Despite recent significant progress in the synthesis of new polymeric materials for solar cells (SCs), the mechanism of conduction in such SCs has not been fully elucidated.

In this work we apply the Kohn-Sham density functional theory (B3LYP / 6-31G**) to study the electronic and spatial structure of the 3,4-ethylenedioxythiopehene oligomer (SCs often use the complex salt of poly-3,4-ethylenedioxythiophene with polystyrenesulfonic acid) consisting of its 12 units (E12), in its various charge states: 0, +1, +2, +3, and +4. The doping extent is thus simulated by the charge increase of the corresponding oligomer species. We employed spin-unrestricted calculations (UB3LYP) for charge states +1 and +3.

The HOMO-LUMO gap in the neutral E12 amounts 2.06 eV. As the positive charge (as a model for an increasing doping extent) grows, we observe a progressive appearance of one (E12⁺¹), two (E12⁺²), three (E12⁺³), and four (E12⁺⁴) polaron levels within the abovementioned HOMO-LUMO gap. A single polaron level in E12⁺¹ is separated from the top of the valence band by 0.54 eV. Two polaron levels in E12⁺² are separated from the valence and conduction bands by 0.50 eV. In the cation E12⁺³, two polaron levels are separated from the top of the valence band by 0.8 eV, and the third level is situated 0.90 eV below the bottom of the conduction band. Finally, four polaron levels of E12⁺⁴, build pairwise a prototype of the polaron band within the HOMO-LUMO gap.

Thus, according to our model, the conductivity of a highly doped (oxidized) 3,4-ethylenedioxythiopehene oligomer consisting of its 12 units is provided by two polarons situated at the ends of the chain. For other oligomers, as well as for poly(3,4-ethylenedioxythiopehene), more sophisticated polaron structures might act as charge carriers.