Let us say we have Germanium which has been doped with antimony. Antinomy has a a fifth valence electron not involved in bonding. Is this electron in the valence band? I ask because all texts on the subject I can find say that an N-type semiconductor has more electrons then holes. But how can this be? if this fifth electron moves out of antinomy's valence band it will leave behind a hole. This means, as I can see it, their is always (do to the overall system been neutral) the same number of holes as electrons. (i.e. all the electrons are initially in the valence band and when they move up to the conduction band they all must leave a hole in the valence band therefore the number of holes = the number of electrons). Please explain why this is not the case for N-type semiconductors.
Antimony is a donor in Germanium. That means that that 5th electron on the Antimony occupies a discrete level in the gap, not as part of the Germanium electronic bands. Since this level is close to the conduction band of the Germanium, it is highly likely that the electron will thermally get enough energy to jump into the conduction band. This leaves behind an unoccupied discrete state within the gap, not within the valence band. This state cannot move - it isn't part of a band. So, the material does remain neutral, you just aren't adding any mobile holes in the valence band.