Electronic band structure

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energies that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it 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.).

Why bands and band gaps occur

The electrons of a single, isolated atom occupy atomic orbitals. Each orbital forms at a discrete energy level. When multiple atoms join together to form into a molecule, their atomic orbitals combine to form molecular orbitals, each of which forms at a discrete energy level. As more atoms are brought together, the molecular orbitals extend larger and larger, and the energy levels of the molecule will become increasingly dense. Eventually, the collection of atoms form a giant molecule, or in other words, a solid. For this giant molecule, the energy levels are so close that they can be considered to form a continuum.