Modeling a Suspended Nanotube Oscillator

Üstünel, Hande; Roundy, David; Arias, T. A.

doi:10.1021/nl0481371

Cited by 80 publications

(92 citation statements)

References 16 publications

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“…18,19 From the small slack we observe in our SEM images, we expect that the nanotube in our device behaves as a stretched string. 18,21 Following a similar analysis as given in ref 18, we find the characteristic vibration amplitude for our system with the given V 0 and V AC is ∼1 nm. A line trace of I versus f is shown in Figure 2b, showing that the resonance has a quality factor Q ∼ 200.…”

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confidence: 72%

Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators

et al. 2008

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Ultraminiaturized mass spectrometers are highly sought-after tools, with numerous applications in areas such as environmental protection, exploration, and drug development. We realize atomic scale mass sensing using doubly clamped suspended carbon nanotube nanomechanical resonators, in which their single-electron transistor properties allows self-detection of the nanotube vibration. We use the detection of shifts in the resonance frequency of the nanotubes to sense and determine the inertial mass of atoms as well as the mass of the nanotube. This highly sensitive mass detection capability may eventually enable applications such as on-chip detection, analysis, and identification of compounds.Because of their small size, nanoscale systems are highly sensitive to their environment, affording great potential for sensing applications. Chemical and biological charge-based sensors using carbon nanotubes 1,2 and nanowires 3 have already been demonstrated. Nanoelectromechanical systems have been proposed for highly sensitive mass detection of neutral species, 4,5 and significant progress has been made in using nanofabricated resonators 6-8 and carbon nanotubes 9-12 for mass sensing. However, the ultimate limit of atomic resolution mass sensitivity remains unrealized. Here we demonstrate that individual double-clamped single-walled carbon nanotube resonators are capable of atomic-scale mass sensing and determining the inertial mass of atomic species. Analysis of our data also yields the nanotube mass, giving a general approach to determining the mass of molecular nanostructures. Our results open the door to ultraminiaturized mass spectroscopy or arrays, potentially enabling on-chip detection and identification of unknown analytes, as well as the study of single atom adsorption and desorption.We fabricate our devices by first growing nanotubes from catalyst islands 13 under either pure CH 4 13 or a CH 4 /H 2 mixture 14 on an oxidized Si wafer. We then attach Pd/Au source/drain electrodes and a side gate using electron beam lithography (EBL). In a second step, a layer of poly(methyl methacrylate) (PMMA) is spun on the chip, and a ∼450 nm window is opened over a segment of the nanotube between the electrodes, again using EBL. The SiO 2 is etched using buffered HF to suspend the carbon nanotube within the window. Following a critical point drying step, the samples are electrically tested at room temperature; we then load selected devices into a custom-built cryostat, which is maintained at a high vacuum. Figure 1a shows a scanning electron microscope (SEM) image of a completed suspended nanotube transistor device.At the temperature T ≈ 6 K of our experiment, the nanotubes act as single-electron transistors (SET) in which the charge on the nanotube is an integer multiple of the electron charge e. 15 As the gate voltage V g is swept, electrons enter the SET one at a time, with each transition between discrete charge states producing a Coulomb peak in the source-drain conductance (see e.g. ref 16). Figure 1b shows this b...

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confidence: 72%

Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators

et al. 2008

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“…Again, fitting the experimental data in Fig. 2(b) with equation (2) SWNT resonators are known to exhibit multiple vibrational states, including in-plane, out-of-plane, and their higher order modes [19][20]. We therefore examined the capacitive softening effect for different vibrational modes.…”

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confidence: 99%

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

Zhong

2011

Nano Lett.

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We report the capacitive spring softening effect observed in single-walled carbon nanotube (SWNT) nanoelectromechanical (NEM) resonators. The nanotube resonators adopt dual-gate configuration with both bottom-gate and side-gate capable of tuning the resonance frequency through capacitive coupling. Interestingly, downward resonance frequency shifting is observed with increasing side-gate voltage, which can be attributed to the capacitive softening of spring constant. Furthermore, in-plane vibrational modes exhibit much stronger spring softening effect than out-of-plan modes. Our dual-gate design should enable the differentiation between these two types of vibrational modes, and open up new possibility for nonlinear operation of nanotube resonators.

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“…Nanotube resonators can also be fabricated without tension, so the restoring force is dominated by the beam's rigidity [48,49]. In this limit, the mechanical frequency is…”

Section: A Mechanical Resonatormentioning

confidence: 99%

“…We consider the nanotube as a beam of length l and diameter D and focus our studies on its fundamental vibrational mode [38][39][40]44,[48][49][50] [51]. The flux coupling is proportional to the area swept out by the nanotube, which is equal to β 0 lX, where β 0 ≡ ½1=ðlXÞ…”

Section: A Mechanical Resonatormentioning

confidence: 99%

Displacemon Electromechanics: How to Detect Quantum Interference in a Nanomechanical Resonator

et al. 2018

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We introduce the "displacemon" electromechanical architecture that comprises a vibrating nanobeam, e.g., a carbon nanotube, flux coupled to a superconducting qubit. This platform can achieve strong and even ultrastrong coupling, enabling a variety of quantum protocols. We use this system to describe a protocol for generating and measuring quantum interference between trajectories of a nanomechanical resonator. The scheme uses a sequence of qubit manipulations and measurements to cool the resonator, to apply two effective diffraction gratings, and then to measure the resulting interference pattern. We demonstrate the feasibility of generating a spatially distinct quantum superposition state of motion containing more than 10 6 nucleons using a vibrating nanotube acting as a junction in this new superconducting qubit configuration.

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Modeling a Suspended Nanotube Oscillator

Cited by 80 publications

References 16 publications

Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators

Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

Displacemon Electromechanics: How to Detect Quantum Interference in a Nanomechanical Resonator

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