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Photoluminescence (abbreviated as PL) is 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 (i.e. photons that excite electrons to a higher energy level in an atom), hence the prefix photo-.IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " photochemistry". Following excitation, various relaxation processes typically occur in which other photons are re-radiated. Time periods between absorption and emission may vary: ranging from short femtosecond-regime for emission involving free-carrier plasma in inorganic semiconductorsHayes, G.R.; Deveaud, B. (2002). "Is Luminescence from Quantum Wells Due to Excitons?". Physica Status Solidi A 190 (3): 637–640. doi:10.1002/1521-396X(200204)190:3<637::AID-PSSA637>3.0.CO;2-7 or metals up to milliseconds for phosphoresence processes in molecular systems; and under special circumstances delay of emission may even span to minutes or hours.
Observation of photoluminescence at a certain energy can be viewed as an indication that an electron transitioned between states separated by this transition energy. 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 systems such as semiconductors or metals. A theoretical approach to handle this is given by the semiconductor luminescence equations.
The latter originate, e.g., from the radiative recombination of excitons, Coulomb-bound electron-hole pair states in solids. Resonance fluorescence may also show significant Quantum optics correlations.Kimble, H. J.; Dagenais, M.; Mandel, L. (1977). "Photon Antibunching in Resonance Fluorescence". Physical Review Letters 39 (11): 691–695. doi:10.1103/PhysRevLett.39.691Carmichael, 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. doi:10.1088/0022-3700/9/4/001
More processes may occur when a substance undergoes internal energy transitions before re-emitting the energy from the absorption event. Electrons change energy states by either resonantly gaining energy from absorption of a photon or losing energy by emitting photons. In chemistry-related disciplines, one often distinguishes between fluorescence and phosphorescence. The former is typically a fast process, yet some amount of the original energy is dissipated so that re-emitted light photons will have lower energy than did the absorbed excitation photons. The re-emitted photon in this case is said to be red shifted, referring to the reduced energy it carries following this loss (as the Jablonski diagram shows). For phosphorescence, electrons which absorbed photons, undergo intersystem crossing where they enter into a state with altered spin multiplicity (see term symbol), usually a triplet state. Once the excited electron is transferred into this triplet state, electron transition (relaxation) back to the lower singlet state energies 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.
Photoluminescence is an important technique for measuring the purity and crystalline quality of semiconductors such as GaN and InP and for quantification of the amount of disorder present in a system.Alfaraj, N.; Mitra, S.; Wu, F.; Ajia, A. A.; Janjua, B.; Prabaswara, A.; Aljefri, R. A.; Sun, H.; Ng, T. K.; Ooi, B. S.; Roqan, I. S.; Li, X. (2017). "Photoinduced entropy of InGaN/GaN p-i-n double-heterostructure nanowires". Applied Physics Letters 110 (16): 161110. [6]
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).
Ideal, defect-free semiconductors are 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 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.
The fictive model structure for this discussion has two confined quantized electronic and two hole , e1, e2 and h1, h2, respectively. The linear absorption spectrum of such a structure shows the exciton resonances of the first (e1h1) and the second quantum well subbands (e2, h2), as well as the absorption from the corresponding continuum states and from the barrier.
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. One has to distinguish between quasi-resonant excitation and barrier excitation.
For quasi-resonant conditions, the energy of the excitation is tuned above the ground state but still below the 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.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. doi:10.1038/nature01676.Chatterjee, S.; Ell, C.; Mosor, S.; Galina Khitrova; 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). doi:10.1103/PhysRevLett.92.067402.
In case of barrier excitation, the initial carrier distribution in the quantum well strongly depends on the carrier scattering between barrier and the well.
The dephasing of the polarization leads to creation of populations of electrons and holes in the conduction and the valence bands, respectively. The lifetime of the carrier populations is rather long, limited by radiative and non-radiative recombination such as Auger recombination. During this lifetime a fraction of electrons and holes may form excitons, this topic is still controversially discussed in the literature. 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.
The characteristic time-scales are in the range of hundreds of in GaAs; they appear to be much shorter in wide-gap semiconductors.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. doi:10.1103/PhysRevB.57.1390.
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 , 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.
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 dispersion and small energies and the temperature decreases much slower beyond the first tens of picoseconds.Kash, Kathleen; Shah, Jagdeep (1984). "Carrier energy relaxation in In0.53Ga0.47As determined from picosecond luminescence studies". Applied Physics Letters 45 (4): 401. doi:10.1063/1.95235.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. doi:10.1103/PhysRevB.35.8273. At elevated excitation densities, the carrier cooling is further inhibited by the so-called hot-phonon effect.Shah, Jagdeep; Leite, R.C.C.; Scott, J.F. (1970). "Photoexcited hot LO phonons in GaAs". Solid State Communications 8 (14): 1089–1093. doi:10.1016/0038-1098(70)90002-5. 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. Thus, a system cools slower, the higher the carrier density is.
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.
Researchers from the King Abdullah University of Science and Technology (KAUST) have studied the photoinduced entropy (i.e. thermodynamic disorder) of InGaN/GaN p-i-n double-heterostructure and AlGaN nanowires using temperature-dependent photoluminescence.Alfaraj, N.; Mumthaz Muhammed, M.; Li, K.; Janjua, B.; Aljefri, R. A.; Sun, H.; Ng, T. K.; Ooi, B. S.; Roqan, I. S.; Li, X. (2017). "Thermodynamic photoinduced disorder in AlGaN nanowires". AIP Advances 7 (12): 125113. [17] They defined the photoinduced entropy as a thermodynamic quantity that represents the unavailability of a system's energy for conversion into useful work due to carrier recombination and photon emission. They have also related the change in entropy generation to the change in photocarrier dynamics in the nanowire active regions using results from time-resolved photoluminescence study. They hypothesized that the amount of generated disorder in the InGaN layers eventually increases as the temperature approaches room temperature because of the thermal activation of surface states, while an insignificant increase was observed in AlGaN nanowires, indicating lower degrees of disorder-induced uncertainty in the wider bandgap semiconductor. To study the photoinduced entropy, the scientists have developed a mathematical model that considers the net energy exchange resulting from photoexcitation and photoluminescence.
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