Local vibrations

Experimentally, local vibrational modes associated witli a defect or impurity may appear in infra-red absorjrtion or Raman spectra. The defect centre may also give rise to new photoluminescence bands and otlier experimentally observable signature. Some defect-related energy levels may be visible by deep-level transient spectroscopy (DLTS) [23]. 

Figure 6. The Bohr-Sommerfeld phase corrections t)(8, ) for k = 0, 1, and 2. The ratio r z,k)lK estimates of the error of primitive Bohr-Sommerfeld eigenvalues as a fraction of their local vibrational spacing.

Defects may be described in terms of thermodynamic constants and equilibria. The presence of defects changes both the local vibrational frequencies in the vicinity of the defect and the local lattice configuration around the defect. 

This new approach enables us to consider all the physical effects due to the interaction of the electron with the medium polarization and local vibrations and to take them into account in the calculation of the transition probability. These physical effects are as follows ... 

Effect of diagonal dynamic disorder (DDD). Fluctuations of the polarization and the local vibrations produce the variation of the positions of the electron energy levels eA(Q) and eB(C ) to meet the requirements of the Franck-Condon principle. 

Effect of off-diagonal dynamic disorder (off-DDD). The interaction of the electron with the fluctuations of the polarization and local vibrations near the other center leads to new terms VeP - V P, Vev - Vev and VeAp - VAPd, VA - VAd in the perturbation operators V°d and Vfd [see Eqs. (14)]. A part of these interactions corresponding to the equilibrium values of the polarization P0l and Po/ results in the renormalization of the electron interactions with ions A and B, due to their partial screening by the dielectric medium. However, at arbitrary values of the polarization P, there is another part of these interactions which is due to the fluctuating electric fields. This part of the interaction depends on the nuclear coordinates and may exceed the renormalized interactions of the electron with the donor and the acceptor. The interaction of the electron with these fluctuations plays an important role in processes involving solvated, trapped, and weakly bound electrons. 

Effect of diagonal-off-diagonal dynamic disorder (D-off-DDD). The polarization fluctuations and the local vibrations give rise to variation of the electron densities in the donor and the acceptor, i.e., they lead to a modulation of the electron wave functions A and B. This leads to a modulation of the overlapping of the electron clouds of the donor and the acceptor and hence to a different transmission coefficient from that calculated in the approximation of constant electron density (ACED). This modulation may change the path of transition on the potential energy surfaces. 

Additional effect of diagonal dynamic disorder. The variations of the electron densities near the centers A and B due to polarization fluctuations and local vibrations lead to changes in the interaction of the electron with the medium and, hence, to changes in the shape of the potential energy surfaces Ut and Uf as compared... 

The quantity Ef is the energy of the reorganization of all the classical degrees of freedom of the local vibrations and of the classical part of the medium polarization, and crc is the tunneling factor for quantum degrees of freedom 1) which do not... 

The effects of the modulation of electron density by local vibrations and polarization fluctuations are most pronounced for reactions involving transfer of weakly bound electrons. These effects were investigated in Ref. 16 for the transfer of weakly bound electrons from a donor Az to an acceptor BZ2 in a polar medium. 

Based on the results obtained in the investigation of the effects of modulation of the electron density by the nuclear vibrations, a lability principle in chemical kinetics and catalysis (electrocatalysis) has been formulated in Ref. 26. This principle is formulated as follows the greater the lability of the electron, transferable atoms or atomic groups with respect to the action of external fields, local vibrations, or fluctuations of the medium polarization, the higher, as a rule, is the transition probability, all other conditions being unchanged. Note that the concept lability is more general than... 

The effects of deviations from the Born-Oppenheimer approximation (BOA) due to the interaction of the electron in the sub-barrier region with the local vibrations of the donor or the acceptor were considered for electron transfer processes in Ref. 68. It was shown that these effects are of importance for long-distance electron transfer since in this case the time when the electron is in the sub-barrier region may be long as compared to the period of the local vibration.68 A similar approach has been used in Ref. 65 to treat non-adiabatic effects in the sub-barrier region in atom transfer processes. However, nonadiabatic effects in the classically attainable region may also be of importance in atom transfer processes. In the harmonic approximation, when these effects are taken into account exactly, they manifest themselves in the noncoincidence of the... 

The maximum of c/T3 is probably due to localized vibrational modes such as excitations in the molecular structure [40], We can see from Fig. 12.14 that the maximum has not been reached in these measurements which are limited to 4.2 K. For the similarity with polypropylene, the maximum in c/T3 for Torlon can be expected at about 10K. 

In Chapter 8, Stavola and Pearton discuss the local vibrational modes of complexes in Si that contain hydrogen or deuterium. They also show how one can use applied stress and polarized light to determine the symmetry of the defects. In the case of the B-H complex, the bond-center location of H is confirmed by vibrational and other measurements, although there are some remaining questions on the stress dependence of the Raman spectrum. The motion of H in different acceptor-H complexes is discussed for the Be-H complex, the H can tunnel between bond-center sites, while for B-H the H must overcome a 0.2 eV barrier to move between equivalent sites about the B. In the case of the H-donor complexes, instead of bonding directly to the donor, H is in the antibonding site beyond the Si atom nearest to the donor. The main experimental evidence for this is that nearly the same vibrational frequency is obtained for the different donor atoms. There is also a discussion of the vibrational modes of H tied to crystal defects such as those introduced by implantation. The relationship of the experimental results to recent theoretical studies is discussed throughout. 

II. Local Vibrational Mode Spectroscopy and Uniaxial Stress Techniques... 

While the BC configuration for the B—H complex is now accepted, several aspects of the vibrational spectra of the acceptor-H complexes are not understood. The temperature dependence of the B—H complex has been examined by Raman spectroscopy (Stutzmann and Herrero, 1987) and IR absorption (Stavola et al., 1988a). The H-stretching vibration shifts from 1875 to 1903 cm 1 between room temperature and liquid He temperature. Frequency shifts of just a few cm 1 are more typical for local vibrational modes. The vibrational bands are also surprisingly broad. 

Fig. 6. Raman spectra of localized vibrations due to nB and 10B in Si before (control) and after passivation by hydrogen or deuterium. [ Reprinted with permission from The Materials Research Society, Stutzmann, M. and Herrero, C.P. (1988). Defects in Electronic Materials, MRS Proceedings 104 (eds. M. Stavola, S.J. Pearson and G. Davies), p. 271. Also from Stutzmann and Herrero, 1988. And with permission from The American Physical Society, Herrero, C.P. and Stutzmann, M. (1988). Phys. Rev. B 38, 12668.]...

The stress parameters Aj and A2 for B—H are large for local vibrational modes. For example, they are an order of magnitude larger than was... 

Besides the electrically active complexes discussed above, there is indirect evidence for the existence of neutral complexes. In close analogy to the observations in silicon and several III-V materials it appears that hydrogen passivates deep and shallow acceptors. Because of the small concentrations of these neutral centers, all attempts to detect them directly with local vibrational mode (LVM) spectroscopy or electron paramagnetic resonance (EPR) have been unsuccessful. 

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