We investigate the influence of gold thin-films subsequently deposited on a set of initially bare, doubly clamped, high-stress silicon nitride string resonators at room temperature. Analytical expressions for resonance frequency, quality factor and damping for both in- and out-of-plane flexural modes of the bilayer system are presented, which allows for the determination of effective elastic parameters of the composite structure from our experimental data. We find the inverse quality factor to scale linearly with the gold film thickness, indicating that the overall damping is governed by losses in the metal. Correspondingly, the mechanical linewidth increases by more than one order of magnitude compared to the bare silicon nitride string resonator. Furthermore, we extract mechanical quality factors of the gold film for both flexural modes and show that they can be enhanced by complete deposition of the metal in a single step, suggesting that surface and interface losses play a vital role in metal thin-films.
References
1.
K. L.
Ekinci
and M. L.
Roukes
, Rev. Sci. Instrum.
76
, 061101
(2005
).2.
S. S.
Verbridge
, J. M.
Parpia
, R. B.
Reichenbach
, L. M.
Bellan
, and H. G.
Craighead
, J. Appl. Phys.
99
, 124304
(2006
).3.
Q. P.
Unterreithmeier
, T.
Faust
, and J. P.
Kotthaus
, Phys. Rev. Lett.
105
, 027205
(2010
).4.
M.
Imboden
and P.
Mohanty
, Phys. Rep.
534
, 89
(2014
).5.
R.
Lifshitz
and M. L.
Roukes
, Phys. Rev. B
61
, 5600
(2000
).6.
I.
Wilson-Rae
, Phys. Rev. B
77
, 245418
(2008
).7.
J.
Rieger
, A.
Isacsson
, M. J.
Seitner
, J. P.
Kotthaus
, and E. M.
Weig
, Nat. Commun.
5
, 3345
(2014
).8.
J.
Yang
, T.
Ono
, and M.
Esashi
, Appl. Phys. Lett.
77
, 3860
(2000
).9.
L. G.
Villanueva
and S.
Schmid
, e-prints arXiv:1405.6115
[cond-mat.mes-hall] (2014
).10.
R. O.
Pohl
, X.
Liu
, and E.
Thompson
, Rev. Mod. Phys.
74
, 991
(2002
).11.
R.
Vacher
, E.
Courtens
, and M.
Foret
, Phys. Rev. B
72
, 214205
(2005
).12.
T.
Faust
, J.
Rieger
, M. J.
Seitner
, J. P.
Kotthaus
, and E. M.
Weig
, Phys. Rev. B
89
, 100102
(2014
).13.
A. N.
Cleland
and M. L.
Roukes
, Sens. Actuators, A
72
, 256
(1999
).14.
J.
Rieger
, T.
Faust
, M. J.
Seitner
, J. P.
Kotthaus
, and E. M.
Weig
, Appl. Phys. Lett.
101
, 103110
(2012
).15.
C. A.
Regal
, J. D.
Teufel
, and K. W.
Lehnert
, Nat. Phys.
4
, 555
(2008
).16.
O.
Kálmán
, T.
Kiss
, J.
Fortágh
, and P.
Domokos
, Nano Lett.
12
, 435
(2012
).17.
A.
Kamra
, M.
Schreier
, H.
Huebl
, and S. T. B.
Goennenwein
, Phys. Rev. B
89
, 184406
(2014
).18.
R.
Sandberg
, K.
Mølhave
, A.
Boisen
, and W.
Svendsen
, J. Micromechan. Microeng.
15
, 2249
(2005
).19.
F. W.
Beil
, R. H.
Blick
, A.
Wixforth
, W.
Wegscheider
, D.
Schuh
, and M.
Bichler
, EPL
76
, 1207
(2006
).20.
G.
Sosale
, K.
Das
, L.
Fréchette
, and S.
Vengallatore
, J. Micromechan. Microeng.
21
, 105010
(2011
).21.
P.-L.
Yu
, T. P.
Purdy
, and C. A.
Regal
, Phys. Rev. Lett.
