When this electron moves, it leaves behind another space. The continual movement of the space for an electron, called a "hole", can be illustrated as the movement of a positively charged particle through the crystal structure. Consequently, the excitation of an electron into the conduction band results in not only an electron in the conduction band but also a hole in the valence band. Thus, both the electron and hole can participate in conduction and are called "carriers". The concept of a moving "hole" is analogous to that of a bubble in a liquid. Although it is actually the liquid that moves, it is easier to describe the motion of the bubble going in the opposite direction.
Skip to main content. When the band gap energy is met, the electron is excited into a free state, and can therefore participate in conduction. The band gap determines how much energy is needed from the sun for conduction, as well as how much energy is generated. A hole is created where the electron was formerly bound. At very high optical intensities , it is possible to have multiphoton absorption e.
Such processes often play a role in laser-induced damage , for example. However, they are generally negligible at moderate intensities, e. A first consequence of the narrow band gap is some electrical conductivity, since thermal excitation e. An applied electric field leads to a slight rearrangement of population within the production and balance brand, which results in an electrical current.
Note, however, that the conductivity varies a lot between different semiconductors, mainly due to the strong dependence on the band gap energy. Another consequence is that photons with moderate energy e. Therefore, semiconductors at least those with a narrow band gap appear opaque and can transmit only infrared light — and that with a rather high refractive index. The details, however, substantially depend on whether we have a direct or indirect band gap — see below.
The table below lists the band gap type and energy of various semiconductors at room temperature. It does not include ternary and quaternary compounds where those properties depend on a composition parameter. In metals, the Fermi energy lies within a band, which is thus only partially occupied. In that situation, it is possible to induce a rearrangement of population within that partially filled band, which turns out to enable a substantial electrical conductivity.
Concerning optical properties of metals, there is strong reflection and absorption of light. Only for optical frequencies above the plasma frequency of the order of a couple of petahertz , a metal becomes transparent. One exploits that for metal-coated mirrors , for example. Semimetals have similar electronic properties, only that the density of states near the Fermi energy is relatively small.
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In case of dielectrics insulators and semiconductors, the band gap energy is understood to be the width of the energy gap between conduction and valence band. For metals, one would have to ask which band gap is meant. For single-photon processes, the optical wavelength corresponding to a given band gap energy E g can be calculated as. Enter input values with units, where appropriate. After you have modified some values, click a "calc" button to recalculate the field left of it.
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The k vector is associated with the position within the Brillouin zone. This is relevant for optical transitions. These involve only a minor change of the magnitude of the k vector, because the optical wavelength is much longer than the interatomic distances or the lattice period. Such a process excites one carrier from the valence band to the conduction band while leaving a hole i.
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It is only that the density of initial and final states is typically quite small just at the band gap energy, but the absorption coefficient then rises steeply for increasing photon energies — in proportion to the square root of the difference of photon energy and band gap energy.
Somewhat above the band gap energy, the absorption length can drop to the order of a micrometer.
It also implies that the refractive index has a large imaginary component. Similarly, emission processes corresponding to transitions from the conduction band to the valence band are easily possible, since every electron in the conduction band typically occupying one of the lowest levels there can find a hole in the valence band which has a very similar k vector, since the holes naturally occur in states with the highest possible energies.
Therefore, the carrier lifetime is usually relatively low, for example a few nanoseconds, even if the crystal structure is of high quality with a low defect density. In case of an indirect band gap, the k vector of the lowest states in the conduction band substantially differs from that for the highest states in the valence band.
As a consequence, absorption processes with photon energies only slightly above the band gap energy are hindered by the fact that there are no target states in the conduction band which have a suitable energy in addition to a suitable k vector.
Semiconductor Band Gaps
Such processes are possible, but occur at much lower rates; therefore, the absorption coefficient is much reduced. Also, the wavelength dependence of the absorption coefficient near the band gap is weaker. The absorption coefficient is also substantially temperature-dependent, since the temperature affects the phonon populations. For substantially higher photon energies, however, it becomes possible to directly excite carriers into the conduction band, not requiring phonons.
In that regime, the absorption coefficient becomes quite high — several orders of magnitude higher than close to the band gap. Similarly, emission processes related to recombination are hindered by the fact that a carrier in the conduction band can hardly find a hole with suitable k vector; any target states with that k vector are occupied. Therefore, emission processes are only possible by also involving the emission of a phonon. Again, this requirement substantially reduces the recombination rate and emission rate. That can also easily reduce the quantum efficiency of fluorescence , since other non-radiative recombination processes, provided e.
Examples for indirect band gap semiconductor materials are silicon Si , germanium Ge , aluminum arsenide AlAs and gallium phosphide GaP. Because of the reduced absorption coefficients, silicon layers in photodiodes and solar cells, for example, need to be substantially thicker — often hundreds of micrometers instead of only a couple of micrometers. For thin-film solar cells, one needs to use direct band gap materials e. Also, silicon is essentially unsuitable for light emitting diodes. Generally, the indirect band gap is often a challenge for silicon photonics.
Ternary and quaternary semiconductor compounds usually have a composition parameter, which influences the band gap properties, in particular the band gap energy. The composition parameter x indicates the fraction of indium which is added to replace gallium. The larger that parameter, the smaller is the band gap energy. The adjustment of such parameters for obtaining the desired band gap energy — for example, in order to obtain a specific emission wavelength of a laser diode or the desired absorption edge of a semiconductor saturable absorber mirror SESAM , is called band gap engineering.
So far, we have considered only homogeneous materials. If a material is inhomogeneous, for example containing quantum well or quantum dot structures, the electronic properties around those structures are modified. Frequently, one has a locally reduced band gap energy, so that quantum wells or dots in a medium can be absorbing even if the surrounding medium is not absorbing due to a too high band gap energy. That often occurs in semiconductor saturable absorber mirrors.