Excitons small radius

Generally, quantum size effects are not expected in lanthanide-doped nanoinsulators such as oxides since the Bohr radius of the exciton in insulating oxides, like Y2O3 and Gd2C>3, is very small. By contrast, the exciton Bohr radius of semiconductors is larger (e.g., 2.5 nm for CdS) resulting in pronounced quantum confinement effects for nanoparticles of about 2.5 nm or smaller (Bol et al., 2002). Therefore, a possible influence of quantum size effects on the luminescence properties of lanthanide ions is expected in semiconductor nanocrystals. 

Because of the strong Coulomb interactions inherent in such low dielectric molecular semiconductors, excitons are characterised by a very small radius (a few nanometres). At the same time the conjugation length can reach... 

The electron and the hole in the crystal attract themselves and can create a bound state. Obviously, the Frenkel exciton corresponds to the situation when the electron and the hole in a bound state are localized in the same lattice cell (the same molecule). Therefore the Frenkel excitons are also called small-radius excitons. When the radius of the electron-hole bound state is much larger than the lattice constant, the corresponding quasiparticle is called a Wannier-Mott exciton, or a large-radius exciton. Let us consider the latter in more detail. 

Higher order multipole terms can also be computed and included in the expression for Hna,m/3 (see, for example, 41, 42 in (13)). An analogous computation of multipole interactions for small-radius excitons can be found in (41). 

We mention here also an excimer (originally short for excited dimer) which is a type of small radius self-trapped exciton state. In organic solids this excited state can be considered as a dimeric molecule formed from two molecules, when one of the molecules is in an electronic excited state. Excimers are usually formed between two molecules that would not bond if both were in the ground state and the molecule pyrene is one of the canonical examples of an excimer. The excimer states play an important role in applications and in photochemistry (more information can be found in (30)). 

Equation (5.44) makes it possible to analyze the dependence of the intensity of impurity absorption on the polarization of the incident light. Rashba has treated this problem within the framework of the theory of small-radius excitons (2), (12) for the isotopic substitutional impurities. 

It should be stressed that the results obtained here for the positions of the lines and the intensities of absorption in such solutions coincide with the results of Broude and Rashba (21) which were derived in the framework of the theory of small-radius excitons using an approximation identical with the mean polarizability approximation (the additive refraction approximation the entire tensor ci j(ui, k) was not found in this study). 

Concerning the choice of materials for the implementation of the system considered here, examples of molecular substances having small-radius (< 0.5 nm) excitons with energies of a few eV, among those already successfully grown (17) as crystalline layers on a variety of inorganic (including semiconductor) crystals, are the acenes, such as tetracene (2 eV) or pentacene (1.5 eV), the metal... 

Many groups have already observed the asymmetrical broadening in Raman experiments on Il-VI-semiconductor dots (see, for example. Refs. 152 and 154), but the observed amount of the redshift lies below the expected one. This can be caused by different effects. The most important one is that the investigated dots are not small enough The dot radius should be smaller than the exciton Bohr radius of the respective semiconductor material to obtain measurable shifts (strong confinement regime). Furthermore, matrices. 

Figure C2.17.12. Exciton energy shift witli particle size. The lowest exciton energy is measured by optical absorjDtion for a number of different CdSe nanocrystal samples, and plotted against tire mean nanocrystal radius. The mean particle radii have been detennined using eitlier small-angle x-ray scattering (open circles) or TEM (squares). The solid curve is tire predicted exciton energy from tire Bms fonnula.

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