In many composites the electrical transport takes place only by tunneling between isolated particles. For a long time it was quite a puzzle how, in spite of the incompatibility of tunneling and percolation networks, these composites conform well to percolation theory. We found, by conductance atomic force microscopy measurements on granular metals, that it is the apparent cut-off of the tunneling to non-nearest neighbors that brings about this behavior. In particular, the percolation cluster is shown to consist of the nearest-neighbors sub-network of the full tunneling network. (grains, crystallites, etc.). In the pioneering works on such systems, these two mechanisms have been considered separately. 1,2,3,4,5,6 In particular, for a high enough content of the metallic phase in granular metals, the continuous network is formed by the

Following the lack of microscopic information about the intriguing well-known electrical-thermal switching mechanism in carbon-black-polymer composites, we applied atomic force microscopy in order to reveal the local nature of the process and correlated it with the characteristics of the widely used commercial switches. We conclude that the switching events take place in critical interparticle tunneling junctions that carry most of the current. The macroscopic switched state is then a result of a dynamic-stationary state of fast switching and slow reconnection of the corresponding junctions.

We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using contact-resistance atomic force microscopy on carbon black/polymer composites. The features in the current images, when presented as a function of the cut-off current, or as a function of the total area covered by the electrically connected objects, appear to obey a cluster statistics that is similar to the one predicted and observed in continuum percolation systems.

Electrical transport measurements through single InAs and CdSe semiconductor nanocrystals embedded in a thin polymer film were performed using conductance atomic force microscopy. The current and topography images showed excellent correlation, where current was detected only over the nanocrystals. A rapid current decay in consecutive scans was observed for positive sample bias, while remaining intact at negative bias. This current decay was accompanied by bias-dependent changes in the height of the nanocrystals. These phenomena, which were not observed for gold nanocrystals, are attributed to long-sustained charging of the nanocrystals.

Subject classification: 61.46.+w; 73.63.BdConsidering the very recent interest in the flow between two sites on a percolation cluster it is obvious that an experimental study of such a problem requires local measurement techniques. Following this observation we report the first study of the voltage dependence of the images derived by contact-resistance atomic force microscopy (C-AFM) in general, and on a binary composite in particular. The results obtained provide an experimental map of the voltage dependence of the realized connectivity between a given pair of sites on a percolation cluster. Our measurements show that the two-dimensional cross-section images of a three-dimensional percolation cluster reveal a systematic behavior that can be described as a phase transition.Introduction While the global aspects of percolation theory [1] are quite well understood by now, the understanding of the more local aspects of this theory is still at a rudimentary level. In fact, in spite of the basic science and applications interests it was only very recently that the problem of flow between two sites on a percolation cluster has been considered [2]. To study this problem experimentally it is obvious that a localprobe technique with driving parameters (such as electrical voltage or hydrostatic pressure) has to be utilized.Following the above considerations we initiated a study of the local currents (conductivity) map via "sites" of a percolation cluster using the contact-resistance atomic force microscopy (C-AFM) technique [3]. We have applied this technique to a binary composite [3-5] made of a conducting component (carbon black) and an insulating component (a polymer) for which it has been established that the observed two-dimensional images represent a cross-section of the three-dimensional percolation cluster [4,5], yielding a bulk fractal dimension of (2.5 AE 0.15), in agreement with the theoretical prediction [1] of 2.53. The relative large conducting particles (known as the aggregates [6]) in this composite [7] on one hand, and the high resolution of the technique on the other hand, provide indeed a local probe that can be considered as touching a single particle (or a single "site"). Hence, the observed currents represent the current or the conductance paths between a "site" and a remote macroscopic counter-electrode of the sample. These paths are parts of the embedded three-dimensional percolation cluster. On the other hand, we realize that each two separated sites on the image, hereafter the "current islands", are electrically connected between themselves via this cluster. In other words, while not being connected in the image, any two current islands are connected by the "hidden" underlying network of the three-dimensional percolation cluster.