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Under open-circuit condition, the current is not extracted and the photogenerated carriers in principle disappear only by recombination. We study the open-circuit voltage $V_{\rm OC}$ and transient photovoltage under the effect of bulk recombination in a medium with energetic disorder by using the multiple trapping (MT) model. The key parameter in the MT model is the dispersion parameter $\alpha$ given by the ratio of thermal energy to the characteristic energy of trap states. We show that $V_{\rm OC}$ depends linearly on the logarithm of the light intensity and the slope depends on the $\alpha$ of the MT model. Under the continuous irradiation of light, the photovoltage response to the weak perturbation by a pulsed light obeys pseudo-first-order decay. The rate as a function of $V_{\rm OC}$ is independent of the dispersion parameter. However, it obeys the power law as a function of light intensity, and the exponent is given by $1/(1+\alpha)$, which reduces to 1/2 in the absence of energetic disorder.

We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the survival probability of the irreversible reaction. Furthermore, we make use of the mean reaction time approximation to write the irreversible survival probability in restricted spaces as a single exponential. In this way, we obtain exact and approximative expressions in the time domain for the reversible survival probability for three different two dimensional diffusion spaces: The infinite and restricted plane as well as the surface of a sphere. Our obtained results should prove useful in the context of membrane-bound reversible diffusion-influenced reactions in cell biology., Comment: 3 figures

We study bulk recombination in a medium with energetic disorder by using the multiple trapping (MT) model under continuous irradiation with excitation light. Charge densities are shown to obey power law as a function of the intensity of excitation light and the exponent is related to the dispersion parameter $\alpha$ of the MT model. The theory is applied to analyze charge densities in bulk heterojunction photovoltaic cells measured by light-induced electron spin resonance (LESR). The values of the exponent are consistent with those obtained from the transient decay of charge densities after pulsed excitations.We show that the value of the exponent is robust against addition of Gaussian trapping energy distribution due to shallow trap states. We also show that open-circuit voltage ($V_{\rm OC}$) depends linearly on logarithm of the light intensity and the slope is equal to $k_B T/e$ when only shallow trap states are present. The same linear relation holds with a slope larger than $k_B T/e$ in the presence of an exponential trapping energy distribution due to deep trap states., Comment: Major changes are required

In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles. The results interpolate between low and high concentrations of the inert particles. Excluded volume interactions by the inert particles hinder the diffusive motion of reactants. When the initial distribution of the inert particles is uniform, the excluded volume interactions slow the decay of the survival probability of a geminate pair in contrast to the acceleration of the decay found for the target problem under the presence of the excluded volume interactions among reactants. We also obtain the escape probability for a non-uniform initial distribution of the inert particles and show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.

Theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is surrounded by other quenchers differently. As a result, each quencher migrates differently in the presence of site blocking effects. However, in the conventional theory, such difference is ignored and quenchers are assumed to move independently of each other. In this paper, theory of diffusion-mediated reactions of target problem is developed by taking into account the site blocking effects for quencher migration and the difference in the configuration of quenchers around each quencher. Our result interpolates between those in high and low limits of quencher concentrations and is a lower bound of the survival probability. In the static limit, the exact result is reproduced for a localized sink. In the presence of diffusion, the approximation is better when intrinsic reaction rates are low.

We study direct energy transfer by multipolar or exchange interactions between diffusive excited donor and diffusive unexcited acceptors. Extending over the case of long-range transfer of an excitation energy a non-perturbative approach by Bray and Blythe [Phys. Rev. Lett. 89, 150601 (2002)], originally developed for contact diffusion-controlled reactions, we determine exactly long-time asymptotics of the donor decay function in one-dimensional systems., Comment: 16 pages

Ivanov-Anderson (IA) model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and supercooled liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first and second rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behaviour observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone., Comment: 14 figures

The photoluminescence in amorphous semiconductors decays according to power law $t^{-delta}$ at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power $alpha$ of the transient current observed in the time-of-flight experiments. Geminate recombination occurs by radiative tunneling which has a distance dependence. In this paper, we formulate ways to calculate reaction rates and survival probabilities in the case carriers execute dispersive diffusion with long-range reactivity. The method is applied to obtain tunneling recombination rates under dispersive diffusion. The theoretical condition of observing the relation $delta = alpha/2 + 1$ is obtained and theoretical recombination rates are compared to the kinetics of observed photoluminescence decay in the whole time range measured., Comment: To appear in Journal of Chemical Physics

The photoluminescence decay in amorphous semiconductors is described by power law $t^{-delta}$ at long times. The power-law decay of photoluminescence at long times is commonly observed but recent experiments have revealed that the exponent, $delta sim 1.2-1.3$, is smaller than the value 1.5 predicted from a geminate recombination model assuming normal diffusion. Transient currents observed in the time-of-flight experiments are highly dispersive characterized by the disorder parameter $alpha$ smaller than 1. Geminate recombination rate should be influenced by the dispersive transport of charge carriers. In this paper we derive the simple relation, $delta = 1+ alpha/2 $. Not only the exponent but also the amplitude of the decay calculated in this study is consistent with measured photoluminescence in a-Si:H., Comment: 18pages. Submitted for the publication in Phys. Rev. B

A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect. The derived equation is applied to the geminate recombination problem. The recombination is shown to depend on the intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem. Phys. {\bf 116}, 2338 (2002)], which were obtained from the fractional reaction-diffusion equation where the diffusion term has a memory effect but the reaction term does not. The reactivity dependence of the recombination probability is confirmed by numerical simulations., Comment: to appear in Journal of Chemical Physics