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In solids, the valence band is the highest range of electron energies where electrons are normally present at absolute zero. In semiconductors and insulators, there's a band gap above the valence band, followed by a conduction band above that. In metals, the conduction band has no energy gap separating it from the valence band (basically, this is correct only for semimetals. All solids have forbidden energy levels between the energy bands). The rest of this article refers to the valence band in semiconductors and insulators.

Semiconductor band structure
See electrical conduction and semiconductor for a more detailed description of band structure.
Semiconductors and insulators owe their low conductivity to the properties of the valence band in those materials. It just so happens that the number of electrons is precisely equal to the number of states available up to the top of the valence band. There are no available states in the band gap. This means that when an electric field is applied, the electrons can't increase their energy (for example, accelerate) because there are no states available to the electrons where they'd be moving faster than they're already going.
   There is some conductivity in insulators, however. This is due to thermal excitation—some of the electrons get enough energy to jump the band gap in one go. Once they're in the conduction band, they can conduct electricity, as can the hole they left behind in the valence band. The hole is an empty state that allows electrons in the valence band some degree of freedom.
   It is a common misconception to refer to electrons in insulators as "bound"—as if they were somehow attached to the nucleus and couldn't move. Electrons in insulators are quite free to move—in fact, they move at a speed on the order of 100 km (60 mi) per second! They are also delocalized, having no well-defined position within the sample.

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