Is the valence band neutral?

Question

While studying about band theory of semiconductors, I observed that when the electrons were excited from the valence band to the conduction band, they left behind holes in the valence band. From my existing knowledge, I believe that the valence electrons alone occupy the valence band which tells me the valence band is negative. For the holes to exist, the valence band has to be neutral. So, why is the valence band neutral?

If my reason for the valence band to be negative was wrong, I would like to know the reason.

Answer 1

A band, in itself, does not have charge. A band is just a collection of possible states where electons might be found. The electrons have charge but the states themselves do not.

If the valence band is fully occupied, the charge of the electrons in the band will be balanced by the charge of the protons in the lattice, and the overall charge of the material will be neutral. As an aside, since the protons are well-localized in position space, they are very spread out in k-space.

If there is an unoccupied state in the valence band, there will be a local (in k-space) net positive charge because the nuclear positive charges are not compensated by valence band electrons. This positve charge behaves as if it were attached to a particle, and we call that particle a hole.

Often the electron removed from the valence band is only moved up to the conduction band, so the net charge in the material may still be neutral, even though there is a hole present. The conduction band particle (electron) and valence band particle (hole) may move apart in k-space (and in position space) so we must keep track of them seperately.