2.1 Introduction

The carrier mobility of organic semiconductors has improved tremendously over the past few years. A field-effect mobility as high as $0.1$cm$^2$/Vs has recently been measured in region-regular poly(thiophenes) [32,33,34]. Because the structure of the polymer depends on the processing conditions, it is not uncommon to find in the literature widely differing mobility values obtained for the same polymer. In particular, the dielectric surface energy prior to the deposition of the polymer [35,36,37,38], the solvent evaporation rate [33], the molecular weight of the polymer [39] and thermal post-processing of the film [40] all influence the carrier mobility.

There is no general consensus on the mechanism of charge transport in these amorphous organic materials. A complete model of the electrical properties should include a description of the energy distribution of carriers and how the conduction varies as a function of carrier energy. Disorder-induced localized states are also important for the transport, and the essential problem is the relation between temperature, electric field, carrier concentration and the transport properties. Generally, charge transport in disordered materials is described either as hopping between localized states, or as trapping and release from localized states into higher energy mobile states. The degree of structural disorder may change the mechanism even within the same class of polymer.

Because the electronic structure of polymer films is not known exactly, a simplified model has to be assumed. The model was proposed by Bassler [9] assuming that the energy distribution is Gaussian due to the random disorder in the material. The standard deviation of Gaussian is around $0.1$eV and increases with increasing disorder of the material. To simplify the calculations, an electronic structure comprising an exponential tail in the bandgap is often used as well.

In this chapter, we present three different models to describe the carrier concentration dependence of the mobility, the temperature and electric field dependence, and a unified mobility model that can explain the temperature, electric field and carrier concentration characteristics together.