Measuring Free Electron Density
Most recent answer: 12/25/2009
- Tam (age 16)
Herndon, VA, USA
The key idea is this. In a magnetic field at right angles to the electric field, electron paths curve due to magnetic forces before they hit anything and scatter. The result is some sideways current or voltage, depending on whether the circuit lets that sideways current flow. That's called the Hall effect. If you have a few electrons with long free paths between scattering, the curvature is important and you get a big Hall effect. If you have the same conductivity but from many electrons with shorter free paths, the Hall effect is reduced.
If the current is carried by 'holes' (missing electrons) it acts like the carriers are positively charged, and the Hall effect has the opposite sign. If there are both electrons and holes, it gets much messier.
So the basic technique is something like this:
Take a thin foil (or evaporated film) of the metal in question. Cut it into a sort of cross shape. Run current one way through the cross. Measure the voltage at right angles in the cross. Now apply a measured magnetic field pointing into the plane of the metal. An extra voltage will appear on the right-angle part of the cross. That's the Hall voltage.
You can calculate the effective concentration of electrons or holes from that, using the more detailed sources I'm sure you can find with the search terms I mentioned.
Good luck on a nice project.
Mike W.
(published on 12/25/2009)
Follow-Up #1: free electrons and conductivity
- Noah (age 13)
Mannassas, VA, U.S.
The conductivity just goes up proportional to the density of free electrons, if other things remain equal. Usually, however, other things don't remain equal.
For example, the extra free electrons in a semiconductor may come from dopant atoms added to the semiconductor. Those dopant atoms also scatter the free electrons, so the conductivity doesn't go up as much as you might expect when there are lots of them
The electrons also interact with each other. That causes all sorts of interesting effects. For example, in the new high-temperature superconductors there's typically an optimum concentration of free electrons to get superconductivity at high temperatures. Either adding or subtracting free electrons (via doping levels( can destroy the superconductivity.
Mike W.
(published on 12/03/2014)