No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
The nature of the plateau on the time-of-flight curves in molecularly doped polymers
Abstract
The transient current curves for a polar molecularly doped polymer were compared for the nearsurface and bulk generation of charge carriers. The horizontal plateau on the first curve was expected to transform into a tilted straight line under the quasiequilibrium transport conditions, but it did not. Instead, for bulk generation, the curve was a hyperbola, on which the slope decreased almost sevenfold during the existence of the plateau. This behavior points to nonequilibrium charge carrier transport. The appearance of a plateau in our case is explained by the effect of the defective surface layer, as indicated in our previous communications.
ResearchGate has not been able to resolve any citations for this publication.
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 charge-dipole 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.
We present the results of Monte Carlo simulations of the charge carrier transport in a disordered molecular system containing spatial and energetic disorders using the dipolar glass model. Model parameters of the material were chosen to fit a typical polar organic photoconductor polycarbonate doped with 30% of aromatic hydrazone, whose transport properties are well documented in literature. Simulated carrier mobility demonstrates a usual Poole-Frenkel field dependence and its slope is very close to the experimental value without using any adjustable parameter. At room temperature transients are universal with respect to the electric field and transport layer thickness. At the same time, carrier mobility does not depend on the layer thickness and transients develop a well-defined plateau where the current does not depend on time, thus demonstrating a non-dispersive transport regime. Tails of the transients decay as power law with the exponent close to -2. This particular feature indicates that transients are close to the boundary between dispersive and non-dispersive transport regimes. Shapes of the simulated transients are in very good agreement with the experimental ones. In summary, we provide a first verification of a self-consistency of the dipolar glass transport model, where major transport parameters, extracted from the experimental transport data, are then used in the transport simulation, and the resulting mobility field dependence and transients are in very good agreement with the initial experimental data.
We examine the published data concerning the shape of the current transients obtained by the time of flight (TOF) technique for molecularly doped polymers and polyvinylcarbazole (PVK) and compare it with the predictions from the existing theories of charge carrier transport in disordered organic solids. We show that TOF current shapes frequently run contrary to theoretical predictions. Plateau appearances on TOF curves may or may not mean the equilibration of the charge carrier transport. Using both TOF and TOF-2 (uniform generation of charge carriers) techniques we demonstrate that hole transport in polycarbonate doped with p-diethylaminobenzaldehyde-diphenylhydrazone (DEH) and in PVK is indeed dispersive despite the fact that samples of these polymers equipped with an a-Se generation layer produce TOF curves with a plateau.
An analytic theory of non-equilibrium hopping charge transport in disordered organic materials is developed. It rests on the concept of effective transport energy and includes quasi-equilibrium (normal) and extremely non-equilibrium (dispersive) regimes of hopping transport as limiting cases at long and short times, respectively. Special attention is paid to the regime of moderately weak non-equilibrium transport. In this regime the quasi-equilibrium value of the mobility is nearly established, whereas the coefficient of field-assisted diffusion continues to increase at long times. Analytic expressions for relaxation times in the context of field-assisted diffusion and carrier drift have been obtained. The results of the theory are in agreement both with the data of time-of-flight experiments for molecularly doped polymers and the results of numerical simulations of the Gaussian disorder model. The impact of non-equilibrium effects on the transit time of charge carriers in thin organic films with a thickness of the order of 100 nm, which is typical for organic light-emitting diodes, is outlined.
Extensive characterization of the hole mobilities mu in dispersions of p-diethylamino- benzaldehyde-diphenyl hydrazone (DEH) in polycarbonate has been carried out. We report the effect of varying the electric field E, temperature T, and spacing between DEH molecules rho on mu. These data are analyzed by a procedure that allows proper separation of the functional dependencies of the mobility on E, T, and rho. It is found that lnmu is proportional to En(T-1-T-10), where n=0.5 and T0 is a fitted parameter which decreases with increasing rho, behavior opposite to the dependence of the glass transition temperature on rho. These experimental results are not yet understood theoretically. Our procedure for separating the rho and T dependence is applied to data taken on DEH-polycarbonate and to data taken from the literature on another molecularly doped polymer system, N,N'-diphenyl-N,N'-bis (3-methylphenyl)-(1,1'-biphenyl)-4,4'-diamine (TPD) in polycarbonate. For DEH-polycarbonate, the activation energy is found to be independent of rho. In contrast, for TPD-polycarbonate the activation energy is strongly dependent on rho. Our data suggest that small-polaron hopping is occurring in molecularly doped polymers; this different dependence of the activation energy on rho is consistent with different small-polaron hopping regimes, adiabatic and nonadiabatic, in these two systems.
