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Transduction

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Fundamentals of Nanomechanical Resonators

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Abstract

The efficient transduction of nanomechanical resonators is quintessential for any practical application. In the context of this book, transduction refers to the translation of mechanical motion to an electrical signal and vice versa for detection and actuation, respectively. In this chapter the most common underlying physical transducing mechanisms are quickly introduced. Most of these mechanisms are of an electrical nature, such as electrodynamic, electrostatic, thermoelastic, piezoresistive, or piezoelectric transduction. Nanomechanical resonators transduced with one of these techniques are therefore known as nanoelectromechanical systems (NEMS). But it is also common practice to transduce nanomechanical resonators by optic means. The full optic transduction and control of nanomechanical resonators is, e.g., employed in the field of cavity optomechanics.

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Notes

  1. 1.

    There is an interesting analogy to electrostatic to be made. The optical radiation pressure observed in optical cavity transduction schemes has an electrostatic analog in the force between two electrodes or capacitor plates (see Sect. 4.2.1.1 on page 121). And the dispersive optical force experienced by a nanomechanical waveguide in a nonuniform optical field has an analog in the force acting on a dielectric nanomechanical structure that is placed in a nonuniform electric field (see Sect. 4.2.1.2 on page 123).

  2. 2.

    UHF-120 Ultra High Frequency Vibrometer from Polytec GmbH Waldbronn Germany.

References

  1. D.V. Scheible, A. Erbe, R.H. Blick, Dynamic control and modal analysis of coupled nano-mechanical resonators. Appl. Phys. Lett. 82, 3333 (2003)

    Article  Google Scholar 

  2. S. Dohn, O. Hansen, A. Boisen, Measurement of the resonant frequency of nano-scale cantilevers by hard contact readout. Microelectron. Eng. 85 (5–6), 1390–1394 (2008)

    Article  Google Scholar 

  3. K. Jensen, J. Weldon, H. Garcia, A. Zettl, Nanotube radio. Nano Lett. 7 (11), 3508–3511 (2007)

    Article  Google Scholar 

  4. O. Cakmak, E. Ermek, N. Kilinc, S. Bulut, I. Baris, I.H. Kavakli, G.G. Yaralioglu, H. Urey, A cartridge based sensor array platform for multiple coagulation measurements from plasma. Lab Chip 15 (1), 113–120 (2015)

    Article  Google Scholar 

  5. M. Suter, O. Ergeneman, J. Zürcher, S. Schmid, A. Camenzind, B.J. Nelson, C. Hierold, Superparamagnetic photocurable nanocomposite for the fabrication of microcantilevers. J. Micromech. Microeng. 21 (2), 025023 (2011)

    Google Scholar 

  6. T.J. Kippenberg, K.J. Vahala, Cavity optomechanics: back-action at the mesoscale. Science 321 (5893), 1172–1176 (2008)

    Article  Google Scholar 

  7. M. Aspelmeyer, T.J. Kippenberg, F. Marquard, Cavity optomechanics. Rev. Mod. Phys. 86 (4), 1391–1452 (2014)

    Article  Google Scholar 

  8. A.N. Cleland, M.L. Roukes, Fabrication of high frequency nanometer scale mechanical resonators from bulk Si crystals. Appl. Phys. Lett. 69, 2653 (1996)

    Article  Google Scholar 

  9. W.J. Venstra, H.J.R. Westra, K.B. Gavan, H.S.J. der Zant, Magnetomotive drive and detection of clamped-clamped mechanical resonators in water. Appl. Phys. Lett. 95 (26), 263103 (2009)

    Google Scholar 

  10. X.L. Feng, C.J. White, A. Hajimiri, M.L. Roukes, A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator. Nat. Nanotechnol. 3 (6), 342–346 (2008)

    Article  Google Scholar 

  11. H.X. Tang, X.M.H. Huang, M.L. Roukes, M. Bichler, W. Wegscheider, Two-dimensional electron-gas actuation and transduction for GaAs nanoelectromechanical systems. Appl. Phys. Lett. 81 (20), 3879–3881 (2002)

    Article  Google Scholar 

  12. S. Schmid, T. Bagci, E. Zeuthen, J.M. Taylor, P.K. Herring, M.C. Cassidy, C.M. Marcus, L.G. Villanueva, B. Amato, A. Boisen, Y.C. Shin, J. Kong, A.S. Sørensen, K. Usami, E.S. Polzik, Single-layer graphene on silicon nitride micromembrane resonators. J. Appl. Phys. 115 (5), 054513 (2014)

