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| '''Photoluminescence''' (abbreviated as '''PL''') describes the phenomenon of light emission from any form of matter after the absorption of [[photons]] (electromagnetic radiation). It is one of many forms of [[luminescence]] (light emission) and is initiated by [[photoexcitation]] (excitation by photons), hence the prefix ''photo-''.<ref>[[IUPAC]], [[Compendium of Chemical Terminology]], 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "[http://goldbook.iupac.org/P04588.html photochemistry]".</ref> The excitation typically undergoes various relaxation processes and then photons are re-radiated. The period between absorption and emission can be extremely short: it ranges from the femtosecond-regime for the emission from, e.g., free-carrier plasma in inorganic semiconductors<ref name="HayesDeveaud2002">Hayes, G.R.; Deveaud, B. (2002). "Is Luminescence from Quantum Wells Due to Excitons?". ''physica status solidi (a)'' '''190''' (3): 637–640. [http://dx.doi.org/10.1002%2F1521-396X%28200204%29190%3A3%3C637%3A%3AAID-PSSA637%3E3.0.CO%3B2-7 doi:10.1002/1521-396X(200204)190:3<637::AID-PSSA637>3.0.CO;2-7]</ref> up to milliseconds for phosphorescent processes in molecular systems; however, it can also be extended into minutes or hours under special circumstances.
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| The observation of photoluminescence at a certain energy can be seen most-straightforwardly as indication of population of the state associated with this transition energy.
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| While this is generally true in [[atoms]] and similar systems, correlations and other more complex phenomena also act as sources for photoluminescence in [[Many-body problem|many-body systems]] such as semiconductors. A theoretical approach to handle this is given by the [[semiconductor luminescence equations]].
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| == Forms of photoluminescence ==
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| Photoluminescence processes can be classified by various parameters such as the energy of the exciting photon with respect to the emission.
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| Resonant excitation describes the situation in which a photon of a particular wavelength is absorbed and an equivalent photon is immediately emitted.This is often referred to as [[resonance fluorescence]]. For materials in solution or in the gas [[Phase (matter)|phase]], this process involves no significant internal energy transitions of the chemical substance between absorption and emission. In crystalline inorganic semiconductors where an electronic [[band structure]] is formed, the secondary emission is more complicated as it contains both [[Coherence (physics)|coherent]] such as resonant [[Rayleigh scattering]] where a fixed phase relation with the driving light field is maintained and [[Coherence (physics)|incoherent]] contributions,<ref name="Kira1999">Kira, M.; Jahnke, F.; Koch, S. W. (1999). "Quantum Theory of Secondary Emission in Optically Excited Semiconductor Quantum Wells". ''Physical Review Letters'' '''82''' (17): 3544–3547. [http://dx.doi.org/10.1103%2FPhysRevLett.82.3544 doi:10.1103/PhysRevLett.82.3544]</ref>
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| The latter originate, e.g., from the radiative recombination of [[excitons]], [[Coulomb interaction|Coulomb]]-bound electron-hole pair states in solids. Resonance fluorescence may also show significant [[Quantum optics|quantum optical]] correlations.<ref name="Kira1999" /><ref name="Kimble1977"> Kimble, H. J.; Dagenais, M.; Mandel, L. (1977). "Photon Antibunching in Resonance Fluorescence". ''Physical Review Letters'' '''39''' (11): 691–695. [http://dx.doi.org/10.1103%2FPhysRevLett.39.691 doi:10.1103/PhysRevLett.39.691]</ref><ref name="Carmichael1976"> Carmichael, H. J.; Walls, D. F. (1976). "Proposal for the measurement of the resonant Stark effect by photon correlation techniques". ''Journal of Physics B: Atomic and Molecular Physics'' '''9''' (4): L43. [http://dx.doi.org/10.1088%2F0022-3700%2F9%2F4%2F001 doi:10.1088/0022-3700/9/4/001]</ref>
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| More processes occur when a substance undergoes internal energy transitions before re-emitting the energy from the absorption event. In [[chemistry]]-related disciplines, one often distinguishes between [[fluorescence]] and [[phosphorescence]]. The prior is typically a fast process, but some of the original energy is dissipated so that the emitted light photons have lower energy than those absorbed. The generated photon in this case is said to be red shifted, referring to the loss of energy (as the [[Jablonski diagram]] shows). For the latter, the energy from absorbed photons undergoes [[intersystem crossing]] into a state of higher [[Spin (physics)|spin]] multiplicity (see [[term symbol]]), usually a [[triplet state]]. Once the energy is trapped in the triplet state, transition back to the lower singlet energy states is quantum mechanically forbidden, meaning that it happens much more slowly than other transitions. The result is a slow process of radiative transition back to the singlet state, sometimes lasting minutes or hours. This is the basis for "glow in the dark" substances.
