What is Band Gap?

A band gap is a range of energy levels in a material in which electrons cannot exist. The absence or presence of a band gap as well as its size can help us understand the electronic behaviour of a material a.nd distinguish electrical insulators, conductors, and semiconductors [1].

In this article you will learn about:

• What is a band gap?
• How are materials classified based on the band gap?
• Optical properties and the bandgap
• What are wide band gap semiconductors?

What is a band gap?

In atoms or molecules, electrons usually occupy distinct energy levels. In solids, however, these energy levels merge together to form bands. The electrons being used in binding the atoms together exist in the valence energy band while the remaining electrons not being used for bonding are free to move around. These exist in the conduction band, and so are available to participate in electrical conduction [1].  

For many materials, the conduction and valence bands overlap, while for others, there is an energy gap between the two bands. This energy gap, in which electrons cannot exist, is called the band gap and is described as the minimum energy needed to excite an electron from the valence band to the conduction band. This means that if enough energy is provided to an electron which is being used for bonding, it can be excited across the band gap to be free for conduction.

Certain properties of materials are heavily influenced by the size of the band gap.

Classification of materials based on the band gap

The electrical behaviour of any material is defined by whether or not there are electrons present in the conduction band. This determined by the band structure.

For conductors, the conduction and valence bands overlap, and so the conduction band can be populated by electrons. In insulators, the bands do not overlap and there is a large band gap between the valence and conduction bands, making it almost impossible for electrons to jump into the conduction band. Semiconductors have a small band gap, just large enough for certain influences to give an electron from the valence band enough energy to cross the barrier to the conduction band. Examples of such influences can include optical or thermal excitations.

An important concept when discussing the band gap is the Fermi energy. This is the energy of the highest energy level occupied by the electrons in a solid at low temperature. The position of the Fermi energy in relation to the energy bands is crucial in determining whether the material is a conductor, insulator or semiconductor.

If the Fermi energy level is within the valence band, all the electrons are participating in bonding (assuming low temperature). If the Fermi energy is inside the conduction band, there are electrons available for participation in conduction. If the Fermi energy lies within the band gap, the valence band is completely filled and the conduction band is empty. This is the situation that gives rise to semiconductors.

This band gap, often represented as Eg, can be illustrated in a “band diagram”. The diagram below shows example band diagrams for a conductor, semiconductor and insulator.

Insulators, conductors, and semiconductors are characterized by [1][3]:

• Insulators: materials in which the band gap is significantly large (about 3 to 7 eV) that it prevents electrons in the valence band being excited into the conduction band. Therefore, the electrons are immobile.  Such materials have very low electrical conductivity and high electrical resistivity. Oxides such as SiO2, or glass, are an example of common electrical insulators.
• Conductors: materials in which the valence and the conduction bands overlap, allowing electrons to freely move in the conduction band. Contrary to insulators, conductors have high electrical conductivity and low electrical resistivity. One of the best electrical conductors is copper but all metals are generally conductive.
• Semiconductors: materials with a small band gap of less than about 3 eV [4], which allows a finite number of electrons to be excited into the conduction band. These excitations can come from thermal or optical sources. The band structure can even be modified through chemical doping or applying an electric field. A semiconductor can, therefore, behave like an insulator or a conductor, depending on the conditions. This is what makes semiconductors useful as switches, or transistors, in integrated circuits. The best-known elemental semiconducting materials are silicon and germanium. Other recognized semiconductors are gallium arsenide, GaAs, and indium phosphide, InP.

The table below presents values of band gaps for some well-known semiconductors [3]:

Material	Symbol	Eg (eV)
		T = 0 K	T = 300 K
Silicon	Si	1.17	1.11
Germanium	Ge	0.74	0.66
Indium antimonide	InSb	0.23	0.17
Indium arsenide	InAs	0.43	0.36
Indium phosphide	InP	1.42	1.27
Gallium nitride	GaP	2.32	2.25
Gallium arsenide	GaAs	1.52	1.43
Gallium antimonide	GaSb	0.81	0.68
Cadmium selenide	CdSe	1.84	1.74
Cadmium telluride	CdTe	1.61	1.44
Zinc oxide	ZnO	3.44	3.2
Zinc sulfide	ZnS	3.91	3.6

Optical properties and the band gap

The colour of a material is dependent upon the interaction of light with atoms and electrons. 

Light can either be absorbed, transmitted or reflected by a material and the extent to which each of these occurs for a specific wavelength determines the material’s colour. The visible range of light is between 390 nm and 700 nm or 1.8 eV and 3.1 eV.

Due to the abundance of free electrons in a metal (in the conduction band), light is usually almost entirely reflected. Some metals, such as copper and gold absorb some wavelengths of light, giving them their colour, whereas others, such as silver do not.

For many insulators, light is usually mostly absorbed, as in the case with most ceramics, transmitted, as with glass, or scattered. 

For semiconductors, light can also be absorbed, and the band gap is an important factor determining which wavelengths are absorbed. Only light with energies (or wavelengths) greater than the band gap energy can be absorbed.

Semiconductors such as Si and GaAs appear dark blue or black because they absorb most wavelengths of light in the visible range. The energy from the electrons being excited to the conduction band can be taken advantage of for photovoltaics. 

Semiconductors can also emit light. When electrons are returned from the conduction band to the valence band they can emit the energy difference in the form of photons. The energy of these photons corresponds to the energy of the band gap, which is unique to the semiconductor.

Examples of semiconductor optical devices which take advantage of these light-emitting properties include light-emitting diodes (LEDs, such as the well-known “blue light-emitting diode”), photodiodes, photodetectors, and diverse optical modulation devices [3].

Wide band gap semiconductors

As the name indicates, wide band gap semiconductors are those with a large band gap. TiO₂, for example, appears white as it only absorbs ultraviolet light and scatters all visible light. Others, such as Fe₂O₃ and CdS, appear reddish-orange-yellow as they absorb green, blue, and violet wavelengths [4].

[1] Kittel C. and McEuen P. (2019), Introduction To Solid State Physics, 8th Ed. Hoboken, NJ: John Wiley & Sons.

[2] Serway, R. A. and Jewett, J. (2010), Physics for Scientists and Engineers with Modern Physics, 8th Ed, Vol. 5, Cengage Learning, Los Angeles, California.

[3] Takashani, K., Yoshikawa, A., and Shandhu A. (2006), Wide Bandgap Semiconductors, Fundamental Properties and Modern Photonic and Electronic Devices, Springer, New York.

[4] University of California at Davis, LibreText, Chemistry, 10.5: Semiconductors - Band Gaps, Colors, Conductivity and Doping [Online].