Curie–Weiss-type law for the strain and stress effects on the dielectric response of ferroelectric thin films

Variations of the dielectric properties of ferroelectric thin films with the misfit strain Sm in the film/substrate system and the associated biaxial stress σ inside the film are analyzed theoretically. Calculations are performed in a mean-field approximation for the dielectric response displayed in a plate-capacitor setup by single crystalline films epitaxially grown on tensile substrates (Sm>0). It is shown that, in the absence of misfit-strain-induced phase transitions, the film dielectric susceptibility η33 obeys the Curie–Weiss-type law η33(Sm)=ε0KS/(Sm−Sm*), η33(σ)=ε0Kσ/(σ−σ*). Theoretical predictions are compared with the measured stress dependence of the dielectric response of polycrystalline Ba0.7Sr0.3TiO3 films grown on Pt/SiO2/Si. The theory explains the observed dielectric behavior and predicts the existence of in-plane polarization state in this film/substrate system.