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Mechanical Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
How is SET applied for detecting the motion of a nanomechanical resonator? This is achieved by capacitively coupling the gate of the SET to a metal electrode on a flexural beam of the resonator and biasing the electrode at a constant voltage, Vbeam. In this scheme, the capacitance C between the SET and the beam has a coupled charge q = VbeamC. As the beam vibrates in the x direction, in the plane of the device, the resulting variation in capacitance modulates the charge induced on the SET, Δq = Vbeam ΔC, changing the SET source−drain current. When the voltage Vbeam is increased, the charge modulation Δq and the sensitivity to the resonator motion increases. However, the source−drain current is due to the stochastic flow of electrons through the SET, so the voltage of the center island fluctuates randomly. This causes a fluctuating “back-action” force on the beam. Increasing the voltage applied to the beam leads to larger coupled-charge signals, but also increases the back-action coupling between the SET and the beam. The force increases as Vbeam increases, resulting in a voltage for which the total noise is minimized. The device had a displacement sensitivity of 2.0 × 10−15 mHz−1/2 at the 116.7 MHz resonance frequency of the mechanical beam at a temperature of 30 mK, which was limited by the noise in the conventional electronics. The sensitivity was roughly two orders of magnitude greater than the quantum limit for this oscillator.
Mechanically Coupled Capacitive Nanomechanical Silicon Resonators
Published in Nguyen Van Toan, Takahito Ono, Capacitive Silicon Resonators, 2019
The single beam nanomechanical resonator (device 1) is shown in Figure 8.1a. It basically consists of silicon resonant body, driving/sensing electrodes, and capacitive gaps. The resonator is electrically excited and vibrated at a flexural mode by the combined influence of direct current (DC) and alternating current (AC) actuation voltages (VDC and VAC). The output voltage of the resonator results from the changes in the capacitive gap on the sensing electrode. In turn, the designed mechanically coupled nanomechanical resonator (device 2) consists of 100 single nanomechanical resonators connected by mechanically coupled elements, as shown in Figure 8.1b. The summarized design parameters of devices 1 and 2 are presented in Table 8.1.
Introduction
Published in Zoran Gajić, Myo-Taeg Lim, Dobrila Škatarić, Wu-Chung Su, Vojislav Kecman, Optimal Control, 2018
Zoran Gajić, Myo-Taeg Lim, Dobrila Škatarić, Wu-Chung Su, Vojislav Kecman
It is interesting to point out that many dynamic nonlinear systems in physics are known to possess the weakly coupled form, for example, acoustic systems (Franzoni and Bliss 1998), temperature dissipation (Ritter and Figueiredo 2005), nonlinear oscillators (Aubry et al. 2001), and systems in photonics (Long et al. 1998). Dynamics of a nanomechanical resonator coupled to a single electron transistor (Averin and Likharev 1986) represents dynamics of a nonlinear weakly coupled system (Armour et al. 2004). Weakly coupled systems have been also studied in mathematics (e.g., Bhaya et al. 1991; Feingold and Varga 1962; Kaskurewics et al. 1990; Zecević and Siljak 1994; Nessyahu 1996; Thompson and Tisdell 1999; Carrive et al. 2002), and in computer science (Jia and Leimkuhler 2003). The applications on nonlinear weakly coupled systems can be found even in medicine for a human scalp-recorded EEG (Sulimov 1998), and in ecology (Auger and Roussarie 1994). In addition, weakly coupled systems have been studied in economics (Simon and Ando 1963; Pierce 1974; Okuguchi 1978), management sciences (You 1998), and power system engineering (Medanić and Avramović 1975; Ilić-Spong et al. 1984; Crow and Ilić 1990; Ilić 2007) under the name of block diagonally dominant matrices and block diagonally dominant systems. Weak coupling linear structures also appear in nearly completely decomposable continuous-and discrete-time Markov chains (Philips and Kokotović 1981; Delebecque and Quadrant 1981; Aldhaheri and Khalil 1991; Stewart 1994; Haurie and Moresino 2007). Applications of weakly coupled systems to networking can be found in Jung et al. (2005). Several journal papers applied the weak coupling approach to linear models of power systems (Avramović and Medanić 1975; Shen and Gajić 1990; Momah and Shen 1991; Nuhanovic et al. 1998; Ilić 2007).
Nicholas A. Besley (1972–2021)
Published in Molecular Physics, 2023
Jonathan D. Hirst, Andrew M. Teale, Anthony J. Stace, Peter J. Knowles
Nick’s early interest in nanotubes [28,36] developed into research on a range of nanoscience problems, often working with colleagues at Nottingham and collaborators further afield. Nick published seven papers with his wife, Elena [45,53,74,101,107,109,130], several of which were in this field. Studies, usually with experimental collaborators, included the transformation of graphene to fullerene [45], reactions of the inner surface of carbon nanotubes and nanoprotrusion processes [53], and adsorption on hexagonal boron nitride [81,101,107]. Nick explored the calculation of the vibrational frequencies of carbon clusters and fullerenes with empirical potentials [75]. He developed a new empirical potential for this purpose [89] with one of his PhD students, Pritesh Tailor (Figure 4). Nick showed that the X-ray emission spectra of carbon nanotubes are weakly dependent on their length and chirality [97]. The new empirical potential was extended to enable the calculation of Raman spectroscopy of multi-layered carbon nanomaterials [108]. To model the physisorption of molecules on surfaces such as graphene and hexagonal boron nitride, Nick developed an approach, called AIRBED, where the constituent atoms of the surface are simply represented by a point charge to capture electrostatic effects [115]. Recently, Nick presented a vibrational analysis of three types of carbon nanotube-based nanomechanical resonator [124].