Quantum cascade laser

Quantum cascade laser

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Quantum cascade lasers are semiconductor lasers that emit in the mid- to far-infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

 portion of the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

 and were first demonstrated by Jerome Faist, Federico Capasso
Federico Capasso
Federico Capasso , a prominent applied physicist, was one of the inventors of the quantum cascade laser during his work at Bell Laboratories. He is currently on the faculty of Harvard University...

, Deborah Sivco, Carlo Sirtori, Albert Hutchinson, and Alfred Cho at Bell Laboratories in 1994.

Unlike typical interband semiconductor lasers that emit electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 through the recombination of electron–hole pairs across the material 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...

, QCLs are unipolar and laser emission is achieved through the use of intersubband transitions in a repeated stack of semiconductor multiple quantum well
Quantum well
A quantum well is a potential well with only discrete energy values.One technology to create quantization is to confine particles, which were originally free to move in three dimensions, to two dimensions, forcing them to occupy a planar region...

 heterostructures, an idea first proposed in the paper "Possibility of amplification of electromagnetic waves in a semiconductor with a superlattice
Superlattice is a periodic structure of layers of two materials. Typically, the thickness of one layer is several nanometers.- Discovery :Superlattices were discovered early in the 20th century through their special X-ray diffraction patterns....

" by R.F. Kazarinov and R.A. Suris in 1971.

Intersubband vs. interband transitions

Within a bulk semiconductor crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

, electrons may occupy states in one of two continuous energy bands - 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....

, which is heavily populated with low energy electrons 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...

, which is sparsely populated with high energy electrons. The two energy bands are separated by an energy band gap in which there are no permitted states available for electrons to occupy. Conventional semiconductor laser diodes generate light by a single 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...

 being emitted when a high energy electron in the conduction band recombines with a 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...

 in the valence band. The energy of the photon and hence the emission wavelength of laser diodes is therefore determined by the band gap of the material system used.

A QCL however does not use bulk semiconductor materials in its optically active region. Instead it comprises a periodic
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...

 series of thin layers of varying material composition forming a superlattice
Superlattice is a periodic structure of layers of two materials. Typically, the thickness of one layer is several nanometers.- Discovery :Superlattices were discovered early in the 20th century through their special X-ray diffraction patterns....

. The superlattice introduces a varying electric potential
Electric potential
In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...

 across the length of the device, meaning that there is a varying probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 of electrons occupying different positions over the length of the device. This is referred to as one-dimensional multiple quantum well confinement and leads to the splitting of the band of permitted energies into a number of discrete electronic subbands. By suitable design of the layer thicknesses it is possible to engineer a population inversion
Population inversion
In physics, specifically statistical mechanics, a population inversion occurs when a system exists in state with more members in an excited state than in lower energy states...

 between two subbands in the system which is required in order to achieve laser emission. Since the position of the energy levels in the system is primarily determined by the layer thicknesses and not the material, it is possible to tune the emission wavelength of QCLs over a wide range in the same material system.

Additionally, in semiconductor laser diodes, electrons and holes are annihilated after recombining across the band gap and can play no further part in photon generation. However in a unipolar QCL, once an 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...

 has undergone an intersubband transition and emitted a 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...

 in one period of the superlattice, it can tunnel
Quantum tunnelling
Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...

 into the next period of the structure where another photon can be emitted. This process of a single electron causing the emission of multiple photons as it traverses through the QCL structure gives rise to the name cascade and makes a quantum efficiency
Quantum efficiency
Quantum efficiency is a quantity defined for a photosensitive device such as photographic film or a charge-coupled device as the percentage of photons hitting the photoreactive surface that will produce an electron–hole pair. It is an accurate measurement of the device's electrical sensitivity to...

 of greater than unity possible which leads to higher output powers than semiconductor laser diodes.

