Band structure

A band structure gives the allowed electron energies in a crystal as a function of crystal momentum. Its bands and gaps help determine how the solid conducts electricity and interacts with light.

Bloch's theorem: A theorem stating that electron wavefunctions in a periodic potential are plane waves multiplied by functions with the crystal’s periodicity. It gives the form of electron states used to derive bands in a periodic crystal.
Band gap: An energy interval in a solid’s electronic spectrum containing no allowed electron states. The size and location of the gap distinguish many electronic and optical behaviors.
Crystal lattice: An idealized periodic arrangement of points that represents the translational symmetry of a crystal. Its periodicity supplies the symmetry underlying electronic bands.
Free electron model: A model treating conduction electrons as independent particles moving without a periodic crystal potential. Unlike a crystal band structure, its simplest form has no lattice-induced gaps.
Brillouin zone: A primitive cell in reciprocal space that contains the distinct crystal momenta of a periodic lattice. Band energies are plotted across this reciprocal-space region.
Effective mass: A parameter describing how a charge carrier responds to forces in a periodic solid, inferred from band curvature. Band curvature determines the effective mass used to model carrier motion.
Reciprocal lattice: The lattice in reciprocal space whose vectors encode the periodicity of a crystal in real space. Crystal momentum and Brillouin zones are defined using reciprocal-lattice vectors.
Energy-level diagram: A diagram showing discrete energy states or transitions without displaying their dependence on momentum. It omits the momentum-dependent dispersion central to a band structure.
Nearly free electron model: A model of crystal electrons as nearly free waves weakly perturbed by a periodic lattice potential. It explains how weak lattice scattering opens gaps at Brillouin-zone boundaries.
Semiconductor: A material whose electrical conductivity can be controlled by temperature, light, doping, or applied fields. Its partially occupied bands and modest gap enable controlled carrier generation.

Linked from 15 pages