    Google Scholar 

  13. P.A. Truitt, J.B. Hertzberg, C.C. Huang, K.L. Ekinci, K.C. Schwab, Efficient and sensitive capacitive readout of nanomechanical resonator arrays. Nano Lett. 7 (1), 120–126 (2007)

    Article  Google Scholar 

  14. P. Weber, J. Güttinger, I. Tsioutsios, D.E. Chang, A. Bachtold, Coupling graphene mechanical resonators to superconducting microwave cavities. Nano Lett. 14 (5), 2854–2860 (2014)

    Article  Google Scholar 

  15. T. Bagci, A. Simonsen, S. Schmid, L.G. Villanueva, E. Zeuthen, J. Appel, J.M. Taylor, A. Sørensen, K. Usami, A. Schliesser, E.S. Polzik, Optical detection of radio waves through a nanomechanical transducer. Nature 507 (7490), 81–85 (2014)

    Article  Google Scholar 

  16. J.D. Teufel, D. Li, M.S. Allman, K. Cicak, A.J. Sirois, J.D. Whittaker, R.W. Simmonds, Circuit cavity electromechanics in the strong-coupling regime. Nature 471 (7337), 204–208 (2011)

    Article  Google Scholar 

  17. C.P. Yuan, T.N. Trick, A simple formula for the estimation of the capacitance of two-dimensional interconnects in VLSI circuits. IEEE Electron Device Lett. 3 (12), 391–393 (1982)

    Article  Google Scholar 

  18. H.A. Haus, J.R. Melcher, Electromagnetic Fields and Energy (Prentice Hall, Englewood Cliffs, NJ, 1989)

    Google Scholar 

  19. T. McRae, K. Lee, G. Harris, J. Knittel, W. Bowen, Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction. Phys. Rev. A 82 (2), 1–7 (2010)

    Article  Google Scholar 

  20. S. Schmid, M. Wendlandt, D. Junker, C. Hierold, Nonconductive polymer microresonators actuated by the Kelvin polarization force. Appl. Phys. Lett. 89 (16), 163506 (2006)

    Google Scholar 

  21. Q.P. Unterreithmeier, E.M. Weig, J.P. Kotthaus, Universal transduction scheme for nanomechanical systems based on dielectric forces. Nature 458 (7241), 1001–1004 (2009)

    Article  Google Scholar 

  22. T.B. Jones, Electromechanics of Particles (Cambridge University Press, Cambridge, 1995)

    Book  Google Scholar 

  23. C.T.-C. Nguyen, R.T. Howe, An integrated CMOS micromechanical resonator high-Q oscillator. IEEE J. Solid State Circuits 34 (4), 440–455 (1999)

    Article  Google Scholar 

  24. S. Schmid, Electrostatically actuated all-polymer microbeam resonators. In: Characterization and Application. Scientific Reports on Micro and Nanosystems, vol. 6 (Der Andere, Uelvesbüll, 2009)

    Google Scholar 

  25. R.G. Knobel, A.N. Cleland, Nanometre-scale displacement sensing using a single electron transistor. Nature 424 (6946), 291–293 (2003)

    Article  Google Scholar 

  26. M.D. LaHaye, O. Buu, B. Camarota, K.C. Schwab, Approaching the quantum limit of a nanomechanical resonator. Science 304 (5667), 74 (2004)

    Google Scholar 

  27. C.A. Regal, J.D. Teufel, K.W. Lehnert, Measuring nanomechanical motion with a microwave cavity interferometer. Nat. Phys. 4 (7), 555–560 (2008)

    Article  Google Scholar 

  28. B. Witkamp, M. Poot, H.S.J. Van Der Zant, Bending-mode vibration of a suspended nanotube resonator. Nano Lett. 6 (12), 2904–2908 (2006)

    Article  Google Scholar 

  29. V. Sazonova, Y. Yaish, H. Üstünel, D. Roundy, T.A. Arias, P.L. McEuen, A tunable carbon nanotube electromechanical oscillator. Nature 431 (7006), 284–287 (2004)

