Damping mechanisms of single-clamped and prestressed double-clamped resonant polymer microbeams

Schmid, Silvan; Hierold, Christofer

doi:10.1063/1.3008032

Cited by 73 publications

(67 citation statements)

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“…It is known that stress can be used to change the quality factor in NEMS systems. 31,33 However, the change in τ 0 from 13 K to 30 K bath temperature is less than 2%, whereas the Q factor changes by 30% (see Figure 4(b)). …”

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confidence: 97%

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Nanoscale Electromechanics To Measure Thermal Conductivity, Expansion, and Interfacial Losses

et al. 2015

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We study the effect of localized Joule heating on the mechanical properties of doubly clamped nanowires under tensile stress. Local heating results in systematic variation of the resonant frequency; these frequency changes result from thermal stresses that depend on temperature dependent thermal conductivity and expansion coefficient. The change in sign of the linear expansion coefficient of InAs is reflected in the resonant response of the system near a bath temperature of 20 K. Using finite element simulations to model the experimentally observed frequency shifts, we show that the thermal conductivity of a nanowire can be approximated in the 10-60 K temperature range by the empirical form κ = bT W/mK, where the value of b for a nanowire was found to be b = 0.035 W/mK 2 , significantly lower than bulk values. Also, local heating allows us to independently vary the temperature of the nanowire relative to the clamping points pinned to the bath temperature. We suggest a loss mechanism

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“…Clamping losses are known to be the dominant damping mechanism in doubly clamped beams under high pre-stress. 31 Here the tension should be more than the flexural rigidity such that the beam mimics the mechanics of a stretched string. This condition is satisfied when τ 0 EI/(AL 2 ).…”

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Nanoscale Electromechanics To Measure Thermal Conductivity, Expansion, and Interfacial Losses

et al. 2015

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“…These features are in contrast to the more complicated harmonics of doubly clamped beams, 16 which are realized in low-stress silicon nitride devices of the same geometry. 17 Furthermore, it has now been shown that very high mechanical Qs exist for nanostrings under tension in a variety of other materials, including the polymer SU-8, 18 aluminum, 6,19 and AuPd. 20 This demonstrates that the high Q is a byproduct of the tension and string-like behavior and not a special material property of the silicon nitride itself.…”

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Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Suhel

Hauer

Biswas

et al. 2012

Applied Physics Letters

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High-stress silicon nitride nanostrings are a promising system for sensing applications because of their ultrahigh mechanical quality factors (Qs). By performing thermomechanical calibration across multiple vibrational modes, we are able to assess the roles of the various dissipation mechanisms in these devices. Specifically, we possess a set of nanostrings in which all measured modes fall upon a single curve of peak displacement versus frequency. This allows us to rule out bulk bending and intrinsic loss mechanisms as dominant sources of dissipation and to conclude that the most significant contribution to dissipation in high-stress nanostrings occurs at the anchor points.The extremely high values of mechanical Q that have been reported in silicon nitride nanostrings 1-3 have generated a great deal of excitement in the nanomechanics community. 4 These devices are ideal for use in mass sensing, 5 temperature sensing, 6 and optomechanics 7-9 and have proved to be an invaluable platform for research into the quantum properties of nanoscale resonators. 10,11 Nanostrings possess all the desired properties for these endeavors, including small mass, high frequency, and high Q, with correspondingly large displacement amplitudes. This combination makes them sensitive to external perturbation yet still within the limits of current detection techniques. 12 In this manuscript, we demonstrate thermomechanically limited detection of up to six mechanical nanostring modes. Furthermore, we present a set of devices in which all harmonics fall upon a single curve of calibrated peak displacement versus frequency. As we discuss below, we are able to infer that the mechanical Q is limited by dissipation processes operating in the vicinity of the anchor points-thus suggesting ways to further engineer the mechanical Q.Silicon nitride nanostrings are devices under extremely high tensile stress (σ = 0.8 GPa for our devices). The accepted understanding is that the tension along their length results in large stored elastic energy and a correspondingly large mechanical Q. 3 Experiments have confirmed that Q increases with mechanical tensioning of non-prestressed (low tension, non-stoichiometric silicon nitride) devices, 13,14 corroborating the tension's central role.In addition to causing the high Q, the tension compels the devices to behave like strings rather than doubly clamped beams, as one would usually expect for this geometry. The harmonics are at integer multiples of the fundamental frequency, 15 ν n = nν 1 , where ν 1 is the fundamental mode frequency and n indicates the mode number; the mode frequency depends only on the length of the string (not on the width or thickness). These features are in contrast to the more complicated harmonics of doubly clamped beams, 16 which are realized in low-stress silicon nitride devices of the same geometry. 17 Furthermore, it has now been shown that very high mechanical Qs exist for nanostrings under tension in a variety of other materials, including the polymer SU-8, 18 aluminum, 6,19 and AuPd...

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“…The total dissipated energy is the sum of energy dissipated by a variety of physical mechanisms. Physical mechanisms of energy dissipation can be described by the two following sets of losses: extrinsic loss and intrinsic loss [19][20][21]. The extrinsic losses include acoustic radiation, surface loss, and air friction.…”

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confidence: 99%

Thermoelastic Damping Depending on Vibration Modes of Nano Beam Resonator

Hoang¹

2016

Comm. in Phys.

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Abstract. The obtainable quality factor for a nano beam resonator is limited due to internal damping such as thermoelastic damping. Therefore, understanding how internal damping varies with the respective resonant modes is very important to design a high performance nanoresonator. In this research, we investigate thermoelastic damping depending on vibration modes of nano beam resonators using finite element method. The study results show that the quality factor of a nanoresonator is lower than at high order modes. The silicon nano beam resonator with the quality factor larger than one million can be achieved by optimizing the dimensions of the resonant beam.

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Damping mechanisms of single-clamped and prestressed double-clamped resonant polymer microbeams

Cited by 73 publications

References 37 publications

Nanoscale Electromechanics To Measure Thermal Conductivity, Expansion, and Interfacial Losses

Nanoscale Electromechanics To Measure Thermal Conductivity, Expansion, and Interfacial Losses

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Thermoelastic Damping Depending on Vibration Modes of Nano Beam Resonator

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