In a solid the atomic levels smear into a filled valence band and an empty conduction band split by a gap E_g. Conductors have no gap; insulators have a huge one; a semiconductor's gap is small enough that heat lifts a few electrons up, leaving holes behind. Doping tilts the balance — pentavalent donors add electrons (n-type), trivalent acceptors add holes (p-type) — while n_e·n_h = n_i² always holds. Heat the lattice and count the carriers appear.

Heat a metal and it conducts worse — the lattice jostles harder and scatters electrons. Heat a semiconductor and it conducts better: the carrier count explodes as n_i ∝ T^{3/2} e^{−E_g/2kT}, and that swamps the drop in mobility. The steepness of the climb reads off the gap E_g directly. Slide the temperature and compare the materials on a log scale.