Conduction direct transitions

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. 

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 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 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 fundamental absorption edge in ZnO corresponds to the direct transition from the highest valence band to the lowest conduction band at the F-point of the Brillouin zone [141]. RT-data for the energy of the lowest / -point band-to-band transition are summarized in Table 3.11. 

The origin of the intense 248-nm emission without band A has not been elucidated yet. A speculation is that the B impurity band is extended deep inside the Brillouin zone, and a direct transition from the conduction band minimum to the impurity band is involved in addition to the ordinal indirect transition... 

Figure 5.35 Graph illustrating the relevant valence-band (VB) and conduction-band (CB) states in the Brillouin zone for a Ti02 crystal in the X and Z edges, and in the crystal centre F. Note that the lowest energy direct transition from the lowest energy of the valence band to the lowest level of the conduction band at F is forbidden the lowest energy transition is an indirect phonon-assisted transition. Adapted with permission from Emeline et al. (2000c). Copyright (2000) American Chemical Society.

Figure 3. The nonrelativistic band structure for AgBr. The lowest energy indirect transition promotes an electron from the highest point in the valence band, L 3, to the minimum in the conduction band, T,. This energy difference is the bandgap energy, Et. The lowest energy direct transition is from r,5 to T,. After [52] and [54],...

There are two possibilities of importance. The first is that the lowest point of the valance band corresponds to the highest point of the conduction band that is, they are at the same value of the wave vector, k (Figure 14.9a). In this case, an optical transition between the bands can take place without a change of k or electron momentum. Such a transition is called a direct transition. In terms of quantum mechanics, the transition has a high probability of occurring when a photon of the correct energy hits the semiconductor, and the efficiency of the process is high. 

Figure 14.9 (a) In a direct transition between the valence band and the conduction band, the wave vector, k, of the excited electron does not change (b) in an indirect transition, the wave vector, k, changes, making the transition much less probable than a direct transition... 

The conduction band where unoccupied MO of CeOg polyhedra form is almost diminished (as expected) because Ca atom is located on the same position of Ce site statistically in this calculation. Interestingly, the structure of valence band was little changed and the top of valence band returned to the T point. This results direct transition of photo-assist excitation. The band edge spectra will be expected as a sharpened one by doping Ca. It can be considered that the band gap was extended by tightly bonded to make new hybridization of orbital both Ca 2s and Ce 4f. Because of this, it can be explained electronically that Ce02 loses the semiconductor property to be more stable compound. 

The family of organic conductors perylene2[M(mnt)2] (mnt = maleonitriledithiolate) has been studied for more than fifteen years, since the Cu and Ni compounds were reported to be semiconductors by Alcacer and Maid [1,2]. Subsequent work paid special attention to the Au, Pt and Pd compounds [3-9], that exhibit quasi one-dimensiond metallic behaviour down to a temperature Tj j, where a metal-insulator transition occurs. These compounds crystallize in space group P2i/c [3,8], and the b axis is the high-conductivity direction (G / 1(P). 

The downward direct transition rate from P to Pg caused by the free conduction electrons in a normal metal, is ... 

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