SelfAssembled Nanoparticle Drumhead
Resonators
Supporting Information
Pongsakorn Kanjanaboos
1
,
XiaoMin Lin
3
,
John E. Sader
4,5
,
Sara M. Rupich
2
,
Heinrich M. Jaeger
1
, Jeffrey R. Guest
3
1
James Franck Institute and Department of Physics, T
he University of Chicago, 929 E. 57
th
St.,
Chicago, Illinois 60637, USA.
2
James Franck Institute and Department of Chemistry
, The University of Chicago, 929 E. 57
th
St., Chicago, Illinois 60637, USA.
3
Center for Nanoscale Materials, Argonne National La
boratory, Argonne, Illinois 60439, USA.
4
Department of Mathematics and Statistics, The Univ
ersity of Melbourne, Victoria 3010,
Australia.
5
Kavli Nanoscience Institute and Department of Phys
ics, California Institute of Technology,
Pasadena, CA 91125, USA
* email: jrguest@anl.gov
Sample Preparation
: Au nanoparticles were synthesized and sizeselect
ed through a digestive
ripening process.
1
Fe
3
O
4
nanoparticles were prepared using the synthetic pr
ocedure described by
Park et al.
2
Nanoparticle monolayers were formed and deposited
onto holecontaining substrates
(siliconnitridecovered silicon chips or TEM grids
) using dryingmediated selfassembly, as
described elsewhere.
35
Briefly, the substrate is placed on a hydrophobic
surface (Teflon tape)
and covered with a water droplet (see Fig. S1). Nex
t, a droplet of nanocrystals suspended in
toluene is deposited on the side of the water dropl
et. A compact monolayer quickly forms at the
watertoluene interface. After the toluene evaporat
es, the substrate is placed on a mesh to aid
drying. As the remaining water evaporates, the mono
layer eventually touches the substrate and
freestanding membranes drape themselves across the
holes, slightly receding below the substrate
surface. Multilayer films can be deposited in a si
milar manner using higher nanoparticle
concentration.
Interferometric
Measurements
: As shown in Fig. 1c, a singlelongitudinalmode,
external
cavity diodelaser beam at
λ
=635 nm was split into a local oscillator and a pro
be beam focused
onto the sample in a diffractionlimited spot (~400n
m). We limited the optical power on the
drumheads to below ~10 FW in air and ~500nW in vacu
um to avoid destruction of the
membrane due to local heating. The reflected probe
beam was interfered with the local oscillator
in a Michelson geometry; the length of the referenc
e arm was locked onto the edge of a fringe for
maximum sensitivity. The optical power from each of
the output ports of the interferometer was
detected and subtracted from one another in a balan
ced detector to maximize the signal and
remove commonmode intensity noise. In order to max
imize the sensitivity to motion, which
scales as
S
~ (
P
loc osc
P
probe
)
1/2
, we mixed the weak probe beam with a ~100
W local oscillator.
Intrinsic thermal excitations were observed through
a spectrum analyzer, and a lockin amplifier
was used for phase sensitive detection of motion dr
iven by a piezo. The sample was mounted in a
enclosure which could be evacuated for measurements
in vacuum.
Mass Density Estimation
: The mass density
σ
is the membrane mass per area (kg/m
2
) due to the
metal cores (gold) and capping ligands. Assuming th
at ~80% of the gold core surface area is
covered by ligands and taking into account the smal
l amount of free ligands added into the
nanoparticle solution, ligands account for addition
al 10% of the weight of metal cores.
Therefore,
σ
can be estimated from
1.1 ∗ 4
3
,
where
and
are the area fraction of the membrane covered by t
he gold cores and the radius of
the core (both estimated from TEM images).
is the density of gold.
Lorentzian Fits
: Deviations from an ideal Lorentzian were observed
during piezoshaker
actuation (See Fig. 4). This is consistent with mea
surements on AFM cantilevers and NEMS
resonators where coupling between the frequency res
ponses of the piezoshaker and the resonator
structure can play a significant role.
