  In crystalline semiconductors, the sharpness of the absorption spectrum onset
is characterized by temperature-dependent Urbach energies. These energies
quantify the static, structural disorder causing localized exponential tail
states, and the dynamic disorder due to electron-phonon scattering. The
applicability of this exponential-tail model to molecular and amorphous solids
has long been debated. Nonetheless, exponential fittings are routinely applied
to the analysis of the sub-gap absorption of organic semiconductors alongside
Gaussian-like spectral line-shapes predicted by non-adiabatic Marcus theory.
Herein, we elucidate the sub-gap spectral line-shapes of organic semiconductors
and their blends by temperature-dependent quantum efficiency measurements in
photovoltaic structures. We find that the Urbach energy associated with singlet
excitons universally equals the thermal energy regardless of static disorder.
These observations are consistent with absorption spectra obtained from a
convolution of Gaussian density of excitonic states weighted by a Boltzmann
factor. A generalized Marcus charge transfer model is presented that explains
the absorption spectral line-shape of disordered molecular matrices, and we
also provide a simple strategy to determine the excitonic disorder energy. Our
findings elaborate the true meaning of the dynamic Urbach energy in molecular
solids and deliver a way of relating the photo-physics to static disorder,
crucial for optimizing molecular electronic devices such as organic solar
cells.
