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Aluminum and holes



Sorry I'm behind in my reading, but there is something to add here....

Larry Woolf wrote:

Taking a look back at Ashcroft and Mermin's Solid State Physics:

The high field Hall coefficient indicates carriers with positive charge for
Be, Mg, In, and Al.

The low field Hall coefficient indicates carriers with negative charge for
Al (there is a graph in my First Edition - p. 15)

The high field Hall coefficient indicates an effective density of carriers a
third of the free electron value.

So Al appears to be predominantly an electron conductor in low magnetic
fields and a hole conductor in high magnetic fields. (pages 299-303)

More complicated than I initially thought!



Indeed more complicated!


If you check Ashcroft and Mermin chapter 15, the section on Al, you'll
find that the factor of 1/3 can be readily explained.

But more importantly, once you get the quantum solid state theory right,
you find that the sign of the Hall coefficient is not all that closely
related to the question of DC conductivity. At least, not as closely as
you might expect based on classical pictures.

In order to honestly say that conduction in a material is via holes, I
think you need to show that the Bloch states providing the conduction
have negative effective mass. That happens at band maxima. So, for
example, "hole conduction" in p-type semiconductors is a very good
picture of what is going on. Negative electrons in negative mass states
are more easily viewed as positive holes with positive mass (the signs
cancel).

The aluminum band structure does have what solid state calls a
"hole-like Fermi surface", and a pretty big one at that. However, the
states at the Fermi surface still have positive effective mass. So it's
a pretty big stretch to say that Al is a hole conductor. I would prefer
to say that it is an electron conductor, but it has an anomalous Hall
coefficient because the electron orbits have reversed orientation due
tot he band structure. (This can be view as a net consequence of the
usual magnetic force plus strong scattering of the electrons by the
Bragg planes.)

If you want a metal with hole conduction, I'd think the place to go is a
semimetal like graphite. Then half of the conduction is by states near
the band maximum, somewhat similar to undoped semiconductors.
--
Dr. James McLean phone: (585) 245-5897
Dept. of Physics and Astronomy FAX: (585) 245-5288
SUNY Geneseo email: mclean@geneseo.edu
1 College Circle
Geneseo, NY 14454-1401