Acoustic phonon modes

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Although no quantum confinement should occur in the electronic energy level structure of lanthanides in nanoparticles because of the localized 4f electronic states, the optical spectrum and luminescence dynamics of an impurity ion in dielectric nanoparticles can be significantly modified through electron-phonon interaction. Confinement effects on electron-phonon interaction are primarily due to the effect that the phonon density of states (PDOS) in a nanocrystal is discrete and therefore the low-energy acoustic phonon modes are cut off. As a consequence of the PDOS modification, luminescence dynamics of optical centers in nanoparticles, particularly, the nonradiative relaxation of ions from the electronically excited states, are expected to behave differently from that in bulk materials. 

As it follows from the (26) and Fig. 6, at the absence of the magnetic field (H = 0) the dynamic coupling does not exist and the unrenormalized acoustic phonon mode active in the CJTE linearly depends upon the wave vector. However when H is not zero the dynamic coupling drastically changes both the phonon and the electronic mode. 

Fig. 4 shows that the lifetime of the 2p impurity level decreases monotonically with the quantum well width. This is likely to be due to the increasing overlap between the impurity state and the confined acoustic phonon modes. 

It has been shown that the binding energy of a Be acceptor can be varied from its bulk value of 28 meV to a maximum of around 55 meV in a narrow GaAs/AlAs quantum well. T he c orresponding s eparation o f t he i mpurities i nternal 1 s a nd 2 p levels is around 21 to 42 meV, which is equivalent to a wavelength of between 60 and 30 mm. Pump probe spectroscopy of the same samples has shown that the lifetime of the upper (2p) level varies from around 350 ps in bulk material to 80 ps in the narrowest quantum well. This variation in lifetime is thought to be due to non-radiative scattering due to zone-folded acoustic phonon modes, which arise from the symmetry of the multiple quantum well potentials. 

Fig. 44. Schematic representation of the influence of different charge relaxation rates of IV rare-earth ions on the frequencies of the optical phonon modes (e.g., (dj and at ) and on the q=0 longitudinal acoustic-phonon modes, represented by the bulk modulus Cg (see text). For the stable n - and (n -1- l) -valent rare-earth compounds we show generalized reference lines. Four typical cases are shown with the representative samples given at the bottom.

Experimentally this effect has been found in dhcp Pr (Houmann et al. 1979) and in PrAlj (Purwins et al. 1976). The latter has cubic site symmetry and the ground and first excited states are Fj (OK) and 7 (27.4K). It orders ferromag-netically at = 33 K. At low temperatures (F T ) only three of the field-split F3-F4 magnetic excitons are seen (fig. 30) and those with 7+ polarization show a strong anti-crossing effect with a transverse acoustic phonon mode in the [001] direction. Detailed model calculations for this mixed-mode spectrum were performed by Aksenov et al. (1981) using an equation of motion approach. 

The coupling of localized electronic states to phonons was first described by Huang and Rhys [56] in their framework, the acoustic phonon modes are discretized and each individual mode forms a new eigenstate (an acoustic polaron) with each confined exciton state. Radiative transitions then occur between these polaron states, possibly leading to photon emission with emission or absorption of acoustic phonons. The probability of emission of an acoustic phonon depends on the coupling strength between the confined electron-hole pair state and the acoustic phonon mode, as well as on the phonon mode population (i.e. on the temperature). 

---