8
Sample Number
2
a
(±0.1 Fm) 2
b
(±0.1 Fm)
f
0,1
(±0.03 MHz)
f
0,
2
(±0.03 MHz)
K
0,1
K
0,2
1
9.6
8.8
2.69
6.61
2.31 5.35
2
8.1
7.0
3.50
8.68
2.25 5.28
3
6.5
5.5
4.33
2.22
4
8.4
7.8
3.04
7.53
2.32 5.37
5
8.9
8.2
2.85
6.87
2.31 5.36
6
7.8
7.0
3.42
8.40
2.28 5.32
7
9.4
8.6
2.81
6.89
2.31 5.35
8
8.0
7.0
3.38
8.29
2.27 5.30
9
8.5
7.9
2.89
7.17
2.33 5.38
10
7.3
7.0
3.42
8.35
2.35 5.41
11
5.0
4.2
6.16
2.22
12
3.7
2.7
8.38
2.10
13
7.2
6.4
3.76
2.29
14
4.3
2.9
8.40
2.05
15
6.1
4.7
4.77
2.15
16
4.6
3.7
6.67
2.19
17
3.5
2.6
9.11
2.12
18
8.4
8.0
3.03
7.34
2.36 5.43
19
5.4
4.7
5.13
2.25
20
6.3
5.5
4.18
2.26
21
7.2
6.8
3.47
2.34
22
8.9
8.5
2.78
6.78
2.36 5.43
23
4.7
4.0
5.62
2.25
24
4.8
4.3
5.80
2.29
25
8.3
7.5
3.30
8.19
2.29 5.32
26
3.9
3.3
8.02
2.22
27
6.0
5.5
4.43
10.83
2.29 5.33
28
7.3
6.6
3.61
8.78
2.30 5.34
29
6.6
5.7
4.16
10.26
2.26 5.29
30
7.0
6.3
4.01
9.82
2.28 5.32
31
4.9
4.1
5.72
2.23
32
3.0
2.7
9.67
2.29
33
2.6
2.2
11.25
2.22
34
3.6
2.7
10.01
2.12
35
5.7
4.6
4.42
2.20
Table 1
:
Resonance peak frequencies of thermal noise measure
ments in air on gold
nanoparticle drumheads
. 2
a
and 2
b
(=
d
) are the major and minor axes measured from optica
l
images (100x) of the samples. As defined in the let
ter, the effective frequency
,
∗
≡
,
/
,
.
Κ
m,n
can be determined numerically.
6,7
The hole shapes fabricated from photolithography w
ere
not perfectly elliptical. The quoted uncertainty in
2
a
and 2
b
is from fitting ellipses to the hole
perimeters in ImageJ.
Figure S1: Membrane Fabrication
. a, Optical image of a silicon nitride chip with p
refabricated
holes. b, Schematic of the dryingmediated process
(from top to bottom). c, Schematic of a cross
section of the freestanding nanoparticle membrane,
clamped along its perimeter. The membrane
recedes slightly into the hole.
nanoparticle solution
Hydrophilic droplet (Water)
Glass
a
b
c
25 m
Figure S2: Quality Factor for a ~ 9()m Au Monolayer
. The data are from the fundamental
resonant peak, mechanically driven, at 2.5x10
6
mbar and room temperature. The peak has a
quality factor of Q ~ 500. The red line is a guide
to the eye.
Figure S3: Freestanding Ordered
Fe
3
O
4
nanoparticle monolayers
.
a
) TEM of Fe
3
O
4
nanoparticle monolayer. Inset: Optical micrograph o
f the grid. Intact drumheads are identified by
their light grey color; empty holes appear black.
b
, Power spectrum for a monolayer drumhead
4.02 4.04 4.06 4.08 4.10 4.12 4.14 4.16
f (MHz)
lA(f)l
2
(a.u.)
Q ~ 500
2
3
4
5
6
a
b
S(f) (a.u.)
f (MHz)
50 nm
near thermally excited fundamental (1,1) resonance
in vacuum (decaying background above 4
MHz is the result of a rolloff in the photodiode r
esponse for this measurement).
Figure S4: Enlarged TEM images of ~ 2()m Au Monolay
er
. The Au monolayers are well
ordered across the hole. Inset: Zoomin of the left
corner region.
References
:
(1)
Lin, X. M.; Jaeger, H. M.; Sorensen, C. M.; Kla
bunde, K. J.
J. Phys. Chem. B
2001
,
105
,
3353.
(2)
Park, J.; An, K.; Hwang, Y.; Park, J.G.; Noh,
H.J.; Kim, J.Y.; Park, J.H.; Hwang, N.
M.; Hyeon, T.
Nature Materials
2004
,
3
, 891.
(3)
Kanjanaboos, P.; JoshiImre, A.; Lin, X.M.; Ja
eger, H. M.
Nano Letters
2011
,
11
, 2567.
200 nm
100 nm
(4)
Mueggenburg, K. E.; Lin, X.M.; Goldsmith, R. H
.; Jaeger, H. M.
Nature Materials
2007
,
6
, 656.
(5)
He, J.; Kanjanaboos, P.; Frazer, N. L.; Weis, A
.; Lin, X.M.; Jaeger, H. M.
Small
2010
,
6
,
1449.
(6)
Troesch, B.; Troesch, H.
Math Comput
1973
,
27
, 755.
(7)
Neves, A. G. M.
Commun Pur Appl Anal
2010
,
9
, 611.
(8)
Bargatin, I. Highfrequency nanomechanical reso
nators for sensor applications, California
Institute of Technology, 2008.