Electronic band structure

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). The electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two identical atoms join to form a molecule, their atomic orbitals overlap. Since electrons are fermions, the Pauli exclusion principle prohibits them from having the same energy. As the atoms get closer together the orbitals split (hybridize) into molecular orbitals with different energies. Similarly, if a large number N of identical atoms come together to form a solid, such as a crystal lattice, the atoms' atomic orbitals overlap with the nearby orbitals. Each discrete energy level splits into N levels, each with a different energy. Since the number of atoms in a macroscopic piece of solid is a very large number (N~1022) the number of orbitals is very large and thus they are very closely spaced in energy (of the order of e-22eV). The energy of the adjacent levels is so close together that they can be considered as a continuum, an energy band. This formation of bands is mostly a feature of the outermost electrons (valence electrons) in the atom, which are the ones involved in chemical bonding and electrical conductivity. The inner electron orbitals do not overlap to a significant degree, so their bands are very narrow. Band gaps are essentially leftover ranges of energy not covered by any band, a result of the finite widths of the energy bands.