Attachment losses of high Q oscillators

Photiadis, Douglas M.; Judge, John A.

doi:10.1063/1.1773928

Cited by 125 publications

(99 citation statements)

References 14 publications

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“…[Pho04], and detailed numerical analysis may be required to estimate support losses. Alternately, more sophisticated designs can be employed to isolate the beam from the supports by creating free-free beams that are attached at their nodal points [Fer05].…”

Section: Theory: Calibration Using Thermoelastic Dampingmentioning

confidence: 99%

A Microcantilever Platform for Measuring Internal Friction in Thin Films Using Thermoelastic Damping for Calibration

Sosale

Prabhakar

Fréchette

et al. 2011

J. Microelectromech. Syst.

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Measuring structural damping due to internal friction in deposited thin films can provide useful guidelines for the design of high-Q micro/nanomechanical resonators utilized used for sensing, communications and vibration energy harvesting. Such measurements can also generate valuable insights into the effects of size and confinement on the mechanisms of damping in these films. Typically, these measurements are carried out by depositing a thin film on a relatively thick cantilevered substrate and measuring the change in damping in the substrate/film composite. However, the measured damping is due to losses from several sources including support losses, clamping losses, thermoelastic damping (TED) and internal friction losses in the substrate/film composite. Accurately identifying the magnitude of internal friction in the film has been a long-standing difficulty in this field. This thesis presents the design and development of a silicon microcantilever platform to resolve this difficulty. At the core of the platform is the ability to reduce the damping in single crystal silicon microcantilevers to low levels of damping approaching the fundamental limits of dissipation established by thermoelastic damping (TED). This demonstrates that all other sources of damping (viscous losses, support losses and internal friction losses) are sufficiently low. These cantilevers can then be coated with the thin film of interest and the damping in the substrate/film composite measured. The measured damping is comprised of the thermoelastic damping in the substrate/film composite and the internal friction in the film. The former can be calculated using accurate models and the initial damping can be substracted from the measured damping in the composite to obtain an accurate estimate of the internal friction in the film. ) with values approaching the TED limit. Subsets of these beams are then used to carry out the first calibrated iii measurements on the effects of thickness and frequency on internal friction in thin films of aluminum, gold and silver at room temperature. The films ranged in thickness from 60 nm to 450 nm and were studied over frequencies from 100 Hz to 1.5 kHz. The results of this study provide two valuable guidelines for the design of low dissipation (high Q) layered composite resonators: gold leads to a smaller increase in damping than either aluminum or silver, and damping in the composite resonators can be decreased by reducing the film thickness. As a third design guideline, a strategy to control and minimize the damping by selective patterning of thin films on the resonator is described. In this work, a simple model is developed to predict the damping in partially metalized cantilevered beams and experimentally validated using the platform. The silicon microcantilever platform, and the results obtained using this platform establish a foundation for studying internal friction in thin films.iv vi

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Section: Theory: Calibration Using Thermoelastic Dampingmentioning

confidence: 99%

A Microcantilever Platform for Measuring Internal Friction in Thin Films Using Thermoelastic Damping for Calibration

Sosale

Prabhakar

Fréchette

et al. 2011

J. Microelectromech. Syst.

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“…There are several models [18][19][20] for quality factors limited by clamping losses, represented as Q clamping , for out of plane flexural cantilever resonators attached to supports of different dimensions. Jimbo et al 20 predicted the quality factor limited by clamping loss of cantilever beam of infinite width attached to semi-infinite base to be given by…”

Section: Dissipation In Microcantileversmentioning

confidence: 99%

“…For the base thickness ͑t b ͒ smaller than the wavelength of the elastic wave in the base ͑ b ͒, quality factors limited by clamping losses to the thickness-matching base are proportional to the aspect ratio of the levers ͑L / w͒. 18,19 However this model does not take into account the fact that thickness-matching bases can be overhangs where the energy can be reflected back to the oscillator. 18 Photiadis et al 19 developed a model for clamping losses of flexural cantilever resonators with finite…”

