Some aspects of charge transport in organic semiconductors : motion of a bipolaron in heterocyclic polymers and charge mobility in conjugated polymers with applications to solar cells

Organic semiconducting materials such as conjugated polymers have many important industrial applications. Understanding the process of charge transport is crucial in order to improve their overall efficiency. The transport of charges in devices made of organic conjugated polymers is a complex process. For example, in organic photovoltaic cells (commonly called solar cells), many steps are involved between the points of absorbing light energy and of ultimately generating a photocurrent; they include the exciton formations followed by their dissociations leading to charge-separated states where the holes and electrons are free to move along the polymer chains (forming polarons or bipolarons) and/or between molecular constituents of the device and finally the collection of charges at the electrodes. The part of the process where the hole and electrons are free to move independently of each other is typically referred to as charge mobility. In this thesis we focus primarily on two aspects of charge mobility. Namely, in the first part of the thesis we study the motion of a bipolaron as a function of the electric field strength since this subject is still relatively controversial and unresolved. In the second part of the thesis we propose a multi-step approach that allows for a calculation of charge mobility (that is primarily due to polarons hopping from site to site) as a function of molecular and morphological structure of the organic materials. -- The motion of a bipolaron is investigated in heterocyclic conjugated polymers such as polythiophene (PT) (Part I of the thesis). In their intrinsic state, heterocyclic conjugated polymers form organic semiconducting materials. When doped, they can become conductors. One of the main goals of studies involving doped conjugated polymers is to describe the transport mechanisms of their charge species when an electric field is applied. We employ the extended Su-Schrieffer-Heeger (SSH) theoretical model to study the transport properties of bipolarons in conjugated polymers in the presence of an electric field. This model involves the solution of coupled equations which include the time-dependent Schrödinger equation and the classical motion equation for the lattice displacement which are solved numerically in a self-consistent way. Our theoretical investigation finds that the bipolaron (when formed in polymers such as PT) moves with little change of its shape along the chain backbone in a weak electric field. However, in the presence of a strong electric field, the bipolaron dissolves and free charges become the main charge carriers. The energy trends of the doped polymer with increasing strength of the electric field provide further support for this conclusion. In addition, we apply the SSH model with electron-electron (e-e) interactions to PT. The parameters employed in the computations are determined by requiring a good agreement between the theoretical and experimental values for PT band gap and bond lengths. We find that, within the extended SSH model, e-e interactions in comparison to electron-phonon coupling do not significantly affect the nature of bipolaron transport in polymers such as PT. -- Recently, organic solar cells, because of their light weight, low cost and processing flexibility, have attracted considerable attention in the field of photovoltaic cells. In Part II of the thesis, the charge mobility of conjugated organic polymers (mostly fluorene and carbazole based) primarily used in the construction of the organic solar cells is investigated using a multi-step computational approach. The proposed approach employs the use of the density functional theory (DFT), semiempirical (ZINDO) and Monte Carlo (MC) theoretical methods to determine transfer integrals, reorganization energies, transfer rates and mobilities of conjugated organic polymers. We find that, in organic polymers, the transfer integrals and the reorganization energies are equally important factors in determining charge transport rates and that the one dimensional (ID) approach to estimating trends in mobilities gives reasonable results, i.e. is in good agreement with experimental trends, provided their relative intermolecular distances can be obtained with some accuracy. However, a greater understanding of the mobilities must take into account the three dimensional (3D) structure and/or the inherent disorder that is present in the organic thin films. We illustrate this requirement with some calculations, for example, the computation of an electron mobility in poly(9,9-di-n-octylfluorene-alt-benzothiadiazole)'s (F8BT's) where their 3D structure is known from x-ray diffraction experiments. The proposed approach illustrates that theoretical computations/simulations based on chemical structure and known morphology of organic semiconductors is an important and reliable approach to studying charge mobility in organic materials used in devices such as solar cells