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| Photoluminescence is an important technique for measuring the purity and crystalline quality of semiconductors such as [[GaAs]] and [[InP]] and for quantification of the amount of disorder present in a system. Several variations of photoluminescence exist, including [[photoluminescence excitation]] (PLE) spectroscopy.
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| Time-resolved photoluminescence (TRPL) is a method where the sample is excited with a light pulse and then the decay in photoluminescence with respect to time is measured. This technique is useful for measuring the [[minority carrier lifetime]] of III-V semiconductors like [[gallium arsenide]] ([[GaAs]]).
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| == Photoluminescence properties of direct-gap semiconductors ==
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| In a typical PL experiment, a semiconductor is excited with a light-source that provides photons with an energy larger than the [[bandgap]] energy.
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| The incoming light excites a polarization that can be described with the [[semiconductor Bloch equations]].<ref name="SQOBook">Kira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics.'' Cambridge University Press. [[ISBN]] [[Special:BookSources/978-0521875097|978-0521875097]].</ref><ref name=Haug2009>Haug, H.; Koch, S. W. (2009). ''Quantum Theory of the Optical and Electronic Properties of Semiconductors'' (5th ed.). World Scientific. p. 216. [[ISBN]] [[Special:BookSources/9812838848|9812838848]].</ref> Once the photons are absorbed, electrons and holes are formed with finite momenta <math>\mathbf{k}</math> in the [[Conduction band|conduction]] and [[valence band]]s, respectively. The excitations then undergo energy and momentum relaxation towards the band gap minimum. Typical mechanisms are [[Coulomb scattering]] and the interaction with [[phonons]]. Finally, the electrons recombine with holes under emission of photons.
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| Ideal, defect-free semiconductors are [[Many-body problem|many-body systems]] where the interactions of charge-carriers and lattice vibrations have to be considered in addition to the light-matter coupling. In general, the PL properties are also extremely sensitive to internal [[electric fields]] and to the dielectric environment (such as in [[photonic crystals]]) which impose further degrees of complexity. A precise microscopic description is provided by the [[semiconductor luminescence equations]].<ref name="SQOBook"/>
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| === Ideal quantum-well structures ===
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| An ideal, defect-free semiconductor [[quantum well]] structure is a useful model system to illustrate the fundamental processes in typical PL experiments. The discussion is based on results published in Klingshirn (2012)<ref>Klingshirn, Claus F. (2012). ''Semiconductor Optics.'' Springer. [[ISBN]] [[Special:BookSources/978-3-642-28361-1|978-3-642-28361-1.]]</ref> and Balkan (1998).<ref>Balkan, Naci (1998). ''Hot Electrons in Semiconductors: Physics and Devices.'' Oxford University Press. [[ISBN]] [[Special:BookSources/0198500580|0198500580.]]</ref>
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| The fictive model structure for this discussion has two confined quantized electronic and two hole [[subband]]s, e1, e2 and h1,h2, respectively.
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| The linear [[absorption spectrum]] of such a structure shows the [[exciton]] resonances of the first (e1h1) and the second quantum well subbands (e2h2), as well as the absorption from the corresponding continuum states and from the barrier.
