  The properties of excitons, or correlated electron-hole pairs, are of
paramount importance to optoelectronic applications of materials. A central
component of exciton physics is the electron-hole interaction, which is
commonly treated as screened solely by electrons within a material. However,
nuclear motion can screen this Coulomb interaction as well, with several recent
studies developing model approaches for approximating the phonon screening to
the properties of excitons. While these model approaches tend to improve
agreement with experiment for exciton properties, they rely on several
approximations that restrict their applicability to a wide range of materials,
and thus far they have neglected the effect of finite temperatures. Here, we
develop a fully first-principles, parameter-free approach to compute the
temperature-dependent effects of phonon screening within the ab initio GW-Bethe
Salpeter equation framework. We recover previously proposed models of phonon
screening as well-defined limits of our general framework, and discuss their
validity by comparing them against our first-principles results. We develop an
efficient computational workflow and apply it to a diverse set of
semiconductors, specifically AlN, CdS, GaN, MgO and SrTiO3. We demonstrate
under different physical scenarios how excitons may be screened by multiple
polar optical or acoustic phonons, how their binding energies can exhibit
strong temperature dependence, and the ultrafast timescales on which they
dissociate into free electron-hole pairs.