    Article  Google Scholar 

  30. B. Lassagne, D. Garcia-Sanchez, A. Aguasca, A. Bachtold, Ultrasensitive mass sensing with a nanotube electromechanical resonator. Nano Lett. 8 (11), 3735–3738 (2008)

    Article  Google Scholar 

  31. V. Gouttenoire, T. Barois, S. Perisanu, J.L. Leclercq, S.T. Purcell, P. Vincent, A. Ayari, Digital and FM demodulation of a doubly clamped single-walled carbon-nanotube oscillator: towards a nanotube cell phone. Small 6 (9), 1060–1065 (2010)

    Article  Google Scholar 

  32. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, A. Bachtold, A nanomechanical mass sensor with yoctogram resolution. Nat. Nanotechnol. 7 (5), 301–304 (2012)

    Article  Google Scholar 

  33. J. Moser, J. Güttinger, A. Eichler, M.J. Esplandiu, D.E. Liu, M.I. Dykman, A. Bachtold, Ultrasensitive force detection with a nanotube mechanical resonator. Nat. Nanotechnol. 8 (7), 493–496 (2013)

    Article  Google Scholar 

  34. B. Ilic, S. Krylov, K. Aubin, R. Reichenbach, H.G. Craighead, Optical excitation of nanoelectromechanical oscillators. Appl. Phys. Lett. 86, 193114 (2005)

    Article  Google Scholar 

  35. I. Bargatin, I. Kozinsky, M.L. Roukes, Efficient electrothermal actuation of multiple modes of high-frequency nanoelectromechanical resonators. Appl. Phys. Lett. 90 (9), 093116 (2007)

    Google Scholar 

  36. I. Bargatin, E.B. Myers, J. Arlett, B. Gudlewski, M.L. Roukes, Sensitive detection of nanomechanical motion using piezoresistive signal downmixing. Appl. Phys. Lett. 86 (13), 1–3 (2005)

    Article  Google Scholar 

  37. R.L. Parker, A. Krinsky, Electrical resistance-strain characteristics of thin evaporated metal films. J. Appl. Phys. 34 (9), 2700–2708 (1963)

    Article  Google Scholar 

  38. Y. Kanda, A graphical representation of the piezoresistance coefficients in silicon. IEEE Trans. Electron Devices 29 (1), 64–70 (1982)

    Article  Google Scholar 

  39. G.C. Kuczynski, Effect of elastic strain on the electrical resistance of metals. Phys. Rev. 94 (1), 61–64 (1954)

    Article  Google Scholar 

  40. S.U. Jen, C.C. Yu, C.H. Liu, G.Y. Lee, Piezoresistance and electrical resistivity of Pd, Au, and Cu films. Thin Solid Films 434 (1–2), 316–322 (2003)

    Article  Google Scholar 

  41. P.J. French, A.G.R. Evans, Piezoresistance in polysilicon and its applications to strain gauges. Solid State Electron. 32 (1), 1–10 (1989)

    Article  Google Scholar 

  42. C.S. Smith, Piezoresistance effect in germanium and silicon. Phys. Rev. 94 (1), 42–49 (1954)

    Article  Google Scholar 

  43. R. He, P. Yang, Giant piezoresistance effect in silicon nanowires. Nat. Nanotechnol. 1 (1), 42–46 (2006)

    Article  Google Scholar 

  44. X. Yu, J. Thaysen, O. Hansen, A. Boisen, Optimization of sensitivity and noise in piezoresistive cantilevers. J. Appl. Phys. 92 (10), 6296–6301 (2002)

    Article  Google Scholar 

  45. A. Boisen, J. Thaysen, H. Jensenius, O. Hansen, Environmental sensors based on micromachined cantilevers with integrated read-out. Ultramicroscopy 82 (1–4), 11–16 (2000)

    Article  Google Scholar 

  46. M. Li, H.X. Tang, M.L. Roukes, Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications. Nat. Nanotechnol. 2 (2), 114–120 (2007)

    Article  Google Scholar 

  47. J. Curie, P. Curie, Development by pressure of polar electricity in hemihedral crystals with inclined faces. Bull. Soc. Min. de France 3, 90 (1880)

    Google Scholar 

  48. W.G. Cady, Piezoelectricity; An Introduction to the Theory and Applications of Electromechanical Phenomena in Crystals, New revised edition (Dover, New York, 1964)

