• Tags: band-theory, conductor, insulator
• Difficulty: Foundation

In isolated atoms, electrons occupy discrete energy levels. In a solid with N atoms, each level splits into N closely spaced levels forming a band. The valence band (highest occupied band) and conduction band (lowest unoccupied band) determine electrical behavior. Conductors: valence and conduction bands overlap (metals like Cu, Ag) — electrons move freely, resistivity ~10^-6 ohm.m. Insulators: large band gap > 3 eV (diamond: 5.5 eV) — negligible conduction at room temperature, resistivity ~10^12 ohm.m. Semiconductors: small band gap ~1 eV (Si: 1.1 eV, Ge: 0.67 eV) — thermal excitation promotes some electrons across the gap, resistivity ~10^-1 to 10^4 ohm.m. Unlike metals, semiconductor conductivity increases with temperature (more electrons get excited across the gap). The Fermi level is the energy where the occupation probability is 50% — it lies at mid-gap for intrinsic semiconductors.