Abstract

Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane’s silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane’s frame so that it assumes the form of a cm-sized bridge featuring a 1-dimensional periodic pattern, whose phononic density of states is tailored to exhibit one, or several, full band gaps around the membrane’s high-Q modes in the MHz-range. We quantify the effectiveness of this phononic bandgap shield by optical interferometry measuring both the suppressed transmission of vibrations, as well as the influence of frame clamping conditions on the membrane modes. We find suppressions up to 40 dB and, for three different realized phononic structures, consistently observe significant suppression of the dependence of the membrane’s modes on sample clamping—if the mode’s frequency lies in the bandgap. As a result, we achieve membrane mode quality factors of 5 × 106 with samples that are tightly bolted to the 8 K-cold finger of a cryostat. Q × f -products of 6 × 1012 Hz at 300 K and 14 × 1012 Hz at 8 K are observed, satisfying one of the main requirements for optical cooling of mechanical vibrations to their quantum ground-state.

© 2014 Optical Society of America

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2014 (1)

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

2013 (2)

T. P. Purdy, R. W. Peterson, C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science 339, 801–804 (2013).
[CrossRef] [PubMed]

M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
[CrossRef] [PubMed]

2012 (3)

T. P. Purdy, R. W. Peterson, P.-L. Yu, C. A. Regal, “Cavity optomechanics with Si3N4 membranes at cryogenic temperatures,” New J. Phys. 14, 115021 (2012).
[CrossRef]

P.-L. Yu, T. P. Purdy, C. A. Regal, “Control of material damping in high-Q membrane microresonators,” Phys. Rev. Lett. 108, 083603 (2012).
[CrossRef] [PubMed]

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

2011 (3)

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

S. Schmid, K. D. Jensen, K. H. Nielsen, A. Boisen, “Damping mechanisms in high-Q micro and nanomechanical string resonators,” Phys. Rev. B 84, 165307 (2011).
[CrossRef]

T. P. Mayer Alegre, A. Safavi-Naeini, M. Winger, O. Painter, “Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap,” Opt. Express 19, 5658–5669 (2011).
[CrossRef]

2010 (3)

A. H. Safavi-Naeini, O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
[CrossRef] [PubMed]

Q. P. Unterreithmeier, T. Faust, J. P. Kotthaus, “Damping of nanomechanical resonators,” Phys. Rev. Lett. 105, 027205 (2010).
[CrossRef] [PubMed]

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

2009 (3)

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

D. J. Wilson, C. A. Regal, S. B. Papp, H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett. 102, 020501 (2009).
[CrossRef] [PubMed]

2008 (3)

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, 72–75 (2008).
[CrossRef] [PubMed]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B 77, 245418 (2008).
[CrossRef]

2006 (2)

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Adibi, A.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

Adiga, V. P.

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

Andrews, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

Aoubiza, B.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

Appel, J.

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,” arXiv:1307.3467 (2013).

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics, 1st ed. (Cengage Learning, 1976).

Aspelmeyer, M.

K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett. 102, 020501 (2009).
[CrossRef] [PubMed]

Bagci, T.

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,” arXiv:1307.3467 (2013).

Barton, R. A.

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

Bawaj, M.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Bellan, L. M.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Biancofiore, C.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Bleszynski Jayich, C.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

Boisen, A.

S. Schmid, K. D. Jensen, K. H. Nielsen, A. Boisen, “Damping mechanisms in high-Q micro and nanomechanical string resonators,” Phys. Rev. B 84, 165307 (2011).
[CrossRef]

Camerer, S.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Chakram, S.

S. Chakram, Y. S. Patil, L. Chang, M. Vengalattore, “Dissipation in ultrahigh quality factor SiN membrane resonators,” arXiv:1311.1234 (2013).

Chang, L.

S. Chakram, Y. S. Patil, L. Chang, M. Vengalattore, “Dissipation in ultrahigh quality factor SiN membrane resonators,” arXiv:1311.1234 (2013).

Cicak, K.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

Craighead, H. G.

