of 9
Superconducting Cavity Electromechanics on a Silicon-on-Insulator Platform
Paul B. Dieterle, Mahmoud Kalaee, Johannes M. Fink,
*
and Oskar Painter
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics,
California Institute of Technology, Pasadena, California 91125, USA
Institute for Quantum Information and Matter, California Institute of Technology,
Pasadena, California 91125, USA
(Received 15 January 2016; revised manuscript received 27 June 2016; published 22 July 2016)
Fabrication processes involving anhydrous hydrofluoric vapor etching are developed to create high-
Q
aluminum superconducting microwave resonators on free-standing silicon membranes formed from a
silicon-on-insulator wafer. Using this fabrication process, a high-impedance 8.9-GHz coil resonator is
coupled capacitively with a large participation ratio to a 9.7-MHz micromechanical resonator. Two-tone
microwave spectroscopy and radiation pressure backaction are used to characterize the coupled system in a
dilution refrigerator down to temperatures of
T
f
¼
11
mK, yielding a measured electromechanical vacuum
coupling rate of
g
0
=
2
π
¼
24
.
6
Hz and a mechanical resonator
Q
factor of
Q
m
¼
1
.
7
×
10
7
. Microwave
backaction cooling of the mechanical resonator is also studied, with a minimum phonon occupancy of
n
m
16
phonons being realized at an elevated fridge temperature of
T
f
¼
211
mK.
DOI:
10.1103/PhysRevApplied.6.014013
I. INTRODUCTION
Recent work in the field of cavity optomechanics has
shown the feasibility of using radiation pressure to cool
micromechanical objects close to their quantum ground
state
[1
3]
, to measure the quantum motion of such objects
[4,5]
, and to prepare nonclassical mechanical states using
backaction-evading techniques
[6
8]
. In a dual role,
mechanical objects may be used to create large electro-
magnetic nonlinearities for slowing
[9
12]
, squeezing
[13,14]
, or even shifting the frequency of light
[15]
.
These experiments have utilized either optical or micro-
wave photons to induce radiation pressure forces, though
recent work has coupled opto- and electromechanical
systems and realized reversible microwave-to-optical con-
version
[16]
. An outstanding problem in the field is to
realize such conversion in a fully integrated, on-chip
platform
[17
19]
.
Here, we develop a fabrication process for the creation of
high-
Q
microwave-superconducting aluminum (Al) reso-
nators on thin-film silicon membranes suitable for integra-
tion with mechanical and photonic devices. As a proof
of concept, we demonstrate parametric radiation pressure
coupling of an 8.9-GHz microwave-superconducting res-
onator to the motion of a 9.7-MHz silicon micromechanical
resonator. The electromechanical circuit, shown schemati-
cally in Fig.
1(a)
, consists of a high-impedance microwave
coil resonator capacitively coupled to the fundamental in-
plane differential mode of a pair of patterned silicon slabs.
Although not a feature exploited in the present study, the
patterned slabs also form a slotted photonic-crystal cavity
which supports an optical resonance in the 1500-nm
telecom wavelength band
[19
21]
. In principle, this
mechanical resonator (what we hereafter refer to as the
H
-slot
resonator) could simultaneously couple to optical
photons in the photonic-crystal cavity and microwave
photons in the superconducting microwave resonator.
II. DEVICE DESIGN
The
H
-slot mechanical resonator is depicted in Fig.
1(b)
,
where finite-element method (FEM) numerical simulations
[22]
are used to solve for the fundamental in-plane
mechanical motion of the structure. The resonator is formed
from a Si layer of 300-nm thickness, and consists of two
patterned slabs that are separated by a central nanoscale slot
and tethered on each end to a central clamp point. As
mentioned, the hole patterning in the two slabs produces a
localized photonic-crystal cavity. The hole patterning on
the left side of the
H
-slot resonator forms a photonic-crystal
optical waveguide which can be used to efficiently excite
the optical cavity. Aluminum electrodes are fed into the
H
-slot resonator from the right side of the structure, and
span the outer edges of the two slabs forming one-half of a
vacuum-gap capacitor [labeled
C
m
in Fig.
