• $summary_{type}$: concept
• $word_{count}$: 170

In solids, atomic energy levels merge into bands. The valence band (highest occupied) and conduction band (lowest unoccupied) determine electrical behavior. Conductors have overlapping bands (metals: ~10^28 free electrons/$m^3$). Insulators have a large band gap > 3 eV (diamond: 5.5 eV). Semiconductors have a small gap: Si = 1.1 eV, Ge = 0.67 eV. At 0 K, semiconductors are insulators (valence band full, conduction band empty). At room temperature (~300 K), thermal energy kT ≈ 0.026 eV excites some electrons across the gap, creating electron-hole pairs. Conductivity sigma = ne($mu_e$ + $mu_h$) where $mu_e$ > $mu_h$ (electron mobility exceeds hole mobility). Unlike metals, semiconductor resistivity decreases with temperature (more carriers excited). The Fermi level (50% occupation probability) lies at mid-gap for intrinsic semiconductors, near the conduction band for n-type, and near the valence band for p-type. GaAs (1.4 eV) and GaN (3.4 eV) are important compound semiconductors.