• Tags: intrinsic, electron-hole, thermal
• Difficulty: Foundation

A pure (undoped) semiconductor is intrinsic. At 0 K, the valence band is full and the conduction band is empty — it behaves as an insulator. At room temperature (300 K), thermal energy kT ≈ 0.026 eV excites some electrons from valence to conduction band. Each excitation creates an electron-hole pair: a free electron in the conduction band and a "hole" (missing electron) in the valence band. In an intrinsic semiconductor: $n_e$ = $n_h$ = $n_i$ (intrinsic carrier concentration). For Si at 300 K: $n_i$ ≈ 1.5 x 10^16 /$m^3$ (compare with ~10^28 free electrons/$m^3$ in copper). Conductivity sigma = $n_i$e($mu_e$ + $mu_h$), where $mu_e$ > $mu_h$ always (electrons are more mobile than holes). Both electrons and holes contribute to current: electrons move opposite to E, holes move along E. Increasing temperature exponentially increases $n_i$, dramatically increasing conductivity.