1(a)
]. The length
(
l
¼
13
.
5
μ
m) of the photonic-crystal slabs is chosen long
enough to support a high-
Q
optical mode and to realize a
motional capacitance on the scale of a few femtofarads. The
width (
w
) of the photonic-crystal slabs is chosen to
accommodate a number of photonic-crystal periods that
should (again) provide high-optical
Q
, but otherwise is
minimized to limit the motional mass of the resonator. The
slab photonic crystals are supported by tethers whose
*
Present address: Institute of Science and Technology Austria
(IST Austria), 3400 Klosterneuburg, Austria.
opainter@caltech.edu
PHYSICAL REVIEW APPLIED
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014013 (2016)
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=
16
=
6(1)
=
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014013-1
© 2016 American Physical Society
length (
l
t
¼
4
μ
m) and width (
w
t
¼
440
nm) produce a
simulated mechanical frequency of
ω
m
=
2
π
9
.
76
MHz for
the fundamental in-plane differential mode, compatible
with resolved-sideband pumping through the coupled
microwave circuit.
The simulated effective mass and zero-point ampli-
tude of the differential mode are
m
eff
¼
42
.
9
pg and
x
zpf
¼
4
.
5
fm, respectively. These figures include the
aluminum wires (width
¼
250
nm, thickness
¼
60
nm)
that form the vacuum-gap capacitor. By using a tuning-
fork design in which the upper and lower slabs are coupled
together at each end through the central tether clamp points,
an acoustic radiation out of the ends of the
H
-slot resonator
can be greatly reduced. Optimization of the tether clamp-
point geometry yields numerically simulated mechanical
quality factors as high as
Q
m
¼
3
.
7
×
10
7
.
The vacuum electromechanical coupling rate of the
H
-slot mechanical resonator to the microwave coil reso-
nator is given by
g
0
¼
x
zpf
ω
r
u
¼
η
x
zpf
ω
r
2
C
m
C
m
u
;
ð
1
Þ
where
u
is the generalized amplitude coordinate of the
fundamental in-plane differential mode of interest,
x
zpf
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
=
ð
2
ω
m
m
eff
Þ
p
is the zero-point amplitude of the mechani-
cal resonance, and
η
¼
C
m
=C
tot
is the participation ratio
of the motional capacitance (
C
m
) to the total capacitance
of the circuit (
C
tot
¼
C
m
þ
C
l
þ
C
s
). In addition to the
motional capacitance, the total circuit capacitance consists
of the intrinsic self-capacitance of the inductor coil (
C
l
)
and any additional stray capacitance of the circuit (
C
s
).
This ratio
and hence the electromechanical coupling
is
maximized for small
C
s
þ
C
l
and large
C
m
. We achieve a
relatively small value of coil capacitance by using a tightly
wound rectangular spiral inductor
[23,24]
with a wire width
of 550 nm and a wire-to-wire pitch of
1
μ
m. A simulation
of the entire circuit layout, including nearby ground plane,
coupling wire, and connecting wires between the coil and
the motional capacitor yields an additional stray capaci-
tance of
C
s
¼
1
.
13
fF. For a coil of 34 turns, with an
estimated inductance of
L
¼
46
.
3
nH and capacitance
C
l
¼
3
.
05
fF, connected in parallel to a motional capaci-
tance of
C
m
¼
2
.
76
fF corresponding to a vacuum gap of
d
¼
60
nm, the microwave resonance frequency of the
coupled circuit is estimated to be
ω
r
=
2
π
¼
8
.
88
GHz.
Using these circuit parameters in conjunction with a
perturbative calculation
[19,25]
of
ð
1
=C
m
Þ
C
m
=
u
based
upon FEM simulations of the differential mechanical mode
and the electric-field distribution in the vacuum-gap
capacitor, yields a calculated vacuum electromechanical
coupling strength of
g
0
=
2
π
¼
29
.
