**2.1 Aspects of the material**

The backbone of conducting polymers is generally formed by aromatic ring systems with delocalized π-electrons that occupy completely the bonding molecule orbitals. Due to the large amount of orbitals with similar energies they form a completely occupied valence band similar to the situation in classical inorganic semiconductors. The conduction band is made up by the antibonding π\*-orbitals and is generally empty. As in the inorganic counterpart the organic polymers as well can be doped with electron abstracting or electron donating agents leading to p- or n-semiconductors. P-dotation withdraws electrons from the valence band while n-dotation adds electrons to the conduction band increasing the conductivity of the material.

The band gap is defined as the energy gap between valence and conduction band. Generally electrons can be promoted by light energy causing π–π\*-transitions. The electron loss results on the site in a mesomerically stabilized radical cation called "polaron" that can be delocalized in the polymer generally over several monomeric units.

With another bond theoretical focus the band gap corresponds to the difference between HOMO and LUMO as they correspond to the highest occupied bonding and the lowest antibonding orbitals (see **Figure 1**). The electrical conductivity in these terms is due to the excitation of an electron from the HOMO passing to the LUMO and its increased mobility in the delocalized antibonding orbital.

As molecules have a finite extension electrons can only occupy a finite number of discrete energies and normally all bonding orbitals are occupied. Electron

#### **Figure 1.**

*Energy of a simple double bond (center), in a conjugated oligomer (aside) band formation in a polymer and the influence of doping.*

#### *Polymers in Solar Cells DOI: http://dx.doi.org/10.5772/intechopen.85312*

mobility is only possible in partly occupied orbitals that can be achieved either by doping the material adding or abstracting electrons with chemical or electrochemical methods. Physically thermal or optical excitation of electrons can be used.

Doping also changes the energies of HOMO and LUMO (or valence-band and conduction band respectively), as these energies are no fixed terms. N-doping—this is adding electrons to the LUMO-orbitals or reduction of the material—will increase the energy level as the electrons will repulse each other while p-doping has the opposite effect and decreases the orbital energy. Additionally doping also alters to a small but significant amount the positions of the atoms as the introduced charges interact with the counter-ions of the doping agent. When the concentration of the doping agent is low it results in the formation or small doped "islands of charge" that can be classified in three types: solitons, polarons and bipolarons. While solitons are wave packets, polaron and bipolaron make reference to quasiparticles.

Polarons and bipolarons can be seen as the polarization of a material due to the presence of charges moving through it. A moving electron, for example, will attract positive charges of the nuclei and push back the negative charges of the electrons in its environment. The polaron is the result of a quantum mechanical treatment of this phenomenon. Bipolarons result from the fact that close polarons may lower their respective energies similar to what happens in Cooper-pairs in superconductors. As the polarization of the surroundings stabilizes the electron lowering the energy of its fundamental state the presence of polarons will result in the formation of new energy bands in the material known as "polaron bands" and new electron transitions may be observed corresponding to this new state could be observed, too. The effect could also be interpreted as a band gap reduction in the semiconducting material [10]. Normally in organic semiconductors polarons and bipolarons are formed due to positive charges found in the polymers. A polaron will correspond to a radical cation while a bipolaron would be formed by a bi-cation. The corresponding energy scheme can be found in **Figure 2**. In organic conducting polymers the presence of various bipolarons at the same time can even lead to the formation of bipolaron bands [11].

The polaron/bipolaron effect has been widely studied on organic semiconducting polymers of different types [12–14]. The effect on bond length has even been confirmed by X-ray diffraction on model substrates with a thiophene backbone similar to the motive found in polythiophenes described later on [15].

While charges are bound to islands where linear parts of molecular chains located in parallel the electron mobility is still relatively low. Anyhow when increasing the doping concentration the charge islands start to overlap giving rise to partly

#### **Figure 2.**

*Energy scheme without polarons (a), in presence of polarons (b) (the black arrow represents the radical electron) and in presence of a bipolaron (c). Blue arrows represent possible electron transitions.*

occupied bands. In these bands charge mobility increases drastically as electrons can move freely along the whole macromolecule and it becomes an electrical conductor. The overall conductivity depends on the electron mobility in an electrical field within the macromolecular chains as well in their "charge islands" as in the intermolecular charge transport. The step that represents the mayor resistance will limit the overall charge mobility and therewith the conductivity.

The electron transport between polymer chains is linked directly to the degree of order that present molecules. The larger the order the more likely it is that polymer chains are located in parallel and with little distance between each other and this favors the electron transfer. When chains enclose an angle or are even located in perpendicular the jump of an electron from one molecule to the other is much more difficult. In long chain polymers it is not even necessary that a charge is transported along the whole molecule but can jump in part to another nearby unity. The shorter the polymer chain the more important is ordered chain morphology as here interchain transport has to occur more often. Unfortunately the general tendency of this type of polymers is to present more disorder or have the chains disposed in a perpendicular manner (see **Figure 3**).

For these reasons long chain per-conjugated polymers are desirable targets for highly conducting materials. The larger the polymer backbone is the larger is the probability to find some ordered region with easy inter-chain electron transport. This is the case even when the crystalline parts are interrupted by amorphous regions. Anyhow chain defects that interrupt the electron delocalization through the chain can make it more appropriate to treat this type of material as an accumulation of several short chain structures. These structures form island-like regions with high conductivity while electron transport between islands is more difficult.

Reasons for the loss of per-conjugation could be torsion between substructures or the formation of neighbored single bonds that do not allow the π-system to extend across the affected site.
