Electron excitation
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Electron excitation is the transfer of a bound
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 ...
to a more energetic, but still bound
state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States * ''Our S ...
. This can be done by
photoexcitation Photoexcitation is the production of an excited state of a quantum system by photon absorption. The excited state originates from the interaction between a photon and the quantum system. Photons carry energy that is determined by the wavelength ...
(PE), where the electron 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 ...
and gains all its energy or by collisional
excitation Excitation, excite, exciting, or excitement may refer to: * Excitation (magnetic), provided with an electrical generator or alternator * Excite Ballpark, located in San Jose, California * Excite (web portal), web portal owned by IAC * Electron exc ...
(CE), where the electron receives energy from a collision with another, energetic electron. Within a semiconductor crystal lattice, thermal excitation is a process where lattice vibrations provide enough energy to transfer electrons to a higher
energy band In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ...
such as a more energetic sublevel or energy level. When an excited electron falls back to a state of lower energy, it undergoes electron relaxation (deexcitation). This is accompanied by the emission of a photon (radiative relaxation/
spontaneous emission Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount of ...
) or by a transfer of energy to another particle. The energy released is equal to the difference in energy levels between the electron energy states. In general, the excitation of electrons in atoms strongly varies from excitation in solids, due to the different nature of the electronic levels and the structural properties of some solids. The electronic excitation (or deexcitation) can take place by several processes such as: * collision with more energetic electrons (
Auger recombination In the solid-state physics of semiconductors, carrier generation and carrier recombination are processes by which mobile charge carriers (electrons and electron holes) are created and eliminated. Carrier generation and recombination processes are ...
,
impact ionization Impact ionization is the process in a material by which one energetic charge carrier can lose energy by the creation of other charge carriers. For example, in semiconductors, an electron (or Electron hole, hole) with enough kinetic energy can kno ...
, ...) *
absorption Absorption may refer to: Chemistry and biology * Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which ...
/ emission of 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 ...
, * absorption of several photons (so called
multiphoton ionization Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and ...
); e.g., quasi-monochromatic
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
light. There are several rules that dictate the transition of an electron to an excited state, known as
selection rules In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, i ...
. First, as previously noted, the electron must absorb an amount of energy equivalent to the energy difference between the electron's current energy level and an unoccupied, higher energy level in order to be promoted to that energy level. The next rule follows from the Frank-Condon Principle, which states that the absorption of a photon by an electron and the subsequent jump in energy levels is near-instantaneous. The atomic nuclei which the electron orbits cannot adjust to the change in electron position on the same time scale as the electron (because nuclei are much heavier), and thus the nuclei may be brought into a vibrational state in response to the electron transition. Then, the rule is that the amount of energy absorbed by an electron may allow for the electron to be promoted from a vibrational and electronic ground state to a vibrational and electronic excited state. A third rule is the
Laporte Rule The Laporte rule is a rule that explains the intensities of absorption spectra for chemical species. It is a selection rule that rigorously applies to chromophores that are centrosymmetric, i.e. with an inversion centre. It states that electronic t ...
, which necessitates that the two energy states between which an electron transitions must have different symmetry. A fourth rule is that when an electron undergoes a transition, the spin state of the molecule/atom that contains the electron must be conserved. Under some circumstances, certain selection rules may be broken and excited electrons may make "forbidden" transitions. The spectral lines associated with such transitions are known as
forbidden lines In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of photons by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particul ...
.


Electron excitation in solids


Ground state preparation

The energy and momentum of electrons in solids can be described by introducing
Bloch Bloch is a surname of German origin. Notable people with this surname include: A–F * (1859-1914), French rabbi *Adele Bloch-Bauer (1881-1925), Austrian entrepreneur *Albert Bloch (1882–1961), American painter * (born 1972), German motor journal ...
waves into the
Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...
with applying
periodic boundary conditions Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a ''unit cell''. PBCs are often used in computer simulations and mathematical mode ...
. Solving this
eigenvalue equation In linear algebra, linear transformations can be represented by matrices. If T is a linear transformation mapping \mathbb^n to \mathbb^m and \mathbf x is a column vector with n entries, then T( \mathbf x ) = A \mathbf x for some m \times n matrix ...
, one obtains sets of solutions that are describing bands of energies that are allowed to the electrons: the
electronic band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or '' ...
. The latter page contains a summary of the techniques that are nowadays available for modeling the properties of solid crystals at equilibrium, i.e., when they are not illuminated by light.


Electron excitation by light: polariton

The behavior of electrons excited by photons can be described by the
quasi-particle 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 ...
named "
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 ...
". A number of methods exist to describe these, both using classical and
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
. One of the methods is to use the concept of
dressed particle In theoretical physics, the term dressed particle refers to a bare particle together with some excitations of other quantum fields that are physically inseparable from the bare particle. For example, a dressed electron includes the cloud of virtu ...
.


See also

*
Energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...
*
Mode (electromagnetism) The mode of electromagnetic radiation describes the field pattern of the propagating waves. Electromagnetic modes are analogous to the normal modes of vibration in other systems, such as mechanical systems. Some of the classifications of electroma ...


References

Electron {{AMO-physics-stub