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Clamp-Tapering Increases the Quality Factor of Stressed Nanobeams
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    Clamp-Tapering Increases the Quality Factor of Stressed Nanobeams
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    • Mohammad. J. Bereyhi
      Mohammad. J. Bereyhi
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
    • Alberto Beccari
      Alberto Beccari
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
    • Sergey A. Fedorov
      Sergey A. Fedorov
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
    • Amir H. Ghadimi
      Amir H. Ghadimi
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
    • Ryan Schilling
      Ryan Schilling
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
    • Dalziel J. Wilson
      Dalziel J. Wilson
      IBM Research, Zürich, Saümerstrasse 4, Rüschlikon 8803, Switzerland
    • Nils J. Engelsen*
      Nils J. Engelsen
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
      *E-mail: [email protected]
    • Tobias J. Kippenberg*
      Tobias J. Kippenberg
      Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
      *E-mail: [email protected]
    Other Access OptionsSupporting Information (1)

    Nano Letters

    Cite this: Nano Lett. 2019, 19, 4, 2329–2333
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    https://doi.org/10.1021/acs.nanolett.8b04942
    Published February 27, 2019
    Copyright © 2019 American Chemical Society

    Abstract

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    Stressed nanomechanical resonators are known to have exceptionally high quality factors (Q) due to the dilution of intrinsic dissipation by stress. Typically, the amount of dissipation dilution and thus the resonator Q is limited by the high mode curvature region near the clamps. Here we study the effect of clamp geometry on the Q of nanobeams made of high-stress Si3N4. We find that tapering the beam near the clamps, thus locally increasing the stress, leads to an increased Q of MHz-frequency low order modes due to enhanced dissipation dilution. Contrary to recent studies of tethered-membrane resonators, we find that widening the clamps leads to a decreased Q despite increased stress in the beam bulk. The tapered-clamping approach has practical advantages compared to the recently developed “soft-clamping” technique, as it enhances the Q of the fundamental mode and can be implemented without increasing the device size.

    Copyright © 2019 American Chemical Society

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    Supporting Information

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    The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.8b04942.

    • FEM simulations of radiation losses, effect of beam width on the Q factor, statistics of yield stress of Si3N4, and observation of thin film transverse buckling in a high stress limit (r < 0.4) (PDF)

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    Cited By

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    This article is cited by 27 publications.

