Band direct transition

Optical absorption measurements give band-gap data for cubic sihcon carbide as 2.2 eV and for the a-form as 2.86 eV at 300 K (55). In the region of low absorption coefficients, optical transitions are indirect whereas direct transitions predominate for quantum energies above 6 eV. The electron affinity is about 4 eV. The electronic bonding in sihcon carbide is considered to be predominantiy covalent in nature, but with some ionic character (55). In a Raman scattering study of vahey-orbit transitions in 6H-sihcon carbide, three electron transitions were observed, one for each of the inequivalent nitrogen donor sites in the sihcon carbide lattice (56). The donor ionization energy for the three sites had values of 0.105, 0.140, and 0.143 eV (57). 

The potentiostatic electrodeposition of iron selenide thin films has been reported recently in aqueous baths of ferric chloride (FeCb) and Se02 onto stainless steel and fluorine-doped TO-glass substrates [193], The films were characterized as polycrystalline and rich in iron, containing in particular a monoclinic FesSea phase. Optical absorption studies showed the presence of direct transition with band gap energy of 1.23 eV. 

It was reported recently [216] that optical-quality PbTe thin films can be directly electrodeposited onto n-type Si(lOO) substrates, without an intermediate buffer layer, from an acidic (pH 1) lead acetate, tellurite, stirred solution at 20 °C. SEM, EDX, and XRD analyses showed that in optimal deposition conditions the films were uniform, compact, and stoichiometric, made of fine, 50-100 nm in size, crystallites of a polycrystalline cubic structure, with a composition of 51.2 at.% Pb and 48.8 at.% Te. According to optical measurements, the band gap of the films was 0.31 eV and of a direct transition. Cyclic voltammetry indicated that the electrodeposition occurred via an induced co-deposition mechanism. 

Indium monoselenide, InSe, is a semiconductor with a weakly allowed direct band gap transition at 1.3 eV and an indirect at 1.2 eV, having a strongly anisotropic... 

The electronic structure of GaN nanotubes was calculated as well (71) and was essentially in accordance with the band structure calculations of the other inorganic nanotubes. The band gap of nanotubes with a diameter >2 nm is >4 eV and shrinks with the nanotube diameter. Zigzag nanotubes are found to have a direct transition, which suggests that they could serve as an ultrasmall blue light-emitting source. The structure and stability of CaSi2 nanotubes have been investigated but a few details are currently available (88b,c). 

This important selection rnle indicates that interband transitions mnst preserve the wave vector. Transitions that preserve the wave vector (snch as those marked by vertical arrows in Figure 4.8(a)) are called direct transitions, and they are easily observed in materials where the top point in the valence band has the same wave vector as the bottom point in the conduction band. These materials are called direct-gap materials. 

Figure 4.8 Interband transitions in solids with band-gap energy Eg-, (a) A direct band gap. Two direct transitions are indicated by arrows, (b) An indirect band gap. Two indirect band-gap transitions are indicated by arrows. The transitions at photon energies lower than Eg require absorption of phonons. The transitions at photon energies higher than Eg involve emission of phonons.

For some direct-gap materials, the quantum electronic selection rules lead to = 0. However, this is only strictly true at / = 0. For 0, it can be assumed, in a first order approximation, that the matrix element involving the top valence and the bottom conduction states is proportional to k that is, Pif k. Within the simplified model of parabolic bands (see Appendix Al), it is obtained that Tuo = Tuog + flp., and therefore Pif k co — cog). Thns, according to Equations (4.31) and (4.32), the absorption coefficient for these transitions (called forbidden direct transitions) has the following spectral dependence ... 

The band structure of Ge, given in Figure 4.11 (a), also shows a second band gap at 0.8 eV, which is now direct and corresponds to the As A transition. Indeed, this direct band gap is also shown experimentally in the linear plot of versus the photon energy for energies larger than about 0.8 eV. According to the observed trend, a ct (Tico — 0.8), we can say that these direct transitions are allowed (see Table 4.3). 

MoS2-type materials are indirect band-gap semiconductors. The energies of the indirect (momentum forbidden) and direct (momentum allowed) band-gap transitions are given in Table 1. The electronic structure of these materials may be qualitatively understood in terms of the crystal structure. 

The lowest-energy-resolved features in the absorption spectrum of M0S2-type semiconductors are the A and B excitons, shown in Fig. 3 for the case of M0S2 [30]. The dissociation limit of peaks built off of the A exciton correspond to the direct band edge. Calculations indicate that these transitions are at K and that the A and B excitons correspond to K4 K5 and K1 K5, respectively [25,26]. The lowest-energy direct-transition excited states have considerably different orbital character than the band-edge state. K1 and K4 correspond to 84% and 82% dyy, respectively corresponds to 77%... 

The photoconductivity and absorption spectra of the multilayer polydiacetylene are shown in Fig. 22 [150]. The continuous and dotted line relate to the blue and red polymer forms respectively. Interpretation is given in terms of a valence to conduction band transition which is buried under the vibronic sidebands of the dominant exciton transition. The associated absorption coefficient follows a law which indicates either an indirect transition or a direct transition between non-parabolic bands. The gap energies are 2.5 eV and 2.6 eV for the two different forms. The transition is three dimensional indicating finite valence and conduction band dispersion in the direction perpendicular to the polymer chain. 

In the delayed emission spectrum of eosin in glycerol or ethanol two bands are present, the relative intensities of which are strongly temperature-dependent (see Fig. 12). The visible band at 1.8 has a contour identical with that of the fluorescence band. It no doubt corresponds to the visible phosphorescence observed by Boudin.26 To interpret the results it was assumed that this band of delayed fluorescence was produced by thermal activation of the eosin triplet to the upper singlet level followed by radiative transition from there to the ground state. The far red band was assumed to correspond to the direct transition from the triplet level to the ground state and was therefore called phosphorescence. To determine the relationship between the intensities of the two bands we write the equations for the formation and consumption of triplet molecules as follows ... 

In addition to energy, the semiconductor band gap is characterized by whether or not transfer of an electron from the valence band to the conduction band involves changing the angular momentum of the electron. Since photons do not have angular momentum, they can only carry out transitions in which the electron angular momentum is conserved. These are known as direct transitions. Momentum-changing transitions are quantum-mechanically forbidden and are termed indirect (see Table 28.1). These transitions come about by coupling... 

The optical absorption coefficient for a single injerband transition is related to the photon energy by a v (hv) (hv - Eg) where Eg is the band gap and n depends upon the character of the transition (n = 0.5 for allowed direct transitions n = 2 for allowed indirect ones). Thus, if experimental values for a are multiplied by hv and are plotted as (ahv) against hv, then a... 

The quantum efficiency data for the defect pyrochlore Bag, -SrQ 5 2 6 iS Presente< i-n Figure 3 (10). It shows an indirect band gap at 3.4 eV with a "tail" extending to nearly 2.6 eV. The higher-energy transition at 4.4 eV shows some curvature of the data, and indeed, corresponds to a direct transition when replotted as (nhv) versus energy (10). 

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