![Moving Wannier exciton](https://upload.wikimedia.org/wikipedia/commons/4/43/Moving_Wannier_exciton.svg)
An exciton is a
bound state
Bound or bounds may refer to:
Mathematics
* Bound variable
* Upper and lower bounds, observed limits of mathematical functions
Physics
* Bound state, a particle that has a tendency to remain localized in one or more regions of space
Geography
* ...
of an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
and an
electron hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...
which are attracted to each other by the electrostatic
Coulomb force. It is an electrically neutral
quasiparticle
In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
For exa ...
that exists in
insulators
Insulator may refer to:
* Insulator (electricity), a substance that resists electricity
** Pin insulator, a device that isolates a wire from a physical support such as a pin on a utility pole
** Strain insulator, a device that is designed to work ...
,
semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s and some liquids. The exciton is regarded as an elementary excitation of
condensed matter
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...
that can transport energy without transporting net electric charge.
An exciton can form when a material absorbs a
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
of higher energy than its
bandgap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (i ...
. This excites an electron from the
valence band
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in w ...
into the
conduction band
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in w ...
. In turn, this leaves behind a positively charged
electron hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...
(an abstraction for the location from which an electron was moved). The electron in the conduction band is then less attracted to this localized hole due to the repulsive
Coulomb forces from large numbers of electrons surrounding the hole and excited electron. These repulsive forces provide a stabilizing energy balance. Consequently, the exciton has slightly less energy than the unbound electron and hole. The
wavefunction
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
of the bound state is said to be ''
hydrogenic
A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron. These atoms are isoelectronic with hydrogen. Examples of hydrogen-like atoms include, but are not limited to, hydrogen itself, all alkali metals such a ...
'', an
exotic atom
An exotic atom is an otherwise normal atom in which one or more sub-atomic particles have been replaced by other particles of the same charge. For example, electrons may be replaced by other negatively charged particles such as muons (muonic atoms) ...
state akin to that of a
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
. However, the
binding energy
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
is much smaller and the particle's size much larger than a hydrogen atom. This is because of both the screening of the Coulomb force by other electrons in the semiconductor (i.e., its
relative permittivity
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
), and the small
effective masses of the excited electron and hole. The recombination of the electron and hole, i.e., the decay of the exciton, is limited by resonance stabilization due to the overlap of the electron and hole wave functions, resulting in an extended lifetime for the exciton.
The electron and hole may have either parallel or anti-parallel
spins. The spins are coupled by the
exchange interaction
In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical ...
, giving rise to exciton
fine structure. In periodic lattices, the properties of an exciton show
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
(k-vector) dependence.
The concept of excitons was first proposed by
Yakov Frenkel
__NOTOC__
Yakov Il'ich Frenkel (russian: Яков Ильич Френкель; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed matter physics. He is also known as Jacov Frenkel, frequ ...
in 1931, when he described the excitation of atoms in a lattice of insulators. He proposed that this excited state would be able to travel in a particle-like fashion through the lattice without the net transfer of charge.
Excitons are often treated in the two limiting cases of small
dielectric constant
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
versus large dielectric constant; corresponding to Frenkel exciton and Wannier–Mott exciton respectively.
Frenkel exciton
In materials with a relatively small
dielectric constant
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
, the Coulomb interaction between an electron and a hole may be strong and the excitons thus tend to be small, of the same order as the size of the unit cell. Molecular excitons may even be entirely located on the same molecule, as in
fullerene
A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms. The molecule may be a hollow sphere, ...
s. This ''Frenkel exciton'', named after
Yakov Frenkel
__NOTOC__
Yakov Il'ich Frenkel (russian: Яков Ильич Френкель; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed matter physics. He is also known as Jacov Frenkel, frequ ...
, has a typical binding energy on the order of 0.1 to 1
eV. Frenkel excitons are typically found in alkali halide crystals and in organic molecular crystals composed of aromatic molecules, such as
anthracene
Anthracene is a solid polycyclic aromatic hydrocarbon (PAH) of formula C14H10, consisting of three fused benzene rings. It is a component of coal tar. Anthracene is used in the Economic production, production of the red dye alizarin and other dyes ...
and
tetracene. Another example of Frenkel exciton includes on-site ''d''-''d'' excitations in transition metal compounds with partially-filled ''d''-shells. While ''d''-''d'' transitions are in principle forbidden by symmetry, they become weakly-allowed in a crystal when the symmetry is broken by structural relaxations or other effects. Absorption of a photon resonant with a ''d''-''d'' transition leads to the creation of an electron-hole pair on a single atomic site, which can be treated as a Frenkel exciton.
