the conduction band

The conduction band is the range of allowed electron energies just above the valence band — the empty shelf sitting above the full one. In a semiconductor or insulator it is normally empty (or nearly so) at low temperature. Its name says its job: an electron that reaches this band is free to roam through the crystal and carry current, because the band has plenty of empty states right nearby for it to accelerate into.

Think of the valence band as a packed ground floor and the conduction band as a wide-open, almost-empty upper floor. Down below, nobody can move because every space is taken; up above, the few electrons present have room to wander in any direction. So conduction-band electrons are the mobile negative carriers of a semiconductor. In a metal there is effectively no gap — the conduction band overlaps the valence band — which is why metals always have electrons roaming an empty band and conduct so freely.

How do electrons get up into the conduction band? Three ways matter for materials. Heat can kick them across the band gap (this is why semiconductors conduct more when warm). Light of high enough energy can knock them up (the basis of solar cells and light sensors). And in n-type doping we add donor atoms that hand electrons almost directly into the conduction band. The number of electrons that make it up there, together with their mobility, sets the semiconductor's conductivity.