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

Abstract

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.

Excited State Dynamics of a Self‐Doped Conjugated Polyelectrolyte

“…For cationic polarons, it is stipulated that a singly occupied energy level located above the highest occupied molecular orbital (HOMO) level and an unoccupied energy level below the lowest unoccupied molecular orbital (LUMO) level of the neutral semiconductor are formed and that the polaronic P 2 transition occurs between localized intragap levels, while the P 1 transition takes place between the HOMO and the singly occupied level, as shown on the right of Figure b . This approach neglects electron–electron interactions on the polaronic site and with neighboring neutral sites, so that modifications to the conventional model have recently been proposed (left of Figure b) . Due to on‐site Coulomb repulsions, the lower intergap polaronic level splits so that the lone electron level is located below the HOMO level of the neutral organic semiconductor, and both the frontier energy levels are stabilized on the doped site.…”

“…This is unambiguously demonstrated by the simultaneous depletion of both the neutral and polaronic transitions, as well as by correlated excited state dynamics, when either transition is photoexcited during femtosecond transient absorption experiments. This result contrasts with the conventional picture of localized intragap polaron states and agrees with a revised model for the electronic structure and optical transitions in doped organic systems . Second, our study shows that intersite Coulomb interactions are present, so that the positive polarons cause a Stark shift in the transitions of nearby neutral sites.…”

“…Our results with films and dissolved CPE‐K systems provide the first experimental evidence that the polaronic sites do not only provoke Coulomb interactions with their surroundings, but also strongly couple electronically to nearby neutral sites of the conjugated backbone. This is consistent with recent electronic structure models of doped organic semiconductors, but cannot be explained within the conventional picture . In the conventional model, the introduction of polarons induces localized intragap states, while the energy levels of the neutral sites remain unaffected.…”

Ohmic transition at contacts key to maximizing fill factor and performance of organic solar cells

“…1b ). This ϕ shift arises from the local Madelung potential effect of the mixed ‒SO 3 H/‒SO 3 ‒ Cs + local ion cluster on the electrochemical potential of the hole carriers 23 , 24 . The valence band edge of PEDT shifts rigidly with FL, which excludes any change in its electronic structure or doping level (Fig.…”

Surface Doping of Organic Single‐Crystal Semiconductors to Produce Strain‐Sensitive Conductive Nanosheets

“…Solvents that are available to dissolve C 8 –DNBDT are limited to only acetonitrile (ACN) and n ‐butyl acetate ( n BA) because both are known to be orthogonal to C 8 –DNBDT. The dopant solutions were then removed by spinning the substrates, [ 49 ] and the residual solvent was evaporated under a flow of N 2 . Doped p ‐mTFF‐F3TSFI solution was prepared by first dissolving the solid form of the undoped mTFF‐TFSI‐Na (annealed for 1 h at 120 °C in a N 2 ‐glovebox prior to dissolution) in anhydrous acetonitrile, 1.0 equiv.…”