Structural entropy in detecting background patterns of AFM images

Abstract

Structural entropy was developed for detecting the type of localization in charge distributions on a finite grid, especially in mesoscopic electronic systems. However, it is possible to detect and analyze superstructures, i.e., topologies consisting of more structures with different types of localization properties. In the definition of the structural entropy, the von Neumann entropy of the system is divided into two parts: first, the extension entropy, which is simply the logarithm of the occupation number; the second part is the structural entropy. On a structural entropy versus logarithm of the spatial filling factor map, the different types of localizations follow different, well-characterized curves. Spatial filling factor measures the percentage of the “filled” (i.e., high intensity) pixels of the image. An atomic force microscopy (AFM) image can be interpreted as some kind of charge distribution on a grid: after normalization, the darkness (or lightness) of the pixels fulfills all the necessary conditions. AFM image artifacts can be detected by plotting the structural entropy versus the logarithm of the spatial filling factor maps of the images. Not only the type of an added large-scale Gaussian, parabolic, exponential, or other function can be identified, but also by careful study of the curves belonging to the structures, the parameters can be detected, too.