## Tuesday, June 30, 2020

### How do hot electrons get hot?

We have a paper that came out today that was very fun.  It's been known for a long time that if you apply a sufficiently large voltage $V$ to a tunnel junction, it is possible to get light emission, as I discussed here a bit over a year ago, and as is shown at the right.  Conventionally, the energy of the emitted photons $\hbar \omega$ is less than $eV$ (give or take the thermal energy scale $k_{\mathrm{B}}T$ ) if the idea is that single-electron processes are all that can happen.

In this new paper looking at planar metal tunnel junctions, we see several neat things:
• The emitted spectra look like thermal radiation with some effective temperature for the electrons and holes $T_{\mathrm{eff}}$, emitted into a device-specific spectral shape and polarization (the density of states for photons doesn't look like that of free space, because the plasmon resonances in the metal modify the emission, an optical antenna effect).    Once the effective temperature is taken into account, the raw spectra (left) all collapse onto a single shape for a given device.
• That temperature $T_{\mathrm{eff}}$ depends linearly on the applied voltage, when looking at a whole big ensemble of devices.  This is different than what others have previously seen.  That temperature, describing a steady-state nonequilibrium tail of the electronic distribution local to the nanoscale gap, can be really high, 2000 K, much higher than that experienced by the atoms in the lattice.
• In a material with really good plasmonic properties, it is possible to have almost all of the emitted light come out at energies larger than $eV$ (as in the spectra above).  That doesn't mean we're breaking conservation of energy, but it does mean that the emission process is a multi-electron one.  Basically, at comparatively high currents, a new hot carrier is generated before the energy from the last (or last few) hot carriers has had a chance to leave the vicinity (either by carrier diffusion or dumping energy to the lattice).
• We find that the plasmonic properties matter immensely, with the number of photons out per tunneling electron being 10000$\times$ larger for pure Au (a good plasmonic material) than for Pd (a poor plasmonic material in this enegy range).
That last point is a major clue.  As we discuss in the paper, we think this implies that plasmons don't just couple the light out efficiently.  Rather, the plasmons also play a key role in generating the hot nonequilibrium carriers themselves.   The idea is that tunneling carriers don't just fly through - they can excite local plasmon modes most of which almost immediately decay into hot electron/hole excitations with energies up to $eV$ away from the Fermi level.  Hot carriers are potentially useful for a lot of things, including chemistry.  I'm also interested in whether some fun quantum optical effects can take place in these extreme nanoscale light sources.  Lots to do!

Don Monroe said...

Very cool. The plots are compelling.

Still, it is a little surprising that the energy is distributed in the electrons so effectively. Even if there is a bottleneck for dumping their energy locally, I might have thought they would transport away before equilibrating.

Usually I think of that as involving inelastic electron-electron scattering, which also gives temperatures above the driving voltage in semiconductor devices. I'm finding it hard to think about how the plasmons accomplish this.

Douglas Natelson said...

Hi Don, I hope you and Alice are well in these chaotic times. I think it's all a question of relative timescales. The farther from the Fermi energy, the faster the relaxation time for e-e scattering, so apparently it's possible to reach some local quasi-thermal Boltzmann-like distribution (as seen in the graphs in the paper) even though carriers are both diffusing away from the junction and, on longer timescale, dumping energy into the lattice. Plugging in some rough numbers (I don't know if the LaTeX formatting is going to work here), if the diffusion constant for the carriers in the polycrystalline gold is around 1e-3 m^2/s (not a crazy value for disordered gold near a surface or tip, implying an elastic mfp of a few nm), then in 100 fs the carriers only diffuse around 10 nm.

I'm also going to edit the post to highlight a couple of other points.

Anonymous said...

Somewhat related is this really quite interesting work directly showing energy transfer from DC current to plasmon/THz frequencies

Stephane Boubanga-Tombet, et al. Phys. Rev. X 10, 031004 (2020)
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.031004

Douglas Natelson said...

Anon@2:24, that's very cute - thanks!

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