Exciton/excitonic

Above mathematics shows that the changes in the model Hamiltonian (1) that do not involve the exciton-phonon coupling terms, - for instance inclusion the exciton-exciton (electron-electron) interaction, lead only to the respective change of in Eqs.(16). 

In a metal, there are excited states for electrons that lie below the ionization energy. This can be conceived as an electron in a "conduction band" and a "hole" that interact so that the combination is neutral but not of lowest energy. Such an excited state is called an exciton. Excitons may move by diffusion of the electron-hole pair or by transfer of a molecular exciton to another molecule. Reversion of the exciton to a lower energy state may be slow enough for the lifetime to be longer that of lattice relaxation processes. 

In another model-based study Gillbro et al. [192] have used exciton-exciton annhilation to determine average EET hopping rates. In this technique the rate of exciton-exciton annhilation depends critically on the domain size and the pairwise EET rate [193, 194]. Average pairwise rates of 2 x 10 s -10 s were calculated for LHCII having EET domain sizes in the range of 300-1000 sites. 

Nguyen TQ, Martini IB, Liu J, Schwartz BJ (2000) Controlling interchain interactions in conjugated polymers the effects of chain morphology on exciton-exciton annihilation and aggregation in MEH-PPV films. J Phys Chem B 104 237... 

The femtosecond fluorescence up-conversion setup has been described elsewhere [13,14]. Briefly, a second harmonic (SH) of a home-made chromium-forsterite femtosecond laser tunable from 610 to 660 nm was used to excite the sample (Fig.2) [14]. The pulse duration of the SH pulses was about 50 fs at the full width at half maximum (FWHM). We were successful in the cavity-dumping operation of this laser [14] and kept the repetition rate as low as 4 MHz. Reduction of the repetition rate was necessary to avoid multiple hits of the same location of the sample as small as possible. The excitation intensity, controlled by a neutral density filter before the sample cell, was (0.5-l)xl012 photons/cm2/pulse. Special care was taken to work at the lowest excitation light intensity so that the effect of the exciton-exciton annihilation process was negligible. 

D. Olness, M. Swicord, and R. C. Jarnagin Photogeneration of free carriers in organic crystals via exciton-exciton interactions. Phys. Rev. Letters 10,12 (1963). 

In case of interaction between excitations, exciton-exciton annihilations (or fusion) are the most likely mechanisms to be employed for an energy density dependence of the transient decays. The dynamics is reflected in a Riccatti rate equation including simultaneous monomolecular and bimolecular processes,... 

Figure 7. Decays of photoinduced absorption in sexithienyl at pump intensities Io and Io/2 (picosecond range). Bi-molecular exciton-exciton annihilation is evidenced [21].

In Fig. 10, the transients exhibit quite different behavior from opal A to opal CT. In particular, a bi-exponential decay (Eq. 2) failed to reproduce the kinetics of opal CT. In this material, the emission is red-shifted towards 2.6 eV and the PL is strongly quenched at shorter time delays, with an unusual, non-linear kinetics in semi-log scale, indicating a complex decay channel either involving multi-exponential relaxation or exciton-exciton annihilations. Runge-Kutta integration of Eq. 5 seems to confirm the latter assumption with satisfactory reproduction of the observed decays. The lifetimes and annihilation rates are Tct = 9.3 ns, ta = 13.5 ns, 7ct o = 650 ps-1 and 7 0 = 241 ps-1, for opal CT and opal A, respectively. 

An alternative quasiparticle description of the optical response is possible using the nonlinear exciton equations (NEE) (39). The response function is then represented in terms of one-exciton Green functions and exciton-exciton scattering matrix. Four coherent ultrafast 2D techniques have been proposed (16,17), and computer simulations of the 2D response were performed for model aggregates made out of a few two-level chromophores. 

In summary, the response function depends on the exciton Green function G, the exciton-exciton scattering matrix T, and the irreducible part G of the density matrix Green function. It has two components ... 

Numerical work involved the calculation of the exciton-exciton scattering matrix T and evaluating the integral in Equation (33). The 2D PE signal for models C-F was averaged over 105 disorder realizations. 

The mobility of excited states, imposed by intermolecular interactions (see Sec. 2.4), can lead to their collision with each other and/or with other types of excited states as well as trapped or free carriers generated in an organic solid. Such collision processes, realizing various excitonic interactions, may result in annihilation of the excitons and/or their transformation into another set of particles and quasi-particles. As different types of excitonic interactions show up in different optical and electrical phenomena, we divide them into two categories corresponding to the interaction between quasiparticles (exciton-exciton interactions) and to the interaction between quasi-particles and particles (exciton-charge carrier interactions). 

Several other charge carrier generation mechanisms involve excitons (1) field or thermal ionization of excitons, (2) exciton interaction with trapped carriers, (3) exciton-exciton interaction, and (4) exciton-photon interaction. 

In addition to surface-enhanced exciton dissociation and geminate recombination, direct photoexcitation (Northrop and Simpson, 1956 Heilmeier et al., 1963 Harima et al., 1989) and exciton-exciton annihilation (Silver et al., 1963 Jortner et al., 1963 Braun, 1968 Johnston and Lyons, 1968 Foumy et al., 1968 Swenberg, 1969 Braun and Dobbs, 1970 Orlowski and Scher, 1983) arguments have been proposed. In direct photoexcitation, a free electron and free hole are created without the involvement of intermediate states. With the exception of the work of Harima et al. and Orlowski and Scher, there have been few references to direct or exciton-exciton photogeneration processes in the past one and a half decades. 

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