3
Hz. The trend of both
C
m
and
g
0
with gap size
d
are shown in Fig.
1(c)
.
III. DEVICE FABRICATION
The devices studied in this work are fabricated from
1
cm ×
1
cm chips diced from a high-resistivity silicon-on-
insulator (SOI) wafer manufactured by SOITEC using the
Smart Cut process
[26]
. The SOI wafer consists of a 300-
nm-thick silicon device layer with (100) surface orientation
and
p
-type (boron) doping with a specified resistivity of
500
Ω
cm. Underneath the device layer is a
3
-
μ
m buried
silicon dioxide (SiO
2
) BOX layer. The device and BOX
layers sit atop a silicon (Si) handle wafer of thickness
(a)
(b)
(c)
(d)
tot
FIG. 1. (a) Schematic of the electromechanical circuit and
measurement setup. The electromechanical circuit (yellow) is
inductively coupled to a
2
-
μ
m-wide wire (turquoise) which
shorts to ground and reflects the signal. Acronyms: SG
i
¼
microwave signal generator, VNA
¼
vector network analyzer,
SA
¼
spectrum analyzer, LNA
¼
low-noise amplifier, HEMT
¼
high-electron-mobility transistor amplifier. (b) FEM simulation
of the differential mechanical mode. In this work,
l
¼
13
.
5
μ
m,
w
t
¼
440
nm, and
l
t
¼
4
μ
m. These values give a simulated
mechanical-mode frequency of
ω
m
=
2
π
¼
9
.
76
MHz. (c) Plot of
FEM simulation values of
C
m
versus slot size
d
. (d) Plot of FEM
simulation values of
g
0
versus slot size
d
for (i)
C
s
¼
C
l
¼
0
fF
corresponding to an ideal
η
¼
1
(blue squares) and
(ii)
C
l
¼
3
.
05
fF and
C
s
¼
1
.
13
fF from FEM simulations of
the circuit (black diamonds). For these plots, the resonance
frequency is fixed at the measured frequency of
ω
r
=
2
π
¼
8
.
872
GHz. At the estimated capacitor gap of
d
60
nm from
SEM images, the theoretical values of the motional capacitance
and the vacuum coupling rate are
C
m
¼
2
.
76
fF and
g
0
=
2
π
¼
29
.
3
Hz, respectively.
DIETERLE, KALAEE, FINK, and PAINTER
PHYS. REV. APPLIED
6,
014013 (2016)
014013-2
675
μ
m and a specified resistivity of
750
Ω
cm. Both the Si
device layer and the handle wafer are grown using the
Czochralski crystal growth method.
Fabrication of the coupled coil resonator and
H
-slot
resonator can be broken down into the following six steps.
In step 1, we pattern the
H
-slot resonator using electron-
beam (
e
-beam) lithography in ZEP-520A resist, and etch
this pattern into the Si device layer using an inductively
coupled plasma-reactive ion etch (ICP-RIE). After the
ICP-RIE etch, we clean the chips with a 4-min piranha
bath and a 12-sec buffered hydrofluoric acid dip. In step 2,
we pattern the capacitor electrodes and ground-plane region
using ZEP-520A resist and use electron-beam evaporation
to deposit 60 nm of Al on the chip. In step 3, we define a
protective scaffold formed out of LOR 5B
e
-beam resist to
create the crossover regions of the spiral inductor coil. In
step 4, we pattern the inductor coil wiring in a double stack
of PMMA 495 and PMMA 950 resists and deposit 120 nm
of Al using electron-beam evaporation. In step 5, we define
a metal contact region that connects the wiring between the
capacitor electrodes and the inductive coil, then perform a
5-min ion mill before evaporating 140 nm of Al. After all
metal-layer depositions, we perform a lift-off process for
1hin
N
-methyl-2-pyrrolidone at
150
°C.
