Nanoscale mapping to assess the asymmetry of local C–V curves obtained from ferroelectric materials

Abstract

The asymmetry in the capacitance-voltage (C-V) curves obtained from a ferroelectric material can provide information concerning the internal microstructure of a specimen. The present study visualized nanoscale switching of a HfO2-based ferroelectric thin film in real space based on assessing asymmetry using a local C-V mapping method. Several parameters were extracted from the local C-V curves at each point. The parameter Vi , indicating the lateral shift of the local C-V curve, was employed as an indicator of local imprint. In addition, the differences in the areas between the C-V curves for the forward and reverse sweeps, Sf − Sr , provided another slightly different indicator of nanoscale switching asymmetry. These parameters obtained from asymmetric C-V curves are thought to be related to internal electric fields and local stresses caused by defects in the film. The work reported herein also involved a cluster analysis of the extracted parameters using the k-means method.

Data-Driven Analysis of High-Resolution Hyperspectral Image Data Sets through Nanoscale Capacitance–Voltage Measurements to Visualize Ferroelectric Domain Dynamics

“…Figures S7 and S8, Supporting Information, show the clustering results when N c = 6 and N c = 12, respectively (the results of the analysis for images acquired at different locations of the same sample are also shown in Figure S11, demonstrating the generality of the method). For both values of N c , the map display of each cluster is more cohesive and shows a clearer pattern than that of the results of the previous analysis presented in ref . No significant differences were found when comparing the general characteristics and trends of the patterns among the methods, suggesting that the structural features inherent in the data set are generally captured regardless of the method used.…”

“…This approach has no major problem if most of the C – V curves in the data set have a typical butterfly shape, as shown in Figure a,b. In contrast, when the data set contains nonswitching (slim arc-shaped) C – V shapes, such as in Figure 8a of ref and in Figure c, or antiferroelectric-like C – V shapes, such as in Figure d, the cluster analysis results may overlook such characteristic and important C – V features because these features cannot be adequately represented by the predefined parameters. Alternatively, it is also possible to perform clustering on the original data set without any special preprocessing.…”

“…Plotting this resynthesis response waveform with bias on the horizontal axis gave a C – V curve for each pixel. Based on the fact that most of the resynthesized C – V curves have a butterfly shape characteristic of ferroelectric materials, we extracted the following features (see also Figure 4 in ref ): V w is the separation between the two peak voltages. V i is the horizontal shift of the butterfly curve.…”

“…The local C−V data set for polycrystalline HfO 2 -based ferroelectric thin films analyzed in this study was obtained from a previous study. 29 To obtain this data set, the response signal of capacitance change to an AC bias of 12 V pp was measured at each point of a 256 × 128 grid in a 4 μm × 2 μm area of a polycrystalline Y:HfO 2 film with a thickness of 17.5 nm (see the Methods section for deposition conditions). The response waveforms obtained at each point were then subjected to Fourier series expansion, and the Fourier coefficients corresponding to the 1 to 30ω harmonics were calculated.…”

Automatic Ferroelectric Domain Pattern Recognition Based on the Analysis of Localized Nonlinear Optical Responses Assisted by Machine Learning

“…In particular, clustering methods are highly suited for the identification of groups with distinct properties in a given data set, based on a concept of similarity between elements within each cluster. [15,30,46,47] In the present analysis, clustering was performed through K-means clustering in order to segment the SHG datasets into regions of interest with distinct behaviors corresponding to ferroelectric domain variants. Euclidean distance criterion is used to segment the data set into spatially indexed clusters, with centroids encoding the differing mean behaviors within each cluster.…”