Multiphonon nonradiative processes

Recombination at and excitation from deep levels are emphasized. Nonradiative transitions at defect levels—Auger, cascade capture, and multiphonon emission processes—are discussed in detail. Factors to be considered in the analysis of optical cross sections which can give information about the parity of the impurity wave function and thus about the symmetry of a particular center are reviewed. 

However, nonradiative return to the ground state is possible if certain conditions are fulfilled that is, the energy difference should be equal to or less than 4-5 times the highest vibrational frequency of the surroundings. In that case this amount of energy can excite simultaneously a few high-energy vibrations and is then lost for the radiative process. Usually this nonradiative process is called multiphonon emission. 

Figure 5.16 Configurational coordinate diagrams to explain (a) radiative and (b) nonradiative (multiphonon emission) de-excitation process. The sinusoidal arrows indicate the nonradiative pathways.

The very low multiphonon decay rates obtained in Example 6.2 from the Po (Pr +) and p5/2 (Yb +) states are due to the large number of effective phonons that need to be emitted -14 and 38, respectively - and so the high-order perturbation processes. As a consequence, luminescence from these two states is usually observed with a quantum efficiency close to one. On the other hand, from the F3/2 state of Er + ions the energy needed to bridge the short energy gap is almost that corresponding to one effective phonon hence depopulation of this state to the next lower state is fully nonradiative. 

The excess free carriers (and excitons) do not represent stable excited states of the solids. A fraction of them recombine directly after thermahzation either radiatively or by multiphonon emission. In most materials, nonradiative transitions to defect states in the gap are the dominant mode of decay. The lifetime of free carriers T = 1/avS is determined by the density a of recombination centers, their thermal velocity v, and the capture cross section S, and may span 10-10 s. Electrons, captured by states above the demarcation level, and holes, captured by states below the hole demarcation level, may get trapped. The condition for trapping is given when the occupied electron trap has a very small cross section for recombining with a free hole. The trapping process has, until recently, not been well understood. 

Some relatively new analyses in the theory of nonradiative transitions have followed from the fact that there is no basic reason why our three primary processes cannot also take place in combination. Thus Gibb et al. (1977) propose a process of cascade capture into an excited electronic state and subsequent multiphonon emission from there. The results of this model were applied to capture and emission properties of the 0.75-eV trap in GaP. A more detailed analysis has since been given by Rees et al. (1980). Similarly, cascade capture followed by an Auger process with a free carrier seems a quite likely process. However, we are not aware that such a model has as yet been suggested. The third possible combination of processes, namely Auger with multiphonon, has been examined by Rebsch (1979) and by Chernysh... 

Nonradiative transitions between the 4f levels of lanthanide ions are caused by multiphonon processes. In the case of band emissions, the quantum efficiency is commonly interpreted by the Mott s model. It should be noted that Struck and Fonger have shown that in fact an unified model can be used for these two types of emission. ... 

The minimum prerequisite for generation of upconversion luminescence by any material is the presence of at least two metastable excited states. In order for upconversion to be efficient, these states must have lifetimes sufficiently long for ions to participate in either luminescence or other photophysical processes with reasonably high probabilities, as opposed to relaxing through nonradiative multiphonon pathways. The observed decay of an excited state in the simplest case scenario, as probed for example by monitoring its luminescence intensity I, behaves as an exponential ... 

Ptutoyujum. (Am +). The energy level scheme and possible lasing transitions for Pu + are very similar to those of Np +. Prospective transitions include 6Hg/2+6H5/2, 9/2 7/2, and h7/2 Hc/2 For efficient fluorescence and laser action from either tne °Hg/2 or j/2 states, hosts should have low phonon frequencies to reduce nonradiative decay by multiphonon processes. Depending upon the host and the exact positions of higher-lying states, excited-state absorption may reduce or prevent net gain. 

The effect of temperature on deep trap emission is similar to that observed for bandgap emission, with the intensity of the emission decreasing as the temperature increases. This can be explained by the involvement of nonradiative recombination processes dominating at higher temperature. Nonradiative relaxation in CdSe nanoclusters has been assigned to the involvement of a multiphonon relaxation mechanism mediated by a vibrational mode of the surface phenylse-lenolate ligands. ... 

The above discussion has focused upon multiphonon decay (i.e., A is greater than the highest energy phonon). When crystal field energy levels are closer together, nonradiative relaxation from the upper to lower level can occur by direct phonon emission, or by Raman or Orbach processes ([2], pp 228-234). 

Reported ranges of output wavelengths for the various types of solid state lasers are shown in the figure. The differences in the ranges of spectral coverage arise in part from the dependence on host properties, in particular the range of transparency and the rate of nonradiative decay due to multiphonon processes. 

The processes competing with luminescence are radiative transfer to another ion and nonradiative transfers such as multiphonon relaxation and energy transfer... 

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