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!

Brief items

Some science items that crossed my path that you may find interesting:

• This article at Quanta is a nice look at the Ising model for a general audience.  When I took graduate statistical mechanics from Lenny Susskind, he told the story of Lars Onsager just casually mentioning on the middle of a conference talk that Onsager had solved the 2D Ising model exactly.
• If you have any interest in the modern history of advanced transistors, the special FinFET ones that are now the mainstays of ultrascaled high performance processors, you might find this article to be fun.
• With all the talk about twisted bilayers of van der Waals materials for exotic electronic properties, it’s cool to see this paper, which looks at the various nonlinear optical processes that can be enabled in similar structures.  Broken structural symmetries are the key to allowing certain nonlinear processes, and the moire plus twist approach is quite the playground.
• This preprint is very cool, where the authors have made basically an interferometer in the fractional quantum Hall regime for electrons confined in 2D, and can show clean results that demonstrate nontrivial statistics.  The aspect of this that I think is hard for non-experimentalists to appreciate is how challenging it is to create a device like this that is so clean - the fractional quantum Hall states are delicate, and it is an art form to create devices to manipulate them without disorder or other problems swamping what you want to measure.

Coming at some point, a post or two about my own research.

A nation of immigrants

Real life has been intruding rudely on my blogging time.  I will try to step up, but nothing seems to be slowing down this summer.

I sense from the comments on my last post that there is some demand to talk about US immigration policy as it pertains to the scientific community (undergraduate and graduate students, postdocs, scholars, faculty members).  I've been doing what little I can to try to push back against what's going on.  I think the US has benefited enormously from being a training destination for many of the world's scientists and engineers - the positive returns to the country overall and the economy have been almost unquantifiably large.  Current policies seem to me to be completely self-defeating.  As I wrote over three years ago alluding to budget cuts (which thankfully Congress never implemented), there is hysteresis and an entropic component in policy-making.  It's depressingly easy to break things that can be very difficult to repair.  Using immigration policy to push away the world's scientists and engineers from the US is a terrible mistake that runs the risk of decades of long-term negative consequences.

The foil electret microphone

Pivoting back toward science by way of technology.... Some very large fraction of the microphones out there in electronic gadgets are based on electrets.  An electret is an insulating material with a locked-in electrical polarization - for example, take a molten or solvated polymer, embed highly polar molecules in there, and solidify in the presence of a large polarizing electric field.  The electrical polarization means that there is an effective surface charge density.  You can make that electret into a free-standing foil or a film coating a backing to make a diaphragm.  When that film vibrates, it will generate an oscillating voltage on a nearby electrode (which could, say, be the gate electrode of a field-effect transistor).  Voila - a microphone that is simple, readily manufacturable, and doesn't need an external power supply.  

While electret microphones are losing some marketshare to microelectromechanical ones in things like airpods, they've played a huge part in now ubiquitous phone and acoustic technologies in the late 20th and early 21st centuries.  When I was a postdoc I was fortunate one day to meet their coinventor, James West, who was still at Bell Labs, when (if I recall correctly) his summer student gave a presentation on some lead-free ultra-adhesive solder they were working on.  He was still patenting inventions within the last two years, in his late 80s - impressive!

Change is a depressingly long time in coming.

People don't read this blog for moralizing, and I surely don't have any particular standing, but staying silent out of concern for saying the wrong thing isn't tenable.  Black lives matter.  There is no more stark reminder of the depressingly long timescales for social progress than the long shadow cast by the US history of slavery.  I have to hope that together we can make lasting change - the scale of the outpouring in the last week has to be a positive sign.  The AAAS announced that on Wednesday June 10 they will be "observing #shutdownSTEM, listening to members of our community who are sharing resources and discussing ways to eliminate racism and make STEM more inclusive of Black people. www.shutdownstem.com. We encourage you to join us."  It's a start.

Non-academic careers and physics PhDs

With so many large-scale events happening right now (the pandemic, resulting economic displacement, the awful killing of George Floyd and resulting protests and unrest, federal moves regarding international students), it's hard not to feel like blogging is a comparatively self-indulgent activity.  Still, it is a way to try to restore a feeling of normalcy.  

The Pizza Perusing Physicist had asked, in this comment, if I could offer any guidance about non-academic careers for physics PhDs (including specific fields and career paths), beyond cliches about how PhD skills are valued by many employers.  I don't have any enormous font of wisdom on which to draw, but I do have a few points:

• I do strongly recommend reading A PhD is Not Enough.  It's a bit older now, but has good insights.
• It is interesting to look at statistics on where people actually land.  According to the AIP, about a half of physics PhDs take initial academic jobs (postdocs and others); a third go to the private sector; and 14% go to government positions.  Similarly, you can see the skills that recent PhDs say they use in their jobs.  
• I found it particularly interesting to read the comments from people ten years out from their degrees, since they have some greater perspective - seriously, check out that document.
• Those latter two AIP documents show why "PhD skills are valued by employers" has become cliched - it's true.
• In terms of non-academic career options for physics PhDs, there really are a wide variety, though like any career trajectory a great deal depends on the skills, flexibility, and foresight of the person.  Technical problem solving is a skill that a PhD should have learned - how to break big problems up into smaller ones, how to consider alternatives and come up with ways to test those, etc.  There is a often a blurry line between physics and some types of engineering, and it is not uncommon for physics doctorates to get jobs at companies that design and manufacture stuff - as a condensed matter person, I have known people who have gone to work at places like Intel, Motorola, Seagate, National Instruments, Keysight (formerly Agilent), Northrup Grumman, Lockheed, Boeing, etc.  It is true that it can be hard to get your foot in the door and even know what options are available.  I wish I had some silver bullet on this, but your best bets are research (into job openings), networking, and career fairs including at professional conferences.  Startups are also a possibility, though those come with their own risks.  Bear in mind that your detailed technical knowledge might not be what companies are looking for - I have seen experimentalist doctoral students go be very successful doing large-scale data analysis for oil services firms, for example.  Likewise, many people in the bioengineering and medical instrumentation fields have physics backgrounds.
• If academia isn't for you, start looking around on the side early on.  Get an idea of the choices and a feel for what interests you. 
• Make sure you're acquiring skills as well as getting your research done.  Learning how to program, how to manipulate and analyze large data sets, statistical methods - these are generally useful, even if the specific techniques evolve rapidly.
• Communication at all levels is a skill - work at it.  Get practice writing, from very short documents (summarize your research in 150 words so that a non-expert can get a sense of it) to papers to the thesis.  Being able to write and explain yourself is essential in any high level career.  Get practice speaking with comfort, from presentations to more informal 1-on-1 interactions.  Stage presence is a skill, meaning it can be learned.  
• Don't discount think tanks/analysis firms/patent firms - people who can tell the difference between reality and creative marketing language (whether about products or policies) are greatly valued.
• Similarly, don't discount public policy or public service.  The fraction of technically skilled people in elected office in the US is woefully small (while the chancellor of Germany has a PhD in quantum chemistry).  These days, governing and policy making would absolutely benefit from an infusion of people who actually know what technology is and how it works, and can tell the difference between an actual study and a press release.

I'm sure more things will occur to me after I publish this.  There is no one-size-fits-all answer, but that's probably a good thing.