Strain-induced non-volatile domain switching and tunable elastic modulus in freestanding Ba_1-xSr_xTiO₃ membrane by phase-field study

Ferroelectrics are key materials in microelectromechanical systems (MEMS), in which the mechanical responses stem from the piezoelectric effect strictly induced by electric fields. Recent advancement of membrane technology offers new opportunities to tune ferroelectric polarizations via strain. However, its influence on the tunability of mechanical responses (such as the effective elastic modulus which is crucial to MEMS) remains underexplored. Here, we developed a phase-field model for free-standing Ba_1-xSr_xTiO₃ membrane with stress-free boundary conditions on top/bottom surfaces, and simulated the non-volatile ferroelectric domain switching driven by the externally applied strain. It is revealed that a tensile/compressive strain favors in-plane orthorhombic/out-of-plane tetragonal domain structures in BaTiO₃, which are stable even after the strain is removed. This results in large difference in elastic modulus of BaTiO₃ membrane under different domain states, i.e., a large tunability of elastic modulus. The maximum tunability is achieved at Sr composition (x=0.5), which is close to the ferroelectric-paraelectric phase boundary. At this point, the free energy of the system becomes degenerate, which facilitates ferroelectric-paraelectric phase transition. Our work demonstrates the nature of and elucidates the mechanism of nonvolatile domain switching and tunable mechanical responses in Ba_1-xSr_xTiO₃ membrane, which is key to its potential applications in MEMS systems.