Quantum recombination model

The quantum recombination model. The photogeneration of an exciton and its luminescent decay occur within a quantum-confined silicon crystallite [Ca6]. 

The approach is ideally suited to the study of IVR on fast timescales, which is the most important primary process in imimolecular reactions. The application of high-resolution rovibrational overtone spectroscopy to this problem has been extensively demonstrated. Effective Hamiltonian analyses alone are insufficient, as has been demonstrated by explicit quantum dynamical models based on ab initio theory [95]. The fast IVR characteristic of the CH cliromophore in various molecular environments is probably the most comprehensively studied example of the kind [96] (see chapter A3.13). The importance of this question to chemical kinetics can perhaps best be illustrated with the following examples. The atom recombination reaction... 

Stein (66) criticized this treatment and reports that although formally the system follows the geminate recombination model, unreasonable parameters are obtained since too-low concentrations of scavengers bring the quantum yield to its limiting value. 

CO2 laser pyrolysis of silane in a gas flow reactor and the extraction of the resulting silicon nanoparticles into a cluster beam apparatus has been shown to offer an excellent means for the production of homogeneous films of size-separated quantum dots. Their photoluminescence varies with the size of the crystalline core. All observations are in perfect agreement with the quantum confinement model, that is, the photoluminescence is the result of the recombination of the electron-hole pair created by the absorption of a UV photon. Other mechanisms involving defects or surface states are not operative in our samples. 

The conclusion that can be drawn from the experiments just discussed is that, except for the very small particles, the photoluminescence of our Si nanocrystals, which are produced by CO2 laser-assisted pyrolysis of silane and which are gently oxidized in air under normal conditions, can be perfectly explained on the basis of the quantum confinement model, that is, by the radiative recombination of electron-hole pairs confined in the nanocrystals [15]. In order to obtain high quantum yields, the nanoparticles must be defect-free in particular, they must be perfectly monocrystalline and all dangling bonds must be passivated, for example by a silicon oxide layer. Indeed, high-resolution electron microscopy (HREM) studies have shown that our Si nanoparticles are composed of a perfect diamond-phase crystalline core and a surrounding layer of SiO [19]. 

The hole current in this LED is space charge limited and the electron current is contact limited. There are many more holes than electrons in the device and all of the injected electrons recombine in the device. The measured external quantum efficiency of the device is about 0.5% al a current density of 0.1 A/cm. The recombination current calculated from the device model is in reasonable agreement with the observed quantum efficiency. The quantum efficiency of this device is limited by the asymmetric charge injection. Most of the injected holes traverse the structure without recombining because there are few electrons available to form excilons. 

Fig. 16.3 Quantum yield (QY) for electron and hole transfer to solution redox acceptors/donors as a function of the reduced variables y (related to the surface properties of the catalyst, i.e., ratio between interfacial electron transfer rate and surface recombination rate) and w (related to the ratio between surface migration currents of hole and electrons to the rate of bulk recombination), according to the proposed kinetic model [23],...

The surface-state model. The absorption of a photon generates an exciton within a quantum-confined silicon crystallite but its radiative recombination occurs at localized electtonic states on the surface of the crystallites [Ko5] or in defects in the oxide coverage of the crystallites [Pr5]. 

All formulas mentioned above are fulfilled for any phenomenological photoconduction model. Microscopic description needs detailed research of the quantum yield, parameters of the generation, recombination and transport processes. 

From the steady state fluorescence spectrum of indole in water a fluorescence quantum yield of about 0.09 is determined. Since the cation appears in less than 80 fs a branching of the excited state population has to occur immediately after photo excitation. We propose the model shown in Fig. 3a). A fraction of 45 % experiences photoionization, whereas the rest of the population relaxes to a fluorescing state, which can not ionize any more. A charge transfer to solvent state (CITS), that was also introduced by other authors [4,7], is created within 80 fs. The presolvated electrons, also known as wet or hot electrons, form solvated electrons with a time constant of 350 fs. Afterwards the solvated electrons show no recombination within the next 160 ps contrary to solvated electrons in pure water as is shown in Fig. 3b). 

Figure 4.16 Example of the inverted region observed in the geminate recombination of an ion pair. Theoretical plots are shown from the top as Rehm-Weller, Marcus with quantum effect correction, and Marcus classical model...

The formation of P -L-Q ion radical pairs upon illumination of the P-L-Q compounds of the kind depicted in Fig. 8 and of their zinc complexes within a notably wider range of temperatures (up to 300 K) was detected by the EPR method [34, 40]. The quantum yield of charge separation and the time of charge recombination at 300 K amount to 5 x 10 3 and 10 3 s, respectively. In accordance with the modern models of electron transfer in condensed media (see Chap. 3) the efficiency of charge separation in P-L-Q grows with increasing solvent polarity [34]. 

The quantum yield of the photocurrent for an electrode illuminated from the front side can be calculated from a simple model described by Gartner (j+) provided some simplifying assumptions are applicable. This model is shown in Figure 1. If surface recombination can be neglected, the quantum yield 4> is obtained as... 

Oxidation of the jc-Si surface has been shown to produce blue PL.15 The blue PL is quite weak in as-prepared 71-Si and becomes intense only after strong oxidation. The blue PL has a much faster decay than the red PL and its origin is of some debate at present. Models currently under consideration include band-to-band recombination in Si nanocrystals, emission from oxide, and emission due to surface states. Blue PL has been observed also in oxide-free zr-Si simply by decreasing the size of the Si crystallites in accordance with the quantum confinement mechanism.51,52 In fact, the PL can be tuned from the c-Si band gap of 1.1 eV all the way up to 3 eV by a judicious choice of the porosity in unoxidized zr-Si.51-53... 

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