Direct/indirect transition

Postcolumn derivatization spectroscopy Direct Indirect Transition metals, high sensitive Used for iodide, nitrate, sulfide Universal application, lacks sensitivity... 

Figure 6.1 A schematic diagram illustrating scattering of electrons from one minimum in the conduction band to another. This occurs especially strongly in alloys near the direct-indirect transition.

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. 

In Ref. 54, XRD showed the deposit to be hexagonal CuSe. Analysis of the absorption spectrum gave a direct bandgap of 2.02 eV. As commonly seen for these compounds, there was still strong absorption at lower energies (e.g., at 1.9 eV, the absorption coefficient was >7 X 10" cm ), possibly due to an indirect transition but likely due, at least in part, to free-carrier absorption. From Hall measurements, the doping (acceptor) density was ca. 10 cm (heavily degenerate) and the mobility ca. 1 cm V sec The dependence of film thickness and deposition rate on the deposition parameters has been studied in a separate paper [62]. 

Fig. 32. Diagram of interband electron transitions under photoemission 1—direct transition, 2—indirect transition.

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. 

Gap transition typed Indirect Indirect Direct Direct Indirect... 

Case A Indirect Transition to Isolated Resonance Here the photodissociation occurs by excitation to a single resonance, followed by a transition from the resonance to the continuum. In this case the sum over s reduces to a single term, and the direct optical transitions to the continuum are suppressed. That is,... 

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

The dependence of the optical absorption in small isolated silicon nanociystals on the photon energy shows a slow increase above the band gap energy which is typical for an indirect gap material [11]. A sharp increase is observed only when the photon energy reaches the value of the direct gap transition (about 3.4 eV) at the F-point k = 0). With decreasing crystallite size below about 4 nm the band gap increases [38] and the PL shows a pronoimced blue shift [39], The results reproduced fi-om ref. [38] and [39] are shown in Fig. 3. 

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 ... 

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. 

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]. 

Figure 1. Schematic presentation of a) direct and b) indirect transitions in semiconductors [24],...

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... 

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