Transition phonon assisted

A simplified schematic diagram of transitions that lead to luminescence in materials containing impurides is shown in Figure 1. In process 1 an electron that has been excited well above the conduction band et e dribbles down, reaching thermal equilibrium with the lattice. This may result in phonon-assisted photon emission or, more likely, the emission of phonons only. Process 2 produces intrinsic luminescence due to direct recombination between an electron in the conduction band... 

Fig. 7.18 The radiative recombination time r as a function of the blue shift of the photon energy AE from the bulk silicon band edge zero-phonon transitions (dots) TO phonon-assisted transitions (line). This scatter plot shows the radiative time for each member of an ensemble uniformly distributed around a cubic geometry. The top scale indicates the equivalent cube size. Redrawn from [Hy2],...

Fluorescence from the Do and Di levels of Eu3+ in doped SrTiOa (cubic perovskite structure) has been observed [618]. The fluorescence decay from the 5Di level consists of radiative transitions to the 7F states and a nonradiative dominant transition to the 5Do level. The decay of the 5X>o state is mainly radiative and is composed of both zero-phonon and phonon-assisted transitions, the latter accounting for much of the temperature dependence of its lifetime. For temperatures upto 300° K, the decrease in the sZ>o lifetime has been correlated [618] with the increased intensity of the vibronic bands [619]. Both 5Z>o 7Fi and 5Do 7F2 transitions as well as 5Di 7F, bD - 7F2 and 5Z>o - 7F show vibronic structures at room temperatures [619] and below. 

Flynn and Stoneham [1970] were the first to suggest that diffusion of the light impurity atom is enhanced by symmetrically coupled vibrations. To incorporate this effect, which is called fluctuational barrier preparation, the authors have proposed to take into account the dependence of the tunneling matrix element on displacements of the heavy nuclei. This approach goes beyond the familiar Condon approximation. In this version of phonon-assisted tunneling, the phonon-dressed incoherent transitions are also induced by a suitable reduction in the barrier height via emission or absorption of phonons. 

Dick [1977] explained this behavior within the framework of a phonon-assisted tunneling mechanisms using the TLS approximation and golden rule formalism (see Sections 2.3 and 6.4). One-phonon transitions dominate the mechanism at low temperatures, resulting in a linear dependence of k with 7 this follows directly from relation (6.27) when j3/Wl. At higher temperatures, the main contribution comes from Raman processes, leading to a T4 dependence of the rate constant. This predicted T4 temperature dependence for RbBr OH- is analogous to results obtained by Silbey and Trommsdorf [1990] for two-proton transfer in benzoic acid crystals (see Section 6.4). 

K. The transition time is 102 s at 1.3 K. Kapphan and Luty proposed a phonon-assisted tunneling mechanism for this process. Although the notion that a mass as heavy as Ag+ can tunnel 0.9 A through a 0.17-kcal/mol barrier at 1.3 K is quite surprising, the experimental data and analysis clearly support this conclusion. 

If there are several AP minima of close energy, then at low temperatures one should take into account two-phonon-assisted transitions between these minima. In Ref. [15] (see also Ref. [14]) it was found that the rate of these transitions depends on temperature as 7 3. However, as it was already mentioned above, in Ref. [9] it was found that the contribution of the two-phonon-assisted transitions between different Jahn-Teller minima of the AP to the ZPL width at low temperatures is described by the T5 law. Note that an increase of the Jahn-Teller interaction leads to a decrease of the rate of these transitions. Therefore, in the strong Jahn-Teller interaction limit this broadening mechanism becomes unimportant. 

When considering the effect of temperature on multiphonon processes, one should take into account stimulated phonon-assisted transitions ([20,21]) and include thermally activated reversed transitions. Account of these factors gives... 

