Semiconductor particle, radius

Colloidal CdS particles 2-7 nm in diameter exhibit a blue shift in their absorption and luminescence characteristics due to quantum confinement effects [45,46]. It is known that particle size has a pronounced effect on semiconductor spectral properties when their size becomes comparable with that of an exciton. This so called quantum size effect occurs when R < as (R = particle radius, ub = Bohr radius see Chapter 4, coinciding with a gradual change in the energy bands of a semiconductor into a set of discrete electronic levels. The observation of a discrete excitonic transition in the absorption and luminescence spectra of such particles, so called Q-particles, requires samples of very narrow size distribution and well-defined crystal structure [47,48]. Semiconductor nanocrystals, or... 

Lanthanides doped into nanocrystalline semiconductors have been the subject of numerous investigations in the past decades. If the size of a semiconductor particle is smaller than the Bohr radius of the excitons, the so-called quantum confinement occurs. As a result, the band gap of the semiconductor increases and discrete energy levels occur at the edges of the valence and conduction bands (Bol et al., 2002 Bras, 1986). These quantum size effects have stimulated extensive interest in both basic and applied research. 

One of the most attractive features of colloidal semiconductor systems is the ability to control the mean particle size and size distribution by judicious choice of experimental conditions (such as reactant concentration, mixing regimen, reaction temperature, type of stabilizer, solvent composition, pH) during particle synthesis. Over the last decade and a half, innovative chemical [69], colloid chemical [69-72] and electrochemical [73-75] methods have been developed for the preparation of relatively monodispersed ultrasmall semiconductor particles. Such particles (typically <10 nm across [50, 59, 60]) are found to exhibit quantum effects when the particle radius becomes smaller than the Bohr radius of the first exciton state. Under this condition, the wave functions associated with photogenerated charge carriers within the particle (vide infra) are subject to extreme... 

The potential distribution, and hence the extent of the band bending, within the space charge layer of a planar macroscopic electrode may be obtained by solution of the one-dimensional Poisson-Boltzmann equation [95]. However, since the particles may be assumed to have spherical geometry, the Poisson-Boltzmann for a sphere must be solved. This has been done by Albery and Bartlett [131] in a treatment that was recently extended by Liver and Nitzan [125]. For an n-type semiconductor particle of radius r0, the Poisson-Boltzmann equation for the case of spherical symmetry takes the form ... 

Thus, it may be seen that, by reducing the particle radius, it is possible to obtain systems where transit from the particle interior to the surface occurs more rapidly than recombination, implying that quantum efficiencies for photoredox reaction of near unity are feasible. However, the achieving of such high quantum efficiencies depends very much upon the rapid removal of one or both types of charge carrier upon their arrival at the semiconductor surface, underlining the importance of the interfacial charge-transfer kinetics. This is the subject of the next section. 

For colloidal materials the small size of the semiconductor particles severely restricts the magnitude of the electric field that a particle can support. Albery and Bartlett first considered the potential distribution within spherical semiconductor particles [144]. For large particles, an expression equivalent to that for planar electrodes given in Eq. 6 was derived. For small semiconductor particles the total band bending within the semiconductor, Fb, is limited by the radius r, Eq. 23 ... 

Several attempts have been carried out to compute the electronic energy levels in such quantum dots [99, 108-110]. According to these concepts, the energy of the lowest excited state of a semiconductor particle with radius R is given approximately by... 

Moller, K. J. Am. Chem. Soc in press.)(17). This is of interest from the standpoint that such small pieces of a bulk semiconductor lattice cannot fully develop the normal semi- conductor band structure and so reside in the so called size-quantized or quantum-confined regime. This is where the electron-hole pair of an excited semiconductor particle has a radius(18) larger than the actual particle size. The electron then behaves as a particle in a box and novel optical properties result. We decided, therefore, to look at preparation of CdS inside the zeolite cavities and then to explore the photo-oxidation chemistry of these species with absorbed olefins. 

An important aspect of nanosized semiconductors is the absence of band bending. Since the number of ionized donors or acceptors in nanosized particles is very small, such particles cannot sustain a large built-in electric field (cf. (2.41) and Fig. 2.13, left). The maximum attainable potential drop within a spherical semiconductor particle with radius R and a donor (or acceptor) density is given by [98] ... 

Semiconductor nanoparticles exhibit size-dependent unique optical and electronic properties that are different from their bulk counterpart due to quantum confinement. Bulk semiconductor crystal is considered as one large molecule, and electronic excitation of semiconductor crystals generates an electron-hole pair. The size of the delocalization area of this electron-hole pair is generally many times larger than the lattice constant. Decrease in the size of a semiconductor crystal down to a size comparable with the delocalization area of the electron-hole pair or to that of the Bohr excitonic radius of those materials modifies the electronic structure of the nanocrystals. When the particle radius decreases below the Bohr excitonic radius, there is widening in the energy band gap, which results in a blue shift in the excitonic absorption band of a semiconductor crystal. For example, in CdS semiconductor material, the blue shift of the excitonic absorption band is observed to begin at a crystal size of 5-6 nm [138-141]. 

Nano-composite materials with fine semiconductor particles dispersed in the matrix have attracted considerable interest because the properties of the particles are much different from their bulks when the diameters are l s than the Bohr exciton radius. Such particles, which are generally named as nano-particles, are characterized by non-stoichiometric surface structure and quantum size effect 2). These properties would lead to new phenomena, new theoretical insights, and new materials and devices. 

The last distinctive feature of small semiconductor partides is the partial screening of Coulomb interaction which takes dace in semiconductor particles if the particle radius is less than the Debye length for semiconducton... 

FIGURE 5.1 A plot of the absorbed photons per incident photons as a function of radius for a hypothetical semiconductor particle suspended in water with an absorptivity of ICf cm- and illuminated at 10 photons cm". (From Gerischer, H. and Heller, A., J. Electrochem. Soc., 139(1), 113, 1992.)... 

Figure C2.17.11. Exciton energy as a function of particle size. The Bms fonnula is used to calculate the energy shift of the exciton state as a function of nanocrystal radius, for several different direct-gap semiconductors. These estimates demonstrate the size below which quantum confinement effects become significant.

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