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.