a thermalized regime (>5 ps) dominated by phonon-limited transport, with orders-of-magnitude lower diffusivity. The initial slope for a diffusivity of D = ke/Ce is shown for comparison. Bottom: Difference Δ between the data and the full model calculation.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaav8965/DC1

    Note S1. General diffusion model

    Note S2. Two-temperature model

    Note S3. Thermo-optical response

    Note S4. Calculation of the transient reflectivity

    Fig. S1. Long-time dynamics of ΔR/R.

    Fig. S2. Scheme of thermo-optical calculations.

    Fig. S3. Schematic of the SUTM setup.

    Fig. S4. Different contributions to the thermo-optical response.

    References (4557)

  • Supplementary Materials

    This PDF file includes:

    • Note S1. General diffusion model
    • Note S2. Two-temperature model
    • Note S3. Thermo-optical response
    • Note S4. Calculation of the transient reflectivity
    • Fig. S1. Long-time dynamics of ΔR/R.
    • Fig. S2. Scheme of thermo-optical calculations.
    • Fig. S3. Schematic of the SUTM setup.
    • Fig. S4. Different contributions to the thermo-optical response.
    • References (4557)

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