Madelung and Hubbard interactions in polaron band model of doped organic semiconductors

The standard polaron band model of doped organic semiconductors predicts that density-of-states shift into the π-π* gap to give a partially filled polaron band that pins the Fermi level. This picture neglects both Madelung and Hubbard interactions. Here we show using ultrahigh workfunction hole-doped model triarylamine-fluorene copolymers that Hubbard interaction strongly splits the singly-occupied molecular orbital from its empty counterpart, while Madelung (Coulomb) interactions with counter-anions and other carriers markedly shift energies of the frontier orbitals. These interactions lower the singly-occupied molecular orbital band below the valence band edge and give rise to an empty low-lying counterpart band. The Fermi level, and hence workfunction, is determined by conjunction of the bottom edge of this empty band and the top edge of the valence band. Calculations are consistent with the observed Fermi-level downshift with counter-anion size and the observed dependence of workfunction on doping level in the strongly doped regime.