Electric Field Dependence of Dielectric Constant of the Sol-Gel Deposited Ba_x Sr_1–x TiO₃ Film—Thermodynamic Analysis

Abstract

The measured dielectric constant as a function of electric field, at a frequency of 1MHz is reported for sol-gel deposited Barium-Strontium Titanate (Ba_xSr_1–x TiO₃) thin films with x = 0.0 to 0.6 at different temperatures and film thicknesses. The experimental data can be explained by Devonshire thermodynamic theory of free energy expansion in terms of power series of polarization. It is shown that the expansion upto the quadratic term is sufficient to explain the field dependence of dielectric constant. The coefficient C₃ of the quadratic term is almost independent of electric field, thickness and temperature but appears to depend on composition and mechanical strains. The effect of strains on C₃ shows that the electrostrictive coefficients Q ₁₁, Q ₁₂ and the elastic constants c ₁₁ and c ₁₂ are different in thin films with respect to the bulk.

Keywords:

• Dielectric thin film
• Barium-Strontium Titanate
• Devonshire thermodynamic theory