Universality of charge-carrier transport in molecularly doped polymers

The charge-carrier transport model based on the multiple-trapping quasi-band theory with the Gaussian or exponential energy distributions of traps for the two-layer structure of the molecularly doped polymer sample is used to explain the experimentally observed constancy of the flat plateau on time-of-flight curves in a wide electric-field range. The constant shape of the time-of-flight curve under the condition of nonequilibrium transport is observed for the exponential, rather than Gaussian, energy trap distribution. This observation may be used to distinguish between these trap distributions. Finding the true Poole–Frenkel constant requires that the nonequilibrium transport in molecularly doped polymers be taken into account during treatment of the data on the field dependence of mobility.     

Effect of charged centers on electron transport in molecularly doped polymers: Theory and experiment

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.     

The universal nature of dispersive transport in molecularly doped polymers

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.     

Dispersive transport in molecularly doped polymers: Theory and experiment

Theoretical and experimental studies of the carrier transport in molecularly doped polymers (MDPs) have been reported. Theoretical analysis uses the multiple trapping (MT) model with an exponential and Gaussian trap distributions. Experimental technique is based on an electron gun technology enabling one to conduct time of flight measurements using the surface and the bulk carrier generation. The list of MDPs tested includes both polar and non-polar systems, some with varying dopant concentration. Experimental results are compared to the MT model predictions as well as the mainstream theories of the hopping conduction in MDPs.     

Field-dependent photogeneration in molecularly doped polymers

The photogeneration of holes in triphenylamine- doped polycarbonate, polystyrene, polyvinyl butyral has been investigated. The field dependence of the photogeneration efficiencies can be explained by the Onsager theory of geminate recombination. The results show that the number of bound electron-hole pairs that are formed per absorbed photon is strongly dependent on the polymer composition whereas the pair disassociation probability is independent of the polymer.     

The effect of charged centers on the transport of charge carriers in molecularly doped polymers

The effect of charged centers on the mobility of charge carriers in molecularly doped polycarbonate is experimentally studied by the method of accelerated electrons for the generation of charge carriers in the surface layer and in the polymer bulk. The hypersensitivity of mobility toward the presence of charged sites that is predicted by the theory of correlated disorder (dipolar glass) is not found. With accumulation of charged centers, transformation of the time-of-flight curves with a well-pronounced plateau region, which is indicative of quasiequilibrium transport according to theory, proceeds in full agreement with the classical concepts on the role of a space charge or bimolecular recombination during high-signal irradiation. Transport of charge carriers in the molecularly doped polymer is not quasiequilibrium but dispersive.     

The field dependence of mobility in molecularly doped polymers under the conditions of nonequilibrium transport

A multiple-trapping model has been used to numerically analyze the effects of the nonequilibrium transport of holes on the field dependence of drift mobility as obtained in a time-of-flight experiment. The intrinsic field dependence has been assigned to the frequency factor in the form of the Poole-Frenkel law. Strongly dispersive transport, as well as a nonequilibrium-charge-transfer regime given by the Gaussian disorder model, has been considered. It has been established that the currently accepted approach to the analysis of the field dependence of mobility needs to be reexamined.     

The features of hole transport in molecularly doped polystyrene

The hole transport in polystyrene doped with 15 wt % tritolylamine is studied via the time-of-flight technique in both the surface carrier generation mode and the bulk carrier generation mode. The hole transport is shown to be dispersive with a dispersion parameter value of 0.99 ± 0.03 at room temperature. The results contradict the widely held view that hole transport in this molecularly doped polymer is quasi-equilibrium. The hole mobility is found to be almost independent of the electric-field intensity.     

The nature of plateau on time-of-flight curves in molecularly doped polymers

Transient current curves in a polar molecularly doped polymer for surface and bulk generations of charge carriers are compared. No transformation of the horizontal plateau on the former to the curve predicted by the diffusion and drift theory was found, contrary to expectations for quasi-equilibrium transport conditions. This behavior indicates a nonequilibrium character of the transport of charge carriers. The plateau appearance is explained in our case by the depleted subsurface layer effect, as we already pointed out earlier.     

The nature of a defective layer in samples of molecularly doped polymers

The shape of time-of-flight curves in the mode of subsurface irradiation of samples with lowenergy electrons is analyzed for free-standing films of a typical molecularly doped polymer of different thicknesses (11?C45 ??m). Special attention is paid to comparison of curves registered for both sides of the samples. The data confirm the hypothesis that the defective layer is formed owing to sublimation of dopant molecules during sample preparation and qualitatively agree with predictions of the two-layer multiple-trapping model.     

Formation of a plateau on time-of-flight curves of molecularly doped polymers

A program for numerical computation of the curves of the transient current in samples of molecularly doped polymers has been developed with allowance for the presence of a defective surface layer in them. Time-of-flight curves are calculated with the multiple-trapping model with a Gaussian energy distribution of traps. The model parameters are determined from the results of independent measurements. Numerical computations are in qualitative agreement with experimental data for a typical molecularly doped polymer. The features of the formation of a flat plateau in samples of different thickness are discussed in terms of the proposed model.     

