of 13
Strong opto-electro-mechanical coupling
in a silicon photonic crystal cavity
Alessandro Pitanti,
1
,
2
Johannes M. Fink,
1
Amir H. Safavi-Naeini,
1
,
3
Jeff T. Hill,
1
,
3
Chan U. Lei,
1
Alessandro Tredicucci,
2
,
4
and Oskar
Painter
1
,
1
Institute for Quantum Information and Matter and Thomas J. Watson, Sr., Laboratory of
Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
2
NEST and Istituto Nanoscienze - CNR, Scuola Normale Superiore, Piazza San Silvestro 12,
56127 Pisa, Italy
3
Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
4
3 Dipartimento di Fisica, Universit di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
opainter@caltech.edu
Abstract:
We fabricate and characterize a microscale silicon opto-electro-
mechanical system whose mechanical motion is coupled capacitively to
an electrical circuit and optically via radiation pressure to a photonic
crystal cavity. To achieve large electromechanical interaction strength,
we implement an inverse shadow mask fabrication scheme which obtains
capacitor gaps as small as 30 nm while maintaining a silicon surface quality
necessary for minimizing optical loss. Using the sensitive optical read-out
of the photonic crystal cavity, we characterize the linear and nonlinear
capacitive coupling to the fundamental
ω
m
/
2
π
=
63 MHz in-plane flexural
motion of the structure, showing that the large electromechanical coupling
in such devices may be suitable for realizing efficient microwave-to-optical
signal conversion.
© 2015 Optical Society of America
OCIS codes:
(230.5298) Photonic crystals; (230.3120) Integrated optics devices;
(220.4880) Optomechanics; (280.4788) Optical sensing and sensors; (350.4238) Nanophoton-
ics and photonic crystals.
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1. Introduction
Microelectromechanical systems (MEMS) are a widespread technology platform with a vast
number of applications. MEMS devices are found, for instance, in a variety of hand-held elec-
tronic devices, often as accelerometers [1], microphones [2] or pressure sensors [3]. Recently,
MEMS have been proposed for energy harvesting applications [4], ultra-high resolution mass
sensors [5] and as a suitable candidate for the development of biological sensors in lab-on-
a-chip technologies [6]. New generation of MEMS have critical dimensions down below the
microscale, and into the nanoscale, opening the possibility to integrate these devices with other
nanotechnologies. In the case of nanophotonics, the emerging field of cavity optomechanics
uses the radiation pressure force to probe and control the state of a mechanical actuator em-
bedded in an optical cavity. Optomechanical nanophotonic devices, such as photonic crystal
“zipper” cavities [7] and optomechanical crystals (OMCs) [8], have been proven effective for
near quantum-limited position read-out [9, 10] and strong back-action effects, as shown by the
cooling of a mechanical mode to its quantum ground state of motion [11].
The integration of MEMS with optomechanical devices may be useful both for micropho-
tonic circuits, where MEMS may be employed to tune the optical properties of devices, as well
as for MEMS sensors, where optomechanical devices may be used for shot-noise-limited read-
out and back-action modification of the mechanical response. Moreover, an integrated MEMS-
optomechanics technology could allow for up-conversion of low-frequency electrical signals
to an optical carrier, mediated by an intermediate mechanical transducer. The ultimate goal of
such a conversion scheme would see the realization of coherent, quantum frequency translation
between an optical and microwave cavity which shares the same mechanical resonator [12–16].
Different approaches to realize such frequency translation include the use of a silicon nitride
membrane vertically stacked within an electronic and optical cavity [17, 18], and the creation
of piezoelectric nanobeam optomechanical crystals [19].
Our approach to integrating optomechanical and electromechanical devices utilizes a silicon
(Si) optomechanical photonic crystal whose mechanical degree of freedom is shared with an
electrical capacitor [20]. Using a nanoslotted planar photonic crystal slab, it is possible to local-
ize the optical field to the center slot of the slab and the capacitor to the other outer edges of the
slab, with both optical and elecrostatic fields connected to the same slab motion. This avoids
losses in the optical path, and in the case of superconducting circuits, avoids optically-induced
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3198
electrical losses from the breaking of Cooper pairs. In this kind of planar device, the capacitive
element is effectively one dimensional, being formed by two parallel metal wires. A strong
coupling between the mechanical motion and the optical or electrical mode (in what follows
we refer to the lower frequency mode as the electrical mode) can be realized by making the
electromagnetic mode volume commensurate with the acoustic wavelength of the mechanical
resonance. In the case of near-infrared optics and GHz mechanical resonances, one finds there
is a common wavelength scale, whereas for radio-frequency or microwave electrical modes,
the mechanical and electrical length scales are vastly different. In the microwave frequency
range this requires decreasing the capacitor gap size to tens of nanometers, where metallic or
superconducting boundaries are used to effectively ”squeeze” the electric field into a small
volume [21, 22].
