  We develop an analytical method for the processing of electron spin resonance
(ESR) spectra. The goal is to obtain the distributions of trapped carriers over
both their degree of localization and their binding energy in semiconductor
crystals or films composed of regularly aligned organic molecules [Phys. Rev.
Lett. v. 104, 056602 (2010)]. Our method has two steps. We first carry out a
fine analysis of the shape of the ESR spectra due to the trapped carriers; this
reveals the distribution of the trap density of the states over the degree of
localization. This analysis is based on the reasonable assumption that the
linewidth of the trapped carriers is predetermined by their degree of
localization because of the hyperfine mechanism. We then transform the
distribution over the degree of localization into a distribution over the
binding energies. The transformation uses the relationships between the binding
energies and the localization parameters of the trapped carriers. The
particular relation for the system under study is obtained by the Holstein
model for trapped polarons using a diagrammatic Monte Carlo analysis. We
illustrate the application of the method to pentacene organic thin-film
transistors.