    Google Scholar 

  49. W.G. Cady, The piezo-electric resonator. Proc. Inst. Radio Eng. 10 (2), 83–114 (1922)

    Google Scholar 

  50. G.A. Racine, P. Muralt, M.A. Dubois, Flexural-standing-wave elastic force motor using ZnO and PZT thin film on micromachined silicon membranes for wristwatch applications. Smart Mater. Struct. 7 (3), 404–416 (1998)

    Article  Google Scholar 

  51. M.A. Dubois, P. Muralt, Pzt thin film actuated elastic fin micromotor. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45 (5), 1169–1177 (1998)

    Article  Google Scholar 

  52. M.A. Dubois, P. Muralt, L. Sagalowicz, Aluminum nitride thin films for high frequency applications. Ferroelectrics 224 (1–4), 671–678 (1999)

    Google Scholar 

  53. F. Martin, P. Muralt, M.A. Dubois, A. Pezous, Thickness dependence of the properties of highly c-axis textured ALN thin films. J. Vac. Sci. Technol. A 22 (2), 361–365 (2004)

    Article  Google Scholar 

  54. T. Itoh, T. Suga, Development of a force sensor for atomic force microscopy using piezoelectric thin films. Nanotechnology 4, 218 (1993)

    Article  Google Scholar 

  55. A. Ansari, M. Rais-Zadeh, A thickness-mode algan/gan resonant body high electron mobility transistor. IEEE Trans. Electron Devices 61 (4), 1006–1013 (2014)

    Article  Google Scholar 

  56. A. Ansari, C.Y. Liu, C.C. Lin, H.C. Kuo, P.C. Ku, M. Rais-Zadeh, Gan micromechanical resonators with meshed metal bottom electrode. Materials 8 (3), 1204–1212 (2015)

    Article  Google Scholar 

  57. S.C. Masmanidis, R.B. Karabalin, I. De Vlaminck, G. Borghs, M.R. Freeman, M.L. Roukes, Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation. Science 317 (5839), 780–783 (2007)

    Article  Google Scholar 

  58. R.B. Karabalin, M.H. Matheny, X.L. Feng, E. Defay, G. Le Rhun, C. Marcoux, S. Hentz, P. Andreucci, M.L. Roukes, Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films. Appl. Phys. Lett. 95 (10), 103111 (2009)

    Google Scholar 

  59. N. Sinha, G.E. Wabiszewski, R. Mahameed, V.V. Felmetsger, S.M. Tanner, R.W. Carpick, G. Piazza, Piezoelectric aluminum nitride nanoelectromechanical actuators. Appl. Phys. Lett. 95 (5), 053106 (2009)

    Google Scholar 

  60. U. Zaghloul, G. Piazza, Synthesis and characterization of 10nm thick piezoelectric ALN films with high c-axis orientation for miniaturized nanoelectromechanical devices. Appl. Phys. Lett. 104 (25), 253101 (2014)

    Google Scholar 

  61. P. Ivaldi, J. Abergel, M.H. Matheny, L.G. Villanueva, R.B. Karabalin, M.L. Roukes, P. Andreucci, S. Hentz, E. Defay, 50 nm thick ALN film-based piezoelectric cantilevers for gravimetric detection. J. Micromech. Microeng. 21 (8), 085023 (2011)

    Google Scholar 

  62. R.B. Karabalin, L.G. Villanueva, M.H. Matheny, J.E. Sader, M.L. Roukes, Stress-induced variations in the stiffness of micro- and nanocantilever beams. Phys. Rev. Lett. 108 (23), 236101 (2012)

    Google Scholar 

  63. A.D. O’Connell, M. Hofheinz, M. Ansmann, R.C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J.M. Martinis, A.N. Cleland, Quantum ground state and single-phonon control of a mechanical resonator. Nature 464 (7289), 697–703 (2010)

    Article  Google Scholar 

  64. G. Piazza, P.J. Stephanou, A.P. Pisano, Piezoelectric aluminum nitride vibrating contour-mode MEMS resonators. J. Microelectromech. Syst. 15 (6), 1406–1418 (2006)

    Article  Google Scholar 

  65. G. Piazza, P.J. Stephanou, A.P. Pisano, Single-chip multiple-frequency ALN MEMS filters based on contour-mode piezoelectric resonators. J. Microelectromech. Syst. 16 (2), 319–328 (2007)

