Domain populations in epitaxial ferroelectric thin films: Theoretical calculations and comparison with experiment

An equilibrium domain theory is used to calculate the thickness and temperature dependencies of relative domain populations in tetragonal ferroelectric thin films epitaxially grown on cubic substrates. The relative coherency strain between the film and substrate that governs domain configurations is evaluated with the account of strain accomodation caused by the generation of misfit dislocations at the growth temperature. The threshold coherency strain, which provides the energetic equivalency of the c and a single‐domain films and plays an important role in predicting multidomain patterns, is computed as a function of temperature with the aid of the Landau–Ginsburg–Devonshire‐type thermodynamic theory. Theoretical predictions are compared with the experimental measurements for PbTiO₃ films grown on (001)‐oriented MgO and KTaO₃ substrates and found to be in good agreement in both the thickness and temperature dependence of the c‐domain volume fraction in these epitaxial heterostructures.