Temperature and field dependence of the mobility of highly ordered conjugated polymer films S. J. Martin, 1 A. Kambili, 1,2, * and A. B. Walker 1 1 Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom 2 Institut fu¨r Theoretische Physik, Universita¨t Regensburg, Universita¨tsstrasse 31, Regensburg D-93053, Germany Received 20 June 2002; revised manuscript received 30 December 2002; published 30 April 2003 The transport properties of organic light-emitting diodes in which the emissive layer is composed of highly ordered conjugated polymers have been investigated. We have performed simulations of the current transient response to an illumination pulse via the Monte Carlo approach, and from the transit times we have extracted the mobility of the charge carriers as a function of both the electric field and the temperature. The transport properties of such films are different from their disordered counterparts, with charge carrier mobilities exhib- iting only a weak dependence on both the electric field and temperature. We show that for spatially ordered polymer films, this weak dependence arises for thermal energy being comparable to the energetic disorder, due to the combined effect of the electrostatic and thermal energies. The inclusion of spatial disorder, on the other hand, does not alter the qualitative behavior of the mobility, but results in decreasing its absolute value. DOI: 10.1103/PhysRevB.67.165214 PACS numbers: 72.10.-d, 72.80.Le I. INTRODUCTION Conjugated polymers, which derive their semiconducting properties from delocalized  bonding along the polymer chain, 1 enable cheap, lightweight, portable, and large area displays, with promising applications for solar cells and photodetectors. 2–4 Since the first observation of polymer light-emitting diodes LED’s 5 , detailed investigation of the aspects of chemistry, physics, and engineering of materials has resulted in rapid progress. 6 In order to commercialize polymer devices, high efficiencies, brightness, and carrier lifetimes are required. 7 It is, therefore, essential to fully un- derstand the fundamental physics of electrical transport through conjugated polymers. For a recent review see Ref. 8. Previous theoretical studies have dealt with strongly dis- ordered organic materials, in which charge transport is mainly attributed to hopping. 9–11 The charge carrier mobili- ties of such systems are low and exhibit a strong temperature and electric field dependence. However, large carrier mobili- ties are generally highly desirable. Most recently, measure- ments in light-emitting diodes 12–14 have demonstrated en- hanced carrier mobilities, varying only weakly with the electric field, for devices characterized by high degree of order in the polymeric material. This weak dependence, which contradicts the theoretical predictions, has been attrib- uted to the purity of the polymer films, but is not yet under- stood. This realization has motivated us to investigate the trans- port properties of highly ordered conjugated polymer films in which the chains are aligned perpendicular to the direction of transport. In a previous paper 15 we looked into the character of transport through such polymer films. By employing the Monte Carlo technique, we showed that it is possible to ob- tain nondispersive transport in such systems. This observa- tion is in agreement with time-of-flight TOF experiments conducted on liquid-crystalline polyfluorene films, 12,13 which demonstrate nondispersive hole transport with enhanced charge carrier mobilities compared to previously examined conjugated polymers. Moreover, we established the condi- tions under which such transport is retained. However, our initial model was a simplistic one, with the film morphology reduced to occupied sites of a two-dimensional lattice, the variation of the hopping probability with the field being rather crude, and there was no temperature dependence. Here, first we have extended the model to allow the detailed description of the geometry of the polymer film, so that vari- ous film morphologies, similar to those appearing in realistic systems, can be considered. Second, we have explicitly in- cluded all parameters of interest, such as the electric field, temperature, and disorder both spatial and energetic. The aim of the present work is to probe in detail the field and temperature dependence of the mobility in highly or- dered conjugated polymer films. In particular, we discuss the effect of the electric field on the interchain mobility of such polymer films, and we attempt to explain the weak depen- dence on the field. The interplay between electric field and temperature on the transport characteristics is also examined. We begin our investigation with spatially ordered films in which all polymer chains are perfectly aligned perpendicular to the direction of the field. The additional effect of spatial disorder in the film configurations on the transport properties of such films is also considered. To account for the chemical regularity and the extended backbone conjugation we have included only a small amount of energetic disorder. II. THE MODEL In order to investigate the transport properties of charge carriers moving within a highly ordered polymer film, we have performed numerical simulations of the TOF technique. The system under study contains a polymer film sandwiched between two electrodes, and charge carriers are generated on one side by illumination of the electrode with an intense pulse of light of short duration. The photogenerated carriers move within the bulk of the film under the effect of an ex- ternal bias, whose sign determines the type of the charge carriers whose transport is studied. The film is composed of conjugated polymer chains of length L =100 nm, which are nematically aligned perpen- dicular to the direction of the electric field. Based on the PHYSICAL REVIEW B 67, 165214 2003 0163-1829/2003/6716/1652147/$20.00 ©2003 The American Physical Society 67 165214-1