Compound two-dimensional thermo-elastic and thermodynamic analysis for c-axis-oriented epitaxial lead titanate thin films

We propose two-dimensional (2D) thermo-elastic model to predict the temperature variation of the lattice constants and volume loss of the epitaxial (0 0 1)PbTiO3 (PT) thin films grown on (1 0 0)SrTiO3 substrates under specific biaxial stress conditions. The stresses resulted from the induced thermal stress and thermo-elastic bending of the PT film and ST substrate are used together with the external stresses to calculate the Landau–Ginsburg–Devonshire (LGD) formalism for PT at any temperature. The dielectric constant and spontaneous polarization could be accurately determined under compound effect of 2D state of stress and temperature variation. Because this study combines thermodynamic with thermo-elastic mechanics; it would be very useful for design and simulate the performance of piezoelectric micro-sensors and micro-actuators which are usually subjected to a various heat and stress under actual working conditions. The present predictions are applicable for a fabrication of piezoelectric MEMS on Si wafers.