Radiative process

Radiative Processes.—A large number of papers concerned with the various aspects of the electronic absorption and emission processes in atomic species have appeared. Of general interest is a paper which presents an expression suitable for the evaluation of the infinite sum describing absorption due to a hydrogenic series of Lorenzian lines.444 The Doppler lineshape in atomic transitions,448 collision effects on lineshapes of atomic transitions,44 the effect of metastable dimers on the radiative transition in pairs of atoms 447 and in donor-acceptor pairs,448 and other aspects of excitation transfer in two-atom systems,449- 480 

The rapid development of lasers has led to the publication of increasing numbers of papers concerned this year with such subjects as superfluorescence and co-operative radiation processes,451 the thermodynamics of co-operative luminescence,452 saturation, collisional dephasing, and quenching of fluorescence of organic vapours in intense laser excitation studies,453 a theoretical model for fluorescence in gases subjected to continuous i.r. excitation,454 a quantum treatment of spontaneous emission from strongly driven two-level atoms,455 the development of site-selection spectroscopy,45 and measurements of relaxation times 457 using laser excitation. 

Radiative Processes. As was stated previously, the fluorescence rate constants of formaldehyde and acetaldehyde are larger than those of the higher aldehydes. When the radiative lifetime, TQ(expt), deduced from observed values of tr and by eq. 8 is compared to the values of tr(SB) calculated from the Strickler-Berg equation, 

Other treatments of the energy-dependent behavior of the radiative lifetime have been applied to formaldehyde, most notably the aforementioned treatments of Lin (145) and Yeung (254). No quantitative test of these theories can be made on the large carbonyls, and complete SVL data on the smaller species such as glyoxal and propynal are still unavailable at this writing. 

Energy-dependent (but not state-dependent) lifetime and quantum yield data are available for some of the more complex carbonyls. With reference to those molecules for which the appropriate data do exist, it can be seen in Table 11 that the radiative lifetime is virtually unaffected over a wide range of energies. This is in sharp contrast to the observed behavior of formaldehyde. The tr values for acetone might be less reliable than the others listed they are calculated using the fluorescence lifetime data of Breuer and Lee (42) and the fluorescence quantum yield data of Heicklen (105). It can be seen that there is no substantial change in tr the apparent (perhaps the real) trend is in the direction opposite that observed for formaldehyde. The values for perfluorocyclobutanone have been calculated using the rp and relative quantum yield values of Lewis and Lee (141) and the absolute fluorescence yield of 0.021 as measured by Phillips (187) as a standard. 

Thayer, et al. (242a) have measured Tp values for the discrete vibrational levels of propynal. While the fluorescence rate constant (or tr) was directly determined for only the vibrationless level of the excited state, their analysis of the higher vibrational data is consistent with the assumption that tr is invariant with the vibrational level excited. Since this observation shows a distinct contrast to the case of formaldehyde, it would be quite interesting to study propynal theoretically and compare the result to formaldehyde. This will require knowledge of the transition moment matrix elements a., which are at present unknown. 

The Tr values of the two fluorinated ketones are much longer than those of their protonated counterparts. The origin of this effect is not clear at this time. Successive chlorination of halogenated acetones appears to lengthen tr somewhat tr values of 1.7 ps for CIF2COCF3, -2.0 ps for CIF2COCIF2, and 3.0 ps for CIF2COCI2F have been reported (94). 

The further text shortly considers all of the three main bulk generation-recombination mechanisms in direct narrow-bandgap semiconductors. A unilied g-r term is presented to be utilized in modeling and optimization of photonic IR detectors. In addition to that, some useful approximations are given that may significantly speed up and simplify modeling. 

In thermal equilibrium the radiative recombination rate is equal to the generation rate due to thermal radiation for each frequency interval dv. If W(v) is the probability for a photon with a frequency v to be absorbed in a unit time, and p(v) energy density of the photon in a given volume of semiconductor crystal per dv, the radiative generation rate in thermal equilibrium is 

Instead of using the dispersion of dielectric permittivity in (1.21), the approximation e(v) fioo is often applied in literature (coo is the high-frequency value of effective dielectric permittivity) [ 13], so that we adopt the same approach in this text. 