In a final step 6, we release the structure by using an
anhydrous vapor hydrofluoric (HF) acid etch using the
SPTS uEtch system. This etch is used to selectively remove
the underlying BOX layer without attacking the Al metal or
Si device layers. Not only is the removal of the SiO
2
BOX
layer desirable from the standpoint of allowing the
mechanical structure to move, but we have also found that
the presence of the underlying BOX layer results in a
significant amount of electrical loss in the microwave
resonator. Measurements of both coplanar waveguide
and lumped-element microwave resonators have shown
that the microwave
Q
factor is substantially degraded
(resonances difficult to detect;
Q
r
100
) with the BOX
layer present. Stripping off the Si device layer and forming
microwave resonators directly on the BOX layer marginally
improves the microwave
Q
factor (
Q
r
300
), whereas
stripping off both the device layer and the BOX layer
realizes microwave resonators with
Q
r
4
×
10
4
when
fabricated directly on the Si handle wafer. The release of
the structure is facilitated by patterning an array of small
(100-nm-diameter) holes into the Si device layer during
step 1. The array of release holes is on a
2
-
μ
m pitch and
covers the region containing the coil and
H
-slot resonator.
A timed etch of 75 min is used to remove
6
μ
m of SiO
2
,
resulting in the complete removal of the BOX layer
underneath the microwave circuit. A scanning electron
microscope (SEM) image of the fully released structure is
shown in Fig.
2(a)
. Enlarged images of the
H
-slot mechani-
cal resonator and undercut inductor coil are shown in
Figs.
2(b)
and
2(c)
, respectively.
IV. ELECTROMECHANICAL MEASUREMENTS
Electromechanical measurements of the fabricated coil
resonator are performed in a dilution refrigerator down
to a temperature of
T
f
11
mK. Microwave signals are
launched onto the SOI chip using a
50
-
Ω
coplanar wave-
guide. The coplanar waveguide is terminated by extending
the center conductor with a
2
-
μ
m-wide wire and then
shorting it into ground. The wire is passed within
9
μ
mof
the side of the inductor coil [see Fig.
2(a)
], thus providing
large inductive coupling to the microwave resonator. A
region extending roughly
10
μ
m from the edge of the
surrounding ground plane of the coplanar waveguide and
FIG. 2. (a) SEM image of the fabricated microwave coil resonator and
H
-slot mechanical resonator. The
H
-slot resonator region is
colored red and the undercut region is outlined in yellow. The coupling wire is colored turquoise. (b) An enlarged SEM image of the
H
-slot mechanical resonator. Inset: a close-up of the 60-nm-wide capacitor gap formed by a 250-nm-wide Al electrode on the photonic-
crystal slab and a 550-nm-wide Al electrode on the outer Si support membrane. Both wires are 60-nm thick, as is the ground plane.
(c) Cross-section image showing the suspended membrane with a coil on top. The Al forming the coil is 120-nm thick. The
3
-
μ
m-thick
dark area underneath the Si membrane is the undercut region where SiO
2
has been etched away. The bottom layer is the Si handle wafer.
SUPERCONDUCTING CAVITY ELECTROMECHANICS ON A
...
PHYS. REV. APPLIED
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inductive coupling wire is also undercut and the BOX layer
fully removed. A readout of the reflected microwave signal
is performed using the measurement scheme shown in
Fig.
1(a)
. The input line is thermalized at each stage of
the fridge with a series of attenuators to eliminate
Johnson thermal noise from the room-temperature envi-
ronment, yielding a calibrated input line attenuation of
A
¼
73
.
9
dB. The reflected signal is redirected using a
pair of circulators at the mixing chamber stage of the fridge
and then sent into an amplifier chain consisting of a HEMT
amplifier at the 4-K fridge stage and a low-noise amplifier
at room temperature. The total amplifier gain is 52 dB with
an equivalent added microwave noise photon number
of
n
add
30
.