    Article  Google Scholar 

  66. G. Piazza, P.J. Stephanou, A.P. Pisano, One and two port piezoelectric higher order contour-mode MEMS resonators for mechanical signal processing. Solid State Electron. 51 (11–12), 1596–1608 (2007)

    Article  Google Scholar 

  67. A. Cho, The first quantum machine. Science 330 (6011), 1604 (2010)

    Google Scholar 

  68. J.M. Gere, B.J. Goodno, Mechanics of Materials, 8th edn. (Cengage Learning, Stamford, CT, 2013)

    Google Scholar 

  69. J. Chan, T.P.M. Alegre, A.H. Safavi-Naeini, J.T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478 (7367), 89–92 (2011)

    Article  Google Scholar 

  70. S. Gröblacher, K. Hammerer, M.R. Vanner, M. Aspelmeyer, Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature 460 (7256), 724–727 (2009)

    Article  Google Scholar 

  71. M. Li, W.H.P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, H.X. Tang, Harnessing optical forces in integrated photonic circuits. Nature 456 (7221), 480–484 (2008)

    Article  Google Scholar 

  72. G. Anetsberger, O. Arcizet, E. Gavartin, Q.P. Unterreithmeier, E.M. Weig, J.P. Kotthaus, T.J. Kippenberg, Near-field cavity optomechanics with nanomechanical oscillators. In: 2010 Conference on Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), vol. 5(12), pp. 1–9 (2010)

    Google Scholar 

  73. J.D. Thompson, B.M. Zwickl, A.M. Jayich, F. Marquardt, S.M. Girvin, J.G.E. Harris, Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452 (7183), 72–75 (2008)

    Article  Google Scholar 

  74. D.W. Carr, L. Sekaric, H.G. Craighead, Measurement of nanomechanical resonant structures in single-crystal silicon. J. Vac. Sci. Technol. B: Microelectron. Nanometer Struct. 16 (6), 3821–3824 (1998)

    Article  Google Scholar 

  75. M. Belov, N.J. Quitoriano, S. Sharma, W.K. Hiebert, T.I. Kamins, S. Evoy, Mechanical resonance of clamped silicon nanowires measured by optical interferometry. J. Appl. Phys. 103, 74304 (2008)

    Article  Google Scholar 

  76. R.W. Andrews, R.W. Peterson, T.P. Purdy, K. Cicak, R.W. Simmonds, C.A. Regal, K.W. Lehnert, Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10, 321–326 (2014)

    Article  Google Scholar 

  77. E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, T.J. Kippenberg, Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482 (7383), 63–67 (2012)

    Article  Google Scholar 

  78. M. Li, W.H.P. Pernice, H.X. Tang, Broadband all-photonic transduction of nanocantilevers. Nat. Nanotechnol. 4 (6), 377–382 (2009)

    Article  Google Scholar 

  79. M. Nordström, D.A. Zauner, M. Calleja, J. Hübner, A. Boisen, Integrated optical readout for miniaturization of cantilever-based sensor system. Appl. Phys. Lett. 91, 103512 (2007)

    Article  Google Scholar 

  80. R. Thijssen, E. Verhagen, T.J. Kippenberg, A. Polman, Plasmon nanomechanical coupling for nanoscale transduction. Nano Lett. 13, 3293–3297 (2013)

    Article  Google Scholar 

  81. J.-Y. Ou, E. Plum, J. Zhang, N.I. Zheludev, An electromechanically reconfigurable plasmonic metamaterial operating in the near-infrared. Nat. Nanotechnol. 8 (4), 252–255 (2013)

    Article  Google Scholar 

  82. R. Thijssen, T.J. Kippenberg, A. Polman, E. Verhagen, Plasmomechanical resonators based on dimer nanoantennas. Nano Lett. 15 (6), 3971–3976 (2015)

    Article  Google Scholar 

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Authors and Affiliations

  1. Vienna University of Technology, Vienna, Austria

    Silvan Schmid

  2. École Polytechnique Fédérale de, Lausanne, Switzerland

    Luis Guillermo Villanueva

  3. California Institute of Technology, Pasadena, CA, USA

    Michael Lee Roukes

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Schmid, S., Villanueva, L.G., Roukes, M.L. (2016). Transduction. In: Fundamentals of Nanomechanical Resonators. Springer, Cham. https://doi.org/10.1007/978-3-319-28691-4_4

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