Exciton Bohr radii

PbS has attracted much attention due to its special direct band gap energy (0.4 eV) and a relatively large exciton Bohr radius (18 nm) and their nanoclusters have potential applications in electroluminescent devices such as light-emitting diodes. PbS nanocrystals with rod like structures with diameters of 20-60 nm and lengths of 1-2 pm have been obtained using the sonochemical method and by using PEG-6000 [66]. Addition of PEG and the time of sonication have been found to play a key role in the formation of these rods. 

As the radius of a semiconductor crystallite approaches the exciton-Bohr-radius its electronic properties begin to change, whereupon quantum size effects can be expected. The Bohr radius ub of an exciton is given by... 

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. 

Yanes et al. (2004) observed a very interesting size selective spectroscopy in 0.4 mol% Eu3+ SnC>2 nanocrystals ( 4 nm) embedded in SiC>2 glass prepared by thermal treatment of sol-gel glasses. The mean size of SnC>2 nanocrystals is comparable to the bulk exciton Bohr radius (4.8 nm). Thus the band-gap excitation energy depends on the nanocrystal size. 

Quantum dots are inorganic semiconductor nanocrystals that possess physical dimensions smaller than the exciton Bohr radius, giving rise to the unique phenom-... 

Ignored in the above quantum confinement model is the fact that when an electron is excited into the conduction band and a positive hole is left behind in the valence band, the hole and electron are coulombically attracted. The pair can be treated as a well-defined qnasiparticle called an exciton, a hydrogen-like system for which a bulk exciton Bohr radius = tfKeJ nfj.f- can be defined. Here k is the dielectric constant (10.2 for bulk CdSe ) and bq is the permittivity of space (8.854 X 10 The quantity a is a... 

As you may recall from Chapter 4, when an electron is promoted from the valence to conduction bands, an electron-hole pair known as an exciton is created in the bulk lattice. The physical separation between the electron and hole is referred to as the exciton Bohr radius (re) that varies depending on the semiconductor composition. In a bulk semiconductor crystal, re is significantly smaller than the overall size of the crystal hence, the exciton is free to migrate throughout the lattice. However, in a quantum dot, re is of the same order of magnitude as the diameter (D) of the nanocrystal, giving rise to quantum confinement of the exciton. Empirically, this translates to the strongest exciton confinement when D < 2r. ... 

Finally, the diameter-range where these size effects are expected can be determined by an exciton Bohr radius, as follows [64] ... 

Silicon nanoparticles (Si NPs) with sizes in the order of bulk exciton Bohr radius [1, 2] present interesting optical properties for fluorescent labeling in biological imaging applications with their potential nontoxicity [3-6], However, the origin of their photoluminescence has been subjected to intense debate for almost two decades. This debate has been focused on whether quantumatomic-scale defects at the surface of the nanocrystals are responsible for the light emission [7]. 

Quantum confinement is defined as the space where the motions of electrons and holes in a semiconductor are restricted in one or more dimensions. This quantum confinement occurs when the size of semiconductor crystallites is smaller than the bulk exciton Bohr radius. Quantum wells, quantum wires, and quantum dots are confined in one, two, and three dimensions, respectively [1, 2]. The confinement can be created due to electrostatic potentials, the presence of an interface between different semiconductor materials, and the presence of a semiconductor surface. A valence band and a conduction band are separated by an energy range known as the band gap ( g). These amounts of energy will be absorbed in order to promote an electron from the valence band to the conduction band and emitted when the electron relaxes directly fi om the conduction band back to the valence band. By changing the size of the semiconductor nanoparticles, the energy width of the band gap can be altered and the optical and electrical responses of these particles are changed (Fig. 1). 

Nanocrystalline semiconductor quantum dots have attracted attention primarily as sensitisers in solar cells, but have also been used as luminescent probes in biological systems, despite concerns over their toxicity (especially with quantum dots containing heavy metals such as Cd and Pb). The recombination of excitons post-excitation can lead to radiative emission with wavelengths shorter than that of the band gap of the bulk semiconductor due to perturbation of the exciton wave-function - so-called quantum confinement effects - at distances shorter than the exciton Bohr radius. For the popular semiconductor cadmium... 

Table 5.3-2 Is exciton Bohr radius for various semiconductors...

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. 

Quantum dots are defined as 0-dimensional semiconductor material as result of quantum confinement of electrons in three dimensions [112, 113]. QDs are generally synthesized from elements in the periodic table belonging to groups 12-14 or 13-15 to form clusters which have dimensions smaller than the exciton Bohr radius [112-115]. QDs have been used to modify electrode surfaces for electrochemical detection of analytes, such as magnesium ions, glutathione and glucose [116-118]. 

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