Non-radiative electron transitions

The results of experimental research have also stimulated the appearance of theoretical papers devoted to the analysis of an elementary act of electron tunneling reactions in terms of the theory of non-radiative electron transitions in condensed media. It has been shown that this theory allows one to explain virtually all the known experimental data on electron tunneling reactions. 

In this paper, the multiphonon relaxation of a local vibrational mode and the non-radiative electronic transitions in molecular systems and in solids are considered using this non-perturbative theory. Results of model calculations are presented. According to the obtained results, the rate of these processes exhibits a critical behavior it sharply increases near specific (critical) value(s) of the interaction. Also the usual increase of the non-radiative transition rate with temperature is reversed at certain value of the non-diagonal interaction and temperature. For a weak interaction, the results coincide with those of the perturbation theory. 

To sum up, we have developed a general non-perturbative method that allows one to calculate the rate of relaxation processes in conditions when perturbation theory is not applicable. Theories describing non-radiative electronic transitions and multiphonon relaxation of a local mode, caused by a high-order anharmonic interaction have been developed on the basis of this method. In the weak coupling limit the obtained results agree with the predictions of the standard perturbation theory. 

Figure 2.23 Schematic illustrating the dye sensitization of a semiconductor electrode via electron transfer straight lines indicate radiative transitions, curved lines electron transfer, and wavy lines non-radiative (nr) transitions. Photoexcitation into the Si state of the dye may result in charge injection into the conduction band of the semiconductor or fluorescence and inter-system crossing, from where charge injection may occur from the triplet state or phosphorescence...

Recombination is either radiative or non-radiative. The radiative process is accompanied by the emission of a photon, the detection of which is the basis of the luminescence experiment. The radiative transition is the inverse of optical absorption and the two rates are related by detailed balance. Non-radiative recombination is commonly mediated by the emission of phonons, although Auger processes are sometimes important, in which a third carrier is excited high into the band. The thermalization process occurs by the emission of single phonons and is consequently very rapid. Non-radiative electron-hole recombination over a large energy requires the cooperation of several phonons, which suppresses the transition probability. 

All non-radiative electronic processes are isoenergetic transitions to another electronic state, which may or may not be the ground state. This other state may be localised on the same molecule, or on molecules produced by unimolecular chemical reaction from the excited-state or the process may involve interaction with states on another system which acts as a quencher of the excited-state, e.g. by energy transfer or bimolecular reaction. (The resultant electronic state(s) may themselves deactivate non-radiatively or radiatively, e.g. the phosphorescence from a triplet state formed from a higher singlet, emission from excimers and exciplexes formed from ground-state excited state interaction (see Sect 1.13.5.5), or emission from quencher states produced by energy transfer or chemical reaction.)... 

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. 

By absorption of light a molecule is promoted to a higher electronic state. The monomolecular physical processes for the dissipation of the excess energy are outlined in Fig. 5 in a so called Jablonski diagramm. In principle one has to differentiate between radiative and non-radiative deactivation on the one side and on the other side one has to consider if the multiplicity of the system is conserved or not. Radiative deactivation, i.e. deactivation accompanied by emission of light, is termed fluorescence if the transition occurs with spin conservation and phosphorescence, if spin inversion occurs. 

The polydiacetylene crystals (1-4) most strikingly corroborate these conjectures. Along this line of thought is also shown that this electron-phonon interaction is intimately interwoven with the polymerisation process in these materials and plays a profound role there. We make the conjecture that this occurs through the motion of an unpaired electron in a non-bonding p-orbital dressed with a bending mode and guided by a classical intermolecular mode. Such a polaron type diffusion combined with the theory of non radiative transitions explains the essentials of the spectral characteristics of the materials as well as their polymerisation dynamics. ... 

Radiative and non-radiative transitions between electronic states... 

Internal conversion is a non-radiative transition between two electronic states of the same spin multiplicity. In solution, this process is followed by a vibrational relaxation towards the lowest vibrational level of the final electronic state. The excess vibrational energy can be indeed transferred to the solvent during collisions of the excited molecule with the surrounding solvent molecules. 

Radiative and non-radiative transitions between electronic states 39 Box 3.2 Spontaneous and stimulated emissions... 

Finally, I refer back to the beginning of this paper, where the assumption of near-adiabaticity for electron transfers between ions of normal size in solution was mentioned. Almost all theoretical approaches which discuss the electron-phonon coupling in detail are, in fact, non-adiabatic, in which the perturbation Golden Rule approach to non-radiative transition is involved. What major differences will we expect from detailed calculations based on a truly adiabatic model—i.e., one in which only one potential surface is considered [Such an approach is, for example, essential for inner-sphere processes.] In work in my laboratory we have, as I have mentioned above,... 

A related phenomenon is the conversion of single visible photons with the result the quantum efficiency can be higher than 100%. If, for example, 0.1% of Pr + is incorporated in YF3 and excited with the mercury spectral line at 185 nm, the electron from 4f5d states decay non-radiatively to the Sq (4p) State. This system is able to generate two visible photons by So- f6> followed by non-radiative decay to the closely adjacent Po and by transition another photon is emitted by transitions to one of the six /-levels of or F. A condition for this cascade process is that the nephelauxetic effect for inter-shell transitions is sufficiently weakly pronounced for the lowest 4/5d state to be above Sq (Reisfeld and Jbrgensen 1977). 

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