Damping of nanomechanical resonators.

We study the transverse oscillatory modes of nanomechanical silicon nitride strings under high tensile stress as a function of geometry and mode index m≤9. Reproducing all observed resonance frequencies with classical elastic theory we extract the relevant elastic constants. Based on the oscillatory local strain we successfully predict the observed mode-dependent damping with a single frequency-independent fit parameter. Our model clarifies the role of tensile stress on damping and hints at the underlying microscopic mechanisms.

[1]  G. J. Iafrate,et al.  Phonon dynamics and phonon assisted losses in Euler-Bernoulli nanobeams , 2008 .

[2]  Eva M. Weig,et al.  Universal transduction scheme for nanomechanical systems based on dielectric forces , 2009, Nature.

[3]  Hiroshi Yamaguchi,et al.  Motion detection of a micromechanical resonator embedded in a d.c. SQUID , 2008 .

[4]  K. Jensen,et al.  An atomic-resolution nanomechanical mass sensor. , 2008, Nature Nanotechnology.

[5]  I. Wilson-Rae,et al.  Intrinsic dissipation in nanomechanical resonators due to phonon tunneling , 2007, 0710.0200.

[6]  P. M. Echternach,et al.  Nanomechanical measurements of a superconducting qubit , 2009, Nature.

[7]  M. Esashi,et al.  Energy dissipation in submicrometer thick single-crystal silicon cantilevers , 2002 .

[8]  K. Vahala,et al.  A picogram- and nanometre-scale photonic-crystal optomechanical cavity , 2008, Nature.

[9]  T. Baehr‐Jones,et al.  Harnessing optical forces in integrated photonic circuits , 2008, Nature.

[10]  Andrew G. Glen,et al.  APPL , 2001 .

[11]  J. Jäckle.  On the ultrasonic attenuation in glasses at low temperatures , 1972 .

[12]  S. Manus,et al.  Coherent detection of nonlinear nanomechanical motion using a stroboscopic downconversion technique , 2009 .

[13]  G. Steele,et al.  Carbon nanotubes as ultrahigh quality factor mechanical resonators. , 2009, Nano letters.

[14]  A. Bachtold,et al.  Ultrasensitive mass sensing with a nanotube electromechanical resonator. , 2008, Nano letters.

[15]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[16]  Scott S. Verbridge,et al.  High quality factor resonance at room temperature with nanostrings under high tensile stress , 2006 .

[17]  J. B. Hertzberg,et al.  Preparation and detection of a mechanical resonator near the ground state of motion , 2009, Nature.

[18]  F. Ayazi,et al.  An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations , 2003 .

[19]  Silvan Schmid,et al.  Damping mechanisms of single-clamped and prestressed double-clamped resonant polymer microbeams , 2008 .

[20]  Xiao Liu,et al.  Low-temperature thermal conductivity and acoustic attenuation in amorphous solids , 2002 .

[21]  A. Cleland,et al.  Noise-enabled precision measurements of a duffing nanomechanical resonator. , 2004, Physical review letters.

[22]  J. Teufel,et al.  Nanomechanical motion measured with an imprecision below that at the standard quantum limit. , 2009, Nature nanotechnology.

[23]  H. Craighead,et al.  Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators. , 2007, Nano letters.

[24]  M. Gad-el-Hak.  The MEMS Handbook , 2001 .

[25]  M. Roukes,et al.  Thermoelastic damping in micro- and nanomechanical systems , 1999, cond-mat/9909271.

[26]  H. Craighead,et al.  Stress and silicon nitride: a crack in the universal dissipation of glasses. , 2009, Physical review letters.

[27]  C. Zener.  INTERNAL FRICTION IN SOLIDS II. GENERAL THEORY OF THERMOELASTIC INTERNAL FRICTION , 1938 .

[28]  Nanomechanical displacement detection using fiber-optic interferometry , 2007 .

[29]  L. Sekaric,et al.  Measurement of mechanical resonance and losses in nanometer scale silicon wires , 1999 .