Nonradiative decay fractionation

Consider, for example, a sensor composed of n phases each with a different nonradiative decay rate. The fraction of the excited sensor molecules Pi in phase ith may decay with an overall decay rate kr + k ri. In this case, the average probability of the sensor molecules of remaining in the excited state is given by... 

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. 

Figure 5. Energy level diagram for the Mo excitation-emission sequence. Initially the diatomic is excited by laser excitation to the state, Mo then decays non-radiatively with rate Ku + K,i. Some fraction is trapped in an intermediate emitting level which has the radiative and nonradiative rates Kcm and K, , respectively.

Figure 19.4C presents data on the phosphorescence decay dynamics on two of the samples in Figure 19.4B, the one without silver and the one having optimum enhancement. These exhibit the characteristic signature of plasmon-enhanced emission, namely that increases in luminescence are accompanied by decreases in excited state lifetime. Ordinarily, radiative rates are fixed by quantum mechanical matrix elements and variation in excited state lifetime is due to changes in nonradiative rates so that increases in lifetime correspond to lower non-radiative rates and increases in luminescence yield. Here, the lifetime is reduced by about a factor of 3 due to increased emissive rate even as the luminescence increases 215 times. These large enhancements cannot be accounted for simply by increase in phosphorescence yield since the yield is greater than 10 % in the absence of silver. It is evident that a substantial fraction of the increase must be accounted for by absorption enhancement. 

Let now q be the difference of the trapping efficiencies in the blend and the bilayer film, and p < 1 be the fraction of trapped excitons that again become exci-plexes and do not decay nonradiatively at the interface. We can then write... 

Since the rate of decay of a vacancy state is the sum of radiative and nonradiative transition rates, the ratios of the intensities of individual X-ray lines are proportional to the ratio of the rates for the corresponding transitions. The fractional emission rates Fij (where i is the munber of subshell and j is the transition e.g.. For L we take Fsa) is defined as ... 

Partitioning of relaxation into radiative and nonradiative channels requires two measurements. A measurement of the quantum yield of fluorescence (defined as the fraction of excited molecules that decays by fluorescence), immediately gives the ratio of the radiative and nonradiative rates of decay. A subsequent measurement of the lifetime of the excited state observed in a time modulated experiment (a lifetime established by the sum of all relaxation processes) then allows assessment of the absolute rate of each type of relaxation. 

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