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| ==== Photoexcitation ====
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| In general, three different excitation conditions are distinguished: resonant, quasi-resonant, and non-resonant. For the resonant excitation, the central energy of the laser corresponds to the lowest [[exciton]] resonance of the [[quantum well]]. No or only a negligible amount of the excess energy is injected to the carrier system. For these conditions, coherent processes contribute significantly to the spontaneous emission.<ref name="Kira1999" /><ref name="KiraJahnke1999">Kira, M.; Jahnke, F.; Hoyer, W.; Koch, S. W. (1999). "Quantum theory of spontaneous emission and coherent effects in semiconductor microstructures". ''Progress in Quantum Electronics'' '''23''' (6): 189–279. [http://dx.doi.org/10.1016%2FS0079-6727%2899%2900008-7 doi:10.1016/S0079-6727(99)00008-7.]</ref> The decay of polarization creates excitons directly. The detection of PL is challenging for resonant excitation as it is difficult to discriminate contributions from the excitation, i.e., stray-light and diffuse scattering from surface roughness. Thus, [[speckle]] and resonant [[Rayleigh scattering|Rayleigh-scattering]] are always superimposed to the [[Coherence (physics)|incoherent]] emission.
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| In case of the non-resonant excitation, the structure is excited with some excess energy. This is the typical situation used in most PL experiments as the excitation energy can be discriminated using a [[spectrometer]] or an [[optical filter]].
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| One has to distinguish between quasi-resonant excitation and barrier excitation.
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| For quasi-resonant conditions, the energy of the excitation is tuned above the ground state but still below the [[Potential barrier|barrier]] [[absorption edge]], for example, into the continuum of the first subband. The polarization decay for these conditions is much faster than for resonant excitation and coherent contributions to the quantum well emission are negligible. The initial temperature of the carrier system is significantly higher than the lattice temperature due to the surplus energy of the injected carriers. Finally, only the electron-hole plasma is initially created. It is then followed by the formation of excitons.<ref name="KaindlCarnahan2003">Kaindl, R. A.; Carnahan, M. A.; Hägele, D.; Lövenich, R.; Chemla, D. S. (2003). "Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas". ''Nature'' '''423''' (6941): 734–738. [http://dx.doi.org/10.1038%2Fnature01676 doi:10.1038/nature01676.]</ref><ref name="ChatterjeeEll2004">Chatterjee, S.; Ell, C.; Mosor, S.; Khitrova, G.; Gibbs, H.; Hoyer, W.; Kira, M.; Koch, S. W.; Prineas, J.; Stolz, H. (2004). "Excitonic Photoluminescence in Semiconductor Quantum Wells: Plasma versus Excitons". ''Physical Review Letters'' '''92''' (6). [http://dx.doi.org/10.1103%2FPhysRevLett.92.067402 doi:10.1103/PhysRevLett.92.067402.]</ref>
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| In case of barrier excitation, the initial carrier distribution in the quantum well strongly depends on the carrier scattering between barrier and the well.
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| ==== Relaxation ====
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| Initially, the laser light induces coherent polarization in the sample, i.e., the transitions between electron and hole states oscillate with the laser frequency and a fixed phase. The polarization dephases typically on a sub-100 fs time-scale in case of nonresonant excitation due to ultra-fast Coulomb- and phonon-scattering.<ref name="ArltSiegner1999">Arlt, S.; Siegner, U.; Kunde, J.; Morier-Genoud, F.; Keller, U. (1999). "Ultrafast dephasing of continuum transitions in bulk semiconductors". ''Physical Review B'' '''59''' (23): 14860–14863. [http://dx.doi.org/10.1103%2FPhysRevB.59.14860 doi:10.1103/PhysRevB.59.14860.]</ref>
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| The dephasing of the polarization leads to creation of populations of electrons and holes in the conduction and the valence bands, respectively.
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| The lifetime of the carrier populations is rather long, limited by radiative and non-radiative recombination such as [[Auger recombination]].
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| During this lifetime a fraction of electrons and holes may form excitons, this topic is still controversially discussed in the literature.
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| The formation rate depends on the experimental conditions such as lattice temperature, excitation density, as well as on the general material parameters, e.g., the strength of the Coulomb-interaction or the exciton binding energy.
