  Nanoscale enables a broad range of electromechanical coupling mechanisms that
are forbidden or negligible in the materials. We conduct a theoretical study of
the electromechanical response of thin paraelectric films with mobile vacancies
(or ions) paradigmatic for capacitor-type measurements in X-ray scattering,
piezoresponse force microscopy (PFM), and electrochemical strain microscopy
(ESM). Using quantum paraelectric SrTiO3 film as a model material with well
known electromechanical, electronic and electrochemical properties, we evaluate
the contributions of electrostriction, Maxwell stress, flexoelectric effect,
deformation potential and compositional Vegard strains caused by mobile
vacancies (or ions) and electrons to the electromechanical response. The local
electromechanical response manifests strong size effects, the scale of which is
determined by the ratio of the SrTiO3 film thickness and PFM/ESM tip size to
the carriers screening radius. Due to the strong dielectric nonlinearity effect
inherent in quantum paraelectrics, the dependence of the SrTiO3 film
electromechanical response on applied voltage demonstrates a pronounced
crossover from the linear to the quadratic law and then to the sub-linear law
with a factor of 2/3 under the voltage increase. The temperature dependence of
the electromechanical response as determined by the interplay between the
dielectric susceptibility and the screening radius is non-monotonic and has a
pronounced maxima, the position and width of which can be tuned by film
thickness. This study provides a comparative framework for analysis of
electromechanical coupling in the non-piezoelectric nanosystems.