Rate equations

QCLs are typically based upon a three-level system. Assuming the formation of the wavefunctions is a fast process compared to the scattering between states, the time independent solutions to the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

 may be applied and the system can be modelled using rate equations. Each subband contains a number of electrons (where is the subband index) which scatter
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

 between levels with a lifetime (reciprocal of the average intersubband scattering rate ), where and are the initial and final subband indices. Assuming that no other subbands are populated, the rate equations for the three level lasers are given by:

In the steady state
Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

, the time derivatives are equal to zero and . The general rate equation for electrons in subband i of an N level system is therefore:

Under the assumption that absorption processes can be ignored, (i.e. , valid at low temperatures) the middle rate equation gives

Therefore if (i.e. ) then and a population inversion will exist. The population ratio is defined as

If all N steady-state rate equations are summed, the right hand side becomes zero, meaning that the system is underdetermined, and it is possible only to find the relative population of each subband. If the total sheet density of carriers in the system is also known, then the absolute population of carriers in each subband may be determined using:

As an approximation, it can be assumed that all the carriers in the system are supplied by doping
Doping (semiconductor)
In semiconductor production, doping intentionally introduces impurities into an extremely pure semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic...

. If the dopant species has a negligible ionisation energy then is approximately equal to the doping density.

Active region designs

The scattering rates are tailored by suitable design of the layer thicknesses in the superlattice which determine the electron wave functions of the subbands. The scattering rate between two subbands is heavily dependent upon the overlap of the wave functions and energy spacing between the subbands. The figure shows the wave functions in a three quantum well (3QW) QCL active region and injector.

In order to decrease , the overlap of the upper and lower laser levels is reduced. This is often achieved through designing the layer thicknesses such that the upper laser level is mostly localised in the left-hand well of the 3QW active region, while the lower laser level wave function is made to mostly reside in the central and right-hand wells. This is known as a diagonal transition. A vertical transition is one in which the upper laser level is localised in mainly the central and right-hand wells. This increases the overlap and hence which reduces the population inversion, but it increases the strength of the radiative transition and therefore the gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...


In order to increase , the lower laser level and the ground level wave functions are designed such that they have a good overlap and to increase further, the energy spacing between the subbands is designed such that it is equal to the longitudinal optical (LO) phonon energy (~36 meV in GaAs) so that resonant LO phonon-electron scattering can quickly depopulate the lower laser level.

Material systems

The first QCL was fabricated in the InGaAs
Indium gallium arsenide
Indium gallium arsenide is a semiconductor composed of indium, gallium and arsenic. It is used in high-power and high-frequency electronics because of its superior electron velocity with respect to the more common semiconductors silicon and gallium arsenide. InGaAs bandgap also makes it the...

Aluminium indium arsenide
Aluminium indium arsenide, also indium aluminium arsenide or AlInAs , is a semiconductor material with very nearly the same lattice constant as GaInAs, but a larger bandgap...

 material system lattice-matched to an InP substrate. This particular material system has a conduction band offset (quantum well depth) of 520 meV
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...

. These InP-based devices have reached very high levels of performance across the mid-infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

 spectral range, achieving high power, above room-temperature, continuous wave
Continuous wave
A continuous wave or continuous waveform is an electromagnetic wave of constant amplitude and frequency; and in mathematical analysis, of infinite duration. Continuous wave is also the name given to an early method of radio transmission, in which a carrier wave is switched on and off...


In 1998 GaAs/AlGaAs
Aluminium gallium arsenide
Aluminium gallium arsenide is a semiconductor material with very nearly the same lattice constant as GaAs, but a larger bandgap. The x in the formula above is a number between 0 and 1 - this indicates an arbitrary alloy between GaAs and AlAs.The bandgap varies between 1.42 eV and 2.16 eV...

 QCLs were demonstrated by Sirtori et al. proving that the QC concept is not restricted to one material system. This material system has a varying quantum well depth depending on the aluminium fraction in the barriers. Although GaAs-based QCLs have not matched the performance levels of InP-based QCLs in the mid-infrared, they have proven to be very successful in the terahertz region of the spectrum.

