The transport of photoinjected charges in disordered organic films is often interpreted using a formula based on a Gaussian disorder model (GDM) that neglects spatial correlations due to chargedipole interactions, even though such correlations have recently been shown to explain the universal electric field dependence observed in these systems. Based on extensive computer simulations of a 3D disorder model that includes such correlations, we present a new formula for analyzing experiments that accurately describes transport in these materials. [S0031-9007(98)07626-1] PACS numbers: 73.50.Yg, 72.10.Bg, 72.80.LeRecent efforts by a number of workers [1-7] have increased our understanding of nearly universal features of photoinjected charge transport in many disordered organic materials, including molecularly doped polymers [8,9], low molecular weight organic glasses [10,11], and certain polyconjugated polymers [12,13]. In particular, it is now recognized that the Poole-Frenkel (PF) dependence [8][9][10][11][12], m~exp͑gof the drift mobility m on electric field E observed in these materials results from slowly varying spatial fluctuations in the potential energy of a charge migrating through the material. Such energetic fluctuations can arise [1] from a random distribution of molecules in the medium possessing permanent electric dipole moments; a carrier's interaction with the latter provides a significant contribution U d to the total site energy. More importantly, the energy correlation function [1,3] C͑r͒ ͗U d ͑0͒U d ͑r͒͘ ϳ s 2 d a͞r (2) decays very slowly with intersite separation r. Here, s d ͗U 2 d ͘ 1͞2 is the rms width of the dipolar energetic disorder, and a is a minimal charge-dipole separation. In a previous Letter [3], an analytical result equivalent to (1) was derived for carriers diffusing along one spatial dimension through a medium with correlations as in (2). This same behavior was also observed in 3D charge transport simulations [4]. Moreover, very recent studies on both 1D and 3D systems suggest that this mechanism producing PF behavior is stable under additional sources of disorder less correlated than those that arise from dipoles [5,6], and indicate that the PF factor g in (1) is insensitive to all but the dipolar component of the disorder.These recent advances raise questions regarding the way materials have been experimentally characterized in the past. Most measurements in the last decade have been interpreted using an uncorrelated Gaussian disorder model, developed and extensively studied by Bässler and co-workers prior to the recent recognition of the importance of spatial correlations [14]. In the GDM, transport occurs through hops among localized states characterized by a Gaussian distribution of site energies, with hopping rates obeying an asymmetric detailed balance relation [14]. Numerical simulations capture well many features of experiment; its Gaussian density of states (DOS) leads to a temperature dependence ln m~2͑T 0 ͞T͒ 2 routinely observed, and the GDM reproduces low temperature...

Using the general result that the mobility m of charge carriers driven in a spatially correlated random potential by an electric field E can be expressed in terms of the Laplace transform of a particular correlation function related to the random potential, we demonstrate that the exponential dependence of m on p E universally observed in molecularly doped polymers arises naturally from the interaction of charge carriers with randomly distributed permanent dipoles. [S0031-9007(96)00689-8] PACS numbers: 72.10.Bg, 72.80.Le High-field time-of-flight experiments have been used for over two decades to characterize carrier mobilities in photoexcited molecularly doped polymers and amorphous molecular glasses [1-3]. Numerous measurements over a large range of fields E and temperatures T have established that, in many materials, the carrier mobility m exhibits a universal Poole-Frenkel behavior [4]where m 0 is a temperature independent prefactor and k is Boltzmann's constant. In a particular form of this phenomenological expression proposed by Gill [5], the activation energy Q is temperature independent, and the Poole-Frenkel factor is written g B͑b 2 b 0 ͒, where b 1͞kT , and B and b 0 1͞kT 0 are constants. In a second form, motivated by extensive numerical simulations on the Gaussian disorder model (GDM) of Bässler and coworkers [2], Q͞kT ͑2s͞3kT͒ 2 , and g C͑b 2 s 2 2 S 2 ͒, where s is the width of the energetic disorder, and C and S are constants. Many recent theoretical attempts to explain this observed proportionality between lnm and p E have focused on the role played by spatial and energetic disorder [2,6-8]. The GDM, for example, describes transport as a biased random walk among dopant molecules with Gaussian-distributed random site energies [2]. Of the various mechanisms proposed as the source of this disorder, it has been shown that the interaction of charge carriers with permanent dipoles (located on either dopant or host molecules) can give rise to a Gaussian-like density of states of the type assumed in the GDM [9,10]. Considerable data establishing a relationship between carrier mobilities and group dipole moments of molecular constituents support this view of charge-dipole interactions as the source of energetic disorder in these systems [9,[11][12][13][14][15].Unfortunately, although the standard GDM satisfactorily explains many features of experiment, such as the time-of-flight transients, it displays a field dependence similar to (1) only in a relatively narrow range and only at large fields (E . 10 5 V͞cm). Indeed, a general feature of Monte Carlo simulations [2,6] and other numerical work [8] on this problem is a significant regime at low fields in which the field dependence is much weaker than that described by (1). In experiments, by contrast, the linear dependence of lnm on p E often [16] persists down to the lowest fields probed (8 3 10 3 V͞cm).In this Letter we develop an analytical theory for the field dependence based upon an idea introduced recently by Gartstein and Conwell [17]. We show, usin...

Polaronic theories for charge transport in disordered organic solids, particularly molecularly doped polymers, have been plagued by issues of internal consistency related to the magnitude of physical parameters. We present a natural resolution of the problem by showing that, in the presence of correlated disorder, polaronic carriers with binding energies Delta approximately 50-500 meV and transfer integrals J approximately 1-20 meV are completely consistent with the magnitudes of field and temperature dependent mobilities observed.

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy p 2 (t) /2 and mean-squared displacement q 2 (t) is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, p 2 (t) ∼ t 2/5 independently of the details of the potential and of the space dimension. Motion is then superballistic in one dimension, with q 2 (t) ∼ t 12/5 , and ballistic in higher dimensions, with q 2 (t) ∼ t 2 . These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: p 2 (t) ∼ t 2/3 and q 2 (t) ∼ t 8/3 in all dimensions d ≥ 1.

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