Determination of model-free Kramers-Kronig consistent optical constants of thin absorbing films from just one spectral measurement: Application to organic semiconductors

Abstract

We present an algorithm which allows to extract the refractive index $n$ and the absorption index $k$ of thin absorbing films from just one spectral measurement. The method makes explicit use of the Kramers-Kronig relation interconnecting $n$ and $k$, thereby yielding an a priori Kramers-Kronig consistent result. No specific model is needed to describe the optical constants. The successful application of the method is demonstrated on both, analytically generated and experimentally recorded examples. Due to the requirement that the absorption index has to approach zero sufficiently at the measurement boundaries we restrict the application of our method to materials exhibiting well defined and distinct absorption bands. Consequently, differential reflectance spectra (DRS) of thin films of the organic semiconductor PTCDA (3,4,9,10-perylenetetracarboxylic dianhydride) on the different substrates transparent mica, opaque gold and opaque HOPG have been chosen as our experimental examples. While we especially focus on the application of our method to differential reflectance measurements, it is anticipated that the method can be applied to other optical quantities likewise.