Theory and simulation of multiple-trapping transport through a finite slab

Transient photocurrent and optical absorption of disordered thin-film semiconductors: In-depth injection and nonlinear response

The time-of-flight method is a fundamental approach for characterizing the transport properties of semiconductors. Recently, the transient photocurrent and optical absorption kinetics have been simultaneously measured for thin films; pulsed-light excitation of thin films should give rise to non-negligible in-depth carrier injection. Yet, the effects of in-depth carrier injection on the transient currents and optical absorption have not yet been elucidated theoretically. Here, by considering the in-depth carrier injection in simulations, we found a 1/t^1-α/2 initial time (t) dependence rather than the conventional 1/t^1-α dependence under a weak external electric field, where α < 1 is the index of dispersive diffusion. The asymptotic transient currents are not influenced by the initial in-depth carrier injection and follow the conventional 1/t^1+α time dependence. We also present the relation between the field-dependent mobility coefficient and the diffusion coefficient when the transport is dispersive. The field dependence of the transport coefficients influences the transit time in the photocurrent kinetics dividing two power-law decay regimes. The classical Scher-Montroll theory predicts that a₁ + a₂ = 2 when the initial photocurrent decay is given by 1/t^a₁ and the asymptotic photocurrent decay is given by 1/t^a₂ . The results shed light on the interpretation of the power-law exponent of 1/t^a₁ when a₁ + a₂ ≠ 2.

Motional narrowing under Markovian and non-Markovian hopping transitions in inhomogeneous broadened absorption line shape

Inspired by recent experiments showing a minimum of electron spin or paramagnetic resonance (ESR and EPR) line width as a function of inverse temperature, we studied the motional narrowing effect by considering a combined model of carrier transitions and static dispersion of the angular frequency giving rise to an inhomogeneous broadening in the spectrum. The dispersion of the angular frequency results from the distribution of the local field. The transition between the sites under inhomogeneous static local field induces adiabatic relaxation of the spin. We also considered the on-site inherent (nonadiabatic) relaxation of the spin. We obtained the exact solution of the spin correlation function by explicitly considering transitions between two sites for both Markovian and non-Markovian transition processes. The absorption line shape is expressed in terms of the Voigt function, which is a convolution of a Gaussian function and a Lorentzian function. Using the known properties of the Voigt function, we discuss the correlation between the change in the full-width at half-maximum and the change in line shape, both of which are induced by motional narrowing. By assuming thermal activation processes for both the hopping transition and the on-site inherent relaxation, we show that the minimum of the width appears as a function of inverse temperature as observed experimentally in organic materials. Contrary to the general belief, we also show that the narrowing of the Gaussian line shape under a local random field did not necessarily lead to a Lorentzian line shape in particular under the presence of heavy tail property in the waiting time distribution of hopping transitions.

Comparative Monte-Carlo simulations of charge carrier transport in amorphous molecular solids as given by three most common models of disorder: The dipolar glass, the Gaussian disorder, and their mix

We have performed Monte-Carlo simulations of the charge carrier transport in a model molecularly doped polymer using three most popular hopping theories (the dipolar glass model, the Gaussian disorder model, and an intermediate between them) in a wide range of applied electric fields and temperatures. Time of flight transients have been computed and analyzed in logarithmic coordinates to study the Poole-Frenkel field dependence, the non-Arrhenius mobility temperature dependence, and the nondispersive versus dispersive current shapes. We also have made an attempt to estimate the total disorder energy directly from simulation data at the lowest electric field thus checking the consistency of the model fitting. Computational results have been compared with the analytical and experimental information available in the literature.

The impact of hot charge carrier mobility on photocurrent losses in polymer-based solar cells

A typical signature of charge extraction in disordered organic systems is dispersive transport, which implies a distribution of charge carrier mobilities that negatively impact on device performance. Dispersive transport has been commonly understood to originate from a time-dependent mobility of hot charge carriers that reduces as excess energy is lost during relaxation in the density of states. In contrast, we show via photon energy, electric field and film thickness independence of carrier mobilities that the dispersive photocurrent in organic solar cells originates not from the loss of excess energy during hot carrier thermalization, but rather from the loss of carrier density to trap states during transport. Our results emphasize that further efforts should be directed to minimizing the density of trap states, rather than controlling energetic relaxation of hot carriers within the density of states.

