Bandstruktuuri

Bandstruktuuri, or band structure, is a description of the allowed energy levels of electrons in a solid as a function of crystal momentum. In a crystalline solid, electrons move in a periodic potential created by the lattice; Bloch's theorem implies that their wavefunctions can be labeled by a wave vector k within the first Brillouin zone, and that energy eigenvalues form bands E_n(k) separated by gaps.

These bands arise from the overlap of atomic orbitals when atoms form a solid. Two common modeling approaches are the nearly-free-electron model and the tight-binding model. Band diagrams plot E versus k and show valence bands that are filled at low temperature, an energy gap to conduction bands, and a Fermi level that depends on temperature and doping. The structure of these bands determines a material’s electronic properties and influences optical response and carrier mobility.

Classification of materials by band structure includes metals, insulators, and semiconductors. Metals have partially filled bands or overlapping bands, insulators have a wide band gap, and semiconductors have a moderate gap. Doping or defects can introduce donor or acceptor states that modify conductivity. A material’s band structure is central to understanding and engineering electronic, optical, and transport properties.

Experimental determination of band structure employs techniques such as angle-resolved photoemission spectroscopy (ARPES) and related methods, while theoretical calculations use density functional theory (DFT), GW corrections, and model Hamiltonians like tight-binding or Kronig-Penney. Band structure calculations extend to bulk crystals and two-dimensional materials, where dimensionality can qualitatively change the bands.

Band engineering uses composition, strain, and dimensionality to tailor band structure for desired functionalities, such as in semiconductors, photovoltaics, and novel quantum materials.