Multi-phonon absorption

We have mentioned the existence of CPs in the one-phonon density of states, but this can be measured only for compound crystals. The situation is different in multi-phonon absorption because the high-frequency phonons of the BZ boundary are mostly involved (note that in three-phonon processes, the q = 0 zone-centre phonons can also be involved without problem for momentum conservation). For the two-phonon absorption, the density of states is proportional to an integral similar to the one in expression 3.20, with wt replaced by the sum of the two pulsations and of the phonons of the combination. Besides the trivial case where = u> = 0, the condition Vq (wt (q) + wt (q)) = 0 is fulfilled when Vq (wt) = Vq(uv) = 0 or when Vq (wt) = — Vq (wt ). The observed two-phonon absorption is the sum of the contributions of the possible two-phonon processes. Figure 3.2 shows the RT absorption of silicon in the two- and three-phonon absorption region. In the two-phonon region, it is fitted with the two-phonon dispersion curves... 

Beyond the intrinsic, multi-phonon absorption bands (between 4000cm and 1500cm ) [30], the transmission of the CVD diamond specimen reaches the maximum reflectivity limited value (Fig. 5) of 71.4% (using a refractive index value of 2.375 [32,3]) and is identical, within experimental accuracy, to that of high-quality single crystal Type Ila samples measured with the same instrument. 

The normalized probability of nuclear inelastic absorption W(E) can be decomposed in terms of a multi-phonon expansion (222,223) ... 

The absorption coefficient for a multi-phonon combination can be expressed as the product of three terms. The first one is the matrix element of the coupling term between the phonons involved in the process. It is non-zero only for specific phonon combinations determined by selection rules derived from symmetry considerations. The second one describes the temperature... 

Estimation of Low-Energy Excitation Modes. An absorption line profile of each dye molecule at low temperature consists of two components a sharp zero-phonon line and a broad phonon side band. Tbe energy difference between the zero-phonon line and the phonon side band coincides with the low-energy excitation mode or phonon frequency of the matrix when multi-phonon processes can be ignored. 

Fig. 3. Schematic representation of emission probability and absorption cross section for nuclei bound in a solid after Visscher (1960). The sharp line arises from zero-phonon processes, the broad distribution from one- and multi-phonon processes. The / factor equals the ratio of the area under the sharp line to the total area. Height and width of the zero-phonon line are not to scale. The energy scale corresponds to the case of Np. [Taken from Dunlap and Kalvius (1985).]...

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