The short wavelength limit of QCLs is determined by the depth of the quantum well and recently QCLs have been developed in material systems with very deep quantum wells in order to achieve short wavelength emission. The InGaAs/AlAsSb material system has quantum wells 1.6 eV deep and has been used to fabricate QCLs emitting at 3 μm. InAs/AlSb QCLs have quantum wells 2.1 eV deep and electroluminescence
Electroluminescence is an optical phenomenon and electrical phenomenon in which a material emits light in response to the passage of an electric current or to a strong electric field...

 at wavelengths as short as 2.5 μm has been observed.

QCLs may also allow laser operation in materials traditionally considered to have poor optical properties. Indirect bandgap materials such as silicon have minimum electron and hole energies at different momentum values. For interband optical transitions, carriers change momentum through a slow, intermediate scattering process, dramatically reducing the optical emission intensity. Intersubband optical transitions however, are independent of the relative momentum of conduction band and valence band minima and theoretical proposals for Si
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...

SiGe , or silicon-germanium, is a general term for the alloy Si1−xGex which consists of any molar ratio of silicon and germanium. It is commonly used as a semiconductor material in integrated circuits for heterojunction bipolar transistors or as a strain-inducing layer for CMOS transistors...

 quantum cascade emitters have been made.

Emission wavelengths

QCLs currently cover the wavelength range from 2.75–250 μm (and extends to 355 μm with the application of a magnetic field).

Optical waveguides

The first step in processing quantum cascade gain material to make a useful light-emitting device is to confine the gain medium in an optical waveguide
Waveguide (optics)
An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber and rectangular waveguides....

. This makes it possible to direct the emitted light into a collimated beam, and allows a laser resonator to be built such that light can be coupled back into the gain medium.

Two types of optical waveguides are in common use. A ridge waveguide is created by etching parallel trenches in the quantum cascade gain material to create an isolated stripe of QC material, typically ~10 um wide, and several mm long. A dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

 material is typically deposited in the trenches to guide injected current into the ridge, then the entire ridge is typically coated with gold to provide electrical contact and to help remove heat from the ridge when it is producing light. Light is emitted from the cleaved ends of the waveguide, with an active area that is typically only a few micrometers in dimension.

The second waveguide type is a buried heterostructure. Here, the QC material is also etched to produce an isolated ridge. Now, however, new semiconductor material is grown over the ridge. The change in index of refraction between the QC material and the overgrown material is sufficient to create a waveguide. Dielectric material is also deposited on the overgrown material around QC ridge to guide the injected current into the QC gain medium. Buried heterostructure waveguides are efficient at removing heat from the QC active area when light is being produced.

Laser types

Although the quantum cascade gain medium can be used to produce incoherent
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

 light in a superluminescent configuration, it is most commonly used in combination with an optical cavity to form a laser.

Fabry–Pérot lasers

This is the simplest of the quantum cascade lasers. An optical waveguide is first fabricated out of the quantum cascade material to form the gain medium. The ends of the crystalline semiconductor device are then cleaved to form two parallel mirrors on either end of the waveguide, thus forming a Fabry–Pérot resonator. The residual reflectivity on the cleaved facets from the semiconductor-to-air interface is sufficient to create a resonator. Fabry–Pérot quantum cascade lasers are capable of producing high powers, but are typically multi-mode
Longitudinal mode
For the longitudinal mode of conduction of electric currents, see Common modeA longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive...

 at higher operating currents. The wavelength can be changed chiefly by changing the temperature of the QC device.

Distributed feedback lasers

A distributed feedback
Distributed feedback laser
A distributed feedback laser is a type of laser diode, quantum cascade laser or optical fibre laser where the active region of the device is periodically structured as a diffraction grating...

