Parametric resonance based scanning probe microscopy

Moreno-Moreno, Miriam; Raman, Arvind; Gomez-Herrero, Julio; Reifenberger, R.

doi:10.1063/1.2202132

Cited by 38 publications

(47 citation statements)

References 20 publications

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“…16,23 We demonstrate this by carrying out similar experiments at atmospheric pressure. The results from the longest available beam ͑device no.…”

Section: A=mentioning

confidence: 80%

“…In previous manifestations of mechanical parametric amplification, the nature of the spring constant modulation was usually capacitive, 11,12 although other methods exploited intrinsic residual stress, 14 Lorentz force, 15 or an external feedback loop. 16 Direct parametric tuning of the tensile stress using piezoelectric electromechanical coupling was introduced earlier in large scale microelectromechanical resonator operating at 140 kHz. 17 Here, we demonstrate piezoelectric parametric amplification and actuation in high frequency and very-high frequency, submicron-scale NEMS resonators.…”

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confidence: 99%

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Efficient parametric amplification in high and very high frequency piezoelectric nanoelectromechanical systems

Karabalin

Masmanidis

Roukes

2010

Applied Physics Letters

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Parametric amplification in nanomechanical structures is demonstrated by modulating a purely intrinsic mechanical parameter of the system-the stress-via piezoelectric electromechanical coupling. Large resonance amplitude and quality factor enhancement due to parametric pumping are observed under both vacuum and ambient pressure conditions. Exploration of the region of parametric instability yields results that agree with parametric amplification theory. © 2010 American Institute of Physics. ͓doi:10.1063/1.3505500͔Recent technological advances have enabled the fabrication of mechanical resonators down to the nanometer scale. 1Resonant nanoelectromechanical systems ͑NEMS͒ possess such properties as extremely high frequencies, 2,3 high mechanical responsivity, large quality factors, and operability at low required power, making NEMS resonators promising in a variety of applications ranging from mass and force sensing 4-6 to quantum limited measurements. 7 However, as electromechanical systems are miniaturized, readout of mechanical motion becomes increasingly difficult, as most forms of electrical transduction signals scale with device size. One potential solution is amplification of the signal in the mechanical domain using parametric effect before applying electrical transduction.Parametric resonance is of interest to many areas of research ranging from quantum optics 8 to plasma physics. 9Since the initial demonstration of a resonant mechanical parametric system by Rugar and Grütter, 10 it has attracted significant attention.11-14 The simplest parametric amplification scheme involves periodic modulation of the spring constant of the system at twice its fundamental resonance frequency. In previous manifestations of mechanical parametric amplification, the nature of the spring constant modulation was usually capacitive, 11,12 although other methods exploited intrinsic residual stress, 14 Lorentz force, 15 or an external feedback loop.16 Direct parametric tuning of the tensile stress using piezoelectric electromechanical coupling was introduced earlier in large scale microelectromechanical resonator operating at 140 kHz.17 Here, we demonstrate piezoelectric parametric amplification and actuation in high frequency and very-high frequency, submicron-scale NEMS resonators.Modulation of the stress of a nanomechanical doubly clamped beam results in resonance frequency change:for length L, Young's modulus E, density , dimension in the direction of vibration t h , and stress . The displacement of the central point of the beam is modeled as harmonic oscillator of effective mass m, spring constant k 1 , and quality factor Q with Duffing 19 nonlinearity we obtain the following equation of motion:where k p = 0.3k 1 L 2 / ͑Et h 2 ͒ is the spring constant modulation amplitude, and F͑t͒ = F 0 cos͑ D t + ͒ is a driving force. The parametric modulation is performed at twice the resonance frequency, leading to a vibrational amplitude gain given by:where k t is the threshold parametric pumping force 2k 1 / Q. The second term in this...

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“…16,23 We demonstrate this by carrying out similar experiments at atmospheric pressure. The results from the longest available beam ͑device no.…”

Section: A=mentioning

confidence: 80%

mentioning

confidence: 99%

Efficient parametric amplification in high and very high frequency piezoelectric nanoelectromechanical systems

Karabalin

Masmanidis

Roukes

2010

Applied Physics Letters

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“…The behavior of a self-excited cantilever far from the sample is governed by equations (2) and (4). We note that, at odd with the AM-AFM case, the dynamics is intrinsically nonlinear and it includes a delay so analytical estimates such as the ones reported in section III-B can not be easily obtained and we have to rely either on analytical approximations or numerical algorithms for characterizing the cantilever response.…”

Section: Self-excited Cantilever: At-afmmentioning

confidence: 99%

“…Thus, the trade-off between sensitivity and scan velocity often limits the effectiveness of this measurement procedure. In this context, parametric P resonance has been proposed as a mean of increasing the effective quality factor without having detrimental effects on the scanning speed [4].…”

Section: Introductionmentioning

confidence: 99%

Analysis of oscillating microcantilever dynamics: A Floquet perspective

Paoletti

Basso

2013

52nd IEEE Conference on Decision and Control

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Dynamic mode atomic force microscopy provides high resolution in imaging biological samples, but it features a reduced scanning velocity. In this paper we investigate a recent scheme in which the cantilever gets excited by a feedback loop containing a saturation function. The proposed modality is then analyzed via Floquet theory and compared to the standard setup, showing better transient performance and elimination of some of the known drawbacks. The analysis results confirm preliminary experiments showing the effectiveness of this operating mode.

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“…[3]. A few relevant recent applications, in micro and nano systems, include quadrupole ion guides and ion traps [4], linear ion crystals in linear Paul traps designed as prototype systems for the implementation of quantum computing [5][6][7], magnetic resonance force microscopy [8], tapping-mode force microscopy [9], axially loaded microelectromechanical systems (MEMS) [10], and torsional MEMS [11]. In the quantum domain we could mention wideband superconducting parametric amplifiers [12] and squeezing in optomechanical cavities below the zero-point motion [13].…”

Section: Introductionmentioning

confidence: 99%

Heating and thermal squeezing in parametrically driven oscillators with added noise

Batista

2012

Phys. Rev. E

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In this paper we report a theoretical model based on Green's functions, Floquet theory, and averaging techniques up to second order that describes the dynamics of parametrically driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincaré map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects causes most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.

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Parametric resonance based scanning probe microscopy

Cited by 38 publications

References 20 publications

Efficient parametric amplification in high and very high frequency piezoelectric nanoelectromechanical systems

Efficient parametric amplification in high and very high frequency piezoelectric nanoelectromechanical systems

Analysis of oscillating microcantilever dynamics: A Floquet perspective

Heating and thermal squeezing in parametrically driven oscillators with added noise

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