Damping mechanisms in high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>micro and nanomechanical string resonators

Schmid, Silvan; Jensen, K.; Nielsen, Katrine; Boisen, Anja

doi:10.1103/physrevb.84.165307

Cited by 180 publications

(207 citation statements)

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“…The extremely high values of mechanical Q that have been reported in silicon nitride nanostrings [1][2][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][8][9] and have proved to be an invaluable platform for research into the quantum properties of nanoscale resonators.…”

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confidence: 99%

“…3(a)]. The smaller this ratio, the smaller the effective loss at the anchors-dissipation is dominated by the anchor points, be it through local curvature 3,15 or the tunneling of phonons. 25,26 Moreover, our analytical results tell us that the peak displacement versus frequency curve contains quantitative information about the dissipation.…”

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confidence: 99%

“…) lying microscopic mechanism and is consistent with a number of different scenarios for losses at the anchor points (including dissipation by phonon tunneling 25,26 and other models of local bending at the anchor points. 3,15 ) Our silicon nitride nanostrings are fabricated from stoichiometric silicon nitride deposited onto silicon dioxide on a silicon handle using LPCVD. This is cost effective as wafers are commercially available for ≈ $50 for a 100 mm wafer (Rogue Valley Microdevices).…”

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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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Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Suhel

Hauer

Biswas

et al. 2012

Applied Physics Letters

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“…The conventional understanding is that the pre-stress of the elastic medium increases the stored elastic energy without affecting intrinsic loss mechanisms [225,226].…”

Section: Stressed Nanostring Coupled To An Optical Microcavitymentioning

confidence: 99%

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Sudhir

2018

Springer Theses

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PAR Vivishek SUDHIR JOSEPH CONRAD, Heart of DarknessExperimental physics demands a certain degree of manual dexterity, the patience to tolerate the mundane, and an inexhaustible supply of optimism. Tobias hired me to work on an immensely sophisticated experiment despite any proof of my possessing these qualities; I am indebted to him for the belief he has placed in me. I would also like to acknowledge his dedication to fostering an environment where the pursuit of science is unencumbered by other worldly concerns. Stefan, Ewold and Samuel bore the brunt of a theorist trying to perform delicate experiments; the stern, yet encouraging, stewardship of this trio ensured that I enjoyed the culture shock. Dal Wilson was more than a colleague and a post-doc; his pragmatic approach to physics provided the ideal counter-point in our attempts to forge a deeper understanding of things ranging from vibration isolation to the subtleties of quantum mechanics. Without the patient efforts of Amir, Ryan and Hendrik in designing, fabricating, and testing of devices, none of the results reported here would have been possible. I hope I have been able to bequeath a better vision of the future of our experiment to Sergey. Conversations with Alexey, Daniel and Nathan have enabled me to vicariously learn how to measure microwave "photons". John Jost once taught me how to decorate a Christmas tree; since then he has imparted some wisdom on frequency metrology, and some on atomic physics. Together with Dal, Victor and Caroline have probably spent the most time with me outside the lab; it was fun to exercise an air of social normalcy with this bunch. Christophe has been an amazing sparring partner on every subject capable of being brought under scientific scrutiny.The personal space required for the pursuit of science comes through the sacrifice of many people. My family back home in India -parents, sister, grand-parents -have had to patiently wait for the brief interludes when I go home. No words can do justice to this and the very many other pleasures they have surrendered over the years for my sake. Before physics attracted me, I was charmed by someone else; I am lucky to have married her. Long time friends, mentorsAjith and Subeesh -have played pivotal roles in my being able to engage in physics; I hope to repay this enormous debt, some day.It was a privilege to have learnt from a few great teachers during my formative years. Their vision of an indelible unity in nature continues to motivate my study of physics. vii AbstractThe precision measurement of position has a long-standing tradition in physics. Cavendish's verification of the universal law of gravitation using a torsion pendulum, Perrin's confirmation of the atomic hypothesis via the precise measurement of the Brownian motion, and, the verification of the mechanical effect of electromagnetic radiation, all belong to this classical heritage. Quantum mechanics posits that the measurement of position results in an uncertain momentum; an idea developed to full maturity within the ...

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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.…”

Section: Model For Analysismentioning

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 in high-Qmicro and nanomechanical string resonators

Cited by 180 publications

References 23 publications

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Dissipation mechanisms in thermomechanically driven silicon nitride nanostrings

Quantum Limits on Measurement and Control of a Mechanical Oscillator

Thermoelastic Damping Depending on Vibration Modes of Nano Beam Resonator

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