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May15-08, 03:26 AM
HW Helper
P: 2,616
This is what I wrote for another thread:

Quote Quote by Defennder View Post
Consider this in 1D:

We all know that J=nev where n is the concentration of electrons, v is the drift velocity.

Suppose the valence band is completely full of N electrons, then it goes without saying there can be no current flow:

[tex]J_{x} = \sum_i^N -ev_{i} = 0[/tex]

But on the other hand suppose there is one missing electron, one vacancy in the valence band where an electron should be:

[tex]J_{x}=\sum_i^{N-1}-ev_{i} = \sum_i^N -ev_{i} -(-ev_{j}) = ev_{j}[/tex]

Notice that the final expression on the right can be thought of as current due to the drift of a single positive charge, since there is no minus sign. That is why we are justified in thinking that we can treat absence of negative charges as positively charged holes.
As for the other question, I'm guessing it's something to do with the magnitude of their effective masses.