Dielectric behavior of point defects on ferroelectric films for different substrate strains by phase–field simulations

Relaxor films constructed by doping point defects are widely applied in various fields, including nanoelectromechanical systems, capacitive energy storage, and pyroelectric energy conversion. Despite their broad utility, the underlying mechanisms by which point defects affect the dielectric properties of these films under varying substrate strains remain insufficiently understood. This work employs a phase–field model to explore the influence of point defects on the domain structure and dielectric properties of BaTiO₃ and Pb(Zr,Ti)O₃ films, with a comparative analysis of their respective responses to different substrate strains. Our results reveal that the domain sizes in both BaTiO₃ and Pb(Zr,Ti)O₃ films decrease with doping, leading to a transition into a relaxor state. Notably, Pb(Zr,Ti)O₃ exhibits a dielectric peak at a lower doping concentration and a more pronounced reduction in dielectric constant, which can be attributed to its smaller domain size and greater susceptibility to phase transitions. As substrate strain increases from −4% to 4%, the dielectric constant initially rises, peaking at zero strain. Moreover, compared with Pb(Zr,Ti)O₃, the BaTiO₃ relaxor films display a higher dielectric constant, due to a larger proportion of noninitial phases and a more uniform phase structure. These findings provide valuable theoretical insights into the manipulation of substrate strain as a strategy to tailor the dielectric properties of relaxor films.