Resonant amplification of vibrational amplitude underpins the application of nanomechanical sensors. For cantilever sensors, this amplification is widely reported to be equal to the sensor’s quality factor, which strongly underestimates its true value. Here, we present a simple analytical formula for this amplification factor, valid for three-dimensional resonators of arbitrary shape, that will find utility in practice.
REFERENCES
1.
R.
Garcia
and R.
Perez
, Surf. Sci. Rep.
47
, 197
(2002
).2.
F. J.
Giessibl
, Rev. Mod. Phys.
75
, 949
(2003
).3.
C.
Acar
and A.
Shkel
, MEMS Vibratory Gyroscopes: Structural Approaches to Improve Robustness
(Springer
, 2009
).4.
M. S.
Hanay
, S.
Kelber
, A. K.
Naik
, D.
Chi
, S.
Hentz
, E. C.
Bullard
, E.
Colinet
, L.
Duraffourg
, and M. L.
Roukes
, Nat. Nanotechnol.
7
, 602
(2012
).5.
M. S.
Hanay
, S. I.
Kelber
, C. D.
O’Connell
, P.
Mulvaney
, J. E.
Sader
, and M. L.
Roukes
, Nat. Nanotechnol.
10
, 339
(2015
).6.
J. P.
Cleveland
, B.
Anczykowski
, A. E.
Schmid
, and V. B.
Elings
, Appl. Phys. Lett.
72
, 2613
(1998
).7.
B.
Anczykowski
, B.
Gotsmann
, H.
Fuchs
, J. P.
Cleveland
, and V. B.
Elings
, Appl. Surf. Sci.
140
, 376
(1999
).8.
A.
Sebastian
, M. V.
Salapaka
, D. J.
Chen
, and J. P.
Cleveland
, J. Appl. Phys.
89
, 6473
(2001
).9.
S.
Morita
, R.
Wiesendanger
, and E.
Meyer
, Noncontact Atomic Force Microscopy
(Springer-Verlag
, Berlin
, 2002
).10.
H.
Holscher
, Appl. Phys. Lett.
89
, 123109
(2006
).11.
S.
Jesse
, S. V.
Kalinin
, R.
Proksch
, A. P.
Baddorf
, and B. J.
Rodriguez
, Nanotechnology
18
, 435503
(2007
).12.
H.
Holscher
and U. D.
Schwarz
, Int. J. Non-Linear Mech.
42
, 608
(2007
).13.
Y.
Song
and B.
Bhushan
, J. Phys.: Condens. Matter
20
, 225012
(2008
).14.
F. J.
Giessibl
, Rev. Sci. Instrum.
90
, 011101
(2019
).15.
The quality factor is not commonly measured from the ratio of the resonator and drive amplitudes, though this is possible.
16.
D.
Kiracofe
and A.
Raman
, Nanotechnology
22
, 485502
(2011
).17.
A.
Maali
and R.
Boisgard
, J. Appl. Phys.
114
, 144302
(2013
).18.
20.
nth flexural mode, where Cn is the nth root of cos Cn cosh Cn = −1. This shows that the coefficient of 1.566 in Eq. (3) depends strongly on the mode number, n.
21.
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