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| The characteristic time-scales are in the range of hundreds of [[picosecond]]s in GaAs;<ref name="KaindlCarnahan2003" /> they appear to be much shorter in [[Wide bandgap semiconductors|wide-gap semiconductors]].<ref name="UmlauffHoffmann1998">Umlauff, M.; Hoffmann, J.; Kalt, H.; Langbein, W.; Hvam, J.; Scholl, M.; Söllner, J.; Heuken, M.; Jobst, B.; Hommel, D. (1998). "Direct observation of free-exciton thermalization in quantum-well structures". ''Physical Review B'' '''57''' (3): 1390–1393. [http://dx.doi.org/10.1103%2FPhysRevB.57.1390 doi:10.1103/PhysRevB.57.1390].</ref>
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| Directly after the excitation with short (femtosecond) pulses and the quasi-instantaneous decay of the polarization, the carrier distribution is mainly determined by the spectral width of the excitation, e.g., a [[laser]] pulse. The distribution is thus highly non-thermal and resembles a [[Gaussian distribution]], centered at a finite momentum. In the first hundreds of [[femtosecond]]s, the carriers are scattered by phonons, or at elevated carrier densities via Coulomb-interaction. The carrier system successively relaxes to the [[Fermi-Dirac distribution]] typically within the first picosecond. Finally, the carrier system cools down under the emission of phonons. This can take up to several [[nanoseconds]], depending on the material system, the lattice temperature, and the excitation conditions such as the surplus energy.
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| Initially, the carrier temperature decreases fast via emission of [[optical phonons]]. This is quite efficient due to the comparatively large energy associated with optical phonons, (36meV or 420K in GaAs) and their rather flat dispersion, allowing for a wide range of scattering processes under conservation of energy and momentum. Once the carrier temperature decreases below the value corresponding to the optical phonon energy, [[acoustic phonons]] dominate the relaxation. Here, cooling is less efficient due their [[Acoustic dispersion|dispersion]] and small energies and the temperature decreases much slower beyond the first tens of picoseconds.<ref name="KashShah1984">Kash, Kathleen; Shah, Jagdeep (1984). "Carrier energy relaxation in In0.53Ga0.47As determined from picosecond luminescence studies". ''Applied Physics Letters'' '''45''' (4): 401. [http://dx.doi.org/10.1063%2F1.95235 doi:10.1063/1.95235.]</ref><ref name="PollandRühle1987">Polland, H.; Rühle, W.; Kuhl, J.; Ploog, K.; Fujiwara, K.; Nakayama, T. (1987). "Nonequilibrium cooling of thermalized electrons and holes in GaAs/Al_{x}Ga_{1-x}As quantum wells". ''Physical Review B'' '''35''' (15): 8273–8276. [http://dx.doi.org/10.1103%2FPhysRevB.35.8273 doi:10.1103/PhysRevB.35.8273.]</ref> At elevated excitation densities, the carrier cooling is further inhibited by the so-called [[hot-phonon effect]].<ref name="ShahLeite1970">Shah, Jagdeep; Leite, R.C.C.; Scott, J.F. (1970). "Photoexcited hot LO phonons in GaAs". ''Solid State Communications'' '''8''' (14): 1089–1093. [http://dx.doi.org/10.1016%2F0038-1098%2870%2990002-5 doi:10.1016/0038-1098(70)90002-5.]</ref> The relaxation of a large number of hot carriers leads to a high generation rate of optical phonons which exceeds the decay rate into acoustic phonons. This creates a non-equilibrium "over-population" of optical phonons and thus causes their increased reabsorption by the charge-carriers significantly suppressing any cooling. A system thus cools slower, the higher the carrier density is.
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| ==== Radiative recombination ====
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| The emission directly after the excitation is spectrally very broad, yet still centered in the vicinity of the strongest exciton resonance.
