Electron-hole pair distance

Fig. 8.16. Distribution of the electron-hole pair distances showing the large range of recombination lifetimes (Biegelsen et al. 1983).

The two above features which modify the simplest theory extend the range of distances z between the fluorophore and the surface over which the results remain valid, from a minimum of several hundred nanometers without the modifications to less than ten nanometers with them. Those two features are incorporated into the results displayed here. Other refinements, not included here, involve consideration of energy transfer to electron-hole pairs (for metals only at z < 10 nm) and nonhomogeneous atomic field effects (z<0.25 nm). We first assume that the intrinsic quantum yield is 100% then we will modify that assumption. 

Fig. 3. Escape probability predicated by On-sager theory for isotropic initial distribution of electron-hole pairs. T = 296 K static permittivity of e = 3 thermalization distance of r0 [11, P 248]...

The use of a bulk-like dielectric constant, such as those in Equations (2.334)-(2.336), neglects the specific contribution given by the surface to the dielectric response of the metal specimen. For metal particles, such a contribution is often introduced in the model by considering the surface as an additional source of scattering for the metal conduction electrons, which consequently affects the relaxation time r [69], Experiments indicate that the precise chemical nature of the surface also plays a role [70], The presence of a surface affects the nonlocal part of the metal response as well, giving rise to surface-assisted excitations of electron-hole pairs. The consequences of these excitations appear to be important for short molecule-metal distances [71], It is worth remarking that, when the size of the metal particle becomes very small (2-3 nm), the electron behaviour is affected by the confinement, and the metal response deviates from that of the bulk (quantum size effects) [70],... 

Fig. 10.28. Model of charge carrier separation and charge transport in a nanocrystalline film. The electrolyte has contact with the individual nanocrystallites. Illumination produces an electron-hole pair in one crystallite. The hole transfers to the electrolyte and the electron traverses several crystallites before reaching the substrate. Note that the photogenerated hole always has a short distance (about the radius of the particle) to pass before reaching the semiconductor/electrolyte interface wherever the electron-hole pair is created in the nanoporous film. The probability for the electron to recombine will, however, depend on the distance between the photoexcited particle and the tin-coated oxide back-contact. (Reprinted with permission from A. Hagfeldt and Michael Gratzel, Light-Induced Redox Reactions in Nanocrystalline Systems Chem. Rev. 95 49-68, copyright 1995, American Chemical Society.)...

Abstract. It is shown, that the photoconductivity of Cgo single crystal essentially depends on a spin state of the intermediate electron-hole pairs. The distance between components of electron-hole pairs in states with uncorrelated spins and their lifetime were estimated as R>3.4 nm and r 10 9 s. 

Influence of EF on magnitude of photoconductivity of fullerene C6o single crystal in a weak MF can be explained in the following way. Increasing intensity of electric field causes the increase of radius of initial distance r0 between the components of electron-hole pairs and, consequently, the decrease of probability of geminate recombination. As a result, AI rises at small values of EF. At higher values of EF the probability of dissociation of pairs in states with uncorrelated spins increases, that causes nonlinear behavior of electrofield dependences of photoconductivity of fullerite C6o in MF. The distance between components of electron-hole pairs in states with uncorrelated spins was estimated as R>3.4 nm. 

Geminate recombination is suppressed when the density of excited electron-hole pairs is large. For example, a pair density of 10 cm results in an average separation of the carriers of 50 A. The geminate pairs overlap when this distance is less than the thermalization length, Z.T, and non-geminate recombination between carriers from different pairs occurs. Geminate recombination is therefore most likely at low temperatures and weak excitation intensities and in a-Si H it is only observed under these conditions. 

The luminescence efficiency is given by the fraction of electron-hole pairs which are created farther than R from the nearest defect (Street et al. 1978). The distribution of distances is the nearest neighbor distribution function, G R), for randomly dispersed defects, which is (Williams 1968)... 

The recombination is modified in a multilayer structiu e whose layer spacing is similar to the carrier tunneling distance and is observed in photoluminescence measurements (Tiedje 1985). Fig. 9.22(a) shows that the luminescence intensity of a-Si H/nitride multilayers decreases as the layer thickness drops below about 500 A. The interface states and bulk nitride defect states cause non-radiative recombination because the electron-hole pairs are never far from an interface. The model of non-radiative tunneling developed in Section 8.4.1 can be adapted for recombination in thin layers. When the layer thickness is less than the critical transfer radius, the luminescence efficiency is (see Eq. (8.52)). 

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