Transient conductivity measurements have been carried out in a hydrazone-polycarbonate molecularly doped polymer over wide dynamic ranges of time and current as a function of the applied electric field. These data are plotted using both linear-linear and log-log axes. The plots on linear-linear axes give familiar results: an initial spike followed by a relatively flat current before the transit time; a mobility that equals published values and precisely follows the Poole-Frenkel law, being exponential in the square root of the electric field; and a current after the transit time that falls much more slowly than can be accounted for using Gaussian statistics. The same data plotted using log-log axes reveals the behavior over long times and low currents. Before the transit time, the decrease of the current can be characterized by two power laws, but it only decreases by about a factor of 2 from 10(-2) of the transit time to the transit time and is almost independent of electric field from 5 to 80 V/mu m. After the transit time the current decreases algebraically as t(-1.75) to a current value of about 10(-2) of the value at the transit time and is also almost independent of electric field. Available theoretical models are not consistent with these data. We note a surprising coincidence: the current transients are virtually identical to the current transients obtained in molecular crystals, as if disorder does not play a role in determining the shape of the current transients in molecularly doped polymers.
The mechanism of charge transport in molecularly doped polymers has been the subject of much discussion over the years. In this paper, data obtained from a new experimental variant of the time-of-Night (TOF) technique, called TOF1a, are compared to the predictions of a two-layer multiple trapping model (MTM) with an exponential distribution of traps. In the recently introduced TOF1a experimental variant, the charge generation depth is varied continuously, from surface generation to bulk generation, by varying the energy of the electron-beam excitation source. This produces systematic changes in the shape of the current transient that can be compared to predictions of the two-layer MTM. In the model, one additional assumption is added to the homogeneous MTM. namely: that there exists a surface region, on the order of a micrometer thick, in which the trap distribution is identical to the bulk, but has a higher trap concentration, We find that the characteristic experimental features of an initial spike, a fiat plateau, and an anomalously broad tail, as well as the sometimes observed cusp or decreasing current occurring near the transit time, can all be described by such a two-layer model; that is, they can arise as a result of carriers delayed by a trap-rich surface layer. We find that we can semiquantitatively fit current transient data over the whole time range of the experiment, but only by using theoretical parameters that lie in a narrow range, the extent of which we quantify here.
Before the invention of the transistor in the 1940s, semiconductors were used as detectors in radios in a device called a “cat’s whisker”. At that time their operation was completely mysterious. Only after the introduction of semiconductor band theory did it become clear that the “cat’s whisker” is a primitive example of a metal-semiconductor Schottky diode. Today organic materials are being investigated for their electronic properties. Such materials are especially attractive for lightweight, flexible, and low-cost solar cells and light emitting devices, as well as transistors and electrophotographic photoreceptors. Yet, even after 40 years of work and a large database, the physics and chemistry that determines the electronic properties of organic materials are not well understood. Practicing organic electronics is like attempting to do silicon device design without semiconductor band theory. It is the purpose of this paper to briefly summarize what is known about the electronic properties of organic materials from charge transport data. It will be shown that our understanding of the charge transport mechanism and the electronic properties of organic materials is at a rudimentary phase which is a limiting factor in applying these materials to practical devices, very similar to the “cat’s whisker” phase of inorganic semiconductor research.
The effect of charged centers on charge-carrier mobility in polycarbonate, a polar molecularly doped polymer, is studied. The nature of this effect is revealed, and a simplified physicomathematical model is proposed to describe it. The performed numerical calculations are qualitatively consistent with experimental results. Preliminary studies are conducted to elucidate the nature of the defective surface layer in molecularly doped polymer samples.