Generation of excess charge carriers in molecularly doped polymers by electron-beam irradiation

The processes of generation and transport of excess charge carriers in molecularly doped polycarbonate and polystyrene were experimentally studied at room temperature. The polymers were ionized by 7-and 50-keV electrons. The radiation-chemical yield of free ions was determined by means of the universal method based on the combination of the time-of-flight technique in two carrier generation modes (surface and bulk generation) with the measurement of nonsteady-state conductivity. It was shown that the radiation-chemical yield of free ions under irradiation by 7-keV electrons is almost the same as that in the case of 50-keV electrons, despite the substantially different values of the linear energy transfer for these electrons.     

The effect of temperature on carrier transport in molecularly doped polycarbonate

Hole transport in low-polarity polystyrene (PS) doped with 10 wt % tritolylamine was studied. The radiation-induced mode of the time-of-flight technique (TOF) with the carrier generation zone of a variable thickness was used. A theoretical treatment of the data in terms of the Gaussian disorder model has shown the mobility value to be fundamentally inconsistent with the flat shape of the plateau, a contradiction that cannot be resolved within the framework of this model. It has been shown that hole transport is actually dispersive, rather than quasi-equilibrium. The contribution of radiation conductivity of the polymer matrix to the TOF signal was evaluated.     

The effect of temperature on carrier transport in molecularly doped polycarbonate

The effect of elevated temperature on the pattern of current transients and the hole mobility in polycarbonate doped with 20 and 30 wt % aromatic hydrazone was studied. With the use of homogeneous carrier generation mode, it was found that the shape of the current transient varies with an increase in the temperature in qualitative agreement with the prediction of the multiple-trapping theory with the exponential trap energy distribution. The apparent activation energy of hole mobility is 0.41 eV in the classical measurement mode and 0.55 eV in the case of homogeneous irradiation.     

The nature of the field dependence of drift mobility in molecularly doped polymers

A direct experimental comparison is performed for the field dependences of drift and effective mobilities of holes in a polar molecularly doped polymer (polycarbonate containing 30 wt % p-diethylaminobenzaldehyde diphenylhydrazone), which are measured by the time-of-flight method during the bulk irradiation of polymer samples with a pulse of fast electrons. A numerical simulation of the time-of-flight experiments is conducted with the use of the multiple-trapping model with the Gaussian energy trap distribution. The parameters of the model are determined during independent measurements. It is shown that, because of the nonequilibrium state of the transport of holes under the conditions of the time-of-flight experiment, the true Poole–Frenkel constant (0.27 (μm/V)^1/2) makes up only a part of the experimentally measured value (0.39 (μm/V)^1/2).     

Electron transport of holes in molecularly doped polycarbonate and its radiation-induced conductivity

The salient features of charge transport in a typical molecularly doped polymer (polycarbonate + 30 wt % DEH hydrazone) were studied by time-of-flight and nonsteady-state radiation-induced conductivity measurements. It was shows that the mobility of holes (major carriers) is due to dispersive transport in the temperature range 296–353 K covering the glass transition temperature at an observation time of up to a few seconds. The appearance of a plateau on the current transient, presumably manifesting the establishing of quasiequilibrium (Gaussian) transport, is the artifact of the time-of-flight technique when the charge carrier generation takes place at the sample surface. All of the obtained results can be satisfactorily rationalized in terms of the Rose-Fowler-Weisberg model with a uniform set of parameters of the model. Such an approach is compatible with the basic concepts of the radiation chemistry of condensed phase (the Onsager theory and the Langevin recombination mechanism), structural features of a disordered medium (transport zone, structural traps), and rotational diffusion of small molecules or their molecular groups in vitrified polymers.     

Effect of preliminary electron-beam irradiation on hole transport in molecularly doped polycarbonate

The effect of preliminary electron-beam irradiation on hole transport in a molecularly doped polymer was studied with the use of the time-of-flight technique in the radiation-induced mode. Specimens that exhibit a plateau on their time-of-flight curves were selected for the study, since they suggest the occurrence of quasi-equilibrium transport in the system according to the conventional point of view. In the extremely small signal mode, current transients in the case of bulk irradiation have a form corresponding to dispersive, rather than Gaussian, transport, although hole movement is observed in the presence of charged sites (trapped electrons). On passing to the moderately large signal mode (preirradiation to a dose of up to 5 Gy), the current transients undergo noticeable changes, which might be mistakenly interpreted as evidence for the influence of charged sites on hole transport in accordance with the predictions of the dipolar glass theory. In actuality, these changes are due to the effect of a space charge field and the hole mobility remains almost unchanged in this case. The appearance of the plateau on the current transients is an artifact of the procedure, and the hole transport is dispersive.