What condition must be met for electrons to contribute to conductivity in a semiconductor?

In a semiconductor, for electrons to contribute to conductivity, they must be able to move from the valence band to the conduction band. This movement occurs when the energy of the electrons is equal to the band gap energy, which is the minimum energy required to bridge the gap between these two bands. When an electron acquires energy that is equal to the band gap energy, it can make this transition, thereby allowing the electron to participate in electrical conduction.

When electrons are below the band gap energy, they do not have enough energy to make the transition needed to move into the conduction band, hence they cannot contribute to conductivity. Conversely, if the energy is much greater than the band gap, this isn't necessary for conductivity; the electron only needs enough energy to cross the gap. Therefore, the specific condition that must be met for electrons to contribute to conductivity is that their energy must equal the band gap.