The electrical conductivity is determined by the mobility of the free electrons in the band model. The band model consists of the valence band and the conduction band.
Conduction band and valence band are separated by the band gap. This is equally true for conductors, semiconductors and non-conductors. The free electrons move in the conduction band. The highest mobility of free electrons is at absolute zero at 0 Kelvin.
In order to transport free electrons from the valence band to the conduction band in semiconductors, the electron energy must exceed the level of the valence band. This can be done by applying an electric field to bridge the energetic difference determined by the band gap.