Transition, radiative

From these equations one also finds the rate coefficient matrix for themial radiative transitions including absorption, induced and spontaneous emission in a themial radiation field following Planck s law [35] ... 

We now discuss the lifetime of an excited electronic state of a molecule. To simplify the discussion we will consider a molecule in a high-pressure gas or in solution where vibrational relaxation occurs rapidly, we will assume that the molecule is in the lowest vibrational level of the upper electronic state, level uO, and we will fiirther assume that we need only consider the zero-order tenn of equation (BE 1.7). A number of radiative transitions are possible, ending on the various vibrational levels a of the lower state, usually the ground state. The total rate constant for radiative decay, which we will call, is the sum of the rate constants,... 

Figure Bl.1.3. State energy diagram for a typical organic molecule. Solid arrows show radiative transitions A absorption, F fluorescence, P phosphorescence. Dotted arrows non-radiative transitions.

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

Semiconductors can be divided into two groups direct and indirect band gap materials. In direct semiconductors the minimum energy in the conduction band and the maximum in the valence band occur for the same value of the electron momentum. This is not the case in indirect materials. The difference has profound consequences for the transitions of electrons across the band gap in which light is emitted, the radiative transitions, of interest here. 

Radiative and non-radiative transitions of rare-earth ions in glasses. R. Reisfeld, Struct. Bonding (Berlin), 1975, 22,123-175 (56). 

Reisfeld R (1975) Radiative and Non-Radiative Transitions of Rare Earth Ions in Glasses. 22 123-175... 

Figure 9.1. A Jablonski diagram. So and Si are singlet states, Ti is atriplet state. Abs, absorption F, fluorescence P, phosphorescence IC, internal conversion and ISC, intersystem crossing. Radiative transitions are represented by full lines and nonradiative transitions by dashed lines...

As a matter of fact low-lying MMCT states can also influence radiative transition probabilities. The long decay time of the VO4 luminescence is considerably shortened by the presence of Bi " [27] due to a Bi(IV)-V(IV) MMCT state (see also above). Such effects are very well-known for LMCT states in case of transition-metal ions and lanthanide ions [6]. They will not be discussed here any further. 

As seen in the radiationless process, intercombinational radiative transitions can also be affected by spin-orbit interaction. As stated previously, spin-orbit coupling serves to mix singlet and triplet states. Although this mixing is of a highly complex nature, some insight can be gained by first-order perturbation theory. From first-order perturbation theory one can write a total wave function for the triplet state as... 

Figure 6.11. Electronic transitions to the first excited singlet (s) and lowest triplet (0 states from the ground states (g) of benzophenone (B) and naphthalene (N) moieties in compounds (4), n = 1-3. Possible radiative transitions are represented by straight arrows, radiationless transitions by wavy arrows.(80> Reprinted by permission of the American Chemical Society.

Of the different kinds of forbiddenness, the spin effect is stronger than symmetry, and transitions that violate both spin and parity are strongly forbidden. There is a similar effect in electron-impact induced transitions. Taken together, they generate a great range of lifetimes of excited states by radiative transitions, 109 to 103 s. If nonradiative transitions are considered, the lifetime has an even wider range at the lower limit. 

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. ... 

Here we outline a dynamical description (42) of the polymerisation of the polydiacetylenes. The approach relies much on the one used (43,44) in the theory of non radiative transitions in crystals and the soliton description of the defects in the lD-or-ganic semiconductors. 

Ion implantation generates many dangling bonds that form centers for nonradiative recombination. These centers decrease the carrier lifetime and compete effectively with radiative transitions. However, after hydrogenation, since hydrogen ties dangling bonds, the luminescence process becomes more efficient. Furthermore, since the 1.0-eV emission is obtained even before hydrogen is introduced, the new radiative center may be formed due to residual hydrogen in the c-Si that combines with the implantation-induced defects. 

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