Relaxation non-radiative

As mentioned in the introductory part of this section, quantum dots exhibit quite complex non-radiative relaxation dynamics. The non-radiative decay is not reproduced by a single exponential function, in contrast to triplet states of fluorescent organic molecules that exhibit monophasic exponential decay. In order to quantitatively analyze fluorescence correlation signals of quantum dots including such complex non-radiative decay, we adopted a fluorescence autocorrelation function including the decay component of a stretched exponential as represented by Eq. (8.11). 

Here, a is a stretched factor, and Xdark is the characteristic time of the non-radiative relaxation. 

In addition to the photoluminescence red shifts, broadening of photoluminescence spectra and decrease in the photoluminescence quantum efficiency are reported with increasing temperature. The spectral broadening is due to scattering by coupling of excitons with acoustic and LO phonons [22]. The decrease in the photoluminescence quantum efficiency is due to non-radiative relaxation from the thermally activated state. The Stark effect also produces photoluminescence spectral shifts in CdSe quantum dots [23]. Large red shifts up to 75 meV are reported in the photoluminescence spectra of CdSe quantum dots under an applied electric field of 350 kVcm . Here, the applied electric field decreases or cancels a component in the excited state dipole that is parallel to the applied field the excited state dipole is contributed by the charge carriers present on the surface of the quantum dots. 

Figure 7.5 Schematic presentation of photoactivation and relaxation processes in a CdSe quantum dot aggregate (a) surface-passivation of photoexcited quantum dots by solvent molecules or dissolved oxygen, (b) thermal activation followed by the formation ofa stabilized state, (c) the formation of deep-trap states, (d) non-radiative relaxation of deep-...

It should be noted that no emission from the zwitterionic form of the proton-transferred tautomer was observed from any of the benzotriazoles studied in the present work. This implies that non-radiative relaxation processes from the excited state of this species are very efficient in all of the solvent and polymer environments studied. Thus no information is available on the effect of the medium polarity on the room-temperature photophysics of the zwitterionic form using fluorescence techniques. 

Turning to the fully quantum mechanical approach, we find that the lowest order rate theory for general non-radiative relaxation processes also provides a factorized rate expression ... 

If the electron enters a Rydberg orbital on one of the protonated amine sites, in addition to undergoing a cascade of radiative or non-radiative relaxation steps to lower-energy Rydberg states, it can subsequently undergo intra-peptide electron transfer to either an SS cr or an OCN n orbital after which disulfide or N-Cr, bond cleavage can occur [3r,3u-3w]. 

Trivalent samarium activated minerals usually display an intense luminescence spectrum with a distinct hne structure in the red-orange part of the spectrum. The radiating term 65/2 is separated from the nearest lower level 11/2 by an energy interval of 7,500 cm This distance is too large compared to the energy of phonons capable to accomplish an effective non-radiative relaxation of excited levels and these processes do not significantly affect the nature of their spectra in minerals. Thus all detected lines of the Sm " luminescence take place from one excited level and usually are characterized by a long decay time. 

In this Chapter we describe the extension of the parametric model used for 4f" spectra to calculations of absorption and emission spectra for the 4f 15d configuration. We also illustrate how they can be applied to calculate other properties of interest, such as non-radiative relaxation rates. Finally, we discuss the relationship between parametrized calculations and other approaches, such as ab initio calculations. 

Once the parameters are determined, we can calculate other spectroscopic properties for the 4f 15d configuration. These include emission spectra and lifetimes, the presence (or lack of) emission from the 4f 15d configuration, and non-radiative relaxation effects upon the linewidths of 4f 15d and 4F excited states. 

Neodymium systems have the potential for quantum cutting because Nd3+ has a high lying 4f" state, 2G(2)9/2, at about 47 000 cm-1, which has a 7000 cm-1 gap above the next lower level, 2F(2)7/2 (Camall et al., 1988). This energy gap is sufficient to prevent non-radiative relaxation between the two states, and emission from the 2G(2)y/2 state can be expected. Exciting the 2G(2)9/2 state directly is impractical, due to the very low transition probability from the ground state. However, if efficient absorption into the 5d band occurs, then the 2G(2)9/2 state may be populated via non-radiative phonon-assisted relaxation, resulting in 2G(2)9/2 emission. 

Efficient excitation from the ground state to the broad 4f5d bands can occur, followed by non-radiative relaxation to the 1 So state, allowing efficient population of1 So. 

Fast non-radiative relaxation of excited states leads to broadening of the spectral lines. The amount of broadening gives information about the nature and rate of the relaxation. We will discuss both qualitative and quantitative effects below. 

It is obvious from figs. 2 and 3 that the fine structure that is observed for the low energy 4f 15d states is not visible for higher-energy states. This is attributed to non-radiative relaxation. In fig. 2 it is clear that the states where the 5d electron is in the lowest-energy orbital (symmetry 2E) have visible fine-structure, whereas the states in which the 5d electron is in a 2T2 orbital do not. The high-energy states are expected to be in the conduction band (Ishii et al., 2001) and the relaxation is presumed to involve ionization to the conduction band. 

Another interesting example of the effect of non-radiative relaxation on linewidths is visible in the two-photon absorption spectrum of Eu2+ in CaF2 (Downer et al., 1983). These experiments involve the excitation of 4f7 states within the 4f65d band, followed by non-radiative decay to 4T55d states. The excitation was measured by monitoring emission from 41fl5d to 4f7. It is apparent from the spectra that the linewidths of the 4f7 states vary significantly. 

Duan et al. (2007) present an alternative approach to these ab initio calculations. They suggest that, rather than attempting to calculate the multitude of 5d energy levels directly, ab initio approaches could concentrate on producing useful parameter values for only the subset of terms in the parametrized Hamiltonian (see section 2) which cannot be experimentally determined. That is, the ab initio calculations could produce reliable values, for example, for the / (fd) and <7v(fd) parameters that could then be incorporated into parametrized calculations. The parameters may then be fine tuned to give a reliable calculation that might be used to investigate other properties of the ions, such as the non-radiative relaxation discussed in section 3.4. 

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