: 200
When atoms combine to form a crystal, their atomic orbitals merge into bands of closely spaced energy levels. Valence band: highest filled band at 0 K. Conduction band: lowest empty band. Band gap: energy difference between them. Metals: valence and conduction bands overlap or band gap = 0 — electrons flow freely. Conductivity: 10^4-10^7 ohm^{-1cm}^{-1}. Decreases with temperature (more lattice vibrations scatter electrons). Insulators: band gap > 3 eV (diamond: 5.5 eV) — electrons cannot jump at room temperature. Semiconductors: small band gap (~1 eV; Si: 1.1 eV, Ge: 0.67 eV) — some electrons jump at room temperature. Conductivity increases with temperature (more electrons gain enough energy). Intrinsic: pure element. Extrinsic: doped. n-type: Group 15 dopant (P, As) adds extra electron — majority carriers are electrons. p-type: Group 13 dopant (B, Al) creates hole — majority carriers are holes. p-n junction: basis of diodes, transistors, solar cells.