Direct and indirect transitions

Optical band gap energies (Eg) for WOx-ZrOa samples calcined at 1073 K were obtained from UV-vis spectra using procedures based on direct and indirect transitions between valence and conduction bands [26]. Direct band gap energies (Egdecreased monotonically from 4.15 to 3.75 eV as the W loading increased from 3.05 to 15.0 W-atomsnm (Table 2). 

Indirect transitions are much weaker thau direct trausitious, because the latter do uot require the participation of photons. However, many indirect-gap materials play an important role in technological applications, as is the case of silicon (band structure diagram iu Figure 4.7(a)) or germanium (baud structure diagram shown later, in Figure 4.11). Hereafter, we will deal with the spectral shape expected for both direct and indirect transitions. 

Case D Sum of Direct and Indirect Transition to Isolated Resonance ... 

Regarding the fundamental interband transition and the corresponding photogeneration of electron-hole pairs, the interband transitions have to be divided into direct and indirect transitions. The meaning of these terms is as follows ... 

Within the present context, the important point to note is that the absorption depths (given by 1 /a) are vastly different for direct and indirect transitions. Whereas in the former case absorption depths span the 100 1000 nm range, they can be as large as 10" nm for an indirect transition [9]. 

C. Douketis, T.L. Haslett, V.M. Shalaev, Z. H. Wang, and M. Moskovits, Fractal Character and Direct and Indirect Transitions in Photoemission from Silver Films, Physica A 207, 352 (1994)... 

The exponent is = 0.5 for semiconductors with direct transition, and = 2 for semiconductors with indirect transition. Direct and indirect transitions are explained in Figure 9.11. 

The better linearity of these plots is used to distinguish direct and indirect transitions and to determine the band gap energy from photocurrent measurements. 

The luminescence mainly originates from the inter-band transitions, which are divided into direct and indirect transitions according to the transition modes. If the electrons jump at the same point between the VBM (valence band maximum) and the CBM (conduction band minimum), this transition is direct. In contrast, there is indirect transition. The semiconductors silicon (Si) and gallium arsenide (GaAs) are typical examples as shown in Fig. 6.6. They have an indirect and direct band gap with the values 1.95 and 0.17 eV, respectively. When the crystal size becomes smaller, e.g., forming quantum dots, the Si becomes a better self-activated luminescence material. 

There are two main regions of absorption, corresponding to so-called direct and indirect transitions. The weaker absorption at longer wavelengths represents the indirect, forbidden transitions, which gain intensity via lattice vibrations (phonons). Absorption of a photon promotes an electron from the valence band to the conduction band, shown by the blue arrow in Fig. 11.8. 

An additional point is related to the temperature-induced direct and indirect transitions of hexosomes to EMEs. In our recent study [14], an example for direct hexosome-EME transitions with increasing temperature is presented. However, an indirect transition sometimes occurs via micellar cubosomes at certain amounts of solubilized oil. A detailed description for these structural transitions is given in Ref. [19]. 

In/X) with a wavelength 1 10 A, while the crystal wave-vectors have typical wavelength values of order the interatomic distances, that is, 1 A. Consequently, the difference between the wave-vectors of the iiutial and final states due to the photon momentum is negligible. Taking q = 0 in the above equation leads to so called direct transitions, that is, transitions at the same value of k in the BZ. These are the only allowed optical transitions when no other excitations are present. When other excitations that can carry crystal momentum are present, such as phonons (see chapter 6), the energy and momentum conservation conditions can be independently satisfied even for indirect transitions, in which case the initial and final photon states can have different momenta. The direct and indirect transitions are illustrated in Fig. 5.3. 

For allowed direct transitions n = 1/2. For indirect transitions, which are only possible by vibrational participation (phonons), n = 2. The proportionality constant A (which is different for direct and indirect transitions) represents a material constant, which depends on the transition dipole moment of the electronic transition and hence on the electron structure of the semiconductor. 

FIGURE 9. Direct and indirect transitions between parabolic semiconductor bands. 

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

Semiconductors can be divided into two groups direct and indirect band gap materials. In direct semiconductors the minimum energy in the conduction band and the maximum in the valence band occur for the same value of the electron momentum. This is not the case in indirect materials. The difference has profound consequences for the transitions of electrons across the band gap in which light is emitted, the radiative transitions, of interest here. 

