Phonon absorption/emission

The single-phonon absorption/emission is dominant at the low temperature limit when A k T and a >> (a is the dimensionless constant). When temperature increases, new factors begin to influence the proton transfer, namely, multiphoton processes and the tunneling through intermediate excited states. 

Excitons eventually decay, however, by electron-hole annihilation, which can be accompanied by the emission of a photon (Luminescence), with or without phonon absorption/emission or the acceleration of a free charge (Auger process). Bulk model predictions break down when the size of the crystal is smaller than the exciton s Bohr radius. The Bohr radius of the exciton is given by [30] ... 

The first term of Ei2) accounts for the broadening and the shift caused by phonon absorption [in ], and the second term for those caused by spontaneous and induced emissions [1 + ]. The Bose Einstein population < ns(q)) has the form... 

Figure 7.6 Schematic representation of fundamental absorption processes in (a) direct bandgap and (b) indirect bandgap semiconductors. Phonon emission and phonon absorption processes are marked in red. (Adapted from Yacobi [211)...

In indirect bandgap semiconductor crystals both the emission and absorption of phonons are allowed to preserve the momentum (see Figure 7.6.). Therefore two contributions to the overall absorption spectrum should be considered aa and ae, associated with phonon absorption and emission, respectively [21] ... 

Indirect band gap means that the minimum of the conduction band and the maximum of the valence band are at different positions in the Brillouin zone, i.e., the electrons in the corresponding quantum states have different wave vectors k. Because the momentum of a photon is very small the optical transitions (absorption, emission) of the electrons have to occur with M = 0. GaAs and many other compound semiconductors are efficient optoelectronic materials because of their direct band gap. In silicon, however, such transitions between the top of the valence and bottom of the conduction bands require assistance of a phonon which delivers the momentum needed [2, 3]. 

Since both phonon and emission absorption are possible when hv> Eg + Bp, the absorphon coefficient is then... 

At very low temperatures, the phonon density is very small and therefore the probability of phonon absorption is also low. In this case one finds that the plot of the square root of a has a linear dependence on hv. At higher temperatures, however, the linear dependence breaks into two linear parts with different slopes corresponding to the emissive and absorptive processes. 

If these holes emit phonons, they will move to the edge of the HOMO band edge, and if they absorb phonons, they will move away from the HOMO band edge. Each hole will experience a different sequence of phonon absorption and emission events that have probabihties given by the carrier-phonon scattering rate, as a function of carrier... 

T. Yamanaka, M. Dutta, T. Rajh, and M. A. Stroscio, Phonon absorption and emission by holes in the HOMO bands of duplex DNA, Proceedings of the International Conference on Hot Carriers in Semiconductors, Springer, in press, 2006. 

The absorption coefficient as a function of energy for a phonon-assisted (Ak 0) indirect transition between indirect valleys consists of two parts, corresponding to phonon absorption and emission ... 

The absorption spectrum of atoms and molecules in low temperature solids is composed of a sharp zero-phonon line and a phonon side band (Table 2.12 ). The phonon side band corresponds to light absorption accompanied by phonon absorption or emission. The absorption shown in bold in Table 2.12 is a zero-phonon line. The sum of the absorption, drawn in a finer line, yields the phonon side band. The phonon side band appears on the higher energy side of the zero-phonon line at low temperatures. A measure of the interaction between guest molecule and host matrix is given by the Debye-Waller factor, DW(T), defined as a function of temperature, T, in Eq. (2.3), using the areas of the zero-phonon line, S0(T), and the phonon side band, SP(T). 

It should be clear that we have now confirmed that phonon absorption and emission from the activator site actually occurs. We have alluded to this fact in prior chapters but no specific data had been presented which actually confirmed this mechanism. The above discussion has proven this. 

Fig. 2 shows of the g(T) in SWCNT film measured by Bae et al. [8, Fig. 1], fitted to the theoretical Wj(E,T) computed using the equation (1). The theory describes well the experimental data. For an explanation of these results in the framework of LL model the authors of [8] involved the additional term with linear temperature dependence. The PhAT model can also explain the crossover of g(T) from semi-conducting-like to metallic-like observed in some works [5,16]. Since the PhAT theory includes an absorption/emission of phonons in the carrier tunneling, the variation of g(T) will be determined by the competition of the absorption and emission of phonons. 

Electrons in excited states are not stable thus, they will return to the ground state releasing energy. The emission probability is R = Pui uf i with the upper and lower energy state electron density n and ni, respectively. In addition, the emission can also be completed by the phonon absorption and emission association... 

Finally, in contrast to the conventional anti-Stokes probes, such as two-phonon absorption or second harmonic generation, upconversion nanophosphors exhibit higher emission efficiency and can be excited by continuous-wave laser rather than the costly femtosecond pulsed laser. 

The Mossbauer measurements makes it possible to study a variety of interesting effects that may be brought about by the introduction of impurity in the lattice as also the modifications brought about by imperfection in the crystal lattice, since the nuclei must be bound in a crystal for this study of resonant emission (or absorption) of y-rays. Three dynamical quantities of interest, which are possible in the Mossbauer studies, are (i) Zero-phonon absorption cross-section giving the Lamb-Mossbauer factor, (ii) One-phonon absorption cross section yielding the time information as well as the information of the localized modes and through this the information on the force constant between impurity and the host atom, (iii) the second order Doppler effect yielding information about the mean square velocity of the Mossbauer probe. 

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