Band Theory, Defects and Why Some Solids Conduct

An isolated atom has discrete electron energy levels. When atoms interact, their orbitals combine into states spread through the solid. N interacting atomic orbitals produce N states. For very large N, their energies are closely spaced and form a band. They remain discrete states, but are often treated as nearly continuous. Gaps separate ranges of allowed electronic energy.

Use the simple independent-electron band model, neglecting localisation and strong electron correlations. In a metal, partly filled or overlapping bands provide occupied and nearby empty states. An electric field can change electron occupation and produce current. An ideal band insulator at zero temperature has full occupied bands separated from empty bands by a gap. At ordinary temperatures, a wide gap strongly suppresses electronic conduction; it does not mean electrons never move.

Heat or suitable light can excite electrons across a semiconductor gap, leaving holes. Both carriers conduct. Warming intrinsic silicon usually increases carrier numbers and conductivity. In copper near room temperature, carrier numbers change little; stronger lattice vibrations increase scattering and lower electron mobility and conductivity.

In lightly doped silicon, shallow donors just below the conduction band release electrons, giving n-type material. Shallow acceptors just above the valence band take electrons from it and leave holes, giving p-type material. Conductivity depends on carrier numbers and mobility; doping need not increase it in every regime.

A vacancy is a missing particle at a normal site. Mobile ions can hop into vacancies and conduct without crossing an electronic band gap. An electron trapped at an anion vacancy can absorb selected visible wavelengths and change colour. This localised optical process need not create a mobile carrier or change the bulk band gap.

For classification, compare band filling and the gap. A pure semiconductor has full valence bands at zero temperature and a relatively small gap allowing thermal electron-hole generation. A wide-gap insulator strongly suppresses that generation. A typical metal has a partly filled band or overlapping bands.