Band gap, of semiconductors

Band gaps of semiconductors carrier lifetimes shallow impurity or defect detection sample quality and structure... 

Hamada, N. and Ohnishi, S. (1986) Self-interaction correction to the local-density approximation in the calculation of the energy band gaps of semiconductors based on the full-potential linearized augmented-plane-wave method, Phys. Rev., B34,9042-9044. 

It is interesting to point out the similarity between the proton level diagram of aqueous solutions and the electron level diagram of semiconductors as shown in Fig. 3-20. The ionic dissodation energy (1.03 eV) of water molecule H2O to form an ion pair of H30 -0H is the energy gap between the imitary acidic proton level and the unitary basic proton level this may correspond to the band gap of semiconductors. The concentration product, of the addic... 

Fig. 5-57. Surface states in the band gap of semiconductors Z> = surface state density.

TABLE 8-1. Preference for the conduction band mechanism (CB) and the valence band mechanism (VB) in outer sphere electron transfer reactions of hydrated redox particles at semiconductor electrodes (SC) Eo = standard redox potential referred to NHE c, = band gap of semiconductors. [From Memming, 1983.]... 

Equation 9-31 indicates that the electron level, er, of the intermediate radical is decisive in determining the ratio of the rates vjv. if the electron level of er is relatively close to the valence band edge Ey, the valence band mechanism, Eqn. 9-24d, will predominate whereas, if the electron level of er is relatively close to the conduction band edge e, the lone pair electron will be excited into the conduction band, and the conduction band mechanism, Eqn. 9-24c, will predominate. As the band gap of semiconductor electrode decreases, the conduction band increasingly participates. 

As it can be seen in the Figure 9, the maximum ideal efficiency corresponds to semiconductors with a band-gap wavelength of 800 < < 950 mn (1.3overall energy losses associated with... 

Thermally-induced network vibrations broaden the absorption edge and shift the band gap of semiconductors. The thermal disorder couples to the optical transition through the deformation potential, which describes how the electronic energy varies with the displacement of the atoms. The bond strain in an amorphous material is also a displacement of atoms from their ideal position, and can be described by a similar approach. The description of static disorder in terms of frozen phonons is a helpful concept which goes back 20 years. Amorphous materials, of course, also have the additional disordering of the real phonon vibrations. 

Consequently, DFT is restricted to ground-state properties. For example, band gaps of semiconductors are notoriously underestimated [142] because they are related to the properties of excited states. Nonetheless, DFT-inspired techniques which also deal with excited states have been developed. These either go by the name of time-dependent density-functional theory (TD-DFT), often for molecular properties [147], or are performed in the context of many-body perturbation theory for solids such as Hedin s GW approximation [148]. 

The quantum effect of reduction of particle size in reducing the band gap of semiconductors and so giving rise to novel optoelectronic properties has stimulated interest in quantum dot inclusion compounds of nanoparticles of semiconductors within zeolite pores.In a pioneering study, Herron and coworkers succeeded in introducing cadmium sulfide clusters within the pores of zeolite Y via the reaction of a cadmium-exchanged zeolite Y with hydrogen sulfide gas (Scheme 6.8). °... 

In Sect. 4.4, we examined the effect of the illumination of semiconductor-electrolyte junctions, using a light source of photon energy greater than the band gap of semiconductor. We shall now try to develop a model to get a quantitative estimation of the photocurrent from the magnitude of the concentration of photogenerated carriers. 

Zhang et al. also investigated the optical properties of ZnO nanostructures dispersed in ethanol. The band at 375 nm corresponds to ZnO nanoparticles. Compared with bulk ZnO, the blue shift observed in the ZnO nanostructures, is due to size effect. This band is also attributed to the band gap of semiconductor ZnO nanoparticles. 

Li M, Li JC (2006) Size effects on the band-gap of semiconductor compounds. Mater Lett 60 2526-2529 Lifshits IM, Slezov VV (1959) Kinetics of diffusive decomposition of supersaturated solid solutions. J Exp Theor Phys 8 331-339... 

We have already mentioned the inaccuracy of LDA-KS when determining the band gap of semiconductors and insulators. This failure is intimately related to a pathological non-analytical behaviour of the xc energy functional, as shown by J. P. Perdew and M. Levy and by L. J. Sham and M. Schliiter [47,48], Namely, the xc potential may be increased by a finite constant of the order of 1 eV as a result of the addition of an extra electron to an extended system, that is, after an infinitesimal change of the electron density. 

In the above equations we have used the traditional symbols tic for electrons and pv for holes, which come from the fact that the former represent negatively charged carriers (with the subscript c to indicate they are related to conduction bands) and the latter represent positively charged carriers (with the subscript v to indicate they are related to valence bands). We have mentioned before (see chapter 5) that in a perfect semiconductor the Fermi level lies in the middle of the band gap, a statement that can be easily proved from the arguments that follow. For the moment, we will use this fact to justify an approximation for the number of electrons or holes. Since the band gap of semiconductors is of order 1 eV and the temperatures of operation are of order 300 K, i.e. 1/40 eV, we can use the approximations... 

Figure 2 Lattice constant versus band gap of semiconductors.

Vijh AK (1970) Chemical approaches to the approximate prediction of band gaps of semiconductors and insulators. J Electrochem Soc 117 173C-178C... 

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