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| As the carrier distribution relaxes and cools, the width of the PL peak decreases and the emission energy shifts to match the ground state of the exciton for ideal samples without disorder. The PL spectrum approaches its quasi-steady-state shape defined by the distribution of electrons and holes. Increasing the excitation density will change the emission spectra. They are dominated by the excitonic ground state for low densities. Additional peaks from higher subband transitions appear as the carrier density or lattice temperature are increased as these states get more and more populated. Also, the width of the main PL peak increases significantly with rising excitation due to excitation-induced dephasing<ref name="WangFerrio1993">Wang, Hailin; Ferrio, Kyle; Steel, Duncan; Hu, Y.; Binder, R.; Koch, S. W. (1993). "Transient nonlinear optical response from excitation induced dephasing in GaAs". ''Physical Review Letters'' '''71''' (8): 1261–1264. [http://dx.doi.org/10.1103%2FPhysRevLett.71.1261 doi:10.1103/PhysRevLett.71.1261.]</ref> and the emission peak experiences a small shift in energy due to the Coulomb-renormalization and phase-filling.<ref name="Haug2009" />
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| In general, both exciton populations and plasma, uncorrelated electrons and holes, can act as sources for photoluminescence as described in the [[semiconductor-luminescence equations]]. Both yield very similar spectral features which are difficult to distinguish; their emission dynamics, however, vary significantly. The decay of excitons yields a single-exponential decay function since the probability of their radiative recombination does not depend on the carrier density. The probability of spontaneous emission for uncorrelated electrons and holes, is approximately proportional to the product of electron and hole populations eventually leading to a non-single-exponential decay described by a [[hyperbolic function]].
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| === Effects of disorder ===
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| Real material systems always incorporate disorder. Examples are structural [[Crystallographic defect|defects]] in the lattice or [[Order and disorder (physics)|disorder]] due to variations of the chemical composition. Their treatment is extremely challenging for microscopic theories due to the lack of detailed knowledge about perturbations of the ideal structure. Thus, the influence of the extrinsic effects on the PL is usually addressed phenomenologically.<ref name="BaranovskiiEichmann1998">Baranovskii, S.; Eichmann, R.; Thomas, P. (1998). "Temperature-dependent exciton luminescence in quantum wells by computer simulation". ''Physical Review B'' '''58''' (19): 13081–13087. [http://dx.doi.org/10.1103%2FPhysRevB.58.13081 doi:10.1103/PhysRevB.58.13081.]</ref> In experiments, disorder can lead to localization of carriers and hence drastically increase the photoluminescence life times as localized carriers cannot as easily find nonradiative recombination centers as can free ones.
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| == Photoluminescent material in safety applications ==
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| One of the major uses of photoluminescent material is for safety and egress marking. It is most commonly seen in the form of "fire exit" signage. The industry is governed by a number of international standards and guidelines that stipulate performance criteria under certain conditions of excitement. A guide to these standards can be found at [http://www.photoluminescent.co.uk/standards photoluminescent.co.uk].
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| == Photoluminescent material for temperature detection ==
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| In [[phosphor thermometry]], the temperature dependence of the photoluminescence process is exploited to measure temperature.
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| ==See also==
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| * [[Luminescence]]
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| * [[Emission (electromagnetic radiation)|Emission]]
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| * [[Secondary emission]]
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| * [[Rayleigh scattering]]
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| * [[Absorption (electromagnetic radiation)|Absorption]]
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| * [[Red shift]]
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| * [[Charge carrier]]
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| * [[Semiconductor Bloch equations]]
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| * [[Elliott formula]]
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| * [[Semiconductor laser theory]]
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| == References ==
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| {{reflist}}
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| ==Further reading==
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| * {{cite book|last1=Klingshirn|first1=C. F.|title=Semiconductor Optics|year=2006|publisher=Springer|isbn=978-3540383451}}
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| * {{cite book|last1=Kalt|first1=H.|last2=Hetterich|first2=M.|title=Optics of Semiconductors and Their Nanostructures|year=2004|publisher=Springer|isbn=978-3540383451}}
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| * {{citation|author=Donald A. McQuarrie, John D. Simon|title=Physical Chemistry, a molecular approach|publisher=University Science Books|year=1997}}
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| * {{cite book|last1=Kira|first1=M.|last2=Koch|first2=S. W.|title=Semiconductor Quantum Optics|year=2011|publisher=Cambridge University Press|isbn=978-0521875097}}
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| * {{cite book|last1=Peygambarian|first1=N.|last2=Koch|first2=S. W.|last3=Mysyrowicz|first3=André|title=Introduction to Semiconductor Optics|year=1993|publisher=Prentice Hall|isbn=978-0-13-638990-3}}
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| [[Category:Spectroscopy]]
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| [[Category:Luminescence]]
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