Thickness scaling of ferroelectricity in BiFeO 3 by tomographic atomic force microscopy

Significance Intrinsic and extrinsic properties of ferroelectric materials are known to have strong dependencies on electrical and mechanical boundary conditions, resulting in finite size effects at length scales below several hundred nanometers. In ferroelectric thin films, equilibrium domain size is proportional to the square root of film thickness, which precludes the use of present tomographic microscopies to accurately resolve complex domain morphologies in submicrometer films. We report a subtractive experimental technique with volumetric resolution below 315 nm 3 , that allows for three-dimensional, tomographic imaging of materials properties using only an atomic force microscope. Multiferroic BiFeO 3 was chosen as a model system for illustrating the capabilities of tomographic atomic force microscopy due to its technological relevance in low-power, electrically switchable magnetic logic.