Wednesday, June 30, 2010
Lies, damned lies, and lying statistics
This is not physics, but it is interesting. According to fivethirtyeight.com (a blog run by Nate Silver that specializes in statistical analysis of political polls), a major polling firm is being sued for fraud by liberal blog DailyKos. The grounds for the suit: this report, which details a number of statistical anomalies suggesting that the polling firm was either cooking their numbers, or outright making them up. Bonus: one of the guys who did this analysis is Mike Weissman, a condensed matter physicist who retired from UIUC. Weissman is an expert on noise measurements, author of this highly cited review article. He's a guy who knows statistics.
Sunday, June 27, 2010
Excitons
A reader emailed me and asked if I had done a posting about excitons. Looking back, I see that I haven't, so here is an attempt to rectify the situation. As I've written previously, condensed matter physicists are fond of giving specific names to excitations of solid state systems when those excitations have well-defined quantum numbers (and are in that sense "particle-like"). An exciton comprises an electron and a "hole" bound together by the attractive Coulomb interaction (since an electron has charge -e and a hole has charge +e). It is the (negative!) binding energy of the exciton that makes it different than a generic "electron-hole" excitation in which an electron is kicked out of an occupied state (leaving behind a hole) and into a previously empty state.
Excitons can exhibit very rich physics. In a 3d crystalline system, excitons can be very analogous to hydrogen-like atoms, or more accurately, positronium, the bound state of an electron and a positron. One can think of the electron and hole as having center-of-mass momentum, and having an exciton wavefunction that describes the relative displacement of the electron and hole, which would look like a hydrogenic orbital (s-like, p-like, etc.). Like positronium, the electron and hole can annihilate each other and emit a photon. Several important features crop up, however, due to the fact that the exciton exists within a solid host. For example, one cannot ignore the screening of the electron-hole Coulomb interaction by the surrounding host. One approximation commonly shown in textbooks is to treat this screening by using the bulk (relative) dielectric constant of the host material when solving for the exciton wavefunctions. As a result, the exciton is much larger, spatially, than positronium - say 5 nm in extent rather than 0.5 nm. (Note that this had better be true! Otherwise the assumption that the bulk material can screen the interaction would not be internally consistent....) Large excitons like this are called Wannier excitons. In contrast, if the screening is relatively weak, the exciton can be small compared to a unit cell of the crystal. Such a small exciton is called a Frenkel exciton.
Furthermore, the electron and hole parts of the exciton wavefunction are really "built" out of the Bloch wave electronic states of the solid. In a semiconductor, the hole states "live" in the valence band, while the electron states live in the conduction band. Hole states often exhibit stronger spin-orbit effects, and as a result, confinement can affect the exciton energy levels quite strongly.
Excitons may be produced by the absorption of light of appropriate energy, and therefore are of intense interest in photovoltaic research. The comparatively strong screening in traditional semiconductors that gives large exciton spatial sizes also leads to modified binding energies. Wannier exciton binding energies in materials like silicon can be on the order of 10 meV (as opposed to electron volts for positronium!). In materials with weaker screening (with Frenkel-like excitons), the exciton binding energy can be higher, more like hundreds of meV. These binding energies are of critical importance. In a silicon pn junction, for example, the built-in electric field due to the junction is large enough to rip apart any light-produced excitons - that's how charge separation happens in a silicon solar cell. In organic semiconductors, in contrast, the binding energies are stronger, and built-in fields are too weak to take apart excitons. Thus, there are no homojunction organic solar cells, and this is one of a number of reasons why organic photovoltaics is challenging.
Excitons can exhibit very rich physics. In a 3d crystalline system, excitons can be very analogous to hydrogen-like atoms, or more accurately, positronium, the bound state of an electron and a positron. One can think of the electron and hole as having center-of-mass momentum, and having an exciton wavefunction that describes the relative displacement of the electron and hole, which would look like a hydrogenic orbital (s-like, p-like, etc.). Like positronium, the electron and hole can annihilate each other and emit a photon. Several important features crop up, however, due to the fact that the exciton exists within a solid host. For example, one cannot ignore the screening of the electron-hole Coulomb interaction by the surrounding host. One approximation commonly shown in textbooks is to treat this screening by using the bulk (relative) dielectric constant of the host material when solving for the exciton wavefunctions. As a result, the exciton is much larger, spatially, than positronium - say 5 nm in extent rather than 0.5 nm. (Note that this had better be true! Otherwise the assumption that the bulk material can screen the interaction would not be internally consistent....) Large excitons like this are called Wannier excitons. In contrast, if the screening is relatively weak, the exciton can be small compared to a unit cell of the crystal. Such a small exciton is called a Frenkel exciton.