The semiconductor absorption coefficient a(v) can be determined from experimental values, munerically calculated according to accurate theoretical dependences or analytically determined using approximations. 

Hall s expression for spontaneous radiative recombination rate, obtained using Bardeen s approximation for the absorption coefficient of narrow-bandgap semiconductors a [E—EgY [18] is often used to calculate the generation rate G,o [19, 20]. A generalization of Hall s expression is given as [29, 351] 

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These rules, A and B (which are not exact) are usefiil for both scattering and radiative processes and are often referenced as Femii s Rules 2 and 1, respectively. 

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

FIGURE 7.4 Modified Jablonski diagram showing transitions between excited states and the ground state. Radiative processes are shown by straight lines, radiationless processes by wavy lines. IC = internal conversion ISC = intersystem crossing, vc = vibrational cascade hvf = fluorescence hVp = phosphorescence. 

Many physical-chemical processes on surfaces of solids involve free atoms and radicals as intermediate particles. The latter diffuse along the adsorbent-catalyst surface and govern not only kinetics of catalytic, photocatalytic, or some heterogeneous radiative processes, but also creation of certain substances as a result of the reaction. 

The efficiency of these radiative processes often increase at low temperatures or in solvents of high viscosity. Consequently emission spectra are generally run in a low-temperature matrix (glass) or in a rigid polymer at room temperature. The variation in efficiency of these processes as a function of temperature and viscosity of the medium indicates that collisional processes compete with radiative and unimolecular nonradiative processes for deactivation of the lowest singlet and triplet states. 

In the radiative process, a real photon is emitted by the donor molecule and the same is absorbed by the acceptor molecule. The effectiveness of this process depends on, among other factors, the degree of overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. 

In radiolysis, a significant proportion of excited states is produced by ion neutralization. Generally speaking, much more is known about the kinetics of the process than about the nature of the excited states produced. In inert gases at pressures of a few torr or more, the positive ion X+ converts to the diatomic ion X2+ very rapidly. On neutralization, dissociation occurs with production of X. Apparently there is no repulsive He2 state crossing the He2+ potential curve near the minimum. Thus, without He2+ in a vibrationally excited state, dissociative neutralization does not occur instead, neutralization is accompanied by a col-lisional radiative process. Luminescences from both He and He2 are known to occur via such a mechanism (Brocklehurst, 1968). 

G. B. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics, Wiley-Interscience 1979. 

The possible fate of excitation energy residing in molecules is also shown in Figure 2. The relaxation of the electron to the initial ground state and accompanying emission of radiation results in the fluorescence spectrum - S0) or phosphorescence spectrum (Tx - S0). In addition to the radiative processes, non-radiative photophysical and photochemical processes can also occur. Internal conversion and intersystem crossing are the non-radiative photophysical processes between electronic states of the same spin multiplicity and different spin multiplicities respectively. 

The lifetime of the excited state will be influenced by the relative magnitudes of these non-radiative processes and thus time-resolved spectroscopy can provide information on the dynamics of excited state depletion... 

The fluoresence lifetimes calculated for TIN in low viscosity alcohols are approximately proportional to the solvent viscosity (12) which suggests that in these solvents there is a non-radiative process related to. the rotational diffusion mobility of the TIN molecule. The observed extent of the quenching, however, is significantly greater than that expected due to viscosity effects alone and cannot be explained by a collisionally-induced, Stern-Volmer type process involving methanol molecules (25.) as the appropriate plot is non-linear. 

The dependence of the fluorescence quantum yields and lifetimes of these stabilizers on the nature of the solvent suggests that the excited-state, non-radiative processes are affected by solvation. In polar, hydroxylic solvents, values of the fluorescence quantum yield for the non proton-transferred form are significantly lower, and the fluorescence lifetimes are shorter, than those calculated for aprotic solvents. This supports the proposal of the formation, in alcoholic solvents, of an excited-state encounter complex which facilitates ESIPT. The observed concentration dependence of the fluorescence lifetime and intensity of the blue emission from TIN in polymer films provides evidence for a non-radiative, self-quenching process, possibly due to aggregation of the stabilizer molecules. 

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