Generalization of Stoney's equation for flexoelectric thin films on elastic substrates

Abstract

When a thin film is deposited on an incompatible elastic substrate, the film develops an elastic mismatch strain, causing the film-substrate system to bend. Stoney's equation relates the curvature of the bent film-substrate system with the residual stress developed in the film, and can be used to infer film properties from curvature measurements. Certain materials exhibit electromechanical coupling, such as piezoelectricity and flexoelectricity, which can alter the curvature and strains. In this work, we generalize Stoney's equation to include flexoelectric and piezoelectric effects in the film. Considering both open and closed circuit configurations, as well as uniform and non-uniform film properties, we compare different cases of electromechanical coupling and discuss their influence on curvature, strains, and electric polarization in the film.

References in corpus (9)

• Piezoelectric thin-film super-lattices without using piezoelectric materials
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters
• Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity
• Modeling flexoelectricity in soft dielectrics at finite deformation
• Cyclic Density Functional Theory : A route to the first principles simulation of bending in nanostructures
• Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes
• Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles
• Modified Stoney formula for obtainment of stress within thin films on large deformed isotropic circular plates