Editing Photoluminescence (section)

==== Relaxation ====

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. [https://dx.doi.org/10.1103%2FPhysRevB.59.14860 doi:10.1103/PhysRevB.59.14860.]</ref>

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 [[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. [https://dx.doi.org/10.1103%2FPhysRevB.57.1390 doi:10.1103/PhysRevB.57.1390].</ref>

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.

Initially, the carrier temperature decreases fast via emission of [[Phonon#Acoustic and optical phonons|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, [[Phonon#Acoustic and optical phonons|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. [https://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. [https://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. [https://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. Thus, a system cools slower, the higher the carrier density is.