In solid state physics and related applied fields, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states exist. For insulators and semiconductors, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band; it is the amount of energy required to free an outer shell electron from its orbit about the nucleus to a free state.

In semiconductor physics

Semiconductor band structure.

A material with a small, but not null or negative, band gap (arbitrarily defined as < 3 eV, although some definitions place the upper limit at 4 eV) is referred to as a semiconductor^[1]. A material with a large band gap is called an insulator.

In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden from other regions. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band; electrons are able to jump from one band to another. In order for an electron to jump from a valence band to a conduction band, it requires a specific amount of energy for the transition. The required energy differs with different materials. Electrons can gain enough energy to jump to the conduction band by absorbing either a phonon (heat) or a photon (light).

The conductivity of intrinsic semiconductors is strongly dependent on the band gap. The only available carriers for conduction are the electrons which have enough thermal energy to be excited across the band gap.

Band gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor alloys, such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors (HBTs), laser diodes and solar cells.

The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as a type of insulator with a low band gap. Insulators with a higher band gap, usually greater than 3 eV, are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. Electron mobility also plays a role in determining a material's informal classification.

The band gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increase, leading to larger interatomic spacing. The interaction between the lattice phonons and the free electrons and holes will also affect the bandgap to a smaller extent^[2]. The relationship between bandgap energy and temperature can be described by Varshni's empirical expression,

In a regular semiconductor crystal, the bandgap is fixed owing to continuous energy states. In a quantum dot crystal, the bandgap is size dependent and can be altered to produce a range of energies between the valence band and conduction band.^[3] It is also known as quantum confinement effect.

, where E_g(0),- and - are material constants.^[4]

Band gaps also depend on pressure. Band gaps can be either direct or indirect bandgaps, depending on the band structure.

Mathematical interpretation

Classically, the ratio of probabilities that two states with an energy difference -E will be occupied by an electron is given by the Boltzmann factor:

where:

is the exponential function

is the energy difference

is Boltzmann's constant

is temperature

At the Fermi level (or chemical potential), the probability of a state being occupied is ½. If the Fermi level is in the middle of a band gap of 1 eV, this ratio is e ^-20 or about 2.0-10^-9 at the room-temperature thermal energy of 25.9 meV.

Photovoltaic cells

The bandgap determines what portion of the solar spectrum a photovoltaic cell absorbs.^[5] A luminescent solar converter uses a luminescent medium to downconvert photons with energies above the bandgap to photon energies closer to the bandgap of the semiconductor comprising the solar cell^[6].

List of band gaps

In photonics and phononics

In photonics band gaps or stop bands are ranges of photon frequencies where, if tunneling effects are neglected, no photons can be transmitted through a material. A material exhibiting this behaviour is known as a photonic crystal.

Similar physics applies to phonons in a phononic crystal.

Materials

• Aluminium gallium arsenide
• Boron nitride
• Indium gallium arsenide
• Gallium arsenide
• Germanium
• Metallic hydrogen

List of electronics topics

• Electronics
• Bandgap voltage reference
• Condensed matter physics
• Direct bandgap
• Electrical conduction
• Electron hole
• Field effect transistor
• Indirect bandgap
• Photodiode
• Photoresistor
• Photovoltaics
• Solar cell
• Solid state physics
• Semiconductor
• Semiconductor devices
• Strongly correlated material
• Valence band

See also

• Spectral density
• Weber and Lambe

References

External links

• Direct Band Gap Energy Calculator