Multiphonon decay

The very low multiphonon decay rates obtained in Example 6.2 from the Po (Pr +) and p5/2 (Yb +) states are due to the large number of effective phonons that need to be emitted -14 and 38, respectively - and so the high-order perturbation processes. As a consequence, luminescence from these two states is usually observed with a quantum efficiency close to one. On the other hand, from the F3/2 state of Er + ions the energy needed to bridge the short energy gap is almost that corresponding to one effective phonon hence depopulation of this state to the next lower state is fully nonradiative. 

Fig. 13.2.7 Relationship between inverse lifetime and temperature. Calculated values based on the multiphonon decay are indicated by solid and broken lines. (From Ref. 22.)...

In the case of luminescence transitions it is usually not appropriate to use the absolute intensities because non-radiative processes such as multiphonon decay or energy transfer processes can effectively change the observed intensities. Similarly, also the experimentally measured lifetime is not suitable because non-radiative processes can effectively shorten the lifetime. However, the radiative branching ratios (1r can still be compared with the calculations. These ratios denote the relative intensities for transitions from the same initial to different final multiplets. 

The above discussion has focused upon multiphonon decay (i.e., A is greater than the highest energy phonon). When crystal field energy levels are closer together, nonradiative relaxation from the upper to lower level can occur by direct phonon emission, or by Raman or Orbach processes ([2], pp 228-234). 

In solids up to now, only a few cases of SF have been observed. This arises from the difficulty to obtain long T2, because in a solid, active centers may be subjected to many perturbations multiphonon decays and ion-ion energy transfers in addition to inhomr eneous contribution and the strong spontaneous radiative decay at optical frequencies. In gas, it has been assumed that in order to avoid dipole-dipole interactions, the atom density should fulfil (Polder et al. 1979)... 

Multiphonon decay rates from excited states of rare earth ions determine three important properties of rare-earth lasers pump conversion efficiency,... 

The multiphonon decay rate from a single excited level to a lower level is given in eq. (36.29). More realistically, it is necessary to consider the total radiationless relaxation rate of a lower Stark multiplet of a rare earth ion in the crystalline lattice. This total thermal average of the individual rates is... 

These include ion-ion energy transfer, which can give rise to concentration quenching and non-exponential decay and relaxation by multiphonon emission, which is usually essential for completing the overall scheme, and can affect the quantum efficiency. For low concentration of rare earth dopant ions the principle nonradiative decay mechanism is a multiphonon emission. 

The excess free carriers (and excitons) do not represent stable excited states of the solids. A fraction of them recombine directly after thermahzation either radiatively or by multiphonon emission. In most materials, nonradiative transitions to defect states in the gap are the dominant mode of decay. The lifetime of free carriers T = 1/avS is determined by the density a of recombination centers, their thermal velocity v, and the capture cross section S, and may span 10-10 s. Electrons, captured by states above the demarcation level, and holes, captured by states below the hole demarcation level, may get trapped. The condition for trapping is given when the occupied electron trap has a very small cross section for recombining with a free hole. The trapping process has, until recently, not been well understood. 

Figure 2 Vibrational energy relaxation (VER) mechanisms in polyatomic molecules, (a) A polyatomic molecule loses energy to the bath (phonons). The bath has a characteristic maximum fundamental frequency D. (b) An excited vibration 2 < D decays by exciting a phonon of frequency ph = 2. (c) An excited vibration >d decays via simultaneous emission of several phonons (multiphonon emission), (d) An excited vibration 2 decays via a ladder process, exciting lower energy vibration a> and a small number of phonons, (e) Intramolecular vibrational relaxation (IVR) where 2 simultaneously excites many lower energy vibrations, (f) A vibrational cascade consisting of many steps down the vibrational ladder. The lowest energy doorway vibration decays directly by exciting phonons. (From Ref. 96.)...

Equation (5), VER involves a higher-order anharmonic coupling matrix element, which gives rise to decay via simultaneous emission of several phonons nftjph (multiphonon emission). In the ACN case, three phonons must be emitted simultaneously via quartic anharmonic coupling (or four phonons via fifth-order coupling, etc.). 

