Photoluminescence is light emission from matter after absorbing photons. It is a form of luminescence initiated by photoexcitation, where photons excite electrons to a higher energy level in an atom. After excitation, various mechanisms release the absorbed energy as new photons. Time between absorption and emission varies, ranging from femtoseconds for free-carrier plasma in inorganic semiconductors or metals to milliseconds for phosphorescence. Under special circumstances the emission delay can be 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.
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Photoluminescent processes can be classified by parameters such as the energy of the exciting photon with respect to the emission. Resonant excitation, also known as resonance fluorescence, is where a wavelength of photons is absorbed and the same wavelength is rapidly re-emitted. For gasses or materials in solution, this process involves electrons but no significant internal energy transitions involving molecular features of the chemical substance between absorption and emission. In crystalline inorganic semiconductors where an electronic band structure is formed, secondary emission can be more complicated as events may contain both coherent contributions such as resonant Rayleigh scattering where a fixed phase relation with the driving light field is maintained (i.e. energetically elastic processes where no losses are involved), and incoherent contributions (or inelastic modes where some energy channels into an auxiliary loss mode), 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 optical correlations. 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, fluorescence and phosphorescence are distinguished. 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 is red shifted, carrying less energy. 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. Time-resolved photoluminescence 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.
Photoluminescence properties of direct-gap semiconductors
In a typical photoluminescence experiment, a semiconductor is excited with a light-source that provides photons with an energy larger than the bandgap energy. The incoming light excites a polarization that can be described with the semiconductor Bloch equations. Once the photons are absorbed, electrons and holes are formed with finite momenta k {\displaystyle \mathbf {k} } in the conduction and valence bands, 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. 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. Photoluminescence is generally 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.
Ideal quantum-well structures An ideal, defect-free semiconductor quantum well structure is a useful model system to illustrate the fundamental processes in typical photoluminescence experiments. The discussion is based on results published in Klingshirn (2012) and Balkan (1998). The fictive model structure for this discussion has two confined quantized electronic and two hole sub-bands, 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 sub-bands (e2, h2), as well as the absorption from the corresponding continuum states and from the barrier.
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