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Di Giuseppe, G.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Enss, C.

C. Enss, S. Hunklinger, Low Temperature Physics (Springer, 2005), Chap. 9, pp. 283–341.

Faust, T.

Q. P. Unterreithmeier, T. Faust, J. P. Kotthaus, “Damping of nanomechanical resonators,” Phys. Rev. Lett. 105, 027205 (2010).
[CrossRef] [PubMed]

T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, E. M. Weig, “Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators,” arXiv:1310.3671 (2013).

Fefferman, A. D.

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

Galassi, M.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Genes, C.

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Girvin, S. M.

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, 72–75 (2008).
[CrossRef] [PubMed]

Hammerer, K.

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett. 102, 020501 (2009).
[CrossRef] [PubMed]

Hänsch, T. W.

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Harris, J. G. E.

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, 72–75 (2008).
[CrossRef] [PubMed]

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

Hunger, D.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Hunklinger, S.

C. Enss, S. Hunklinger, Low Temperature Physics (Springer, 2005), Chap. 9, pp. 283–341.

Ilic, B.

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

Jayich, A. M.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

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, 72–75 (2008).
[CrossRef] [PubMed]

Jensen, K. D.

S. Schmid, K. D. Jensen, K. H. Nielsen, A. Boisen, “Damping mechanisms in high-Q micro and nanomechanical string resonators,” Phys. Rev. B 84, 165307 (2011).
[CrossRef]

Jockel, A.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

Kampel, N. S.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X3, 031012 (2013).

Karuza, M.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Khelif, A.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

Kimble, H. J.

D. J. Wilson, C. A. Regal, S. B. Papp, H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

Korppi, M.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

Kotthaus, J. P.

Q. P. Unterreithmeier, T. Faust, J. P. Kotthaus, “Damping of nanomechanical resonators,” Phys. Rev. Lett. 105, 027205 (2010).
[CrossRef] [PubMed]

T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, E. M. Weig, “Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators,” arXiv:1310.3671 (2013).

Laude, V.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

Lehnert, K. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

Mader, M.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

Maldovan, M.

M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
[CrossRef] [PubMed]

M. Maldovan, E. L. Thomas, Periodic Materials and Interference Lithography for Photonics, Phononics and Mechanics (Wiley-VCH, 2009), Chap. 7, pp. 183–213.

Marquardt, F.

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, 72–75 (2008).
[CrossRef] [PubMed]

May, G. S.

G. S. May, S. M. Sze, Fundamentals of Semiconductor Fabrication, 1st ed. (John Wiley, 2003).

Mayer Alegre, T. P.

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics, 1st ed. (Cengage Learning, 1976).

Mohammadi, S.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

Molinelli, C.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Natali, R.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Nielsen, K. H.

S. Schmid, K. D. Jensen, K. H. Nielsen, A. Boisen, “Damping mechanisms in high-Q micro and nanomechanical string resonators,” Phys. Rev. B 84, 165307 (2011).
[CrossRef]

Painter, O.

Papp, S. B.

D. J. Wilson, C. A. Regal, S. B. Papp, H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

Parpia, J. M.

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Patil, Y. S.

S. Chakram, Y. S. Patil, L. Chang, M. Vengalattore, “Dissipation in ultrahigh quality factor SiN membrane resonators,” arXiv:1311.1234 (2013).

Peterson, R. W.

T. P. Purdy, R. W. Peterson, C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science 339, 801–804 (2013).
[CrossRef] [PubMed]

T. P. Purdy, R. W. Peterson, P.-L. Yu, C. A. Regal, “Cavity optomechanics with Si3N4 membranes at cryogenic temperatures,” New J. Phys. 14, 115021 (2012).
[CrossRef]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X3, 031012 (2013).

Polzik, E.

K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett. 102, 020501 (2009).
[CrossRef] [PubMed]

Polzik, E. S.

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,” arXiv:1307.3467 (2013).

