We have investigated the dependence of hole mobility on thickness in free-standing films of bisphenol-Apolycarbonate (PC) doped with 30 wt% p-diethylaminobenzaldehyde diphenylhydrazone (DEH). Carrier generation in a time-of-flight (TOF) experiment was achieved through direct ionization of dopant molecules by electron impact using an electron gun supplying pulses of monoenergetic electrons in the range of 2–50 keV. The position of dopant ionization depends upon the electron energy and three TOF variants have been recently developed and used in this study. We have found that the hole mobility generally decreased with increasing film thickness with concomitant acceleration of the post-flight current decay indicating that the transport process approaches the steady-state regime, this process happening slightly faster than our model predicts. Numerical calculations have been compared with experimental data. The results are discussed in detail. The way to reconcile ostensibly contradictory interpretations of our results and those commonly reported in literature relying on photo injection technique has been proposed.
We have performed the comprehensive analysis of the time of flight curves using the multiple trapping model with the Gaussian trap distribution. Our analysis shows that flat plateaus on the computed curves are rare events. We have shown numerically that plateau formation for the non-equilibrium transport may be due to the presence of a thin defective (depletion) layer on the sample surface (two-layer model of a polymer film). Also, to escribe the Poole–Frenkel effect, we have explicitly introduced an analogous field dependence for the frequency factor.
We have investigated the bimolecular recombination of holes and electrons in a typical hole-conducting molecularly doped polymer (DEH-doped polycarbonate). The method used is a variant of the time-offlight technique with the bulk generation of charge carriers. A small signal regime has been used to extract parameters of the multiple trapping model with an exponential as well as the Gaussian trap distributions.Then, using a large signal regime with the generation rate increasing sequentially in a power of 10, we compared model predictions with experiment. It was found that the best agreement is achieved once the Langevin recombination coefficient is used, this being defined by the microscopic mobility featuring in the models. The relevance of this fact to the published data has been addressed as well. 2013 Elsevier B.V. All rights reserved.
We have compared time-of-flight curves predicted by hopping and multiple trapping models with the Gaussian and exponential site/trap energy distributions, fitting Monte-Carlo predictions of the former with numerical calculations of the latter in a wide time domain using logarithmic coordinates lg j–lgt for the characterization of current shapes and an estimation of transit times. As a prototype hopping theory, we used the Gaussian disorder model while for representing the quasi-band theories we relied on the multiple trapping model, both of these for two types of the site/trap energy distributions. In case of the Gaussian distribution of trap depths, fitting procedure requires adjusting of the two model parameters (an energy distribution parameter r and a frequency factor m 0 ). For an exponential distribution, a one-parameter ( m 0 ) fitting suffices. The dipolar glass model, unlike the Gaussian disorder model, is basically different from the multiple trapping formalism, but a recently introduced two-layer multiple trapping model seems capable of reproducing TOF current shapes rather well.
We have compared time-of-flight curves predicted by hopping and multiple trapping models with the Gaussian and exponential site/trap energy distributions, fitting Monte-Carlo predictions of the former with numerical calculations of the latter in a wide time domain using logarithmic coordinates lg j–lg t for the characterization of current shapes and an estimation of transit times. As a prototype hopping theory, we used the Gaussian disorder model while for representing the quasi-band theories we relied on the multiple trapping model, both of these for two types of the site/trap energy distributions. In case of the Gaussian distribution of trap depths, fitting procedure requires adjusting of the two model parameters (an energy distribution parameter σ and a frequency factor ν0). For an exponential distribution, a one-parameter (ν0) fitting suffices. The dipolar glass model, unlike the Gaussian disorder model, is basically different from the multiple trapping formalism, but a recently introduced two-layer multiple trapping model seems capable of reproducing TOF current shapes rather well.
The dipolar disorder formalism (DDF) of Borsenberger and Bдssler has been further developed based on a unified approach treating the van der Waals and the dipolar disorder energies as being roportional to mean intersite distance in a certain power. Tested against real molecularly doped polymers with the concentration of the dopant changing in a wide range, this approach gives values of the exponent lying in the interval from _1.5 to _2.5. The total disorder is represented by an algebraic combination of four material parameters relating to the dopant and the polymer matrix weighted by their relative weight concentrations. What is important, we seem to get able to explain the near constancy of the total disorder when the concentration of the polar dopant changes. Until recently, this unusual behavior of the total disorder defied any reasonable explanation.
