Carrier generation and recombination
Encyclopedia
In the solid state physics of semiconductor
s, carrier generation and recombination are processes by which mobile charge carriers (electron
s and electron hole
s) are created and eliminated. Carrier generation and recombination processes are fundamental to the operation of many optoelectronic semiconductor device
s, such as photodiode
s, LED
s and laser diode
s. They are also critical to a full analysis of p-n junction
devices such as bipolar junction transistor
s and p-n junction diode
s.
The electron–hole pair is the fundamental unit of generation and recombination, corresponding to an electron transitioning between the valence band and the conduction band.
determined by the crystal properties of the material. The actual energy distribution among the electrons is described by the Fermi energy
and the temperature
of the electrons. At absolute zero
temperature, all of the electrons have energy below the Fermi energy; but at non-zero temperatures the energy levels are filled following a Boltzmann distribution.
In semiconductors the Fermi energy lies in the middle of a forbidden band or band gap
between two allowed bands called the valence band
and the conduction band
. The valence band, immediately below the forbidden band, is normally very nearly completely occupied. The conduction band, above the Fermi level, is normally nearly completely empty. Because the valence band is so nearly full, its electrons are not mobile, and cannot flow as electrical current.
However, if an electron in the valence band acquires enough energy to reach the conduction band, it can flow freely among the nearly empty conduction band energy states. Furthermore it will also leave behind an electron hole that can flow as current exactly like a physical charged particle. Carrier generation describes processes by which electrons gain energy and move from the valence band to the conduction band, producing two mobile carriers; while recombination describes processes by which a conduction band electron loses energy and re-occupies the energy state of an electron hole in the valence band.
In a material at thermal equilibrium
generation and recombination are balanced, so that the net charge carrier
density remains constant. The equilibrium carrier density that results from the balance of these interactions is predicted by thermodynamics
. The resulting probability of occupation of energy states in each energy band is given by Fermi-Dirac statistics
.
s and other carriers, either with the lattice
of the material, or with optical photons. As the electron moves from one energy band to another, its gained or lost energy must take some other form, and the form of energy distinguishes various types of generation and recombination:
between the carriers, and so this process is the dominant generation and recombination process in silicon
and other indirect bandgap materials. It can also dominate in direct bandgap materials under conditions of very low carrier densities
(very low level injection). The energy is exchanged in the form of lattice vibration, or a phonon
exchanging thermal energy with the material. The impurities create energy level
s within the band gap
, forming deep-level trap
s.
, a photon
is emitted with the wavelength corresponding to the energy released. This effect is the basis of LEDs
. Because the photon carries relatively little momentum
, radiative recombination is significant only in direct bandgap materials.
When photons are present in the material, they can either be absorbed, generating a pair of free carriers, or they can stimulate a recombination event, resulting in a generated photon with similar properties to the one responsible for the event. Absorption is the active process in photodiode
s, solar cell
s, and other semiconductor photodetector
s, while stimulated emission
is responsible for laser action in laser diode
s.
The Auger recombination can be calculated from the equation :
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
s, carrier generation and recombination are processes by which mobile charge carriers (electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s and electron hole
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
s) are created and eliminated. Carrier generation and recombination processes are fundamental to the operation of many optoelectronic semiconductor device
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...
s, such as photodiode
Photodiode
A photodiode is a type of photodetector capable of converting light into either current or voltage, depending upon the mode of operation.The common, traditional solar cell used to generateelectric solar power is a large area photodiode....
s, LED
LEd
LEd is a TeX/LaTeX editing software working under Microsoft Windows. It is a freeware product....
s and laser diode
Laser diode
The laser diode is a laser where the active medium is a semiconductor similar to that found in a light-emitting diode. The most common type of laser diode is formed from a p-n junction and powered by injected electric current...
s. They are also critical to a full analysis of p-n junction
P-n junction
A p–n junction is formed at the boundary between a P-type and N-type semiconductor created in a single crystal of semiconductor by doping, for example by ion implantation, diffusion of dopants, or by epitaxy .If two separate pieces of material were used, this would...
devices such as bipolar junction transistor
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...
s and p-n junction diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
s.
The electron–hole pair is the fundamental unit of generation and recombination, corresponding to an electron transitioning between the valence band and the conduction band.
Band structure
Like other solids, semiconductor materials have electronic band structureElectronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
determined by the crystal properties of the material. The actual energy distribution among the electrons is described by the Fermi energy
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
and the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
of the electrons. At absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
temperature, all of the electrons have energy below the Fermi energy; but at non-zero temperatures the energy levels are filled following a Boltzmann distribution.
