Multi-Probe Atomic Force Microscopy Using Piezoelectric Cantilevers

Abstract

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

Adaptive tilting angles to achieve high‐precision scanning of a dual probes AFM

“…Satoh et al [14] developed a self-sensing multi-probe AFM system by integrating the piezo-resistor with cantilever. Satoh et al [14] developed a self-sensing multi-probe AFM system by integrating the piezo-resistor with cantilever.…”

“…For years, dual-probe AFM (DP-AFM) has been developed and shown excellent performance in applications of measurement and manipulation. Satoh et al [14] developed a self-sensing multi-probe AFM system by integrating the piezo-resistor with cantilever. Mancevski et al [15] designed a dual-probes CD-AFM, the two probes of which operate as a caliper for sidewall measurement of high-aspect-ratio features.…”

Using dynamic force microscopy with piezoelectric cantilever for indentation and high-speed observation

“…We have developed the MP-AFM system using such self-sensing cantilevers, which allowed us not to use any complex optical elements. We chose the piezoelectric thin-film cantilever (referred to as a PZT cantilever [11]) where the cantilever deflection was measured using the piezoelectric effect on the PZT thin-film [12].…”

Effective Tilting Angles for a Dual Probes AFM System to Achieve High-Precision Scanning

“…With the improvement of technology, there were some attempts to develop the dual probe AFM system, and the technology behind can be expected to provide high precision measurements and manipulations in a lot of applications. Satoh et al [10] have developed a multi-probe AFM system with a self-sensitive cantilever, which is a micro cantilever with an integrated piezoresistor serving as a deflection sensor. Intuitively, the use of the self-sensitive cantilever reduces the complexity of the setup since the optical sensing elements can be saved.…”