Wannier–Mott exciton
In semiconductors, the dielectric constant is generally large. Consequently,
electric field screening
In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases (classical plasmas), electrolytes, and charge c ...
tends to reduce the Coulomb interaction between electrons and holes. The result is a ''Wannier–Mott exciton'', which has a radius larger than the lattice spacing. Small effective mass of electrons that is typical of semiconductors also favors large exciton radii. As a result, the effect of the lattice potential can be incorporated into the effective masses of the electron and hole. Likewise, because of the lower masses and the screened Coulomb interaction, the binding energy is usually much less than that of a hydrogen atom, typically on the order of . This type of exciton was named for
Gregory Wannier
Gregory Hugh Wannier (1911–1983) was a Swiss physicist.
Biography
Wannier received his physics PhD under Ernst Stueckelberg at the University of Basel in 1935. He worked with Professor Eugene P. Wigner as a post-doc exchange student at Prince ...
and
Nevill Francis Mott
Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. ...
. Wannier–Mott excitons are typically found in semiconductor crystals with small energy gaps and high dielectric constants, but have also been identified in liquids, such as liquid
xenon
Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...
. They are also known as ''large excitons''.
In single-wall
carbon nanotubes
A scanning tunneling microscopy image of a single-walled carbon nanotube
Rotating single-walled zigzag carbon nanotube
A carbon nanotube (CNT) is a tube made of carbon with diameters typically measured in nanometers.
''Single-wall carbon nan ...
, excitons have both Wannier–Mott and Frenkel character. This is due to the nature of the Coulomb interaction between electrons and holes in one-dimension. The dielectric function of the nanotube itself is large enough to allow for the spatial extent of the
wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
to extend over a few to several nanometers along the tube axis, while poor screening in the vacuum or dielectric environment outside of the nanotube allows for large (0.4 to ) binding energies.
Often more than one band can be chosen as source for the electron and the hole, leading to different types of excitons in the same material. Even high-lying bands can be effective as
femtosecond two-photon experiments have shown. At cryogenic temperatures, many higher excitonic levels can be observed approaching the edge of the band, forming a series of spectral absorption lines that are in principle similar to
hydrogen spectral series
The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an ...
.
Equations for 3D semiconductors
In a bulk semiconductor, a Wannier exciton has an energy and radius associated with it, called exciton Rydberg energy and exciton Bohr radius respectively. For the energy, we have
:
where
is the Rydberg unit of energy (cf.
Rydberg constant
In spectroscopy, the Rydberg constant, symbol R_\infty for
heavy atoms or R_\text for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first aro ...
),
is the (static) relative permittivity,
is the reduced mass of the electron and hole, and
is the electron mass. Concerning the radius, we have
:
where
is the
Bohr radius
The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an ...
.
So for example in
GaAs
Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a zinc blende crystal structure.
Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monolithic microwave integrated circui ...
, we have relative permittivity of 12.8 and effective electron and hole masses as 0.067''m
0'' and 0.2''m
0'' respectively; and that gives us
meV and
nm.
Equations for 2D semiconductors
In
two-dimensional (2D) materials, the system is
quantum confined in the direction perpendicular to the plane of the material. The reduced dimensionality of the system has an effect on the binding energies and radii of Wannier excitons. In fact, excitonic effects are enhanced in such systems.
For a simple screened Coulomb potential, the binding energies take the form of the 2D hydrogen atom
:
.
In most 2D semiconductors, the Rytova–Keldysh form is a more accurate approximation to the exciton interaction
:
where
is the so-called screening length,
the average dielectric constant of the surrounding media, and
the exciton radius. For this potential, no general expression for the exciton energies may be found. One must instead turn to numerical procedures, and it is precisely this potential that gives rise to the nonhydrogenic Rydberg series of the energies in 2D semiconductors.
Example: excitons in transition metal dichalcogenides (TMDs)
Monolayers of a transition metal dichalcogenide (TMD) are a good and cutting edge example where excitons play a major role. In particular, in these systems, they exhibit a bounding energy of the order of 0.5 eV
with a Coulomb attraction between the hole and the electrons stronger than in other traditional quantum wells. As a result, optical excitonic peaks are present in these materials even at room temperatures.
Charge-transfer exciton
An intermediate case between Frenkel and Wannier excitons is the ''charge-transfer (CT) exciton''. In molecular physics, CT excitons form when the electron and the hole occupy adjacent molecules. They occur primarily in organic and molecular crystals; in this case, unlike Frenkel and Wannier excitons, CT excitons display a static
electric dipole moment
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...
