Relation between Charge-Dipole Interactions and the Sqrt(E)-Dependent Mobility in Molecularly Doped Polymers

Time-of-flight measurements on a wide variety of molecularly-doped polymers reveal carrier mobilities that exhibit an exponential dependence on the square root of the applied electric field. Recent attempts to explain the observed field dependence have focused on the role played by spatial and energetic disorder. It as also been conjectured that the charge-dipole interactions often identified as the source of energetic disorder could be of sufficient range to lead to correlations in the energies of neighboring hopping sites. We have analytically explored the effect of such correlations on high field carrier transport in random potentials, and discuss how particular features of the correlations associated with charge-dipole interactions might lead to behavior similar to that seen in experiment

Long-Range Hopping in Substitutionally Disordered Solids

A theoretical approach for studying charge-carrier and energy diffusion due to long-range hopping in substitutionally disordered solids is presented. Unlike some earlier theories, which invoke a pair approximation to treat back-transfer processes, the current theory makes use of the exact solution to an appropriate single-defect problemone in which long-range jumps into, out of, and between both the defect site and all other active sites in the lattice are explicitly included. From this exact solution a new long-range effective-medium theory is constructed to describe the configurationally averaged transport properties of the disordered system

Low-Field Hopping among Randomly-Distributed Sites with Uncorrelated Energetic Disorder

The low-field mobility μ of a small concentration of charge carriers hopping among a random distribution of transport sites is studied, as a function of the mean interparticle spacing ρ and the temperature T, for model systems having different site-energy distribution functions. For a uniform density of states our calculations show that the mobility obeys empirical scaling laws similar to those found in the theory of variable-range hopping. For a binary distribution of site energies we observe a crossover as a function of site density between trap-limited conduction and trap-mediated conduction. For a Gaussian density of states our results confirm the quadratic inverse temperature dependence of lnμ found in Monte Carlo studies, although quantitative characterization of this dependence is found to depend sensitively on the degree of spatial disorder in ways that could impact the extraction of microscopic parameters from experimental data

One-Dimensional Trapping Kinetics at Zero Temperature

The asymptotic decay of the survival probability is calculated for a quantum particle moving at zero temperature on a one-dimensional tight-binding chain possessing randomly placed irreversible traps of strength γ. The survival probability exhibits a decay, P(t) ~ exp(-At1/4), which is slower than that associated with a diffusing particle

Site-Diagonal T-Matrix Expansion for Anisotropic Transport and Percolation on Bond-Disordered Lattices

A study is made of the dynamical behavior of an electron or exciton undergoing anisotropic hopping on a d-dimensional bond-disordered lattice. Starting with a master equation for the site probabilities, an exact equation of motion is obtained for the probability currents that flow along the bonds connecting nearest-neighbor sites. Unlike the original master equation, the equation of motion which couples the microscopic currents contains the randomly distributed hopping rates in a form which is strictly site diagonal. The simplification that results leads to a new and exact expansion for the diffusion tensor in powers of an appropriately defined single-bond t matrix. From the lowest term of this expansion, a frequency-dependent effective-medium theory for anisotropic solids is constructed. The theory is then used to study the vanishing transport anisotropy that occurs for an anisotropic random walk on an isotropically percolating lattice near the critical point

Exciton Diffusion at Finite Frequency: Luminescence Observables for Anisotropic Percolating Solids

A study is made of the luminescence intensities associated with exciton diffusion and trapping on a three-dimensional anisotropic percolating lattice. The calculation is based upon a relationship that exists between the frequency dependent diffusion tensor at frequencies comparable to the inverse excitation lifetime, and luminescence observables such as the host and trap luminescence intensities for conditions of constant illumination. The present approach allows the study of crossover behavior in percolative systems that are of intermediate transport dimensionality 2 \u3c dt \u3c 3. Our results suggest that curvature seen in luminescence observables near the transition need not always be a direct reflection of the critical indices associated with classical isotropic percolation. We have identified three possible sources of deviation from the classical behavior: (1) the radiative time scale of the luminescence measurements, (2) the functional dependence of the luminescence yields on the diffusion tensor, and (3) the demands of dimensional crossover in the critical region arising from the anisotropy of the medium

Quantum Transport in the Presence of Random Traps

We calculate the asymptotic decay of a quantum particle moving in a d-dimensional medium doped with randomly placed trapping impurities, focusing on contributions from slowly decaying long-wavelength modes centered in large compact regions devoid of traps. By averaging the decay over the statistical distribution associated with these regions we find that the survival probability, P(t) ~exp(-Atd/(d+3)), decays more slowly in any dimension than for diffusive transport

Trapping-to-Percolation Transition in the Hopping Diffusion of Substitutionally Disordered Solids with a Binary Energy Distribution

We consider charge carriers that undergo nearest-neighbor hopping among the sites of a binary random lattice, each site of which is associated with one of two possible energies E1 or E2. A general and recently observed feature of this problem not predicted by previous treatments of disordered hopping models is a crossover between trap-limited conduction and percolation. We introduce new energy-projected equations of motion whose solutions reveal the deep conductivity minimum associated with this phenomenon, and compare the results predicted to numerical simulations

Low Temperature Tunneling Dynamics in Condensed Media

There has been considerable interest recently in the low temperature dynamics of condensed phase tunneling phenomena. In this paper we consider the interplay between quasiparticle transport and vibrational relaxation; the former taking place via tunneling in a double well potential, and the latter occurring due to interactions of the tunneling system with a harmonic bath. Taking the system-bath interactions to be linear in the bath coordinates, and explicitly allowing for a vibrationally excited well, we present a unified treatment of the weak and strong coupling regimes and obtain reduced equations of motion for the tunneling particle position operator. Solutions are obtained for several important limiting cases. In particular, we find that at sufficiently low temperatures, the dynamical behavior strongly resembles that of multisite spin jump model

Variational Treatment of a Harmonic Oscillator Coupled to a Dissipative Heat Bath

We consider the problem of a single quantum oscillator coupled linearly to a heat bath of independent harmonic modes. An exact solution is presented for the system-oscillator observables of interest. The exact results are then used to evaluate the utility of a variational approach to the problem that has proven useful recently in elucidating the dynamics of dissipatively coupled systems. We find that the variational approach does provide a good description for most, but not all, observables of interest. Both the exact and the variational treatment demonstrate the important role played by the low-frequency bath modes in determining qualitative features of the dynamical behavior