Dimensionality of electronic excitations in organic semiconductors: A dielectric function approach

Abstract

We present a detailed investigation on the effective dimensionality (associated with the degree of delocalization) of electronic excitations in thin organic films using the dielectric function as obtained from ellipsometry. To this end, we study first the best analytical representation of the optical dielectric function of these materials and compare different approaches found in the literature: (i) the harmonic oscillator approximation, (ii) the standard critical-point model (SCP), (iii) the model dielectric function (MDF), and (iv) the Forouhi-Bloomer model. We use these models to analyze variable angle spectroscopic ellipsometry raw data for a thin poly(9,9-dioctylfluorene) (PFO) film deposited on quartz (taken as an archetypal sample). The superiority of the SCP model for PFO films and a wide range of other spin-coated conjugated polymers (and guest-molecules in polymers) is demonstrated. Moreover, we show how the SCP model can be used to gain physical information on the microscopic structure. As an example, we show that the delocalization of excitons decreases for nonconjugated polymers, such as polymethylmethacrylate and polyimide, while the conjugation length and exciton delocalization are, respectively, enhanced in cases where a planar conformation (e.g., $\ensuremath{\beta}$ phase of PFO) or a high degree of crystallinity [e.g., poly(3-hexylthiophene)] is achieved. As an additional example, we employ the SCP excitonic model to investigate the temperature dependence of the dielectric function of crystalline and glassy PFO films. We propose that the SCP excitonic model should be adopted as the standard choice to model the optical properties of polymer thin films from ellipsometry data.