 (DFB) quantum cascade laser is similar to a Fabry–Pérot laser, except for a distributed Bragg reflector (DBR)
Distributed Bragg reflector
A distributed Bragg reflector is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with varying refractive index, or by periodic variation of some characteristic of a dielectric waveguide, resulting in periodic variation...

 built on top of the waveguide to prevent it from emitting at other than the desired wavelength. This forces single mode operation of the laser, even at higher operating currents. DFB lasers can be tuned chiefly by changing the temperature, although an interesting variant on tuning can be obtained by pulsing a DFB laser. In this mode, the wavelength of the laser is rapidly “chirp
A chirp is a signal in which the frequency increases or decreases with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly used in sonar and radar, but has other applications, such as in spread spectrum communications...

ed” during the course of the pulse, allowing rapid scanning of a spectral region.

External cavity lasers

In an external cavity (EC) quantum cascade laser, the quantum cascade device serves as the laser gain medium. One, or both, of the waveguide facets have an anti-reflection coating that defeats the optical cavity action of the cleaved facets. Mirrors are then arranged in a configuration external to the QC device to create the optical cavity.

If a frequency-selective element is included in the external cavity, it is possible to reduce the laser emission to a single wavelength, and even tune the radiation. For example, diffraction gratings have been used to create a tunable laser that can tune over 15% of its center wavelength.


The alternating layers of the two different semiconductors which form the quantum heterostructure
Quantum heterostructure
Quantum heterostructure is a heterostructure in a substrate , where size restricts the movements of the charge carriers forcing them into a quantum confinement. This leads to the formation of a set of discrete energy levels at which the carriers can exist...

 may be grown on to a substrate using a variety of methods such as molecular beam epitaxy
Molecular beam epitaxy
Molecular beam epitaxy is one of several methods of depositing single crystals. It was invented in the late 1960s at Bell Telephone Laboratories by J. R. Arthur and Alfred Y. Cho.-Method:...

 (MBE) , metalorganic vapour phase epitaxy
Metalorganic vapour phase epitaxy
Metalorganic vapour phase epitaxy , also known as organometallic vapour phase epitaxy or metalorganic chemical vapour deposition , is a chemical vapour deposition method of epitaxial growth of materials, especially compound semiconductors, from the surface reaction of organic compounds or...

 (MOVPE), or metalorganic chemical vapor deposition (MOCVD).


Distributed feedback (DFB) quantum cascade lasers were first commercialized in 2004, and broadly-tunable external cavity quantum cascade lasers first commercialized in 2006. The high optical power output, tuning range and room temperature operation make QCLs useful for spectroscopic applications such as remote sensing of environmental gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es and pollutant
A pollutant is a waste material that pollutes air, water or soil, and is the cause of pollution.Three factors determine the severity of a pollutant: its chemical nature, its concentration and its persistence. Some pollutants are biodegradable and therefore will not persist in the environment in the...

s in the atmosphere and homeland security. They may eventually be used for vehicular cruise control
Cruise control
Cruise control is a system that automatically controls the speed of a motor vehicle. The system takes over the throttle of the car to maintain a steady speed as set by the driver.-History:...

 in conditions of poor visibility
In meteorology, visibility is a measure of the distance at which an object or light can be clearly discerned. It is reported within surface weather observations and METAR code either in meters or statute miles, depending upon the country. Visibility affects all forms of traffic: roads, sailing...

, collision avoidance radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

, industrial process control, and medical diagnostics
Diagnosis is the identification of the nature and cause of anything. Diagnosis is used in many different disciplines with variations in the use of logics, analytics, and experience to determine the cause and effect relationships...

 such as breath analyzers. QCLs are also used to study plasma chemistry.

Their large dynamic range, excellent sensitivity, and failsafe operation combined with the solid-state reliability should easily overcome many of the technological hurdles that impede existing technology in these markets. When used in multiple-laser systems, intrapulse QCL spectroscopy offers broadband spectral coverage that can potentially be used to identify and quantify complex heavy molecules such as those in toxic chemicals, explosives, and drugs.

Unguided QCL emission in the 3–5 μm atmospheric window could be used as a cheaper alternative to optical fibres for high-speed Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

access in built up areas.

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