Friday, May 19, 2017

What are "hot" electrons?

In basic chemistry or introductory quantum mechanics, you learn about the idea of energy levels for electrons.  If you throw a bunch of electrons into some system, you also learn about the ground state, the lowest energy state of the whole system, where the electrons fill up* the levels from the bottom up, in accord with the Pauli principle.   In statistical physics, there are often a whole lot of energy levels and a whole lot of electrons (like \(10^{22}\) per cc), so we have to talk about distribution functions, and how many electrons are in the levels with energies between \(E\) and \(E + dE\).   In thermal equilibrium (meaning our system of interest is free to exchange energy in the form of heat with some large reservoir described by a well-defined temperature \(T\)), the distribution of electrons as a function of energy is given by the Fermi-Dirac distribution.

So, what are "hot" electrons?  If we have a system driven out of equilibrium, it's possible to have the electrons arranged in a non-thermal (non-FD distribution!) way.  Two examples are of particular interest at the nanoscale.  In a transistor, say, or other nanoelectronic device, it is possible to apply a voltage across the system so that \(eV >> k_{\mathrm{B}}T\) and inject charge carriers at energies well above the thermally distributed population.  Often electron-electron scattering on the 10-100 fs timescale redistributes the energy across the electrons, restoring a thermal distribution at some higher effective temperature (and on longer timescales, that energy cascades down into the vibrations of the lattice).  Electrons in a metal like Au at the top of the distribution are typically moving at speeds of \(\sim 10^{6}\) m/s (!!), so that means that near where the current is injected, on distance scales like 10-100 nm, there can be "hot" electrons well above the FD distribution.  

The other key way to generate "hot" electrons is by optical absorption.  A visible photon (perhaps a green one with an energy \(\hbar \omega\) of 2 eV) can be absorbed by a metal or a semiconductor, and this can excite an electron at an energy \(\hbar \omega\) above the top of the FD distribution.  Often, on the 10-100 fs timescale, as above, that energy gets redistributed among many electrons, and then later into the lattice.  That's heating by optical absorption.  In recent years, there has been an enormous amount of interest in trying to capture and use those hot electrons or their energy before there is a chance for that energy go become converted to heat.  See here, for instance, for thoughts about solar energy harvesting, or here for a discussion of hot electron photochemistry.  Nanoscale systems are of great interest in this field for several reasons, including the essential fact that hot electrons generated in them can access the system surface or boundary in the crucial timespan before energy relaxation.

(Talking about this and thermoelectricity now sets the stage so I can talk about our recent paper in an upcoming post.)

*Really, the whole many-body electron wavefunction has to be antisymmetric under the exchange of any two electrons, so it's wrong to talk as if one particular electron is sitting in one particular state, but let's ignore that for now.  Also, in general, the energy levels of the many-electron system actually depend on the number and arrangement of the electrons in the system (correlation effects!), but let's ignore that, too.

Tuesday, May 16, 2017

More coming, soon.

I will be posting more soon.  I'm in the midst of finally shifting my group webpage to a more modern design.  In the meantime, if there are requests for particular topics, please put them in the comments and I'll see what I can do.

Update:  Victory.  After a battle with weird permissions issues associated with the way Rice does webhosting, it's up here:  natelson.web.rice.edu/group.html

Still a few things that should be updated and cleaned up (including my personal homepage), but the major work is done.

