Spatial modeling for refining and predicting surface potential mapping with enhanced resolution

Quantitatively mapping surface properties with nanometer or even subnanometer resolutions is critical for advanced scanning probe microscopy (SPM) characterization. However, the characterization performance often suffers from noises and artifacts due to instrumentation or environmental limitations. In this paper, we proposed a novel statistical approach with bivariate spatial modeling to efficiently refine and predict surface property mapping. Scanning Kelvin probe microscopy (SKPM) was selected as a representative example to test our proposed method on lateral nanowire assemblies. We revealed that the proposed method can effectively retrieve the artifact-free surface potential distribution by automatically identifying topological artifacts from surface potential maps. Furthermore, the statistical model built upon low spatial resolution was successfully used to predict the potential values from higher-resolution topography data. Compared to conventional regression model, our model is able to predict the surface potential distribution from less raw-data but yields much higher accuracy. Through this means, the spatial resolution of SKPM surface potential maps can be significantly improved. This statistics-enabled predictive method opens a new route toward high-precision and high-resolution SPM characterizations without the enhancement of instrumentation capabilities.