Section: Dissipation In Microcantileversmentioning

confidence: 99%

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Mechanical stiffness and dissipation in ultrananocrystalline diamond microresonators

et al. 2009

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We have characterized mechanical properties of ultrananocrystalline diamond UNCD thin films grown using the hot filament chemical vapor deposition HFCVD technique at 680 °C, significantly lower than the conventional growth temperature of 800 °C. The films have 4.3% sp2 content in the near-surface region as revealed by near edge x-ray absorption fine structure spectroscopy. The films, 1 m thick, exhibit a net residual compressive stress of 3701 MPa averaged over the entire 150 mm wafer. UNCD microcantilever resonator structures and overhanging ledges were fabricated using lithography, dry etching, and wet release techniques. Overhanging ledges of the films released from the substrate exhibited periodic undulations due to stress relaxation. This was used to determine a biaxial modulus of 8382 GPa. Resonant excitation and ring-down measurements in the kHz frequency range of the microcantilevers were conducted under ultrahigh vacuum UHV conditions in a customized UHV atomic force microscope system to determine Young's modulus as well as mechanical dissipation of cantilever structures at room temperature. Young's modulus is found to be 79030 GPa. Based on these measurements, Poisson's ratio is estimated to be 0.0570.038. The quality factors Q of these resonators ranged from 5000 to 16000. These Q values are lower than theoretically expected from the intrinsic properties of diamond. The results indicate that surface and bulk defects are the main contributors to the observed dissipation in UNCD resonators. We have characterized mechanical properties of ultrananocrystalline diamond ͑UNCD͒ thin films grown using the hot filament chemical vapor deposition ͑HFCVD͒ technique at 680°C, significantly lower than the conventional growth temperature of ϳ800°C. The films have ϳ4.3% sp 2 content in the near-surface region as revealed by near edge x-ray absorption fine structure spectroscopy. The films, ϳ1 m thick, exhibit a net residual compressive stress of 370Ϯ 1 MPa averaged over the entire 150 mm wafer. UNCD microcantilever resonator structures and overhanging ledges were fabricated using lithography, dry etching, and wet release techniques. Overhanging ledges of the films released from the substrate exhibited periodic undulations due to stress relaxation. This was used to determine a biaxial modulus of 838Ϯ 2 GPa. Resonant excitation and ring-down measurements in the kHz frequency range of the microcantilevers were conducted under ultrahigh vacuum ͑UHV͒ conditions in a customized UHV atomic force microscope system to determine Young's modulus as well as mechanical dissipation of cantilever structures at room temperature. Young's modulus is found to be 790Ϯ 30 GPa. Based on these measurements, Poisson's ratio is estimated to be 0.057Ϯ 0.038. The quality factors ͑Q͒ of these resonators ranged from 5000 to 16000. These Q values are lower than theoretically expected from the intrinsic properties of diamond. The results indicate that surface and bulk defects are the main contributors to the observed dissipation in UNCD re...

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“…Besides, it has been demonstrated that not only the nature of the clamping but also its geometry greatly determines the amount of energy that is lost through the clamping. 42,43 Therefore, lower values of F min should be achievable through the optimization of the size of the rods (by reducing their thickness) and their clamping geometry (by reducing its curvature radius or increasing the lateral size of the supporting medium).…”

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confidence: 99%

High quality factor indium oxide mechanical microresonators

Bartolomé

Cremades

Piqueras

2015

Applied Physics Letters

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The mechanical resonance behavior of as-grown In2O3 microrods has been studied in this work by in-situ scanning electron microscopy (SEM) electrically induced mechanical oscillations. Indium oxide microrods grown by a vapor–solid method are naturally clamped to an aluminum oxide ceramic substrate, showing a high quality factor due to reduced energy losses during mechanical vibrations. Quality factors of more than 105 and minimum detectable forces of the order of 10−16 N/Hz1/2 demonstrate their potential as mechanical microresonators for real applications. Measurements at low-vacuum using the SEM environmental operation mode were performed to study the effect of extrinsic damping on the resonators behavior. The damping coefficient has been determined as a function of pressure.

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Attachment losses of high Q oscillators

Cited by 125 publications

References 14 publications

A Microcantilever Platform for Measuring Internal Friction in Thin Films Using Thermoelastic Damping for Calibration

A Microcantilever Platform for Measuring Internal Friction in Thin Films Using Thermoelastic Damping for Calibration

Mechanical stiffness and dissipation in ultrananocrystalline diamond microresonators

High quality factor indium oxide mechanical microresonators

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