. CT excitons can also occur in transition metal oxides, where they involve an electron in the transition metal 3''d'' orbitals and a hole in the oxygen 2''p'' orbitals. Notable examples include the lowest-energy excitons in correlated cuprates or the two-dimensional exciton of TiO
2. Irrespective of the origin, the concept of CT exciton is always related to a transfer of charge from one atomic site to another, thus spreading the wave-function over a few lattice sites.
Surface exciton
At surfaces it is possible for so called ''image states'' to occur, where the hole is inside the solid and the electron is in the vacuum. These electron-hole pairs can only move along the surface.
Atomic and molecular excitons
Alternatively, an exciton may be described as an excited state of an atom,
ion
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
, or molecule, if the excitation is wandering from one cell of the lattice to another.
When a molecule absorbs a quantum of energy that corresponds to a transition from one
molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of findin ...
to another molecular orbital, the resulting electronic excited state is also properly described as an exciton. An
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
is said to be found in the
lowest unoccupied orbital and an
electron hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...
in the
highest occupied molecular orbital
In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for ''highest occupied molecular orbital'' and ''lowest unoccupied molecular orbital'', respectively. HOMO and LUMO are sometimes collectively called the ''frontie ...
, and since they are found within the same molecular orbital manifold, the electron-hole state is said to be bound. Molecular excitons typically have characteristic lifetimes on the order of
nanoseconds
A nanosecond (ns) is a unit of time in the International System of Units (SI) equal to one billionth of a second, that is, of a second, or 10 seconds.
The term combines the SI prefix ''nano-'' indicating a 1 billionth submultiple of an SI unit ( ...
, after which the ground electronic state is restored and the molecule undergoes photon or
phonon
In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
emission. Molecular excitons have several interesting properties, one of which is energy transfer (see
Förster resonance energy transfer
Förster resonance energy transfer (FRET), fluorescence resonance energy transfer, resonance energy transfer (RET) or electronic energy transfer (EET) is a mechanism describing energy transfer between two light-sensitive molecules ( chromophores). ...
) whereby if a molecular exciton has proper energetic matching to a second molecule's spectral absorbance, then an exciton may transfer (''hop'') from one molecule to another. The process is strongly dependent on intermolecular distance between the species in solution, and so the process has found application in sensing and ''molecular rulers''.
The hallmark of molecular excitons in organic molecular crystals are doublets and/or triplets of exciton absorption bands strongly polarized along crystallographic axes. In these crystals an elementary cell includes several molecules sitting in symmetrically identical positions, which results in the level degeneracy that is lifted by intermolecular interaction. As a result, absorption bands are polarized along the symmetry axes of the crystal. Such multiplets were discovered by
Antonina Prikhot'ko
Antonina Fedorivna Prykhotko (; 26 April 1906, Pyatigorsk – 29 September 1995, Kyiv), was a Soviet and Ukrainian experimental physicist. She was an Academician of the National Academy of Sciences of Ukraine and is known for her fundamental co ...
and their genesis was proposed by Alexander Davydov. It is known as 'Davydov splitting'.
Giant oscillator strength of bound excitons
Excitons are lowest excited states of the electronic subsystem of pure crystals. Impurities can bind excitons, and when the bound state is shallow, the oscillator strength for producing bound excitons is so high that impurity absorption can compete with intrinsic exciton absorption even at rather low impurity concentrations. This phenomenon is generic and applicable both to the large radius (Wannier–Mott) excitons and molecular (Frenkel) excitons. Hence, excitons bound to impurities and defects possess
giant oscillator strength Giant oscillator strength is inherent in excitons that are weakly bound to impurities or defects in crystals.
The spectrum of fundamental absorption of direct-gap semiconductors such as gallium arsenide (GaAs) and cadmium sulfide (CdS) is continuo ...
.
Self-trapping of excitons
In crystals, excitons interact with phonons, the lattice vibrations. If this coupling is weak as in typical semiconductors such as GaAs or Si, excitons are scattered by phonons. However, when the coupling is strong, excitons can be self-trapped. Self-trapping results in dressing excitons with a dense cloud of virtual phonons which strongly suppresses the ability of excitons to move across the crystal. In simpler terms, this means a local deformation of the crystal lattice around the exciton. Self-trapping can be achieved only if the energy of this deformation can compete with the width of the exciton band. Hence, it should be of atomic scale, of about an electron volt.