In this Article, we push the fabrication limits of the silicon-on-insulator (SOI) cavity-electro-
optomechanics platform first presented in Ref. [20], to achieve large electromechanical cou-
pling by engineering a narrow electrode gap while retaining a high optical
Q
-factor. To this
end, we use an
inverse
shadow-mask evaporation which allows us to fabricate electrode gaps
as small as
d
30 nm. Compared to other fabrication techniques, such as focused ion beam
milling [22], this method maintains a pristine semiconductor surface, avoiding damage to the
optical resonator [23]. An outline of the paper is as follows. We begin with a review of the opti-
cal, electrical, and mechanical design of the structure, followed by a description of the methods
used for device fabrication. Optical and mechanical characterization of the device are then pre-
sented. This is followed by a characterization of both the linear and nonlinear electromechanical
coupling. We conclude by discussing the potential application of these devices for efficient and
noise-free microwave-to-optical signal conversion.
2. Design and Fabrication
As shown in Fig. 1, the electro-optomechanical device studied here is based around a silicon
thin-film photonic crystal in which a linear waveguide is formed around a central nanoscale air
slot (a so-called W1 slotted waveguide) [20, 24]. An optical resonant cavity is formed from the
waveguide by creating a defect along the axial length of the waveguide in which the parameters
of the waveguide are slowly modified. This results in an optical mode confined in the
s
80 nm air slot and localized to the defect region, as shown in the finite-element-method (FEM)
simulation of Fig. 1(a). Mechanical motion of the structure is allowed by undercutting, and
suspending the Si device layer. Two additional gaps are fabricated on the outer edge of the
two photonic crystal slabs to accommodate capacitor electrodes which connect the mechanical
motion of the slabs to an electrical circuit (see Fig. 1c). The whole slab structure is clamped
on the ends to the underlying SiO
2
(BOX) layer and Si substrate, resulting in a fundamental in-
plane mode with simulated frequency of
ω
m
/
2
π
=
67 MHz. The deformation profile,
|
Q
(
r
)
|
, of
the differential motion of the two slabs is shown in Fig. 1(b). A spatial separation between light
and metals, as in our device, has a twofold benefit. From the photonic side it makes metallic-
related losses negligible, and from the electrical side it avoids any stray light on the electrodes,
which can be crucial if superconducting materials are used.
The main difference between the device studied here and the one reported in Ref. [20] resides
in the electrode gap size, which has been reduced from 250 nm to less than 30 nm using an
inverted shadow-mask evaporation technique in a two-layer lithography process (see Fig. 1d).
In the first step of the device fabrication, a ZEP resist mask is defined with electron beam
lithography. The 220 nm Si device layer of the SOI wafer used in this work is dry etched with
an inductively-coupled SF
6
/C
4
F
8
plasma reactive-ion etching process. After a H
2
SO
4
/H
2
O
2
Piranha clean, the device layer is partially undercut in a 15 second hydrofluoric acid (HF) wet
etching step. The electrical circuit is then defined in a ZEP lift-off process using an aligned
electron beam lithography step, followed by deposition of chromium (5 nm) and gold (50 nm)
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3 | DOI:10.1364/OE.23.003196
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EXPRESS
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through optical transmission measurements using a tunable external cavity semiconductor
diode laser (Newfocus Velocity series) whose frequency tuning is calibrated with an unbal-
anced fiber Mach-Zender interferometer. Optical coupling to a given device is achieved via a
tapered and dimpled optical fiber probe, which when placed in near-field of the photonic crys-
tal cavity allows for evanescent coupling of light between the fiber and cavity [25]. An optical
transmission scan, shown in Fig. 2(b) for a typical device (device A in what follows), shows a
fundamental optical resonance with center wavelength
λ
c
=
1522
.
94 nm and intrinsic quality
factor
Q
c
=
8
.
9
×
10
4
.