Doorway vibration decay is particularly interesting because it is the one situation where polyatomic molecule VER looks just like diatomic molecule VER. The doorway vibrations of polyatomic molecules decay by exactly the same multiphonon mechanism as the VER of a diatomic molecule. Diatomic molecules have been extensively studied (7). One prediction for diatomic molecules is an exponential energy-gap law (2). As the vibrational frequency is increased, with everything else held constant, the number of emitted phonons increases (the order of the multiphonon process increases) and the VER rate should decrease exponentially with increasing vibrational frequency. 

Indirect transfer occurs by a two-part mechanism, as shown in Fig. 18. First a vibrational excitation decays by generating phonons. The phonons then produce vibrational excitation on other molecules by multiphonon up-pumping. Indirect transfer will not occur unless the density of vibrational excitations is large enough to produce a real increase in the bath temperature. 

Relaxation from a high-energy level of the 4f configuration occurs by multiphonon transitions between closely spaced levels down to a level whose energy gap to the next-lower level is wide enough to allow radiative decay (Section 2.3). 

The minimum prerequisite for generation of upconversion luminescence by any material is the presence of at least two metastable excited states. In order for upconversion to be efficient, these states must have lifetimes sufficiently long for ions to participate in either luminescence or other photophysical processes with reasonably high probabilities, as opposed to relaxing through nonradiative multiphonon pathways. The observed decay of an excited state in the simplest case scenario, as probed for example by monitoring its luminescence intensity I, behaves as an exponential ... 

Fig. 13.2 The relaxation of different vibrational levels of the ground electronic state of 2 in a sohd Ar matrix. Analysis of these results indicates that the relaxation of the v < 9 levels is dominated by radiative decay and possible transfer to impurities. The relaxation ofthe upper levels probably takes place by the multiphonon mechanism discussed here. (From A. Salloum and H. Dubust, Chem. Phys. 189, 179 (1994).)...

Single-ion nonradiative decay for Ln3+ diluted into transparent host elpa-solite crystals, where the energy gap is greater than the Debye cutoff, is primarily due to multiphonon relaxation (with rate kmp). In some cases, first order selection rules restrict phonon relaxation between states, such as between Tig and T4g, or between T2g and T5g, CF states for MX63- systems. The dependence of the multiphonon relaxation rate, kmp, upon the energy gap to the next-lowest state (AE) has been investigated for other systems and is given by a relation such as [353, 354]... 

W(0) is the asymptotic transfer probability for AE — 0 and ft a parameter determined by the strength of the electron-lattice coupling as well as by the nature of phonons involved. This expression is similar to that for multiphonon radiationless decay except for the fact that fi represents the coupling between the two species involved. 

The vibrational spectrum of the host is particularly important for determining the rate of nonradiative decay and fluorescence quantum efficiency of lanthanides ions. Studies show that in both crystals and glasses, the rate of multiphonon emission is determined principally by the size of the energy gap to the next lower level and the number of phonons required to conserve energy (29J. Therefore hosts in which the maximum phonons energies are relatively small, e.g.,... 

Various broadband sources employed to optically pump Ha include tungsten, mercury, xenon, and krypton lamps. The last source provides an especially good spectral match to the near-infrared absorption bands of Nd3+ in YAG. To reduce lattice heating resulting from the multiphonon emission decay to the F3/2 state, semiconductor diodes and laser sources at 0.8-0.9 ym nave pumped Nd lasers (58). Sun-pumped Nd and chromium-sensitized Nd lasers have been demonstrated and considered for space applications (59). Lasing of Nd3+ by electron beam excitation has also been reported (bO). 

Ptutoyujum. (Am +). The energy level scheme and possible lasing transitions for Pu + are very similar to those of Np +. Prospective transitions include 6Hg/2+6H5/2, 9/2 7/2, and h7/2 Hc/2 For efficient fluorescence and laser action from either tne °Hg/2 or j/2 states, hosts should have low phonon frequencies to reduce nonradiative decay by multiphonon processes. Depending upon the host and the exact positions of higher-lying states, excited-state absorption may reduce or prevent net gain. 

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