Date of Completion


Embargo Period


Major Advisor

Bryan D. Huey

Associate Advisor

George Rossetti

Associate Advisor

C. Barry Carter

Field of Study

Materials Science and Engineering


Doctor of Philosophy

Open Access

Open Access


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 ability for current tomographic microscopies to accurately resolve complex domain morphologies in sub-micron films. Nanometer-scale three-dimensional imaging of spontaneous polarization is critical for understanding equilibrium states in polar materials, as well as for engineering devices based on such phenomena, however such capabilities remain a substantial experimental challenge. Tomographic atomic force microscopy (AFM) is presented as a novel experimental modality for three-dimensional ferroelectric property measurements with 20 nm spatial resolution.

This dissertation presents the results of an investigation into the size-dependence of ferroelectricity in the room temperature multiferroic BiFeO3 across two decades of thickness to below 5 nm. Multiferroic BiFeO3 was chosen for this research due its technological relevance in low-power, electrically-switchable magnetic logic. Tomographic AFM provides unprecedented tomographic imaging capabilities of ferroelectric domains in BiFeO3 with a significant improvement in spatial resolution compared to existing tomographic microscopies capable of resolving ferroelectric domains. In addition to volumetric imaging, tomographic AFM is employed for direct, thickness-dependent measurements of the local spontaneous polarization and ferroelectric coercive field in BiFeO3. The thickness-resolved ferroelectric properties of BiFeO3 strongly correlate with cross-sectional TEM, Landau-Ginzburg-Devonshire phenomenological theory, and the semi-empirical Kay-Dunn scaling law for ferroelectric coercive fields. These results provide an unambiguous determination of a stable and switchable polar state in BiFeO3 to thicknesses below 5 nm. Electrically conductive, filamentary defects are found to exist at nonlinearities the ferroelectric domain structure of BiFeO3, and are shown to be localized to such defects throughout the entire thickness of the film, again to below 5 nm. A novel first principles-based model is derived for the electric field applied during tomographic AFM, allowing for direct confirmation of Schottky emission as the relevant mechanism of electrical conduction for filamentary, conductive defects in BiFeO3. Such findings demonstrate the accuracy and utility of tomographic AFM for nanoscale three-dimensional property measurements, thereby providing novel insight into finite-size effects in ferroelectric and multiferroic materials.