By defining the structural entropy the von Neumann entropy of a charge distribution on a finite grid is divided into two parts. The first one, the extension entropy, is simply the logarithm of the occupation number (i.e., the number of the average grid sites occupied by the charge distribution), while the second part is the structural entropy itself. On a structural entropy versus participation ratio map the different types of localizations follow different, well characterized curves, and every distribution is represented by a vector on the map. By a structural entropy-filling factor map of any charge distributions on a finite grid (e.g., finite representation of an electron density, or a grayscale atomic force microscope (AFM) image) superstructures of different scale topologies with different decay types can be traced as well. However it is rather hard to distinguish elements of an additive superstructure, especially if the numerical parameters of the different scale patterns are necessary. In the AFM practice the background patterns are sometimes hard to compensate, and by simple structural entropy based calculations it is almost impossible to separate the superstructure of the atomic scale and the image-scale pattern. The reason is the following. Superstructures manifest on the structural entropy map as sum of the sub-structures vector, thus since none of the structures are known, only the sum of their vectors, the sub-vectors are not unique. Multiresolution or wavelet analysis (MRA) uses a system of basis functions with various time and frequency (space and spatial frequency) parameters for expanding functions. This system makes the time-frequency localization possible. Using some selected MRA resolution levels of the AFM image and carrying out the structural entropy based localization study on each of these levels will determine the decay type of the image at the length scales corresponding to the selected frequencies. This approach is promising for determining the large-scale patterns on AFM pictures.

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. © 2009 Elsevier Ltd. All rights reserved.

The thermal interactions of thin AlGe and AlNiGe layers with a bulk GaAs monocrystal were investigated. The heat treatment of these systems was carried out in the working chamber of a scanning electron microscope. The SEM pictures were analysed using a fractal mathematical technique. It was found that the surface of the samples has fractal character. No temperature dependence of the fractal dimension was observed. The samples were also studied using the structural entropy versus filling factor maps of the samples in order to find their localization properties. The SEM pictures of AlGe perform mostly as a Gaussian functions, whereas the AlNiGe samples show usually a behaviour with exponential decay. © 2009 Elsevier Ltd. All rights reserved.

In the present work nanowires are investigated, which were prepared with the help of encapsulated metal induced growth method on GaAs and InP substrate. As our former investigations how, we can receive nanowires with substrate-like composition in the case of InP. In the case of GaAs substrate the situation is entirely different, while the growth technology in both cases was the same. The difference between the nanoproducts in the cases of different substrates originate in the reactivity of the components, which is explained in the following considerations. Furthermore we have observed that the diameter of the nanowires depends on the electron energy of the irradiation. If the electron beam was 5 kV and 20 kV, the diameter lasting increases and decreases, respectively. This effect can be explained by the change of the nanowires structure influenced by the electron beam. © 2008 IEEE.