Purdy, T. P.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

T. P. Purdy, R. W. Peterson, C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science 339, 801–804 (2013).
[CrossRef] [PubMed]

T. P. Purdy, R. W. Peterson, P.-L. Yu, C. A. Regal, “Cavity optomechanics with Si3N4 membranes at cryogenic temperatures,” New J. Phys. 14, 115021 (2012).
[CrossRef]

P.-L. Yu, T. P. Purdy, C. A. Regal, “Control of material damping in high-Q membrane microresonators,” Phys. Rev. Lett. 108, 083603 (2012).
[CrossRef] [PubMed]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X3, 031012 (2013).

Rakher, M. T.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

Regal, C. A.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

T. P. Purdy, R. W. Peterson, C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science 339, 801–804 (2013).
[CrossRef] [PubMed]

P.-L. Yu, T. P. Purdy, C. A. Regal, “Control of material damping in high-Q membrane microresonators,” Phys. Rev. Lett. 108, 083603 (2012).
[CrossRef] [PubMed]

T. P. Purdy, R. W. Peterson, P.-L. Yu, C. A. Regal, “Cavity optomechanics with Si3N4 membranes at cryogenic temperatures,” New J. Phys. 14, 115021 (2012).
[CrossRef]

D. J. Wilson, C. A. Regal, S. B. Papp, H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X3, 031012 (2013).

Reichenbach, R. B.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Rieger, J.

T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, E. M. Weig, “Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators,” arXiv:1310.3671 (2013).

Safavi-Naeini, A.

Safavi-Naeini, A. H.

Schliesser, A.

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,” arXiv:1307.3467 (2013).

Schmid, S.

S. Schmid, K. D. Jensen, K. H. Nielsen, A. Boisen, “Damping mechanisms in high-Q micro and nanomechanical string resonators,” Phys. Rev. B 84, 165307 (2011).
[CrossRef]

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,” arXiv:1307.3467 (2013).

Seitner, M. J.

T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, E. M. Weig, “Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators,” arXiv:1310.3671 (2013).

Shanks, W. E.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

Simmonds, R. W.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

Simonsen, A.

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,” arXiv:1307.3467 (2013).

Sørensen, A.

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,” arXiv:1307.3467 (2013).

Southworth, D. R.

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

Stannigel, K.

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Sze, S. M.

G. S. May, S. M. Sze, Fundamentals of Semiconductor Fabrication, 1st ed. (John Wiley, 2003).

Taylor, J. M.

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,” arXiv:1307.3467 (2013).

Thomas, E. L.

M. Maldovan, E. L. Thomas, Periodic Materials and Interference Lithography for Photonics, Phononics and Mechanics (Wiley-VCH, 2009), Chap. 7, pp. 183–213.

Thompson, J. D.

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, 72–75 (2008).
[CrossRef] [PubMed]

Thomson, J. D.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

Tombesi, P.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Treutlein, P.

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Tsaturyan, Y.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

Unterreithmeier, Q. P.

Q. P. Unterreithmeier, T. Faust, J. P. Kotthaus, “Damping of nanomechanical resonators,” Phys. Rev. Lett. 105, 027205 (2010).
[CrossRef] [PubMed]

Usami, K.

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,” arXiv:1307.3467 (2013).

Vengalattore, M.

S. Chakram, Y. S. Patil, L. Chang, M. Vengalattore, “Dissipation in ultrahigh quality factor SiN membrane resonators,” arXiv:1311.1234 (2013).

Verbridge, S. S.

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Villanueva, L. G.

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,” arXiv:1307.3467 (2013).

Vitali, D.

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

Weig, E. M.

T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, E. M. Weig, “Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators,” arXiv:1310.3671 (2013).

Wilson, D. J.

D. J. Wilson, C. A. Regal, S. B. Papp, H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

Wilson-Rae, I.

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B 77, 245418 (2008).
[CrossRef]

Winger, M.

Yang, C.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

Yu, P.-L.

