The Electronic Band Gap

The electronic band gap is one of the properties that is relevant in solid-state physics, and it describes the “gap” in the energy range of the solid where no electron states can exist. Since electrons are quantized and can only exist at certain levels, there are natural gaps that occur when an electron moves from one energy level to the next highest energy level.

In practical terms, the band gap can be described in terms of the valence band and the conduction band in insulators and semiconductors. These bands are specific to each material and help determine the electrical conductivity of a solid and are closest to the Fermi level, which is the total chemical potential for electrons. The conduction band is the lowest range of vacant electronic states, while the valence band is the highest range of electron energies where electrons are normally present. Since the band gap is the space that is traversed by the electron when it moves from one energy level to another, there will be a minimum amount of energy required for the transition. If the energy put into the material does not meet the minimum, then the transition to a higher energy state will not occur. Therefore, when the electronic band gap is smaller for the solid, then the material will be more conductive, such as a semiconductor, and vice versa for an insulator. For conductors, the valence and conduction bands may overlap, which eliminates the band gap.

The use of the electronic band gap can also exploited through engineering for different materials. Since materials have varying band gaps, the composition of an alloy can help determine the overall band gap of the material. In addition, the materials can be used in a variety of areas, such as photovoltaic cells or laser diodes. The band gap can also be experimentally determined using a variety of different methods. One relation is the band gap energy decreasing as the temperature increases. This phenomenon is observed because the amplitude of atomic vibrations will increase as the temperature increases and leads to larger interatomic spacing. So by measuring changes that occur as the temperature varies, properties of the band gap can be determined. Another way that the surface electronic structure of compounds can be elucidated is by using scanning tunneling spectroscopy and interpreting results. For example, the electron transfer processes at pyrite surfaces can be closely examined using this method, and the band gap can be determined. Overall the band gap is important because other properties can be evaluated after finding the gap, such as electrochemical processes relevant to corrosion and solar energy conversion.

Citations
1. Herbert, F.W., Krishnamoorthy, A., Van Vliet, K.J., Yildiz, B. Quantification of electronic band gap and surface states on FeS2(100). Surface Science. [Online] 2013, 1-9.