108
, 083603
(2012
).22.
F.
Hocke
, M.
Pernpeintner
, X.
Zhou
, A.
Schliesser
, T. J.
Kippenberg
, H.
Huebl
, and R.
Gross
, Appl. Phys. Lett.
105
, 133102
(2014
).23.
W.
Weaver
, S. P.
Timoshenko
, and D. H.
Young
, Vibration Problems in Engineering
, 5th ed. (John Wiley & Sons
, 1990
).24.
See supplementary material at http://dx.doi.org/10.1063/1.4902430 for theoretical derivations and additional information.
25.
J. M.
Gere
and B. J.
Goodno
, Mechanics of Materials
(Cenegage Learning
, 2013
), Chap. 6.3.26.
X.-S.
Wang
and T.-Y.
Zhang
, Metall. Mater. Trans. A
38
, 2273
(2007
).27.
Y. T.
Yang
, K. L.
Ekinci
, X. M. H.
Huang
, L. M.
Schiavone
, M. L.
Roukes
, C. A.
Zorman
, and M.
Mehregany
, Appl. Phys. Lett.
78
, 162
(2001
).28.
T. S.
Biswas
, A.
Suhel
, B. D.
Hauer
, A.
Palomino
, K. S. D.
Beach
, and J. P.
Davis
, Appl. Phys. Lett.
101
, 093105
(2012
).29.
Springer Handbook of Condensed Matter and Materials Data
, edited by W.
Martienssen
and H.
Warlimont
(Springer
, Berlin Heidelberg, New York
, 2005
).30.
C. A.
Neugebauer
, J. Appl. Phys.
31
, 1096
(1960
).31.
X.
Liu
, E.
Thompson
, B. E.
White
, Jr., and R. O.
Pohl
, Phys. Rev. B
59
, 11767
(1999
).32.
A. B.
Hutchinson
, P. A.
Truitt
, K. C.
Schwab
, L.
Sekaric
, J. M.
Parpia
, H. G.
Craighead
, and J. E.
Butler
, Appl. Phys. Lett.
84
, 972
(2004
).33.
X. L.
Feng
, C. A.
Zorman
, M.
Mehregany
, and M. L.
Roukes
, Tech. Digest, Solid-State Sensors, Actuators and Microsystems Workshop (Hilton Head 2006), 342–346, South Carolina, June 4–8 (2006
); e-print arXiv:hep-th/0606711.34.
B. E.
White
, Jr. and R. O.
Pohl
, Phys. Rev. Lett.
75
, 4437
(1995
).35.
A.
Olkhovets
, S.
Evoy
, D. W.
Carr
, J. M.
Parpia
, and H. G.
Craighead
, J. Vac. Sci. Technol. B: Microelectron. Nanometer Struct.
18
, 3549
(2000
).36.
F.
Hoehne
, Y. A.
Pashkin
, O.
Astafiev
, L.
Faoro
, L. B.
Ioffe
, Y.
Nakamura
, and J. S.
Tsai
, Phys. Rev. B
81
, 184112
(2010
).37.
A.
Venkatesan
, K. J.
Lulla
, M. J.
Patton
, A. D.
Armour
, C. J.
Mellor
, and J. R.
Owers-Bradley
, Phys. Rev. B
81
, 073410
(2010
).38.
S.
Prabhakar
and S.
Vengallatore
, J. Micromech. Microengineering
17
, 532
(2007
).39.
J. L.
Arlett
, E. B.
Myers
, and M. L.
Roukes
, Nat. Nanotechnol.
6
, 203
(2011
).40.
Z.
Darázs
, Z.
Kurucz
, O.
Kálmán
, T.
Kiss
, J.
Fortágh
, and P.
Domokos
, Phys. Rev. Lett.
112
, 133603
(2014
).41.
E.
Collin
, J.
Kofler
, S.
Lakhloufi
, S.
Pairis
, Y. M.
Bunkov
, and H.
Godfrin
, J. Appl. Phys.
107
, 114905
(2010
).© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
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