Electronic Band Structure

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© Wikimedia Commons, Public Domain. Author: Pieter Kuiper, 6 June 2007.

The energy bands in the crystals shown here have their physical origin in the electronic energy levels of their individual atoms: when the atoms are brought together in the crystal, their interaction broadens each atomic level into energy bands, which may be completely or partially filled. Insulators are materials in which their lowest lying bands, known as valence bands, are completely filled, while the higher lying bands are empty, i.e., contain no electrons; as a result the electrons in an insulator cannot physically move in response to an applied electric field. Metals, on the other hand, contain a partially filled band, the conduction band, whose conduction electrons move easily in response to an external electric field. Semiconductors are insulators in which the energy gap between its valence and conduction bands is sufficiently small that at temperatures of interest, a fraction of the electrons in the valence band are thermally excited to the conduction band (leaving behind holes, unoccupied states in the valence band) and both the conduction electrons and the holes can move in response to an applied electric field. Because the density of mobile electrons in a semiconductor is very much smaller than that found for metals, that response is much weaker, hence their name. We note that conduction is an emergent property of materials, since their individual atoms do not conduct, and that the interband transitions between electron energy levels in different bands require a finite amount of energy, while intra-band transitions, where allowed, form a continuum starting at zero energy. (Unit: 8)