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.     

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.     

Drift mobility of excess charge carriers in molecularly doped polymers upon photo-and radiation-induced charge generation

Comparative experiments on molecularly doped (with aromatic hydrazone) polycarbonate were performed to measure the drift mobility of excess charge carriers using carrier generation by exposure to light and ionizing radiation. Measurements showed practically complete coincidence of both mobility values and signal shapes. Compared were the results of measurements on polymer specimens with various thicknesses supported on substrates with different surface roughness, as well as for samples with or without an injecting amorphous-selenium layer. Dispersive carrier transport was observed in all cases. However, current transients sometimes displayed a plateau, depending on the sample preparation conditions. As the magnitude of generated (injected to the polymer layer) charge increased, a current spike appeared by the end of the transit time, thus indicating the emergence of local space-charge-limited current.     

Bimolecular recombination of charge carriers in molecularly doped polycarbonate

The general problems of the bimolecular recombination of charge carriers in molecularly doped polycarbonate are discussed. Experimental studies are performed via the transient radiation-induced conductivity method. Transient-current curves are numerically calculated via the multiple trapping model. The calculated and experimental curves are in good agreement. It is shown that the studied molecularly doped polymer undergoes bimolecular recombination via the Langevin mechanism.     

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.     

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.     

Hole transport and bimolecular recombination of charge carriers in polycarbonate molecularly doped with aromatic hydrazone

General questions about hole transport and bimolecular recombination of charge carriers in molecularly doped polycarbonate with a low dopant concentration (10 wt %) are considered. The experiment is performed via a radiation-induced time-of-flight technique with bulk generation of charge carriers. Transient-current curves are calculated numerically via a multiple-trapping model. There is good agreement between the calculated and experimental results on the transient-current waveform. Nonequilibrium hole transport is observed in the studied molecularly doped polymer, and the bimolecular recombination is close to the Langevin recombination as described by the multiple-trapping model.     

Theoretical description of electron transport in homo-and molecularly doped polymers

The general aspects of electron transport in disordered organic media (polymers, organic glasses, molecularly doped polymers) are considered. A critical analysis of experimental results and their interpretation in terms of basic theoretical models and experimental methods used in research in this area is presented. Particular attention is given to the comparative analysis of the data obtained by the time-of-flight technique and in studying the radiation conductivity of polymers, in particular, to the possibility of describing the conductivity data in terms of the Gaussian disorder model.     

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.     

Bimolecular recombination of charge carriers in pure and molecularly doped branched polyphenylenevinylenes

General problems of bimolecular recombination of charge carriers in both pure and molecularly doped branched polyphenylenevinylenes are addressed. Experiments are performed via the nonstationary radiation-induced conductivity method. Transient-current curves are numerically calculated in terms of the multiple-trapping model. Good agreement between the calculated and experimental curves is attained. In the investigated polymers, the Langevin mechanism of bimolecular recombination is active.     

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.     

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.     

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 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 charge carrier mobility’s activation energies and pre-factor dependence on dopant concentration in molecularly doped polymers

The elucidation of the charge transport mechanism in molecularly doped polymers MDP has been confused by disagreement on the role of disorder, which has led to disagreement on how to analyze the experimental mobility data. Plotting the mobility vs. T⁻¹ or T⁻² where T is temperature gives an Arrhenius activation energy or disorder energy respectively, which cannot be compared. A methodology is suggested to convert disorder energies into activation energies. This allows a compilation of a list of the activation energies of all MDP’s which have been characterized as a function of dopant concentration and a correlation of the activation energies with material properties.     

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 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).