Estimating Damping in Microresonators by Measuring Thermomechanical Noise Using Laser Doppler Vibrometry

Kuter-Arnebeck, Ottoleo; Labuda, Aleksander; Joshi, Surabhi; Das, Kaushik; Vengallatore, Srikar

doi:10.1109/jmems.2013.2286199

Cited by 10 publications

(9 citation statements)

References 43 publications

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“…For the three major classes of linear damping (viscous, viscoelastic, and anelastic), the first peak (corresponding to the fundamental natural frequency) is symmetric and well-approximated by a simple Lorentzian function given by [18], [33] ( ) ( ) ( )…”

Section: Estimating Q From Thermomechanical Noisementioning

confidence: 99%

Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

Nourmohammadi

Mukherjee

Joshi

et al. 2015

J. Microelectromech. Syst.

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Abstract-Atomistic simulations can be used to compute damping from first principles and gain unprecedented insights into the mechanisms of dissipation. However, the technique is still in its infancy and many foundational aspects remain unexplored. As a step towards addressing these issues, we present here a comparative study of five different methods for estimating damping under isothermal conditions. Classical molecular dynamics was used to simulate the fundamental longitudinalmode oscillations of nanowires and nanofilms of silicon and nickel at room temperature (300 K) in the canonical ensemble using the Nosé-Hoover thermostat. In the sub-resonant regime, damping was quantified using the loss tangent and loss factor during steady-state harmonic vibration. The quality factor was obtained by analyzing the spectrum of thermomechanical noise and also from the Duffing-like nonlinearity in the frequency response under harmonic excitation. In addition, the nonlinear logarithmic decrement was obtained from the Hilbert transform of freely-decaying oscillations. We discuss the factors that must be considered while selecting simulation parameters; establish criteria for convergence and linearity; and highlight the relative merits and limitations of each method.

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Section: Estimating Q From Thermomechanical Noisementioning

confidence: 99%

Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

Nourmohammadi

Mukherjee

Joshi

et al. 2015

J. Microelectromech. Syst.

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“…Harmonic excitation is associated with two dimensionless measures of damping: the loss angle, ϕ, by which the stress (σ) leads the strain (ɛ); and the quality factor, Q ≡ (ω n /Δω), where Δω is the half-power bandwidth of the resonance peak and ω n is the angular natural frequency. Alternately, the quality factor can be estimated by fitting the resonance peak in the thermomechanical noise spectrum [10][11][12]. The free decay technique quantifies damping in terms of the logarithmic decrement, δ, and wave propagation techniques measure the attenuation,α, of the amplitude of elastic waves with wavelength λ [9].…”

Section: Foundations Of Dampingmentioning

confidence: 99%

Design strategies for controlling damping in micromechanical and nanomechanical resonators

2014

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Damping is a critical design parameter for miniaturized mechanical resonators usedin microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS),optomechanical systems, and atomic force microscopy for a large and diverse set ofapplications ranging from sensing, timing, and signal processing to precisionmeasurements for fundamental studies of materials science and quantum mechanics.This paper presents an overview of recent advances in damping from the viewpointof device design. The primary goal is to collect and organize methods, tools, andtechniques for the rational and effective control of linear damping in miniaturizedmechanical resonators. After reviewing some fundamental links between dynamicsand dissipation for systems with small linear damping, we explore the space ofdesign and operating parameters for micromechanical and nanomechanicalresonators; classify the mechanisms of dissipation into fluid–structure interactions(viscous damping, squeezed-film damping, and acoustic radiation), boundarydamping (stress-wave radiation, microsliding, and viscoelasticity), and materialdamping (thermoelastic damping, dissipation mediated by phonons and electrons,and internal friction due to crystallographic defects); discuss strategies for minimizingeach source using a combination of models for dissipation and measurements of material properties; and formulate design principles for low-loss micromechanical and nanomechanical resonators

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“…In this case, deterministic noise peaks can be clearly identified and removed before fitting an SHO model to the PSD, thereby allowing robust and accurate calibration of the cantilever stiffness and damping. The removal of electronic noise peaks is especially useful for very high Q cantilevers, 51,52 such as in vacuum experiments, where the cantilever thermal noise can easily be mistaken for electronic noise and vice versa. Reducing the burden in distinguishing between stochastic and deterministic noise sources paves the way for accurate and robust automated PSD fitting software and AFM automation algorithms.…”

Section: Discussionmentioning

confidence: 99%

Daniell method for power spectral density estimation in atomic force microscopy

Labuda

2016

Review of Scientific Instruments

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An alternative method for power spectral density (PSD) estimation--the Daniell method--is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion--the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum.

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Estimating Damping in Microresonators by Measuring Thermomechanical Noise Using Laser Doppler Vibrometry

Cited by 10 publications

References 43 publications

Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

Design strategies for controlling damping in micromechanical and nanomechanical resonators

Daniell method for power spectral density estimation in atomic force microscopy

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