Phonon absorption

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

Lastly, in order to use Eq. (A. 12) to compute the phonon absorption due to this particular mechanism, we need to estimate the density of the active domain walls. It will suffice for our purposes here to consider as active the defects that contribute to the specihc heat, that is, roughly, n /Tg. A more... 

As a consequence, expression (A2.21) turns into the sum of two quantities, namely, the probabilities for transitions per unit time accompanied by phonon absorption,... 

Figure 6.17 The energy-level diagram (not to scale) for the Yb ion in ZBLANP. To make the cooling mechanism clear, the pump and emitted frequencies have been indicated by arrows and the phonon absorption processes by sinusoidal arrows (reproduced with permission from Epstein et al., 1995).

However, the situation becomes already more complicated for ternary single crystals like lanthanum-aluminate (LaAlC>3, er = 23.4). The temperature dependence of the loss tangent depicted in Figure 5.3 exhibits a pronounced peak at about 70 K, which cannot be explained by phonon absorption. Typically, such peaks, which have also been observed at lower frequencies for quartz, can be explained by defect dipole relaxation. The most important relaxation processes with relevance for microwave absorption are local motion of ions on interstitial lattice positions giving rise to double well potentials with activation energies in the 50 to 100 meV range and color-center dipole relaxation with activation energies of about 5 meV. 

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... 

To find the low-energy absorption, we iterate the expression (2.107) retaining only the phonon absorption term in , and stopping at the second-order term for the last real process, which leads to the excitonic band at the energy + vh s(q) and provides an imaginary part for E 2) ( + vhQ(q)). We may evaluate the optical absorption using the simplification [ (< ) =, hiis(q) = h i0, E independent of fc]... 

In the last subsection, we invoked phonons to explain the nonradiative broadening of the surface structures. However, at very low temperature, the surface state at the bottom of the excitonic band cannot undergo broadening either by phonon absorption or by phonon creation the phonon bath at 2 K does not suffice to account for the 3- to 4-cm 1 nonradiative width of the first surface resonance. Nevertheless, we assume the intrinsic nature of this broadening, since it is observed, constant, for all our best crystals.67120... 

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] ... 

The origin of these transformations is very difficult to investigate. Yet it appears that the optical study should be very helpful for this purpose. An analysis of T dependence of the phase phonon absorptions at 317 and 253 cm -1 show that the 54 K metal-insulator transition is driven by the Peierls distortion on the TCNQ sublattice, whereas the distortion on the TTF chains increases markedly around 49-K phase transition [100]. It is a typical example of a close relationship between the optical properties of organic conductors and a molecular mechanism of the phenomena that occur in the material. 

Similarly, for transitions in the reverse direction with phonon absorption ... 

The silicon raw material can be analyzed by FT-IR spectroscopy. The oxygen and carbon content is determined by comparing the ratios of the oxygen and carbon bands with those of the characteristic phonon absorptions of the silicon lattice (see Fig. 5.1-9 Zachmann, 1987). The measurements are calibrated by a reference wafer of similar thickness and surface condition in order to avoid complicated correction calculations. In a special manufacturing process for integrated circuits. Si wafers are coated with very thin films... 

Fig. 7. Spectral position of the principal zero phonon absorption lines of the three photoproduct series as a function of the chain length n in monomer units. The calculated curves have been fitted to the experimental points. The data are given in Table 3...

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. 

Ri92 M. J. Rice and H. Y. Choi, Charged-Phonon Absorption in Doped Ceoi Phya. Rev. B45, 10173-10176 (1992). 

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. 

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... 

Fig. 2. Phonon absorption rate as a function of phonon energy.

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. 

Figure 3.12 Hot phonon bottleneck to slow hot-electron cooling in QWs. At high light intensity, hot electrons produce hot phonons which can reheat electrons via phonon absorption to keep them hot. Pioss is power loss per electron.

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