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

P.-L. Yu, T. P. Purdy, C. A. Regal, “Control of material damping in high-Q membrane microresonators,” Phys. Rev. Lett. 108, 083603 (2012).
[CrossRef] [PubMed]

T. P. Purdy, R. W. Peterson, P.-L. Yu, C. A. Regal, “Cavity optomechanics with Si3N4 membranes at cryogenic temperatures,” New J. Phys. 14, 115021 (2012).
[CrossRef]

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X3, 031012 (2013).

Zeuthen, E.

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,” arXiv:1307.3467 (2013).

Zoller, P.

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett. 102, 020501 (2009).
[CrossRef] [PubMed]

Zwickl, B. M.

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

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, 72–75 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, C. Bleszynski Jayich, J. D. Thomson, J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125 (2008).
[CrossRef]

A. Jockel, M. T. Rakher, M. Korppi, S. Camerer, D. Hunger, M. Mader, P. Treutlein, “Spectroscopy of mechanical dissipation in micro-mechanical membranes,” Appl. Phys. Lett. 99, 143109 (2011).
[CrossRef]

P.-L. Yu, K. Cicak, N. S. Kampel, Y. Tsaturyan, T. P. Purdy, R. W. Simmonds, C. A. Regal, “A phononic bandgap shield for high-q membrane microresonators,” Appl. Phys. Lett. 104, 023510 (2014).
[CrossRef]

J. Appl. Phys. (2)

V. P. Adiga, B. Ilic, R. A. Barton, I. Wilson-Rae, H. G. Craighead, J. M. Parpia, “Approaching intrinsic performance in ultra-thin silicon nitride drum resonators,” J. Appl. Phys. 112, 064323 (2012).
[CrossRef]

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Nature (2)

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, 72–75 (2008).
[CrossRef] [PubMed]

M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
[CrossRef] [PubMed]

New J. Phys. (1)

T. P. Purdy, R. W. Peterson, P.-L. Yu, C. A. Regal, “Cavity optomechanics with Si3N4 membranes at cryogenic temperatures,” New J. Phys. 14, 115021 (2012).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (1)

K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch, “Optical lattices with micromechanical mirrors,” Phys. Rev. A 82, 021803 (2010).
[CrossRef]

Phys. Rev. B (2)

S. Schmid, K. D. Jensen, K. H. Nielsen, A. Boisen, “Damping mechanisms in high-Q micro and nanomechanical string resonators,” Phys. Rev. B 84, 165307 (2011).
[CrossRef]

I. Wilson-Rae, “Intrinsic dissipation in nanomechanical resonators due to phonon tunneling,” Phys. Rev. B 77, 245418 (2008).
[CrossRef]

Phys. Rev. E (1)

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller, “Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles,” Phys. Rev. Lett. 102, 020501 (2009).
[CrossRef] [PubMed]

D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses,” Phys. Rev. Lett. 102, 225503 (2009).
[CrossRef] [PubMed]

P.-L. Yu, T. P. Purdy, C. A. Regal, “Control of material damping in high-Q membrane microresonators,” Phys. Rev. Lett. 108, 083603 (2012).
[CrossRef] [PubMed]

Q. P. Unterreithmeier, T. Faust, J. P. Kotthaus, “Damping of nanomechanical resonators,” Phys. Rev. Lett. 105, 027205 (2010).
[CrossRef] [PubMed]

D. J. Wilson, C. A. Regal, S. B. Papp, H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

Science (1)

T. P. Purdy, R. W. Peterson, C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science 339, 801–804 (2013).
[CrossRef] [PubMed]

Other (10)

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X3, 031012 (2013).

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A88(2013).
[CrossRef]

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,” arXiv:1307.3467 (2013).

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, K. W. Lehnert, “Reversible and efficient conversion between microwave and optical light,” arXiv:1310.5276 (2013).

T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, E. M. Weig, “Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators,” arXiv:1310.3671 (2013).

S. Chakram, Y. S. Patil, L. Chang, M. Vengalattore, “Dissipation in ultrahigh quality factor SiN membrane resonators,” arXiv:1311.1234 (2013).