Using Monte Carlo simulation we investigated time of flight current transients predicted by the dipolar glass model for a random spatial distribution of hopping centers. Behavior of the carrier drift mobility was studied at room temperature over a broad range of electric field and sample thickness. A flat plateau followed by j∝t-2j∝t-2 current decay is the most common feature of the simulated transients. Poole–Frenkel mobility field dependence was confirmed over 5–200 V/μμm as well as its independence of the sample thickness. Universality of transients with respect to both field and sample thickness has been observed. A simple phenomenological model to describe simulated current transients has been proposed. Simulation results agree well with the reported Poole–Frenkel slope and shape of the transients for a prototype molecularly doped polymer.
The data on the influence of an applied electric field (field dependence) on the mobility of holes in molecularly doped polycarbonate
samples prepared at Eastman Kodak laboratories and at the Institute of Physical Chemistry and Electrochemistry, Russian Academy
of Sciences, were compared. The results were generally close (the dispersive transport and almost coinciding mobilities in
medium fields), but, at high fields, substantial differences in the field dependence were observed. This is at variance with
the almost universal applicability of the Pool-Frenkel law reported in the literature.
The field and temperature dependencies of the hole mobility of 1,1‐bis(di‐4‐tolylaminophenyl)cyclohexane (TAPC) doped polystyrene have been measured and compared to results obtained for the TAPC doped polycarbonate and pure TAPC. The results are described by the disorder formalism, due to Bässler and co‐workers. The mobility of TAPC doped polystyrene is approximately 100‐fold greater than that observed for TAPC doped polycarbonate. This effect is interpreted in terms of (1) the elimination of random dipolar fields due to static dipole moments of the polycarbonate that affect the energetic disorder, and (2) improved electronic intermolecular coupling with a concomitant reduction of positional disorder.
It is shown that the relative widths of photoconductive current transients, obtained in molecularly doped polymers, are independent of the electric field and sample thickness, even when the current before the transit time is nearly time independent. Such a result has been termed universality in the Scher-Montroll theory of dispersive transport. The implications of these results for the field and temperature dependence of the mobility are considered.
Energetic disorder plays a central role in many of the theories of charge transport in molecularly doped polymers, MDP. In these theories, energetic disorder determines the energy width of the hopping site manifold. It is generally assumed that the disorder-created energy width arises from interactions between the charge on a dopant molecule and its environment, including the dipole moments of neighboring dopant molecules, the dipole moments of the molecules of the polymer matrix, and van der Waals interactions with neighboring molecules. This assumption can be tested experimentally. Bassler's formulation of the Gaussian Disorder Model predicts that the energy width can be obtained from the temperature dependence of the mobility: it appears as an activation energy. A review of experimentally characterized MDP systems reveals that there is almost no experimental evidence to support the prediction that the experimentally observed activation energy is due to energetic disorder. Instead, the data appear to suggest that the activation energy is primarily intramolecular in origin.
The time-of-flight technique is used to measure hole mobility in molecularly doped polycarbonate and polystyrene that contain
both polar and weakly polar additives. The two versions of the technique with the bulk and surface generation of charge carriers
under small-signal conditions are employed. Numerical calculations show that the time dependence of the transient-current
curves obtained with the first version of the technique is in agreement with the theory of multiple trapping for an exponential
energy distribution of traps. In the case of time-of-flight curves with surface generation, the run of the post-transit branch
is likewise consistent with the theory, whereas this consistency is often violated for the pretransit branch of the curves.
This result is due to the effect of the defective surface layer of a polymer, which is not taken into account in numerical
calculations. The results show that the hole transport in the studied molecularly doped polymers is dispersive. An increase
in the polarity of the polymer matrix and the dopant drastically decreases the hole mobility and, at the same time, increases
its field and temperature dependence.
Hole‐drift‐mobility measurements are presented for a molecularly doped polymer, p‐diethylaminobenzaldehyde‐diphenyl hydrazone in polycarbonate, over the widest temperature (213–373 K) and electric‐field range (3.3–111 V/μm) yet reported. Use of these data and graphical techniques which we introduce allow us to unambiguously determine for the first time the functional form of the electric field and temperature dependence of the mobility. Consistent with results obtained by others, the observed field dependence cannot be accounted for by any known hopping model. The observed temperature dependence suggests that the activation energy may be temperature dependent.