Band gap
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...
between two allowed bands called the valence band
Valence band
In solids, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature....
and the conduction band
Conduction band
In the solid-state physics field of semiconductors and insulators, the conduction band is the range of electron energies, higher than that of the valence band, sufficient to free an electron from binding with its individual atom and allow it to move freely within the atomic lattice of the material...
. The valence band, immediately below the forbidden band, is normally very nearly completely occupied. The conduction band, above the Fermi level, is normally nearly completely empty. Because the valence band is so nearly full, its electrons are not mobile, and cannot flow as electrical current.
However, if an electron in the valence band acquires enough energy to reach the conduction band, it can flow freely among the nearly empty conduction band energy states. Furthermore it will also leave behind an electron hole that can flow as current exactly like a physical charged particle. Carrier generation describes processes by which electrons gain energy and move from the valence band to the conduction band, producing two mobile carriers; while recombination describes processes by which a conduction band electron loses energy and re-occupies the energy state of an electron hole in the valence band.
In a material at thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
generation and recombination are balanced, so that the net charge carrier
Charge carriers in semiconductors
There are two recognized types of charge carriers in semiconductors. One of them is electrons, which carry negative electric charge. In addition, it is convenient to treat the traveling vacancies in the valence-band electron population as the second type of charge carriers, which carry a positive...
density remains constant. The equilibrium carrier density that results from the balance of these interactions is predicted by thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
. The resulting probability of occupation of energy states in each energy band is given by Fermi-Dirac statistics
Fermi-Dirac statistics
Fermi–Dirac statistics is a part of the science of physics that describes the energies of single particles in a system comprising many identical particles that obey the Pauli Exclusion Principle...
.
Generation and recombination processes
Carrier generation and recombination result from interaction between electronElectron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s and other carriers, either with the lattice
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
of the material, or with optical photons. As the electron moves from one energy band to another, its gained or lost energy must take some other form, and the form of energy distinguishes various types of generation and recombination:
Shockley–Read–Hall (SRH) process
The electron in transition between bands passes through a new energy state created within the band gap by an impurity in the lattice. The impurity state can absorb differences in momentumMomentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
between the carriers, and so this process is the dominant generation and recombination process in silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
and other indirect bandgap materials. It can also dominate in direct bandgap materials under conditions of very low carrier densities
Charge carrier density
The charge carrier density denotes the number of charge carriers per volume. It is measured in m−3. As any density it can depend on position.It should not be confused with the charge density, which is the number of charges per volume at a given energy....
(very low level injection). The energy is exchanged in the form of lattice vibration, or a phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
exchanging thermal energy with the material. The impurities create energy level
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
s within the band gap
Band gap
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...
, forming deep-level trap
Deep-level trap
Deep-level traps or deep-level defects are a generally undesirable type of electronic defect in semiconductors. They are "deep" in the sense that the energy required to remove an electron or hole from the trap to the valence or conduction band is much larger than the characteristic thermal energy...
s.
Photon exchange
During radiative recombination, a form of spontaneous emissionSpontaneous emission
Spontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...
, a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
is emitted with the wavelength corresponding to the energy released. This effect is the basis of LEDs
Light-emitting diode
A light-emitting diode is a semiconductor light source. LEDs are used as indicator lamps in many devices and are increasingly used for other lighting...
. Because the photon carries relatively little momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
, radiative recombination is significant only in direct bandgap materials.
When photons are present in the material, they can either be absorbed, generating a pair of free carriers, or they can stimulate a recombination event, resulting in a generated photon with similar properties to the one responsible for the event. Absorption is the active process in photodiode
Photodiode
A photodiode is a type of photodetector capable of converting light into either current or voltage, depending upon the mode of operation.The common, traditional solar cell used to generateelectric solar power is a large area photodiode....
s, solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....
s, and other semiconductor photodetector
Photodetector
Photosensors or photodetectors are sensors of light or other electromagnetic energy. There are several varieties:*Active pixel sensors are image sensors consisting of an integrated circuit that contains an array of pixel sensors, each pixel containing a both a light sensor and an active amplifier...
s, while stimulated emission
Stimulated emission
In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...
is responsible for laser action in laser diode
Laser diode
The laser diode is a laser where the active medium is a semiconductor similar to that found in a light-emitting diode. The most common type of laser diode is formed from a p-n junction and powered by injected electric current...
s.
Auger recombination
The energy is given to a third carrier, which is excited to a higher energy level without moving to another energy band. After the interaction, the third carrier normally loses its excess energy to thermal vibrations. Since this process is a three-particle interaction, it is normally only significant in non-equilibrium conditions when the carrier density is very high. The Auger effect process is not easily produced, because the third particle would have to begin the process in the unstable high-energy state.The Auger recombination can be calculated from the equation :