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Figures (9)

Fig. 1
Fig. 1

Photographs of SiN membranes held in the center of a periodically modulated silicon bridge. The silicon appears golden as the entire wafer has been coated with SiN, but it is etched from the backside only in the center to release the membrane. From left to right, three different unit cells of the periodic pattern were chosen, which we refer to as the drum structure, hollow drum structure and cross structure, respectively. The periodic arrangement of these cells leads to a bandgap in the phonon density of states, whose frequency span contains the membranes’ mechanical modes of interest.

Fig. 2
Fig. 2

Unit cells (top) and band diagrams (bottom) for the drum, hollow drum and cross structures (left to right). The bandgaps relevant for our devices have been highlighted. Central row shows displacement patterns of the unit cells, as simuated numerically, for the modes at the band edges labeled in the band diagrams. The dimensions for the unit cells presented above lay the basis for the photomasks, used in the fabrication process. Also, the unit cell sizes a are indicated (top).

Fig. 3
Fig. 3

Illustration of the fabrication process flow. The inset in step 2 shows a cross-sectional view of the wafer after the first lithography step. Prior to photoresist (AZ 5214-E) removal, the wafer is exposed to chemically active plasma, removing silicon nitride and silicon (∼ 1 μm combined thickness) in regions with photoresist openings. In the second step of photolithography we use a thicker layer of photoresist (AZ 4562), in order to protect the SiN membranes during the DRIE.

Fig. 4
Fig. 4

a) Measurement of the driven response on the defect and the frame, and the non-driven response on the defect. The data constitutes an average of 29 measurement points on the defect and the frame and has been normalized to a trace without actuation (optical shot noise, 0 dB). A calibration peak is positioned around 2.6 MHz (green). b) Illustration of a cross structure device, with the measured regions on the frame (gray) and defect (red) highlighted. c) Comparison of measured (top row) and simulated (bottom row) defect modes, indicated in the response spectrum. The colors indicates the magnitude of vertical displacement.

Fig. 5
Fig. 5

The response measurements of a cross structure (a–b) and a hollow drum structure device (c–d), accompanied with the mechanical Q-factors. The error bars for the quality factors are the standard deviation of all measured ringdowns for a given mode (typically 20 ringdown measurements for each mode). The response data is an average of 8 measurement points on the defect and the frame. The regions assumed to be the phononic bandgaps are shown in orange, while the calibration peak is indicated in green. The labels in (b) and (d) indicate the membrane modes. For the two devices the membrane sizes are (b) L ∼ 290 μm and (d) L ∼ 370 μm.

Fig. 6
Fig. 6

Frequency dependence of the Q-factor for a (2,2) inside (blue) and outside (red) a phononic bandgap. The change in frequency is induced by a temperature sweep from 303 K to 319 K (in-bandgap mode) and 326 K (mode outside the bandgap). The starting frequencies for the in-bandgap mode is f0 = 2.811 MHz and f0 = 3.022 MHz for the mode outside the bandgap.

Fig. 7
Fig. 7

The quality factors for the devices bolted firmly down, compared to the quality factors of the free-standing devices. The 77 mechanical modes are distributed among 7 devices, all three phononic structures (Fig. 1), different membrane sizes, and mode numbers. We distinguish between membrane modes (a) outside and (b) inside phononic bandgaps.

Fig. 8
Fig. 8

Results of two ringdown measurements used to determine the quality factor of a in-bandgap (2,2) mode for a cross structure device measured at 300 K (a) and 8 K (b). The frequencies are f = 2.81 × 106 Hz and f = 2.73 × 106 Hz at 300 K and 8 K, respectively. The vacuum pressure for the room temperature measurement is ∼ 5 × 10−7 mbar. The membrane size is L ∼ 285 μm.

Fig. 9
Fig. 9

Unit cell geometries found by genetic optimization. The cross structure (left) and the new geometry (right) have bandgap sizes of ∼ 540 kHz and ∼ 170 kHz, centered around ∼ 2.6 MHz and ∼ 1.1 MHz, respectively.

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