Distinguishing spin relaxation mechanisms in organic semiconductors

A theory is introduced for spin relaxation and spin diffusion of hopping carriers in a disordered system. For disorder described by a distribution of waiting times between hops (e.g., from multiple traps, site-energy disorder, and/or positional disorder) the dominant spin relaxation mechanisms in organic semiconductors (hyperfine, hopping-induced spin-orbit, and intrasite spin relaxation) each produce different characteristic spin relaxation and spin diffusion dependences on temperature. The resulting unique experimental signatures predicted by the theory for each mechanism in organic semiconductors provide a prescription for determining the dominant spin relaxation mechanism.

Analysis of the time-of-flight transients in molecularly doped polymers using the Gaussian disorder model

Using published data for four molecularly doped polymers, which exhibit flat plateaus on the time-of-flight transients, we compared theoretical curves with experimental ones. The numerical calculations as well as parameter values were based on the Gaussian disorder model. In no case were flat plateaus predicted to appear. According to theory carrier transit should proceed in the non-equilibrium regime. We saw close agreement for the transit times in weakly polar polymers even at high fields but only at elevated temperatures, while in highly polar polymers similar agreement occurred only at low fields. In addition, the Gaussian disorder model does not account for the current shape universality (regarding field variation) frequently observed experimentally in polar molecularly doped polymers.

Porosity Effects on Electron Transport in TiO2 Films and Its Application to Dye-Sensitized Solar Cells

Porosity (P) of TiO2 film in dye-sensitized solar cells affects the light absorption coefficient and electron diffusion coefficient. A theoretical analytical expression of the intensity-modulated photocurrent spectroscopy (IMPS) response involving the light absorption coefficient and the electron diffusion coefficient as a function of the porosity has been proposed to investigate the influence of TiO2 film porosity on the characteristics of electron transport. The incident photon-to-current conversion efficiency (IPCE) and electron transit time depending on the porosity have been analyzed illuminating from both the electrolyte side (IE) and the substrate side (IS). The IPCE derived from the IMPS response reaches its maximum at a porosity of around 30% for IE and 41% for IS, respectively. Electron transit time increases with increasing the porosity for IE, while it declines when P < 0.41 for IS, which is attributable to the influence of the RC time constant. It has also been found that a larger RC time constant will lead to a longer transit time. The electron diffusion coefficient calculated from the transit time for IE corresponds to the results from the porosity reported in previous literature, which indicates that the dependence of the electron transit time tau(d) on the porosity is justifiable. The diffusion coefficient calculated for a larger RC time constant approaches the value from the literature when P > or = 0.41, while it is not practicable when P < 0.41 for IS.

Dispersive-diffusion-controlled distance-dependent recombination in amorphous semiconductors

The photoluminescence in amorphous semiconductors decays according to the 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.

Grain Morphology and Trapping Effects on Electron Transport in Dye-Sensitized Nanocrystalline Solar Cells

We have examined the combined effects of grain morphology and electron trapping on the transient response of photoelectrons moving through the TiO2 grains in a dye-sensitized nanocrystalline solar cell using a multi-time-scale random walk Monte Carlo model. Our use of a multi-time-scale approach enables us to simulate transport for electrons moving through spherical connected grains in a three-dimensional (3D) voided network and look at the effect of the size of interparticle boundaries on carrier dynamics. We can also address similar times to those over which measurements are taken, namely, 0.1 ms. These times are long because of deep traps in the TiO2 grains. The grains have 2-fold connectivity in one dimension (linear chains) or 4-fold or 6-fold connectivity in three dimensions and traps with an exponential distribution of energies. Photoelectrons are generated by a light pulse of short duration. The spatial distribution of the photogenerated electron density from this pulse either has a uniform profile or is peaked on the electrolyte side. We show that the constrictions at the grain necks slow the electrons, making trapping more likely and hence further delaying their passage to the extracting electrode. By comparing our results for 4-fold and 6-fold coordinated particles on a cubic lattice with 2-fold coordinated particles on linear chains, we show that transport is slowed in the former case due to the additional paths available to the electrons in the 3D network. We also find that the charge and current transients cannot be fit to an analytical solution of the continuum equations with an effective diffusion coefficient even at long times. Therefore, caution must be exercised when attempting to fit experimental transient data with an effective diffusion coefficient.