A. Pump-probe microwave spectroscopy
Figure
3(a)
shows the measured magnitude and phase of
the reflected microwave signal versus frequency from a
vector network analyzer (VNA) used to probe the electrical
properties of the device. The microwave resonance fre-
quency is measured to be
ω
r
=
2
π
¼
8
.
872
GHz, in close
correspondence to the resonance frequency based upon the
simulated values of the coil inductance and the motional
and stray capacitance of the circuit. At the lowest base
temperature of our fridge,
T
f
11
mK, we measure an
intrinsic microwave cavity loss rate of
κ
i
=
2
π
¼
1
.
8
MHz at
an intracavity photon number on a resonance of
n
p
¼
3
.
3
,
corresponding to an internal quality factor of
Q
r;i
¼
4890
.
The external coupling rate to the resonator is measured to
be
κ
e
¼
2
.
7
MHz, putting the device well into the over-
coupled regime. We note that for similar coil resonators
(without an
H
-slot resonator and coil crossovers) which
were coupled more weakly using a transmission as opposed
to reflection geometry, we have observed internal quality
factors as high as
Q
r;i
2
×
10
4
, close to the measured
Q
values for resonators fabricated directly on the Si handle
wafer. Further investigation is needed to determine the
source of the additional microwave loss in the electro-
mechanical devices studied here.
To characterize the mechanical properties of the
H
-slot
resonator, and to determine the strength of its radiation
pressure coupling to the microwave coil resonator, we
perform two-tone pump and probe measurements as
illustrated in Fig.
3(b)
. Here, a strong drive tone of power
P
d
is applied at frequency
ω
d
on the red motional sideband
of the microwave cavity resonance while a weak probe
tone is scanned across the cavity resonance. Interference
between the anti-Stokes sideband of the drive tone and the
weak probe tone results in a form of mechanically mediated
electromagnetically induced transparency (EIT)
[9
12]
,
which for pump detuning near two-photon resonance
(
Δ
r;d
ω
r
ω
d
ω
m
) yields a reflection spectrum given
by
S
11
ð
δ
Þ¼
1
κ
e
κ
=
2
þ
i
δ
þ
2
G
2
γ
i
þ
i
2
½
δ
ð
ω
m
Δ
r;d
Þ
;
ð
2
Þ
arg
Δ
Δ
×
×
×
(a)
(c)
(d)
(b)
FIG. 3. (a) Phase and amplitude response of the microwave resonator at fridge temperature
T
f
11
mK and on-resonance cavity
photon number of
n
p
¼
3
.
3
. The intrinsic loss rate
κ
i
and external coupling rate
κ
e
are extracted by fitting the curves with a modified
Lorentzian cavity model to take into account the asymmetry in the background frequency response. (b) Schematic showing two-tone
EIT measurement procedure. A strong drive tone at frequency
ω
d
is placed on the red sideband of the microwave cavity and the cavity
response is swept by a weak VNA probe at
ω
p
. (c) Plot of the measured EIT spectra at a series of drive intracavity photon numbers for a
fridge temperature of
T
f
11
mK. From top to bottom:
n
d
¼
484
(orange curve),
1
.
20
×
10
5
(maroon curve), and
2
.
38
×
10
6
(blue
curve). Note for the blue curve at
n
d
¼
2
.
38
×
10
6
, a weakly coupled auxiliary mechanical mode can be observed. The frequency range
between the vertical red dashed lines, surrounding the auxiliary mechanical resonance, is omitted for fitting purposes. (d) Plot of the fit
values from the measured EIT spectra using Eq.
(2)
for cavity coupling rates (top), intrinsic mechanical damping rate (middle), and
parametrically enhanced coupling rate (bottom). Error bars correspond to a 95% confidence interval in the estimated fit parameter.
DIETERLE, KALAEE, FINK, and PAINTER
PHYS. REV. APPLIED
6,
014013 (2016)
014013-4