Scaling of dissipation in megahertz-range micromechanical diamond oscillators

Imboden, Matthias; Mohanty, Pritiraj; Gaidarzhy, A.; Rankin, Janet; Sheldon, Brian W.

doi:10.1063/1.2732163

Cited by 47 publications

(54 citation statements)

References 15 publications

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“…Higher dissipation in the NCD resonators can be attributed to the fact that as the resonator dimensions become smaller, dissipation due to surface effects also play a role. 15,16 This argument is supported by the investigations of scaling of dissipation with the dimension of the NCD fixed-fixed resonators, as reported by Imboden et al 44 Factors that contribute to the higher dissipation in highfrequency fixed-fixed flexural resonators may also include clamping losses, losses that occur at metal-diamond interfaces between metal-diamond interfaces, and the dissipation in the metal layer of the composite beams. 15 Cantilever resonator structures made from tetrahedral amorphous carbon ͑ta-C͒, which have a significant sp 3 content, ͑80% sp 3 , 20% sp 2 ͒ showed a lower Q of 3500.…”

Section: Dissipation In Diamondsupporting

confidence: 63%

“…11 Recent investigation 36 of the quality factor of metalcoated UNCD fixed-fixed beams at extremely low temperatures ͑Ͻ10 K͒ indicated the presence of TLS processes. Table II summarizes the results reported by other groups [9][10][11]24,44,45 as compared to ours for different flexural beams fabricated using NCD, UNCD, or ta-C films.…”

Section: Dissipation In Diamondmentioning

confidence: 76%

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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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Section: Dissipation In Diamondsupporting

confidence: 63%

Section: Dissipation In Diamondmentioning

confidence: 76%

Mechanical stiffness and dissipation in ultrananocrystalline diamond microresonators

et al. 2009

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“…Figure 2 a) depicts the temperature dependence for three resonance frequencies; the insert illustrates how dissipation varies with frequency at two applied magnetic field strengths. Short, doubly-clamped beams often suffer from clamping losses and dissipation is dominated by energy loss into the pads [17]. For this case, dissipation rapidly grows with decreasing resonator length.…”

Section: Resultsmentioning

confidence: 99%

Evidence of universality in the dynamical response of micromechanical diamond resonators at millikelvin temperatures

Imboden

Mohanty

2009

Phys. Rev. B

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We report kelvin to millikelvin-temperature measurements of dissipation and frequency shift in megahertz-range resonators fabricated from ultra-nanocrystalline diamond. Frequency shift δf /f0 and dissipation Q −1 demonstrate temperature dependence in the millikelvin range similar to that predicted by the glass model of tunneling two level systems. The logarithmic temperature dependence of δf /f0 is in good agreement with such models, which include phonon relaxation and phonon resonant absorption. Dissipation shows a weak power law, Q −1 ∝ T 1 3 , followed by saturation at low temperature. A comparison of both the scaled frequency shift and dissipation in equivalent micromechanical structures made of single-crystal silicon and gallium arsenide indicates universality in the dynamical response.

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“…Hutchinson et al [5] measured the temperature dependence of dissipation of metal / nanocrystalline diamond (NCD) composite fixed-fixed beams which showed the presence of a Debye peak at 55 K and a dramatic increase in dissipation above 100 K. However for these high frequency (MHz) beams they measured a lower quality factor (Q∼3000, at room temperature) than the low frequency UNCD cantilever resonators. Higher dissipation in these high frequency resonator beams has been attributed to surface effects and the clamping losses [26,27] is supported by investigations of the scaling of dissipation with the dimensions of NCD fixed-fixed resonators by Imboden et al [28]. Factors that contribute to the higher dissipation in high frequency resonators may also include TED, and the dissipation in the metal layer of the composite beams.…”

Section: Dissipation In Uncd Cantileversmentioning

confidence: 55%

Temperature dependence of mechanical stiffness and dissipation in ultrananocrystalline diamond

et al. 2009

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Ultrananocrystalline diamond (UNCD) films are promising for radio frequency micro electro mechanical systems (RF-MEMS) resonators due to the extraordinary physical properties of diamond, such as high Young's modulus, quality factor, and stable surface chemistry. UNCD films used for this study are grown on 150 mm silicon wafers using hot filament chemical vapor deposition (HFCVD) at 680°C. UNCD fixed free (cantilever) resonator structures designed for the resonant frequencies in the kHz range have been fabricated using conventional microfabrication techniques and are wet released. Resonant excitation and ring down measurements in the temperature range of 138 K to 300 K were conducted under ultra high vacuum (UHV) conditions in a custom built UHV AFM stage to determine the temperature dependence of Young's Modulus and dissipation (quality factor) in these UNCD cantilever structures. We measured a temperature coefficient of frequency (TCF) of 121 and 133 ppm/K for the cantilevers of 350 ìm and 400 ìm length respectively. Young's modulus of the cantilevers increased by about 3.1% as the temperature was reduced from 300 K to 138 K. This is the first such measurement for UNCD and suggests that the nanostructure plays a significant role in modifying the thermo-mechanical response of the material. The quality factor of these resonators showed a moderate increase as the cantilevers were cooled from 300 K to 138 K. The results suggest that surface and bulk defects significantly contribute to the observed dissipation in UNCD resonators. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Ultrananocrystalline diamond (UNCD) films are promising for radio frequency micro electro mechanical systems (RF-MEMS) resonators due to the extraordinary physical properties of diamond, such as high Young's modulus, quality factor, and stable surface chemistry. UNCD films used for this study are grown on 150 mm silicon wafers using hot filament chemical vapor deposition (HFCVD) at 680°C. UNCD fixed free (cantilever) resonator structures designed for the resonant frequencies in the kHz range have been fabricated using conventional microfabrication techniques and are wet released. Resonant excitation and ring down measurements in the temperature range of 138 K to 300 K were conducted under ultra high vacuum (UHV) conditions in a custom built UHV AFM stage to determine the temperature dependence of Young's Modulus and dissipation (quality factor) in these UNCD cantilever structures. We measured a temperature coefficient of frequency (TCF) of 121 and 133 ppm/K for the cantilevers of 350 μm and 400 μm length respectively. Young's modulus of the cantilevers increased by about 3.1% as the temperature was reduced from 300 K to 138 K. This is the first such measurement for UNCD and suggests that the nanostructure plays a significant role in modifyi...

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Scaling of dissipation in megahertz-range micromechanical diamond oscillators

Cited by 47 publications

References 15 publications

Mechanical stiffness and dissipation in ultrananocrystalline diamond microresonators

Mechanical stiffness and dissipation in ultrananocrystalline diamond microresonators

Evidence of universality in the dynamical response of micromechanical diamond resonators at millikelvin temperatures

Temperature dependence of mechanical stiffness and dissipation in ultrananocrystalline diamond

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