## Saturday, October 08, 2022

### Getting light out of plasmonic tunnel junctions - the sequel

A couple of years ago I wrote about our work on "above threshold" light emission in planar metal tunnel junctions.  In that work, we showed that in a planar tunnel junction, you can apply a bias voltage $V$ and get lots of photons out at energies quite a bit greater than $\hbar \omega = eV$.  In the high current regime when there are strong local plasmon resonances, it is possible to drive (steady state) some part of the electronic distribution to very high effective electron temperatures, and then observe radiation from the recombination of those hot carriers.  One neat thing about this is that by analyzing the spectra, it is possible to back out the actual plasmon-modified density of photonic states for emission to the far-field, $\rho(\hbar \omega)$ of a particular junction.

In our new paper published this week, we have been able to take this quite a bit further.  In the low current regime with weaker local plasmon resonances, the energy deposited by tunneling electrons is able to diffuse away rapidly compared to the arrival of more carriers, so that kind of carrier heating above isn't important.  Instead, it's been known for a while that the right way to think about light emission in that case is as a process connected to fluctuations (shot noise) in the tunneling current, as demonstrated very prettily here.  Within that mechanism, it should be possible to predict with precision what the actual emission spectrum should look like, given the tunneling conductance, the bias voltage, and $\rho(\hbar \omega)$.  As shown in the figure, we can now test this, and it works very well.  Take a planar aluminum tunnel junction made by electromigration, and in the high conductance/high current limit, use the hot carrier emission to determine $\rho(\hbar \omega)$.  Then gently migrate the junction further to lower the conductance and fall out of the hot carrier emission regime.  Using the measured conductance and the previously found $\rho(\hbar \omega)$, the theory (dashed lines in the right panel) agrees extremely well with the measured spectra (colored data points) with only two adjustable parameters (an overall prefactor, and a slightly elevated electronic temperature that gets the rounding of the emission at the $eV$ cutoff, indicated by the arrows in the right panel).

I think this agreement is pretty darn impressive.  It confirms that we have a quantitative understanding of how shot noise (due to the discreteness of charge!) affects light emission processes all the way up to optical frequencies.

Anonymous said...

Very cool! Could you realistically get EUV photons out of an aluminum junction? I think the plasma frequency of aluminum was above 12V if I'm not mistaken. Though it seems maybe the surface plasmon polariton frequency is more relevant here?

Douglas Natelson said...

Anon@2:20, one reason we started playing with Al junctions was to see how far into the blue we could push the luminescence. The big limitation really seems to be the vulnerability of Al to electromigration. In our configuration it just doesn't seem possible to get the junctions to be stable up at biases of, e.g., 2.5 V and the currents where you might to see blue to UV emission. At those current densities and field conditions, the atoms move around and lower the conductance.

Anonymous said...

I guess cooling to low temp also doesn't help with electromigration in this case because of the large Joule heating?

Douglas Natelson said...

Anon@11:33, yep. Aluminum is so easy to push around (hence one reason the chip industry switched to copper for interconnects) that even cooling the substrate to 5 K doesn't help if the current density is sufficiently high.