The mechanical mode studied in this work is not the fundamental in-plane differential slab
mode, but rather the fundamental in-plane mode of only a single slab. This is an artifact of the
measurement technique we employ, in which to mechanically stabilize the optical fiber taper
we place it in direct contact with one of the photonic crystal slabs. This effectively decouples
the one slab from the other, and thus we only measure and actuate the motion of the free slab
without the taper on it. The fundamental in-plane mode of the free slab still modifies the air slot
gap size in the center of the photonic crystal, and thus induces a frequency shift of the optical
cavity resonance which we quantify by an optomechanical coupling parameter
g
OM
(defined
below) in units of GHz/nm. The transmitted optical power for a laser, frequency locked on the
side of the optical cavity resonance, carries a signal corresponding to the thermal Brownian
motion of the structure, as shown in Fig. 2(c) for device A. The measured fundamental me-
chanical mode of this device is centered at
ω
m
/
2
π
=
63 MHz with a corresponding quality
factor of
Q
m
=
150, limited by atmospheric pressure squeeze-film damping [26]. The smaller
peaks in the optically-transduced mechanical spectrum are (predominantly) out-of-plane slab
modes which are weakly coupled to the optical cavity resonance.
The optomechanical coupling parameter,
g
OM
, is defined as the fractional change in the en-
ergy stored in the optical resonance per unit displacement of the mechanical resonance. The
fractional energy shift (
δ
̄
U
E
) can be numerically calculated with a perturbative approach, eval-
uating an integral of the electric and displacement fields of the optical resonance over the di-
electric boundaries of the structure (here we assume no change in the magnetic energy due
to the fact that the magnetic permeability of most materials is approximately unity at optical
frequencies) [8, 28]:
δ
̄
U
E
=
́
V
(
̃
Q
(
r
)
·
~
n
)(
∆ε
|
E
|
2
∆ε
1
|
D
|
2
)
d
2
r
́
V
ε
|
E
|
2
d
3
r
,
(1)
where
ε
is the dielectric constant,
∆ε
(
ε
1
ε
2
)
is the difference in the dielectric constant
across the boundary between material 1 and material 2,
∆ε
1
(
1
/
ε
1
1
/
ε
2
)
, and
E
(
D
)
is the parallel (perpendicular) component with respect to the boundary,
V
, of the electric
(displacement) field. Here, a generalized coordinate for the mechanical resonance of
u
=
max
(
|
Q
(
r
)
|
)
is chosen, corresponding to a normalized displacement field of
̃
Q
=
Q
/
max
(
|
Q
|
)
in eq. (1). The optomechanical coupling, representing the optical resonance frequency shift per
unit displacement amplitude
u
of the mechanical resonance, is given by
g
OM
= (
1
/
2
)
ω
c
δ
̄
U
E
,
where
ω
c
is the optical resonance frequency and the factor of 1
/
2 accounts for the energy in the
magnetic field which is decoupled from the mechanical motion. For the fundamental optical
mode coupled to the fundamental in-plane mechanical mode of a single slab, the optomechani-
cal coupling is evaluated to be
g
OM
/
2
π
=
36 GHz/nm. This value is in good agreement with the
experimentally measured value of 37
±
6 GHz/nm for device A, determined from the radiation
pressure induced mechanical frequency shift (see for example Ref. [20]). Note that we have
implicitly chosen a positive amplitude
u
to correspond to outward motion of the photonic crys-
tal slabs as shown in Fig. 1(b), resulting in a reduced capacitor gap,
d
, and an increased central
slot width,
s
. In what follows we continue to use the same generalized mechanical coordinate,
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| OPTICS
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| OPTICS
EXPRESS
3202
U
es
=
Q
2
/
2
C
m
. For fixed charge, the fractional electrostatic energy shift due to motion of the
mechanical resonance can be numerically calculated for an arbitrary mechanical displacement
profile from the unperturbed fields in the capacitor using the same integral as for the calculation
of the optomechanical coupling in eq. (1), with
G
e,1
=
δ
̄
U
E
. Here we assume perfectly con-
ducting boundary conditions and zero fields within the metal wires, a good approximation at
microwave frequencies and below. Typically, one would like to couple the mechanical motion
to an electrical resonant circuit. In such a case, the coupling capacitance is closed by an inductor
(
L
) to form an LC resonant circuit of frequency
ω
LC
/
2
π
= (
LC
)
1
/
2
. Assuming capacitive cou-
pling only to the mechanical resonator, the corresponding electromechanical coupling is given
by,
g
EM
= (
ω
LC
/
2
)
G
e,1
, in direct analogy to the optomechanical coupling. Addition of the
inductor usually accompanies an unwanted parasitic capacitance,
C
s
, which is not coupled to
the mechanical resonator and which reduces
G
e,1
by a participation factor
η
e
=
C
m
/
(
C
m
+
C
s
)
.
Here we will concern ourselves primarily with the coupling parameter
G
e,1
, however, in the
conclusion we will further discuss coupling to a microwave LC resonator.
To measure the linear electromechanical coupling parameter we apply a voltage to the elec-
trodes and measure the resulting mechanical displacement using optical read-out. This is done
for both a static voltage (
V
DC
) and for a small modulated voltage (
V
AC
) at half the resonance
frequency of the fundamental in-plane differential mode. For example, Fig. 3(a) shows a water-
fall plot of the transmission through the optical cavity for an applied bias voltage of
V
DC
=
0 to
5
.