Furthermore, the electron and hole parts of the exciton wavefunction are really "built" out of the Bloch wave electronic states of the solid. In a semiconductor, the hole states "live" in the valence band, while the electron states live in the conduction band. Hole states often exhibit stronger spin-orbit effects, and as a result, confinement can affect the exciton energy levels quite strongly.
Excitons may be produced by the absorption of light of appropriate energy, and therefore are of intense interest in photovoltaic research. The comparatively strong screening in traditional semiconductors that gives large exciton spatial sizes also leads to modified binding energies. Wannier exciton binding energies in materials like silicon can be on the order of 10 meV (as opposed to electron volts for positronium!). In materials with weaker screening (with Frenkel-like excitons), the exciton binding energy can be higher, more like hundreds of meV. These binding energies are of critical importance. In a silicon pn junction, for example, the built-in electric field due to the junction is large enough to rip apart any light-produced excitons - that's how charge separation happens in a silicon solar cell. In organic semiconductors, in contrast, the binding energies are stronger, and built-in fields are too weak to take apart excitons. Thus, there are no homojunction organic solar cells, and this is one of a number of reasons why organic photovoltaics is challenging.
Wednesday, June 23, 2010
Travel + interesting review article
I'm traveling this week, so blogging is thin. I did want to point out an interesting review article from the arviv: arxiv:1006.3736, Force-detected nuclear magnetic resonance: Recent advances and future challenges, Poggio and Degen. This article take a look at the progress over the years in this micro mechanical approach to incredibly sensitive spin measurements.
Monday, June 14, 2010
Kavli Prizes for Nanoscience
This post is a bit late, but real life has been busy recently. The Kavli Foundation recently announced their 2010 Kavli Prize for Nanoscience, which they awarded to Don Eigler and Nadrian Seeman, for "their development of unprecedented methods to control matter on the nanoscale". As in their previous 2008 award to Louis Brus and Sumio Iijima, this prize is richly deserved by the awardees.
Don Eigler ran the scanning tunneling microscopy (STM) research group at IBM Almaden, where he and co-workers constructed incredibly stable STMs that functioned in ultrahigh vacuum and at low temperatures. With the resulting stability and surface cleanliness, Eigler et al. were able to demonstrate manipulation of matter on the atomic scale, giving us several of the most iconic images in nanoscience. Eigler's intellectual progeny have gone on to many faculty positions and trained generations of practitioners in the art and science of working at the atomic scale.
Nadrian Seeman had the foresight to realize what an incredible toolkit nature has provided for us in the form of DNA. While most people are familiar with double-helix structure of DNA, Seeman and co-workers developed techniques to make nanoscale DNA building blocks that can assemble into complex, three-dimensional structures. This is DNA as a construction tool rather than DNA as a carrier of genetic information. Who knows what the end result will be of this capability - I have been very impressed by some related work.
Thursday, June 10, 2010
Nanomechanical mass sensing in fluid
The idea of using mechanical resonators as mass sensors is an old one, and one that may be explained to a first-year physics undergrad. The (angular) frequency of a mass on a simple Hooke's Law spring is (k/m)0.5, where k is the spring constant. Change the mass, and the resonant frequency changes. With the development of micromachining techniques, there has been a great deal of interest in using tiny, high frequency resonators (e.g., doubly clamped Si beams) as mass sensors. One can have a metal wire along the resonator, and in the presence of a dc magnetic field perpendicular to the wire, an ac current may be used to apply a driving force to the structure. This is the same principle used to move the filament back and forth in those cheesy old flicker light bulbs. By measuring the induced voltage along the wire as it moves through the static magnetic field, the resonator's motion may be detected. Michael Roukes' group at Cal Tech been enthusiastic about the possibility of achieving sensitivities high enough to resolve a single atomic mass unit (1.66 x 10-27 kg).
There are many situations where one would love to have great mass detection capabilities in a liquid environment (e.g., to detect the binding of some cancer marker). The problem is, if you immerse a mechanical resonator in a liquid, viscous damping completely kills your sensitivity by damping the resonance. An old acquaintance of mine from graduate school, Scott Manalis at MIT, has come up with a solution to this problem. Don't put the resonator inside liquid; rather, put liquid inside the resonator. His group has been making mechanical resonators with micro (and now nano)fluidic flow channels inside them. In their latest work, they report a sensitivity of 30 attograms. I think this is very elegant, and a tour de force fabrication exercise.
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