Posted by Steve Simon on February 23, 2014, 9:19 pm, in reply to "Holes"
First Question First:
Why does the hall coefficient have the wrong sign.
Yes, it does look a bit like holes are just a bookkeeping trick and the electrons still carry the charge so why should the sign of the Hall effect care?
There are several ways to explain this.
(1) If you insist on speaking in terms of electrons, then you have to live with the fact that the electrons near the top of the band have velocity opposite to their wavevector k, since the dispersion is bent downwards not upwards. So the electrons are actually moving reverse of what you think electrons should move!
(2) It is easier to think in terms of holes with positive mass, but also positive charge. As we showed in lecture, you can describe the (Drude) dynamics of the k-state orbitals either in terms of electrons with negative mass or holes with positive charge. Either way, they end up curving the "wrong" way in a magnetic field.
Second (unrelated) question:
How to calculate the number of charge carriers.
You have Law of mass action which always gives you the product of n and p. Then you have n - p given by the number of donors minus acceptors. That is two equations in two unknowns.
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