TO phonon assisted transition

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],...

Table I. Theoretical expressions for the "oscillator strengths" of the LA, LO, TA, and TO phonon-assisted transitions in indirect materials. The subscript I refers to the phonon branch being considered. The spin orbit split band, is considered.

Although in Ge a piezospectroscopy experiment has been performed on the LA phonon-assisted transition its interpretation is more complex due to the fact that there are two intermediate electron states. However, from this work as well as the WMA spectrum of the TO-phonon assisted transition at zero stress valuable information about Sg pjj and S -ph both these transitions was obtained. 

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. 

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. 

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. 

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. 

Figure 5.35 Graph illustrating the relevant valence-band (VB) and conduction-band (CB) states in the Brillouin zone for a Ti02 crystal in the X and Z edges, and in the crystal centre F. Note that the lowest energy direct transition from the lowest energy of the valence band to the lowest level of the conduction band at F is forbidden the lowest energy transition is an indirect phonon-assisted transition. Adapted with permission from Emeline et al. (2000c). Copyright (2000) American Chemical Society.

Other transitions have been observed in the Se and Te spectra at energies higher than those of the above-reported lines. They have been attributed to phonon-assisted donor transitions involving the emission of A/Sb TO(T) and LO(T) phonons at 323 and 344 cm-1, respectively [4]. 

In this case, relaxation takes place from a level close to the ground state. And, we have specified rates in terms of Einstein probability coefficients. This allows us to determine under what conditions the threshold for stimulated emission can be reached. Note that in our three level diagram relaxation from Level 2. involves a phonon-assisted transition or a phonon emission to the lattice. 

In parallel with these experimental studies of PL for SQD suspensions, the role of the observed linewidth broadening has been examined. In particular, the linewidth broadening due to acoustic-phonon-assisted transitions is expected [1] to contribute to satellite lines in PL spectra that are downshifted by the acoustic phonon energies. Within the elastic continuum approach [6], the phonon mode frequencies sensitive to the boundary conditions at the SQD surface were calculated. The lowest-order spherical acoustic mode frequency for CdS for different matrix materials differ by as much as a factor of three for a given SQD radius. 

Lying at a lower energy than E2 is an energy level El- This energy level is due to an electron configuration in which two electrons are spin-paired, (tit ) A transition from Eq. 2 or E3 to Ei is not allowed under the total electron spin rule. None of these transitions would normally be involved in transitions that produce colour. However, in ruby, excited Cr ions in states E2 or 3 can lose energy to the crystal stmcture and drop down to level Ei. This process operates under different conditions from the optical transitions and is independent of spin. The energy is taken up in lattice vibrations and the ruby crystal warms up. This is called a radiationless or phonon-assisted transition. Typical rates of the transitions are ... 

Polymer photophysics is determined by a series of alternating odd (B ) and even (Ag) parity excited states that correspond to one-photon and two-photon allowed transitions, respectively [23]. Optical excitation into either of these states is followed by subpicosecond nonradiative relaxation to the lowest excited state [90]. This relaxation is due to either vibrational cooling within vibronic sidebands of the same electronic state, or phonon-assisted transitions between two different electronic states. In molecular spectroscopy [146], the latter process is termed internal conversion. Internal conversion is usually the fastest relaxation channel that provides efficient nonradiative transfer from a higher excited state into the lowest excited state of the same spin multiplicity. As a result, the vast majority of molecular systems follow Vavilov-Kasha s rule, stating that FT typically occurs from the lowest excited electronic state and its quantum yield is independent of the excitation wavelength [91]. 

The relative intensities of the phonon assisted transitions in a given material are determined by the product f (Uq + h + h) -The effects of the oscillator strength are clearly manifested in phonon emission processes, for which ng <<1. For temperatures up to room ten5)erature this conditions is satisfied and fj becomes the principal factor governing the relative strengths. For phonon absorption processes, the phonon occupation number has a large effect on the relative intensities. In this case the role of... 

The general theoretical expression for the intensities of the excitonic lines in the optical spectra, corresponding to TO phonon assisted indirect transitions between the stress-split Tg y valence and Al,c conduction bands via T] 5 conduction and A5 y valence band intermediate states are listed in Table IV. 

Table VI. Experimental and theoretical values of the intensities for the TO-phonon assisted indirect transitions in silicon. The relative and actual (in parentheses in units of cm ) experimental values were obtained by multiplying da/dE by the broadening parameter F. The theoretical values were calculated using... 

For Ge reliable experimental data exists for Af A snd the polarization dependent relative intensities of the LA phonon in the strained crystal, as shown in Fig. 10. Reference 41 could not resolve the TO transition and thus there is no known value for the quantity Af pQ The lack of data for the TO phonon can be remedied by making use of the WMA spectra of Fig. 10 at zero stress. A line is found approximately 9 meV higher in energy than the strong LA peak and is a result of TO phonon assisted indirect transitions. This conclusion is based on the fact that at L the LA and TO phonons differ in energy by 9 meV. 

Fig. 10. Wavelength-modulated absorption spectra of the LA-phonon assisted indirect transition in Ge at 77K for X = 0 and 3.73 x 10 dyn-cm along [ lll for E 1 X and E X It. For the X = 0 spectra the TO-phonon assisted peak is also observed as marked.

Table XI. Theoretical and experimental values for the intensities of the LA-phonon assisted transition in Ge for stress, X, along fill and fool for the electric field vector, E, of the incident light polarized parallel and perpendicular to X.

Due to the electron-phonon interactions, which contribute to the emission process by phonon-assisted transitions, the above expression may be modified to take into account the vibrational states. In that case, the dipole momentum matrix elements include both electronic... 

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... 

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