Spectroscopy of Polarons in Organic Semiconductors: A New Theoretical Model

Abstract

The spectral line-shape of the mid-IR absorption spectrum provides valuable information about the "hole" polaron coherence length in doped and undoped conjugated polymer films. In poly(3-hexylthiophene) (P3HT) films the spectrum generally consists of a narrow, low-energy peak A (700-1000 $cm^{-1}$) followed by a much broader, higher-energy peak B (2500-5000 $cm^{-1}$). Using a theory based on the Holstein Hamiltonian for mobile holes in P3HT, the IR line-shape is successfully reproduced for several recently measured spectra recorded in doped and undoped films, confirming the association of an enhanced peak ratio (A/B) with extended polaron coherence. Emphasis is placed on the origin of components polarized along the intra- and inter-chain directions and their dependence on the spatial distribution of disorder as well as the position of the dopant relative to the $\pi$-stack. The model is further adapted to treat donor-acceptor copolymers where the local HOMO energy varies periodically from donor unit to acceptor unit. The calculated line shape for a diketopyrrolopyrrole-based copolymer agrees well with the recently measured spectrum.