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Abstract Domain switching pathways in ferroelectric materials visualized by dynamic piezoresponse force microscopy (PFM) are explored via variational autoencoder, which simplifies the elements of the observed domain structure, crucially allowing for rotational invariance, thereby reducing the variability of local polarization distributions to a small number of latent variables. For small sampling window sizes the latent space is degenerate, and variability is observed only in the direction of a single latent variable that can be identified with the presence of domain wall. For larger window sizes, the latent space is 2D, and the disentangled latent variables can be generally interpreted as the degree of switching and complexity of domain structure. Applied to multiple consecutive PFM images acquired while monitoring domain switching, the polarization switching mechanism can thus be visualized in the latent space, providing insight into domain evolution mechanisms and their correlation with the microstructure. 

Abstract While grain boundaries (GBs) in conventional inorganic semiconductors are frequently considered as detrimental for photogenerated carrier transport, their exact role remains obscure for the emerging hybrid perovskite semiconductors. A primary challenge for GB-property investigations is that experimentally they need to be performed at the top surface, which is not only insensitive to depth-dependent inhomogeneities but also could be susceptible to topographic artifacts. Accordingly, we have developed a unique approach based on tomographic atomic force microscopy, achieving a fully-3D, photogenerated carrier transport map at the nanoscale in hybrid perovskites. This reveals GBs serving as highly interconnected conducting channels for carrier transport. We have further discovered the coexistence of two GB types in hybrid perovskites, one exhibiting enhanced carrier mobilities, while the other is insipid. Our approach reveals otherwise inaccessible buried features and previously unresolved conduction pathways, crucial for optimizing hybrid perovskites for various optoelectronic applications including solar cells and photodetectors. 

Nanometer-scale 3D imaging of materials properties is critical for understanding equilibrium states in electronic materials, as well as for optimization of device performance and reliability, even though such capabilities remain a substantial experimental challenge. Tomographic atomic force microscopy (TAFM) is presented as a subtractive scanning probe technique for high-resolution, 3D ferroelectric property measurements. Volumetric property resolution below 315 nm 3 , as well as unit-cell-scale vertical material removal, are demonstrated. Specifically, TAFM is applied to investigate the size dependence of ferroelectricity in the room-temperature multiferroic BiFeO 3 across two decades of thickness to below 1 nm. TAFM enables volumetric imaging of ferroelectric domains in BiFeO 3 with a significant improvement in spatial resolution compared with existing domain tomography techniques. We additionally employ TAFM for direct, thickness-dependent measurements of the local spontaneous polarization and ferroelectric coercive field in BiFeO 3 . The thickness-resolved ferroelectric properties strongly correlate with cross-sectional transmission electron microscopy (TEM), Landau–Ginzburg–Devonshire phenomenological theory, and the semiempirical Kay–Dunn scaling law for ferroelectric coercive fields. These results provide an unambiguous determination of a stable and switchable polar state in BiFeO 3 to thicknesses below 5 nm. The accuracy and utility of these findings on finite size effects in ferroelectric and multiferroic materials more broadly exemplifies the potential for novel insight into nanoscale 3D property measurements via other variations of TAFM. 

Polyamide thickness and roughness have been identified as critical properties that affect thin-film composite membrane performance for reverse osmosis. Conventional formation methodologies lack the ability to control these properties independently with high resolution or precision. An additive approach is presented that uses electrospraying to deposit monomers directly onto a substrate, where they react to form polyamide. The small droplet size coupled with low monomer concentrations result in polyamide films that are smoother and thinner than conventional polyamides, while the additive nature of the approach allows for control of thickness and roughness. Polyamide films are formed with a thickness that is controllable down to 4-nanometer increments and a roughness as low as 2 nanometers while still exhibiting good permselectivity relative to a commercial benchmarking membrane.