Abstrad. ? l e lacunarity is computed for randomly diluted two-dimensional lattices in terms of the chemical distance. The crossover behaviour and the question of universality are discussed.Fractal lattices are not translationally invariant and the mass distribution around each occupied site is different from site to site. The fractal dimension characterizes only the average of the mass distribution; the fluctuation around the average is characterized by the lacunarity which may be defined as the relative mean-square width of the distribution. The lacunarity has been studied in thermal phase transitions as a parameter which may prove relevant for the king critical behaviour in deterministic fractals [l-81. The purpose of this letter is to study the lacunarity with random fractals.Random fractals do indeed show remarkable fluctuation phenomena (for a review, see [9]). Some time ago, Coniglio et a/ [lo] asked the question: when large percolation clusters are simulated on a computer many times, does the cluster number N , fluctuate from sample to sample in the 'usual' way like the particle number in an ideal gas for which the compressibility never diverges, or does it fluctuate in the 'critical' way like the particle number in a real gas for which the compressibility diverges near the critical point? The fluctuation turns out to be equal to the square root of the average cluster number, as in the 'usual' way. But the average cluster number itself sharply peaks only near the percolation threshold, as in the 'critical' way. Stauffer [ l l ] and Coniglio and Stauffer [12] studied the fluctuation of S,.,, the number of lattice sites of the largest cluster, and Kapitulnik et al [ 131 studied the fluctuation of M( L), the number of sites

We developed a multi-probe atomic force microscope (AFM) having two AFM cantilevers independently controlled using the optical beam deflection method. We succeeded in simultaneously obtaining images with two independent probes by frequency modulation (FM) detection method. To evaluate the distance between the AFM tips of the cantilevers, we used a new the address-patterned sample, which was also developed for this study. The images obtained show that the distance between the probes was 2 µm. The development of the multi-probe AFM opens a wide variety of applications in the present nanoscience and engineering field.

The floating memory properties of thiolateprotected gold (Au:SR) nanoclusters, Au 25 (SR) 18 , Au 38 (SR) 24 , Au 144 (SR) 60 , and Au 333 (SR) 79 (R = C 12 H 25 ), and Au colloids were investigated using four-probe measurements in vacuum. Uniform and monolayer films of Au:SR nanoclusters or Au colloids were formed as floating memory layers on p-type Si substrates by Langmuir−Blodgett method. The fluoropolymer (CYTOP, ∼15 nm thick) was spin-coated on top to form a hydrophobic insulating layer. Using Au dot (∼40 nm thick) as the anode electrode, the capacitance−voltage (C−V) measurements were performed using the Au and Cu plate electrodes as contact points for the two probes. Clockwise hysteresis curves originating from the Au:SR nanoclusters or Au colloids were observed, and the hysteresis width was dependent on the size of the Au:SR nanoclusters and the sample temperature. In particular, for the Au 38 (SR) 24 nanocluster, multiple phases were observed in the C−V curve, implying their application in multivalued memory devices.

We performed electrical transport measurements on α-sexithiophene crystalline grains using a dual-probe atomic force microscopy system having two independently controlled cantilever probes. The field-effect transistor characteristics were measured by varying the distances between the two probes brought in contact with the surface of the grains. It was clearly shown by the transfer line method that the grain boundary is the dominant factor limiting the electrical properties of organic thin films. Moreover, the hole transport across the grain boundary was found to be more affected by the oxygen hole doping than that within the crystalline grain.

We developed a dual-probe (DP) atomic force microscopy (AFM) system that has two independently controlled probes. The deflection of each cantilever is measured by the optical beam deflection (OBD) method. In order to keep a large space over the two probes for an objective lens with a large numerical aperture, we employed the OBD sensors with obliquely incident laser beams. In this paper, we describe the details of our developed DP-AFM system, including analysis of the sensitivity of the OBD sensor for detection of the cantilever deflection. We also describe a method to eliminate the crosstalk caused by the vertical translation of the cantilever. In addition, we demonstrate simultaneous topographic imaging of a test sample by the two probes and surface potential measurement on an α-sexithiophene (α-6T) thin film by one probe while electrical charges were injected by the other probe.