We reinvestigate the applicability of the concept of trap-free carrier transport in molecularly doped polymers and the possibility of realistically describing time-of-flight (TOF) current transients in these materials using the classical convection–diffusion equation (CDE). The problem is treated as rigorously as possible using boundary conditions appropriate to conventional time of flight experiments. Two types of pulsed carrier generation are considered. In addition to the traditional case of surface excitation, we also consider the case where carrier generation is spatially uniform. In our analysis, the front electrode is treated as a reflecting boundary, while the counter electrode is assumed to act either as a neutral contact (not disturbing the current flow) or as an absorbing boundary at which the carrier concentration vanishes. As expected, at low fields transient currents exhibit unusual behavior, as diffusion currents overwhelm drift currents to such an extent that it becomes impossible to determine transit times (and hence, carrier mobilities). At high fields, computed transients are more like those typically observed, with well-defined plateaus and sharp transit times. Careful analysis, however, reveals that the non-dispersive picture, and predictions of the CDE contradict both experiment and existing disorder-based theories in important ways, and that the CDE should be applied rather cautiously, and even then only for engineering purposes.
We have performed numerical analysis of the charge carrier transport in a specific molecularly doped polymer using the multiple trapping model. The computations covered a wide range of applied electric fields, temperatures and most importantly, of the initial energies of photo injected one-sign carriers (in our case, holes). Special attention has been given to comparison of time of flight curves measured by the photo-injection and radiation-induced techniques which has led to a problematic situation concerning an interpretation of the experimental data. Computational results have been compared with both analytical and experimental results available in literature.
We have examined the Poole-Frenkel mobility field dependence in a molecularly doped polymer (MDP) both experimentally and theoretically trying to separate two physically different contributions to this phenomenon, one constituting a real physical effect and the other arising from the fact that the charge carrier transport in MDP is not fully equilibrated. The former is ascribed to the influence of an electric field on the transport process itself affecting at least one of the model parameters. The latter should be associated with the mobility field effect under conditions when neither model parameter is field sensitive. Numerical calculations have been used to achieve their deconvolution. On the experimental front, we relied on the time of flight technique specifically modified to suit this task. Both approaches show that the contribution of the second (operational) field effect in the investigated MDP is quite appreciable. This result is compared with the traditional interpretation of the Poole-Frenkel effect in molecularly doped polymers.
We have examined the temporal evolution of an ion pair with fully suppressed geminate recombination. For this purpose, the Smoluchowski–Debye equation for a pure Coulomb potential with a reflecting boundary condition on the recombination sphere has been solved numerically and analytically (in the last case, only approximately). It has been shown that the probability of the pair non-dissociation decreases in time roughly as a power law. We also discussed the applicability of the conductivity method for studying the non-Langevin recombination in low mobility solids. An example of such an analysis is given for one technical polymer. The relation of these results to the concept of the coulombic traps has also been discussed.
We have studied effects of the negative charged centers on the time of flight (TOF) curves measured in a typical hole-conducting molecularly doped polymer. The main effects are the unusual TOF (surface generation) current rise in the preflight region (be it a flat plateau or a cusp) due to the accumulated space charge and the current reduction at all times because of the monomolecular recombination. TOF-2 (bulk generation) transients are less sensitive to charged centers. Analysis of these effects has proved that charged centers do not change the carrier mobility provided that the space charge field and bimolecular recombination are properly accounted for in terms of the proposed two-layer MT model. We have shown that combination of TOF, TOF-1a and TOF-2 variants of the electron-gun based technique allows one to establish definitively the character of the charge carrier transport in MDPs.
The influence of diffusion on the current shape in the time-of-flight (TOF) experiment under conditions of the quasiequilibrium transport has been considered. An analytical expression for the transient current density has been obtained for the case of the reflecting front electrode. The expression has been found to be in a better agreement with the Monte-Carlo numerical modeling than the usual expression based on the standard convection–diffusion equation. We found an estimate of the minimum layer thickness for a flat plateau appearance on TOF current transients.