Tuesday, May 09, 2017

Brief items

Some interesting items of note:

  • Gil Refael at Cal Tech has a discussion going on the Institute for Quantum Information and Matter blog about the content of "modern physics" undergraduate courses.  The dilemma as usual is how to get exciting, genuinely modern physics developments into an already-packed undergrad curriculum.  
  • The variety and quality of 3d printed materials continues to grow and impress.  Last month a team of folks from Karlsruhe demonstrated very nice printing of (after some processing) fused silica.  Then last week I ran across this little toy.  I want one.  (Actually, I want to know how much they cost without getting on their sales engineer call list.)  We very recently acquired one of these at Rice for our shared equipment facility, thanks to generous support of the NSF MRI program.   There are reasons to be skeptical that additive manufacturing will scale in such a way as to have enormous impact, but it sure is cool and making impressive progress.
  • There is a news release about our latest paper that has been picked up by a few places, including the NSF's electronic newsletter.  I'll write more about that very soon.
  • The NSF and the SRC are having a joint program in "SemiSynBio", trying to work at the interface of semiconductor devices and synthetic biology to do information processing and storage.  That's some far out stuff for the SRC - they're usually pretty conservative.
  • Don Lincoln has won the AIP's 2017 Gemant Award for his work presenting science to the public - congratulations!  You have likely seen his videos put out by Fermilab - they're frequently featured on ZapperZ's blog

Friday, May 05, 2017

What is thermoelectricity?

I noticed I'd never written up anything about thermoelectricity, and while the wikipedia entry is rather good, it couldn't hurt to have another take on the concept.   Thermoelectricity is the mutual interaction of the flow of heat and the flow of charge - this includes creating a voltage gradient by applying a temperature gradient (the Seebeck Effect) and driving a heating or cooling thermal flow by pushing an electrical current (the Peltier Effect).  Recently there have been new generalizations, like using a temperature gradient to drive a net accumulation of electronic spin (the spin Seebeck effect).

First, the basic physics.  To grossly oversimplify, all other things being equal, particles tend to diffuse from hot locations to cold locations.  (This is not entirely obvious in generality, at least not to me, from our definitions of temperature or chemical potential, and clearly in some situations there are still research questions about this.  There is certainly a hand-waving argument that hotter particles, be they molecules in a gas or electrons in a solid, tend to have higher kinetic energies, and therefore tend to diffuse more rapidly.  That's basically the argument made here.)

Let's take a bar of a conductor and force there to be a temperature gradient across it.  The mobile charge carriers will tend to diffuse away from the hot end.  Moreover, there will be a net flux of lattice vibrations (phonons) away from the hot end.  Those phonons can also tend to scatter charge carriers - an effect called phonon drag.   For an isolated bar, though, there can't be any net current, so a voltage gradient develops such that the drift current balances out the diffusion tendency.  This is the Seebeck effect, and the Seebeck coefficient is the constant of proportionality between the temperature gradient and the voltage gradient.   If you hook up two materials with different (known) Seebeck coefficients as shown, you make a thermocouple and can use the thermoelectric voltage generated as thermometer.

Ignoring the phonon drag bit, the Seebeck coefficient depends on particular material properties - the sign of the charge carriers (thermoelectric measurements are one way to tell if your system is conducting via electrons or holes, leading to some dramatic effects in quantum dots), and the energy dependence of their conductivity (which has wrapped up in it the band structure of the material and extrinsic factors like the mean free path for scattering off impurities and boundaries).

Because of this dependence on extrinsic factors, it is possible to manipulate the Seebeck coefficient through nanoscale structuring or alteration of materials.  Using boundary scattering as a tuning parameter for the mean free path is enough to let you make thermocouples just by controlling the geometry of a single metal.  This has been pointed out here and here, and in our own group we have seen those effects here.   Hopefully I'll have time to write more on this later....

(By the way, as I write this, Amazon is having some kind of sale on my book, at $19 below publisher list price.  No idea why or how long that will last, but I thought I'd point it out.  I'll delete this text when that expires.)

Monday, April 24, 2017

Quantum conduction in bad metals, and jphys+

I've written previously about bad metals.  We recently published a result (also here) looking at what happens to conduction in an example of such a material at low temperatures, when quantum corrections to conduction (like these) should become increasingly important.   If you're interested, please take a look at a blog post I wrote about this that is appearing on jphys+, the very nice blogging and news/views site run by the Institute of Physics.

