In solid-state physics, a band gap, also called an energy gap or bandgap, is an energy range
in a solid where no electron states can exist. In graphs of the electronic band structure
of solids, the band gap generally refers to the energy difference between the top of the
valence band and the bottom of the conduction band in insulators and semiconductors. This
is equivalent to the energy required to free an outer shell electron from its orbit about
the nucleus to become a mobile charge carrier, able to move freely within the solid material,
so the band gap is a major factor determining the electrical conductivity of a solid. Substances
with large band gaps are generally insulators, those with smaller band gaps are semiconductors,
while conductors either have very small band gaps or none, because the valence and conduction
bands overlap.
In semiconductor physics
Every solid has its own characteristic energy-band structure. This variation in band structure
is responsible for the wide range of electrical characteristics observed in various materials.
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. However, in order for an electron to jump from a valence
band to a conduction band, it requires a specific minimum 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 or a photon.
A semiconductor is a material with a small but non-zero band gap that behaves as an insulator
at absolute zero but allows thermal excitation of electrons into its conduction band at temperatures
that are below its melting point. In contrast, a material with a large band gap is an insulator.
In conductors, the valence and conduction bands may overlap, so they may not have a
band gap. The conductivity of intrinsic semiconductors
is strongly dependent on the band gap. The only available charge carriers for conduction
are the electrons that have enough thermal energy to be excited across the band gap and
the electron holes that are left off when such an excitation occurs.
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, 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 narrow band gap.
Insulators with a larger 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 band gap to a smaller extent. The relationship between band gap energy and
temperature can be described by Varshni's empirical expression,
, where Eg(0), α and β are material constants. In a regular semiconductor crystal, the band
gap is fixed owing to continuous energy states. In a quantum dot crystal, the band gap is
size dependent and can be altered to produce a range of energies between the valence band
and conduction band. It is also known as quantum confinement effect.
Band gaps also depend on pressure. Band gaps can be either direct or indirect, depending
on the electronic band structure. Mathematical interpretation
Classically, the ratio of probabilities that two states with an energy difference ΔE will
be occupied by an electron is given by the Boltzmann factor:
where: ΔE is the energy difference
k is Boltzmann's constant T is temperature.
At the Fermi level, 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 optical band gap determines what portion of the solar spectrum a photovoltaic cell
absorbs. A luminescent solar converter uses a luminescent medium to downconvert photons
with energies above the band gap to photon energies closer to the band gap of the semiconductor
comprising the solar cell. List of band gaps
Below are band gap values for some selected materials. For a comprehensive list of band
gaps in semiconductors, see List of semiconductor materials.
Optical versus electronic bandgap In materials with a large exciton binding
energy, it is possible for a photon to have just barely enough energy to create an exciton,
but not enough energy to separate the electron and hole. In this situation, there is a distinction
between "optical bandgap" and "electrical band gap". The optical bandgap is the threshold
for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole
pair that is not bound together. In almost all inorganic semiconductors, such
as silicon, gallium arsenide, etc., there is very little interaction between electrons
and holes, and therefore the optical and electronic bandgap are essentially identical, and the
distinction between them is ignored. However, in some systems, including organic semiconductors,
the distinction may be significant. 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
List of electronics topics
See also Wide bandgap semiconductors
Band bending Spectral density
Pseudogap References
External links Direct Band Gap Energy Calculator
Moriarty, Philip. "Energy Gap". Sixty Symbols. Brady Haran for the University of Nottingham.