Band Theory

Band theory is similar to molecular orbital theory and provides a model for electronic behavior in solids. Recall that when two or more atoms come together to become a molecule, their atomic orbitals overlap to form molecular orbitals of discrete energy levels. As the number of atoms in the molecule increases, so does the number of molecular orbitals. Solids typically have an exceedingly large number of atoms, so the entire solid would be represented with an exceedingly large number of closely spaced molecular orbitals. As a result, groups of the molecular orbitals will be so closely spaced that they can be thought of as continuous ranges, or bands, of energy that electrons can occupy. Like molecular orbitals, these bands are separated by energy gaps. If the gaps are too wide, electrons cannot cross them. In conductors like copper, the valence electrons are in a band that also has many empty orbitals. The valence electrons can readily move between orbitals, allowing electrons to flow freely through the solid. These mobile electrons are responsible for the good electrical conductivity of the solid. Models of semiconductors and insulators consider two bands: the valence band, which is the highest-energy band that contains electrons in the ground state, and the conduction band, which is the band just above the valence band. The valence band has few to no empty orbitals, limiting the ability of valence electrons to move through the solid if they cannot reach the empty orbitals of the conduction band. This is the behavior seen in insulators like glass, which have a large energy gap, or band gap, between the valence and conduction bands. Insulators, therefore, exhibit poor electrical conductivity. If the band gap is small, valence electrons can be excited to the conduction band and move freely between the empty orbitals there. The empty orbitals that the excited electrons leave behind also make it easier for electrons to move within the valence band. This is the behavior seen in semiconductors like silicon, which are less conductive than metals but more conductive than insulators.