Sunday, April 23, 2017

Thoughts after the March for Science

About 10000 people turned out (according to the Houston Chronicle) for our local version of the March for Science.   Observations:

  • While there were some overtly partisan participants and signs, the overarching messages that came through were "We're all in this together!", "Science has made the world a better place, with much less disease and famine, a much higher standard of living for billions, and a greater understanding of the amazingness of the universe.", "Science does actually provide factual answers to properly formulated scientific questions", and "Facts are not opinions, and should feed into policy decisions, rather than policy positions altering what people claim are facts."
  • For a bunch of people often stereotyped as humorless, scientists had some pretty funny, creative signs.  A personal favorite:  "The last time scientists were silenced, Krypton exploded!"  One I saw online:  "I can't believe I have to march for facts."
  • Based on what I saw, it's hard for me to believe that this would have the negative backlash that some were worrying about before the event.  It simply wasn't done in a sufficiently controversial or antagonistic way.  Anyone who would have found the messages in the first point above to be offensive and polarizing likely already had negative perceptions of scientists, and (for good or ill) most of the population wasn't paying much attention anyway.
So what now?

  • Hopefully this will actually get more people who support the main messages above to engage, both with the larger community and with their political representatives.  
  • It would be great to see some more scientists and engineers actually run for office.  
  • It would also be great if more of the media would get on board with the concept that there really are facts.  Policy-making is complicated and must take into account many factors about which people can have legitimate disagreements, but that does not mean that every statement has two sides.  "Teach the controversy" is not a legitimate response to questions of testable fact.  In other words, Science is Real
  • Try to stay positive and keep the humor and creativity flowing.  We are never going to persuade a skeptical, very-busy-with-their-lives public if all we do is sound like doomsayers.

Thursday, April 20, 2017

Ready-to-peel semiconductors!

Every now and then there is an article that makes you sit up and say "Wow!"  

Epitaxy is the growth of crystalline material on top of a substrate with a matching (or very close to it) crystal structure.  For example, it is possible to grow InAs epitaxially on top of GaSb, or SiGe epitaxially on top of Si.  The idea is that the lattice of the underlying material guides the growth of the new layers of atoms, and if the lattice mismatch isn't too bad and the conditions are right, you can get extremely high quality growth (that is, with nearly perfect structure).  The ability to grow semiconductor films epitaxially has given us a ton of electronic devices that are everywhere around us, including light emitting diodes, diode lasers, photodiodes, high mobility transistors, etc.   Note that when you grow, say, AlGaAs epitaxially on a GaAs substrate, you end up with one big crystal, all covalently bonded.  You can't readily split off just the newly grown material mechanically.  If you did homoepitaxy, growing GaAs on GaAs, you likely would not even be able to figure out where the substrate ended and the overgrown film began.

In this paper (sorry about the Nature paywall - I couldn't find another source), a group from MIT has done something very interesting.  They have shown that a monolayer of graphene on top of a substrate does not screw up overgrowth of material that is epitaxially registered with the underlying substrate.  That is, if you have an atomically flat, clean GaAs substrate ("epiready"), and cover it with a single atomic layer of graphene, you can grow new GaAs on top of the graphene (!), and despite the intervening carbon atoms (with their own hexagonal lattice in the way), the overgrown GaAs will have registry (crystallographic alignment and orientation) with the underlying substrate.  Somehow the short-ranged potentials that guide the overgrowth are able to penetrate through the graphene.  Moreover, after you've done the overgrowth, you can actually peel off the epitaxial film (!!), since it's only weakly van der Waals bound to the graphene.  They demonstrate this with a variety of overgrown materials, including a III-V semiconductor stack that functions as a LED.  

I found this pretty amazing.  It suggests that there may be real opportunities for using layered van der Waals materials to grow new and unusual systems, perhaps helping with epitaxy even when lattice mismatch would otherwise be a problem.  I suspect the physics at work here (chemical interactions from the substrate "passing through" overlying graphene) is closely related to this work from several years ago.