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

Abstract

The ultrafast response of metals to light is governed by intriguing nonequilibrium dynamics involving the interplay of excited electrons and phonons. The coupling between them leads to nonlinear diffusion behavior on ultrashort time scales. Here, we use scanning ultrafast thermomodulation microscopy to image the spatiotemporal hot-electron diffusion in thin gold films. By tracking local transient reflectivity with 20-nm spatial precision and 0.25-ps temporal resolution, we reveal two distinct diffusion regimes: an initial rapid diffusion during the first few picoseconds, followed by about 100-fold slower diffusion at longer times. We find a slower initial diffusion than previously predicted for purely electronic diffusion. We develop a comprehensive three-dimensional model based on a two-temperature model and evaluation of the thermo-optical response, taking into account the delaying effect of electron-phonon coupling. Our simulations describe well the observed diffusion dynamics and let us identify the two diffusion regimes as hot-electron and phonon-limited thermal diffusion, respectively.

Heat Transport without Heating?—An Ultrafast X‐Ray Perspective into a Metal Heterostructure

“…This text-book model was recently applied to model the in-plane heat transport in a nanometric metal film. [35] The thermophysical parameters used in our modeling are listed in Table 1. For an incident excitation fluence of 20 mJ cm −2 we obtain the spatio-temporal temperature maps T e/ph (z, t) of the electron and phonon systems shown in Figure 2.…”

Selective excitation of individual nanoantennas by pure spectral phase control in the ultrafast coherent regime

“…The first photon in this picture creates a nonequilibrium situation (hot electrons) that has to decay to the thermal equilibrium. Typical internal thermalization times of the hot electron gas in noble metals were determined to be in the range of 350 fs-3 ps [42][43][44]. Biagioni et al [19] reported on crystalline gold gap-antennas, while we study amorphous gold nanorod antennas, which will explain our shorter value of T 1 .…”

Ultrafast Dynamics of Optically Induced Heat Gratings in Metals

“…Specifically, the phonon diffusion does not change the dynamics described above (indeed, it is a much weaker effect compared with the electron-induced phonon diffusion); there is no sensitivity to the pump duration nor to the metal layer thickness. Indeed, previous studies (e.g., [35,24,26] showed that accounting for the finite thickness accounts only to modest quantitative changes in the temperature dynamics.…”

“…However, it is clear that a proper model for ballistic transport has to be derived from the Boltzmann equation, something that to the best of our knowledge, was not done so far. Experimentally, there have been some studies of vertical heat transport based on a configuration in which the pump and probe are incident on opposing interfaces of a metal film (see [27,28]), however, for lateral heat transport, there has been no evidence for ballistic diffusion even when using 10 femtosecond temporal resolution, see [26]. Convincing models and measurements of heat transport in this regime will also be useful for resolving arguments regarding charge transfer on the femtosecond scale which are relevant for non-thermal (the so called "hot") electron studies, and their application for photocatalysis and photodetection [4,5,52] and should eventually be combined with models of additional transport effects associated with interband transitions (see e.g., [53,54]).…”

“…(c) Peculiarly, the later stages of the dynamics reveal that the rapid grating contrast slows down significantly. Additional numerical simulations of the complete eTTM (not shown) show that the diffusion proceeds at the phonon diffusion rate [35,26]; c;early, this occurs due to the coupling the of the electrons to the phonons (the grating erasure is indeed complete if the electrons are artificially decoupled from the phonons (not shown)). Within the few picosecond range, the residual contrast is 1%, specifically, it is a few degrees for the local case but, as one might expect, it is much lower, a fraction of a degree, in the non-local case; naturally, the contrast decreases for a stronger electron thermal conductivity.…”