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 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. 
A.N. Morozovska, E.A. Eliseev, G.S. Svechnikov and S.V. Kalinin
cond-mat.mtrl-sci