# Question on semiconductors and band gap at absolute zero

I was reading a book on Solid State Physics which stated that insulators have a band gap larger than 3eV, insulators <3eV and metals have no gap. It also states that semiconductors become insulators at absolute zero. However, at 0 K the band gaps for semiconductors remain very low (1.4eV for example) and barely change from room temperature (1.2eV). Does this mean that they do not act as insulators at 0 K?

• You've written "insulators have a band gap larger than 3eV, insulators <3eV ...", did you mean "semiconductors <3eV", perhaps? Commented Jun 17, 2021 at 5:04

## 1 Answer

It would be useful to understand the difference between conductivity in metals and in semiconductors/insulators. The electrical conductivity depends on the concentration of electrons in the conduction band and the mobility of the electrons. In semiconductors and insulators, at zero K the conduction band is empty. So teher are no free electrons and the conductivity is zero. As the temperature increases some electrons from the valence band are excited into the conduction band. So the conductivity becomes non-zero but it is still much lower than in metals. This is due to the fact that the concentration of free electrons is much lower than in metals, even at room temperature. This can be related to the fact that the average thermal energy at room temperature is about 1/40 eV whereas the band gap of typical semiconductors is of the order of 1eV and more (germanium has a little less than 1 eV, about 0.6 eV). Insulators have even higher band gaps so the free electron concentration is negligible at tempretaures below their melting points. This also explains the fact that the conductivity of the semiconductors increases with temperature. The mobility decreases with temperature but the increase in free electron concentration dominates.

In metals the concentration of free electrons is pretty much independent of temperature, the electrons are already in the conduction band even at zero Kelvin (there is no band gap). So the conductivity is controlled by the mobility which decreases with temperature and so the conductivity of metals decreases at higher temperatures.