Monte Carlo calculations have been carried out to simulate the spin transition behaviour in both mono- and dinuclear systems [197]. The stepwise transition in [Fe(2-pic)3]Cl2-EtOH as well as its modification by metal dilution and application of pressure have been similarly modelled by considering short- and long-range interactions [52, 198, 199]. An additional study of the effect of metal dilution was successfully simulated with the Monte Carlo treatment considering direct and indirect inter-molecular interactions [200]. A very recent report deals with the application of the Monte Carlo method to mimic short- and long-range interactions in cooperative photo-induced LS—>HS conversion phenomena in two- and three-dimensional systems [201],... 

From a study of overall rate constant k(T) for a reaction in the bulk and its dependence on concentrations of reactants, catalyst/inhibitor, temperature etc., the kinetics come up with a mechanism by putting together a lot of direct and indirect evidences. The determination of the overall rate constant k(T) using transition state theory was a more sophisticated approach. But the macroscopic theories such as transition state theory in different versions are split to some extent in some cases, e.g. for very fast reactions. The experimental and theoretical studies in reaction dynamics have given the indications under which it becomes less satisfactory and further work in this direction may contribute much more to solve this problem. 

Another possibility for distinguishing between direct and indirect channels arises from an analysis of the angular dependence of the fragments. If the photodissociation is direct, there will be a correlation between the angular distribution and and direction of the radiation. For indirect photodissociation the correlation vanishes, because the appearance of the photofragments is a result of the radiationless transition. 

Now, use the effective non-Hermitean Hamiltonians (228) to get the time dependence of the transition moment operator through Heisenberg transformation, but ignore non-Hermitean part for the Boltzmann operator. Then, the ACF taking into account both direct and indirect dampings, appears to be given by... 

Direct and indirect audits. There are instances in which an indirect audit will prove of benefit within the organization. Examples of these may be the transition of information from another audit process or source such as drug accountability information from manufacturing s receipt of investigator returns with drug accountability logs and patient compliance information. 

Depending upon the relationship between the momentum in the initial and final states (which, in turn, depend on the profile of the parabolic energy valley ) direct or indirect transitions can occur, as shown in Figure 2.4, and this affects all the three terms Pn, vk and Uf. It must be noted that in transitions between indirect valleys (Figure 2.4B) momentum is conserved via interaction with a phonon (i.e. a quantum lattice vibration), which can be either emitted or adsorbed. Some additional detail on such transitions will be given in the section deaUng with semiconductor oxides. 

Figure 4 Direct and indirect models of metal ion activation of ribozyme catalysis. Model of classes of metal sites that influence ribozyme activity. The scheme on top depicts the binding of a metal ion important for ribozyme folding that binds distant from the active site but promotes a structural transition that permits catalysis or the binding of catalytic metal ions. Such binding interactions may result directly in overall folding or may merely foster small stmctural changes near the active site that are critical to ribozyme chemistry. The scheme below depicts the direct activation of ribozyme activity by binding of metal ions that interact with the reactive phosphate and are involved in metal ion catalysis. Adapted from Reference 38.

The optical band-gap of the semiconductor (Section 1.2) is an important parameter in defining its light absorption behavior. In this quantized process, an electron-hole pair is generated in the semiconductor when a photon of energy hv (v = frequency and hv > Ef) is absorbed. Optical excitation thus results in a delocalized electron in the CB, leaving behind a delocalized hole in the VB this is the band-to-band transition. Such transitions are of two types direct and indirect. In the former, momentum is conserved and the top of VB and the bottom of CB are both located at /c = 0 (A is the electron wavevector). The absorption coefficient (a) for such transitions is given by [202]... 

The evolution of primary producers in the oceans profoundly changed the chemistry of the atmosphere, ocean, and hthosphere of Earth. The photosynthesis processes catalyzed by ensemble of these organisms not only influences the six major hght elements, but directly and indirectly affect every major soluble redox-sensitive trace element and transition metal on Earth s surface. These processes continue to provide, primarily through the utihzation of solar... 

The formation of the anhydride (N2O3) from equation (3) can lead to both direct and indirect DNA damage. Direct action results from nitrosation of primary amines on DNA bases which leads to deamination and at physiological pH, N2O3 has been demonstrated to be the most important species [130]. Indirect actions are due to mutations that can arise from the deamination of bases where guanine deaminates to xanthine, mispairing of which can cause a G C to A T transition which will ultimately lead to single strand breaks [131]. 

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