Self-trapping of excitons is similar to forming strong-coupling
polaron
A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electro ...
s but with three essential differences. First, self-trapped exciton states are always of a small radius, of the order of lattice constant, due to their electric neutrality. Second, there exists a self-trapping barrier separating free and self-trapped states, hence, free excitons are metastable. Third, this barrier enables coexistence of free and self-trapped states of excitons. This means that spectral lines of free excitons and wide bands of self-trapped excitons can be seen simultaneously in absorption and luminescence spectra. While the self-trapped states are of lattice-spacing scale, the barrier has typically much larger scale. Indeed, its spatial scale is about
where
is effective mass of the exciton,
is the exciton-phonon coupling constant, and
is the characteristic frequency of optical phonons. Excitons are self-trapped when
and
are large, and then the spatial size of the barrier is large compared with the lattice spacing. Transforming a free exciton state into a self-trapped one proceeds as a collective tunneling of coupled exciton-lattice system (an
instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. Mo ...
). Because
is large, tunneling can be described by a continuum theory. The height of the barrier
. Because both
and
appear in the denominator of
, the barriers are basically low. Therefore, free excitons can be seen in crystals with strong exciton-phonon coupling only in pure samples and at low temperatures. Coexistence of free and self-trapped excitons was observed in rare-gas solids, alkali-halides, and in molecular crystal of pyrene.
Interaction
Excitons are the main mechanism for
light emission
This is a list of sources of light, the visible part of the electromagnetic spectrum. Light sources produce photons from another energy source, such as heat, chemical reactions, or conversion of mass or a different frequency of electromagnetic ener ...
in semiconductors at low
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
(when the characteristic thermal energy ''
kT'' is less than the exciton
binding energy
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
), replacing the free electron-hole recombination at higher temperatures.
The existence of exciton states may be inferred from the absorption of light associated with their excitation. Typically, excitons are observed just below the
band gap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in ...
.
When excitons interact with photons a so-called
polariton
In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also ...
(or more specifically
exciton-polariton
In physics the Exciton–polariton is a type of polariton; a hybrid light and matter quasiparticle arising from the strong coupling of the electromagnetic dipolar oscillations of excitons (either in bulk or quantum wells) and photons. Because lig ...
) is formed. These excitons are sometimes referred to as ''dressed excitons''.
Provided the interaction is attractive, an exciton can bind with other excitons to form a
biexciton
In condensed matter physics, biexcitons are created from two free excitons.
Formation of biexcitons
In quantum information and computation, it is essential to construct coherent combinations of quantum states.
The basic quantum operations can b ...
, analogous to a dihydrogen
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
. If a large density of excitons is created in a material, they can interact with one another to form an
electron-hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or crystal structure, atomic lattice. Since in ...
liquid, a state observed in k-space indirect semiconductors.
Additionally, excitons are integer-spin particles obeying
Bose
Bose may refer to:
* Bose (crater), a lunar crater
* ''Bose'' (film), a 2004 Indian Tamil film starring Srikanth and Sneha
* Bose (surname), a surname (and list of people with the name)
* Bose, Italy, a ''frazioni'' in Magnano, Province of Biella ...
statistics in the low-density limit. In some systems, where the interactions are repulsive, a
Bose–Einstein condensed state, called excitonium, is predicted to be the ground state. Some evidence of excitonium has existed since the 1970s, but has often been difficult to discern from a Peierls phase. Exciton condensates have allegedly been seen in a double quantum well systems. In 2017 Kogar et al. found "compelling evidence" for observed excitons condensing in the three-dimensional semimetal 1T-TiSe2
Spatially direct and indirect excitons
Normally, excitons in a semiconductor have a very short lifetime due to the close proximity of the electron and hole. However, by placing the electron and hole in spatially separated quantum wells with an insulating barrier layer in between so called 'spatially indirect' excitons can be created. In contrast to ordinary (spatially direct), these spatially indirect excitons can have large spatial separation between the electron and hole, and thus possess a much longer lifetime. This is often used to cool excitons to very low temperatures in order to study Bose–Einstein condensation (or rather its two-dimensional analog).
Excitons in nanoparticles
In semiconducting crystallite
nanoparticles
A nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 1 ...
which exhibit quantum confinement effects and hence behave as quantum dots, excitonic radii are given by
[
][
]
:
where
is the
relative permittivity
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
,
is the reduced mass of the electron-hole system,
is the electron mass, and
is the
Bohr radius
The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an ...
.
See also
*
Orbiton
Orbitons are one of three quasiparticles, along with holons and spinons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero. The e ...
*
Oscillator strength In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule. For example, if an emissive state ha ...
*
Plasmon
In physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quantiz ...
*
Polariton superfluid Polariton superfluid is predicted to be a state of the exciton-polaritons system that combines the characteristics of lasers with those of excellent electrical conductors. Researchers look for this state in a solid state optical microcavity coupled ...
*
Trion
References
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Quasiparticles
Bosons