Size-dependent buckling in freestanding films driven by flexoelectricity

The flexibility in recently developed freestanding oxide films makes them fertile for exploring buckling-based flexible electronic devices at nanoscale. However, the rigorous flexoelectric theoretical model has not been established for accurately describing the buckling in a delamination film-substrate system yet. In this paper, we establish an electromechanical model by taking flexoelectricity into account to investigate the buckling properties of freestanding films. The results demonstrate the strain gradient of up to 10⁶ m⁻¹ in buckling films induces a giant flexoelectric effect. The flexoelectricity significantly suppresses the buckling deformation, of which the critical strain increases nearly tenfold as well as the buckling amplitude reduces by half. Meanwhile, flexoelectricity drives a size-dependent buckling behavior that differs from classical elastic buckling, in which the films with a smaller size exhibit a larger buckling resistance. These theoretical findings are well-confirmed experimentally. This work highlights the critical role of flexoelectricity in buckling films at nanoscale and provides guidelines for the design of buckling film-based flexoelectric devices.