thank you, there can be hole in metal as well, if i understand well it says "Their motion is much too much restrained by a lack of available empty energy states " it means that there is not enough hole in a metal to have a significant current, as i think or that there will be a recombination of this hole with a free electron, that is actually the same. It's linked to fermi dirac distribution of hole, depending on temperature but do not remember where it comes from and why it s so low for metal. Any way another question for a semi conductor if you just have "hole" for the last energy state of valance band and completed free electron on conduction band how could you have a hole current because there is no valence electron that can pass trough tunnel effect to the hole to build the "hole" current ? and if you have your valence band that is full, why does your electron could not move due to the electrical potential ? i means the + (cathode) will catch an electron valence and then you have an hole and so on.
Why does this effect is impossible if you have the band full ?