Imaging mechanisms in contact Kelvin probe force microscopy (cKPFM) are explored via information theory-based methods. Gaussian processes are used to achieve super-resolution in the cKPFM signal, effectively extrapolating across the spatial and parameter space. Tensor factorization is applied to reduce the multidimensional signal to the tensor convolution of the scalar functions that show a clear trending behavior with the imaging parameters. These methods establish a workflow for the analysis of the multidimensional datasets that can then be related to the relevant physical mechanisms. We also provide an interactive Google Colab notebook that goes through all the analyses discussed in the paper.
Research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility (M.Z., R.K.V., L.C., S.J., and S.V.K.). Part of the BE SHO data processing and experimental setup was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division (SN). D.K. and M.A. acknowledge support from CNMS User Facility, Project No. CNMS2019-272. The authors would like to thank Amit Kumar (Queen\u2019s University Belfast) and Dipanjan Mazumdar (Southern Illinois University) for providing the BiFeO3 sample.
