11.18: Band Theory

When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.

The energy difference between these bands is known as the band gap.

Conductor, Semiconductor, and Insulators

In order to conduct electricity, valence electrons must cross orbitals of different energies to move throughout the solid. This is determined by the band gap. The valence electrons in conductors occupy a band that has many empty orbitals. Thus, only a small amount of energy is required to move the electrons to these empty orbitals. This small energy difference is “easy” to overcome, so they are good conductors of electricity. Semiconductors and insulators observe two types of bands - a valence band, with few to no empty orbitals, and a conduction band, with empty orbitals. The energy difference or the band gap between the valence band and the conduction band decides the ease with which the electrons can move. In insulators, the band gap is so “large” that very few electrons can reach the empty orbitals of the conduction band; as a result, insulators are poor conductors of electricity. Semiconductors, on the other hand, have comparatively small band gaps. As a result, they can conduct electricity when “moderate” amounts of energy are provided to move electrons out of the filled orbitals of the valence band and into the empty orbitals of the conduction band. Thus, semiconductors are better than insulators but not as efficient as conductors in terms of electrical conductivity.

This text has been adapted from Openstax, Chemistry 2e, Section 8.4 Molecular Orbital 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.