Nanoscale electromechanics of paraelectric materials with mobile charges: Size effects and nonlinearity of electromechanical response of SrTiO3 films

Nanoscale enables a broad range of electromechanical coupling mechanisms that are forbidden or are 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 a quantum paraelectric SrTiO3 (STO) 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 STO 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 STO film electromechanical response on the applied voltage demonstrates a pronounced crossover from the linear to the quadratic law and then to the sublinear 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 nonmonotonic and has pronounced maxima, the position and width of which can be tuned by film thickness. This paper provides a comparative framework for the analysis of electromechanical coupling in the nonpiezoelectric nanosystems.