Finite element analysis of domain structures in epitaxial PbTiO3 thin films

Abstract

Equilibrium domain structures commonly observed in epitaxial Pb-based ferroelectric thin films are analyzed by the finite element method (FEM) using a commercial package, ABAQUS (Hibbit, Karlsson & Sorensen, Inc., 1080 Main Street, Pawtucket, RI 02860-4847). Structures of periodic 90° domains in epitaxial PbTiO3 thin films on cubic single crystalline substrates are analyzed as a function of decreasing temperature in order to simulate cooling process after the film deposition at elevated temperature (TG). The degree of c-axis orientation (α) is determined as a function of temperature below the Curie temperature and compared to the experimental results. It is then possible to calculate the magnitude of misfit strain during film growth and its relaxation due to dislocation generation. The effect of PZT composition on c-domain abundance is also simulated. FEM simulation is performed with the assumption that the major driving force for such domain formation is thermoelastic strains arising from the film–substrate interaction and the cubic-tetragonal phase transformation. The FEM analysis also suggests that initial misfit stress at TG is not fully relaxed and the unrelaxed misfit stress is inversely related to final c-domain abundance.