On the contrary, the semiclassical approach in the problem of the optical absorption is restricted to a great extent and the adequate description of the phonon-assisted optical bands with a complicated structure caused by the dynamic JTE cannot be done in the framework of this approach [13]. An expressive example is represented by the two-humped absorption band of A —> E <8> e transition. The dip of absorption curve for A —> E <8> e transition to zero has no physical meaning because of the invalidity of the semiclassical approximation for this spectral range due to essentially quantum nature of the density of the vibronic states in the conical intersection of the adiabatic surface. This result is peculiar for the resonance (optical) phenomena in JT systems full discussion of the condition of the applicability of the adiabatic approximation is given in Ref. [13]. 

The dispersionless optical phonon mode />, splits the degenerated unperturbed electron level (j = 1,2) while the mode b2 mediates the electron transitions between the levels. This latter term represents phonon-assisted tunneling, a mechanism of the... 

Fig. 6 Schematic illustration of the phonon-assisted exciton dissociation process. Due to the electronic state couplings, the photogenerated exciton (XT) wavepacket undergoes transitions to an interfacial charge transfer (CT) state, along with indirect XT — IS — CT transitions via an intermediate (IS) state (see panel (b)). In Ref. [52], the diabatic Hamiltonian of Eqs. (19)-(20) was parametrized for two relevant interface configurations (eclipsed (E) vs. staggered (S) as shown in panel (a)) which correspond to the configurations of Fig. 3.

Neodymium systems have the potential for quantum cutting because Nd3+ has a high lying 4f" state, 2G(2)9/2, at about 47 000 cm-1, which has a 7000 cm-1 gap above the next lower level, 2F(2)7/2 (Camall et al., 1988). This energy gap is sufficient to prevent non-radiative relaxation between the two states, and emission from the 2G(2)y/2 state can be expected. Exciting the 2G(2)9/2 state directly is impractical, due to the very low transition probability from the ground state. However, if efficient absorption into the 5d band occurs, then the 2G(2)9/2 state may be populated via non-radiative phonon-assisted relaxation, resulting in 2G(2)9/2 emission. 

In conclusion, on phonon-assisted absorption, the investigation of the phonon modes involved in the broadening of an excitonic transition is greatly... 

Fig. 8.3. Configurational coordinate diagram representing optical absorption and recombination in a material with a strong phonon coupling. A and B illustrate phonon-assisted non-radiative transitions.

The maximum rate of the phonon-assisted transitions is 10 -10 times greater than the fastest radiative rate and 10 times greater than the average rate (see Fig. 8.14). Luminescence therefore occurs only after the majority of carriers have thermalized to a sufficiently low density of states that further phonon-assisted transitions are suppressed by the weak overlap to neighboring sites. 

A spin-dependent recombination rate is another consequence of the electron-hole correlation. The conservation of spin selection rule is preserved in amorphous materials. The final state of the recombination process has zero spin and both radiative and phonon-assisted non-radiative transitions occur without change in spin, so that recombination can only proceed from an initial state of zero spin. A weakly interacting electron-hole pair forms four possible spin states, one singlet and one triplet. Of the four states, only the singlet and one... 

However, very soon it became clear that the situation is more complex (e.g. [9, 10]). The obvious problem arises with the fact that the red-yellow PL from PS is relatively slow with a decay time in the range of tens of microseconds, which, together with some further experimental observations [11] and theoretical calculations [9,10,12], is considered as strong evidence for an indirect band gap. However, as pointed out by Hybertsen [13], the electron and hole wave functions in small crystallites are spread in k space so that it is no longer meaningful to debate whether the gap is direct or indirect. Detailed calculations show that the phonon assisted transitions dominate in crystallites larger than about 1.5 nm, where an important part of the phonon contribution comes from scattering at the surface of the crystallites and a part from the bulk phonons. 

The direct transitions dominate only in much smaller crystallites [13]. As the size of the crystallites covered in the current experiments is 2 nm or more, the porous and nanocrystalline light emitting silicon is "indirect" gap material. The calculated radiative life time decreases with decreasing crystallite size for both the phonon assisted and direct transitions. The predicted dependence [13] correlates reasonably with... 

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