    1. Sushanth Kini Manjeshwar, Anastasiia Ciers, Fia Hellman, Jürgen Bläsing, André Strittmatter, Witlef Wieczorek. High-Q Trampoline Resonators from Strained Crystalline InGaP for Integrated Free-Space Optomechanics. Nano Letters 2023, 23 (11) , 5076-5082. https://doi.org/10.1021/acs.nanolett.3c00996
    2. David Hoch, Xiong Yao, Menno Poot. Geometric Tuning of Stress in Predisplaced Silicon Nitride Resonators. Nano Letters 2022, 22 (10) , 4013-4019. https://doi.org/10.1021/acs.nanolett.2c00613
    3. Anastasiia Ciers, Alexander Jung, Joachim Ciers, Laurentius Radit Nindito, Hannes Pfeifer, Armin Dadgar, André Strittmatter, Witlef Wieczorek. Nanomechanical Crystalline AlN Resonators with High Quality Factors for Quantum Optoelectromechanics. Advanced Materials 2024, 36 (44) https://doi.org/10.1002/adma.202403155
    4. Nils Johan Engelsen, Alberto Beccari, Tobias Jan Kippenberg. Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution. Nature Nanotechnology 2024, 19 (6) , 725-737. https://doi.org/10.1038/s41565-023-01597-8
    5. F. Fung, E. Rosenfeld, J. D. Schaefer, A. Kabcenell, J. Gieseler, T. X. Zhou, T. Madhavan, N. Aslam, A. Yacoby, M. D. Lukin. Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport. Physical Review Letters 2024, 132 (26) https://doi.org/10.1103/PhysRevLett.132.263602
    6. Minxing Xu, Dongil Shin, Paolo M. Sberna, Roald van der Kolk, Andrea Cupertino, Miguel A. Bessa, Richard A. Norte. High‐Strength Amorphous Silicon Carbide for Nanomechanics. Advanced Materials 2024, 36 (5) https://doi.org/10.1002/adma.202306513
    7. Toan Dinh, Mina Rais‐Zadeh, Thanh Nguyen, Hoang‐Phuong Phan, Pingan Song, Ravinesh Deo, Dzung Dao, Nam‐Trung Nguyen, John Bell. Micromachined Mechanical Resonant Sensors: From Materials, Structural Designs to Applications. Advanced Materials Technologies 2024, 9 (2) https://doi.org/10.1002/admt.202300913
    8. R. Shaniv, S. Kumar Keshava, C. Reetz, C.A. Regal. Understanding the Quality Factor of Mass-Loaded Tensioned Resonators. Physical Review Applied 2023, 19 (3) https://doi.org/10.1103/PhysRevApplied.19.L031006
    9. Roghayeh Nikbakht, Xitong Xie, Arnaud Weck, Raphael St-Gelais. High quality factor silicon nitride nanomechanical resonators fabricated by maskless femtosecond laser micromachining. Journal of Vacuum Science & Technology B 2023, 41 (2) https://doi.org/10.1116/5.0124150
    10. Ting-Yi Chen, Wei-Chang Li. A CMOS-MEMS Beam Resonator with Q > 10,000. 2023, 1151-1154. https://doi.org/10.1109/MEMS49605.2023.10052474
    11. Silvan Schmid, Luis Guillermo Villanueva, Michael Lee Roukes. Damping. 2023, 69-106. https://doi.org/10.1007/978-3-031-29628-4_3
    12. Xiong Yao, David Hoch, Menno Poot. Relaxation and dynamics of stressed predisplaced string resonators. Physical Review B 2022, 106 (17) https://doi.org/10.1103/PhysRevB.106.174109
    13. Le Tri Dat, Vinh N. T. Pham, Nguyen Duy Vy, Amir F. Payam. Frequency equation and semi‐empirical mechanical coupling strength of microcantilevers in an array. Microscopy Research and Technique 2022, 85 (9) , 3237-3244. https://doi.org/10.1002/jemt.24180
    14. Matthijs H. J. de Jong, Malte A. ten Wolde, Andrea Cupertino, Simon Gröblacher, Peter G. Steeneken, Richard A. Norte. Mechanical dissipation by substrate–mode coupling in SiN resonators. Applied Physics Letters 2022, 121 (3) https://doi.org/10.1063/5.0092894
    15. Mohammad J. Bereyhi, Amirali Arabmoheghi, Alberto Beccari, Sergey A. Fedorov, Guanhao Huang, Tobias J. Kippenberg, Nils J. Engelsen. Perimeter Modes of Nanomechanical Resonators Exhibit Quality Factors Exceeding 10 9 at Room Temperature. Physical Review X 2022, 12 (2) https://doi.org/10.1103/PhysRevX.12.021036
    16. A. Beccari, D. A. Visani, S. A. Fedorov, M. J. Bereyhi, V. Boureau, N. J. Engelsen, T. J. Kippenberg. Strained crystalline nanomechanical resonators with quality factors above 10 billion. Nature Physics 2022, 18 (4) , 436-441. https://doi.org/10.1038/s41567-021-01498-4
    17. Leo Sementilli, Erick Romero, Warwick P. Bowen. Nanomechanical Dissipation and Strain Engineering. Advanced Functional Materials 2022, 32 (3) https://doi.org/10.1002/adfm.202105247
    18. Dennis Høj, Fengwen Wang, Wenjun Gao, Ulrich Busk Hoff, Ole Sigmund, Ulrik Lund Andersen. Ultra-coherent nanomechanical resonators based on inverse design. Nature Communications 2021, 12 (1) https://doi.org/10.1038/s41467-021-26102-4
    19. Enrico Serra, Antonio Borrielli, Francesco Marin, Francesco Marino, Nicola Malossi, Bruno Morana, Paolo Piergentili, Giovanni Andrea Prodi, Pasqualina Maria Sarro, Paolo Vezio, David Vitali, Michele Bonaldi. Silicon-nitride nanosensors toward room temperature quantum optomechanics. Journal of Applied Physics 2021, 130 (6) https://doi.org/10.1063/5.0055954
    20. Mohammad J. Bereyhi, Amirali Arabmoheghi, Nils J. Engelsen, Tobias J. Kippenberg. A High Cooperativity Silicon Nitride Optomechanical Transducer. 2021, 1-1. https://doi.org/10.1109/CLEO/Europe-EQEC52157.2021.9541851
    21. Nils J. Engelsen, Aman R. Agrawal, Dalziel J. Wilson. Ultra-High-Q Nanomechanics Through Dissipation Dilution: Trends and Perspectives. 2021, 201-205. https://doi.org/10.1109/Transducers50396.2021.9495394
    22. Maximilian Bückle, Yannick S. Klaß, Felix B. Nägele, Rémy Braive, Eva M. Weig. Universal Length Dependence of Tensile Stress in Nanomechanical String Resonators. Physical Review Applied 2021, 15 (3) https://doi.org/10.1103/PhysRevApplied.15.034063
    23. Mohammad J. Bereyhi, Amirali Arabmoheghi, Nils J. Engelsen, Tobias J. Kippenberg. A high-cooperativity, nano-optomechanical system comprised of high stress Si3N4. 2021, FTh2P.6. https://doi.org/10.1364/CLEO_QELS.2021.FTh2P.6
    24. Erick Romero, Victor M. Valenzuela, Atieh R. Kermany, Leo Sementilli, Francesca Iacopi, Warwick P. Bowen. Engineering the Dissipation of Crystalline Micromechanical Resonators. Physical Review Applied 2020, 13 (4) https://doi.org/10.1103/PhysRevApplied.13.044007
    25. Vassil Tzanov, Jordi Llobet, Francesc Torres, Francesc Perez-Murano, Nuria Barniol. Multi-Frequency Resonance Behaviour of a Si Fractal NEMS Resonator. Nanomaterials 2020, 10 (4) , 811. https://doi.org/10.3390/nano10040811
    26. S. A. Fedorov, A. Beccari, N. J. Engelsen, T. J. Kippenberg. Fractal-like Mechanical Resonators with a Soft-Clamped Fundamental Mode. Physical Review Letters 2020, 124 (2) https://doi.org/10.1103/PhysRevLett.124.025502
    27. Pedram Sadeghi, Manuel Tanzer, Simon L. Christensen, Silvan Schmid. Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators. Journal of Applied Physics 2019, 126 (16) https://doi.org/10.1063/1.5111712

    Nano Letters

    Cite this: Nano Lett. 2019, 19, 4, 2329–2333
    Click to copy citationCitation copied!
    https://doi.org/10.1021/acs.nanolett.8b04942
    Published February 27, 2019
    Copyright © 2019 American Chemical Society

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