6 V for device A. In order to determine the electromechanical coupling from this tuning data,
we first consider the force exerted on the fundamental in-plane mechanical mode for a potential
difference
V
across the capacitor,
F
cap
=
1
2
C
m
V
2
G
e,1
,
(2)
where again
G
e,1
is specific to the amplitude coordinate
u
of a given mechanical resonance.
For a static voltage, the resulting mechanical displacement amplitude
u
due to
F
cap
is inversely
proportional to the mode effective spring constant,
k
eff
=
m
eff
ω
2
m
. Here,
m
eff
(
=
10
.
4 pg) is the
effective motional mass of the fundamental in-plane mechanical mode of a single slab defined
as:
m
eff
=
́
Q
(
r
)
ρ
(
r
)
Q
(
r
)
d
3
r
max
(
|
Q
|
2
)
,
(3)
where
ρ
is the mass density of Si. This definition of
m
eff
is consistent with our choice of def-
inition of
u
corresponding to the maximum amplitude of the mechanical displacement profile.
The effective spring constant, obtained by combining the simulated
m
eff
and the measured me-
chanical frequency, is equal to
k
eff
=
1
.
8 kN/m for device A. This agrees within 18% of the
full numerical simulation of the deformation under a constant load applied to the center point
of the mechanical mode. The mechanical deformation shifts the optical resonance frequency
according to,
∆ω
c,DC
(
V
) =
g
OM
C
m
G
e,1
2
k
eff
V
2
DC
=
α
V
2
DC
,
(4)
where
α
(
g
OM
C
m
G
e,1
)
/
(
2
k
eff
)
is the optical tunability of the structure.
Alternatively, if a modulated voltage
V
AC
=
V
0
cos
(
ω
AC
t
)
is applied to the capacitor, the re-
sulting mechanical displacement is filtered by the mechanical response function, with the max-
imum displacement being enhanced by the mechanical
Q
-factor for an on-resonance capacitive
force,
ω
AC
=
ω
m
/
2. In this case, the time-average of the optical transmission spectrum assumes
a double-dip lineshape (see Ref. [20]) with a separation between the minima given by,
∆ω
c,AC
=
α
Q
m
V
2
0
.
(5)
#228907 - $15.00 USD
Received 3 Dec 2014; revised 28 Jan 2015; accepted 29 Jan 2015; published 3 Feb 2015
©
2015
OSA
9 Feb
2015
| Vol.
23,
No.
3 | DOI:10.1364/OE.23.003196
| OPTICS
EXPRESS
3203
#228907 - $15.00 USD
Received 3 Dec 2014; revised 28 Jan 2015; accepted 29 Jan 2015; published 3 Feb 2015
©
2015
OSA
9 Feb
2015
| Vol.
23,
No.
3 | DOI:10.1364/OE.23.003196
| OPTICS
EXPRESS
3204
5. Nonlinear electromechanical coupling
The small capacitor gaps in our devices makes nonlinear terms in the electromechanical in-
teraction relevant. Electromechanical nonlinearities can be used to generate squeezing [29–31]
and mechanical parametric amplification [32, 33], as well as for logic operation in the classi-
cal [34] and quantum regime [35]. Assuming the voltage across the capacitor electrodes follows
the applied voltage during the mechanical motion of the electrodes (This assumption requires
that the drive circuit be able to provide the current necessary to the electrodes such that as the
electrodes undergo mechanical motion the capacitor voltage follows the applied voltage. This
feedback from the drive circuit modifies the electrostatic force curve similar to the optical feed-
back in cavity-optomechanics, resulting in a dynamic spring effect. A wholly different force
curve and nonlinear coupling parameter results if we assume a closed capacitor system with
fixed charge on the electrodes.), and expanding the capacitive force to linear order in amplitude
u
, we can define the second order nonlinear coupling parameter as
G
e,2
= (
1
/
C
m
)(
2
C
m
/
u
2
)
.
The effective spring constant of the mechanical system is
k
tot
=
k
eff
(
1
/
2
)
C
m
V
2
G
e,2
[29, 36],
resulting in an electrical shift of the
mechanical
resonance frequency given by,
∆ω
m
=
(
ω
m
C
m
G
e,2
4
k
eff
)
V
2
=
β
V
2
,
(6)
where
β
≡−
(
ω
m
C
m
G
e,2
)
/
(
4
k
eff
)
is defined as the
mechanical
tunability. From the mechanical
frequency shift versus applied voltage, we can obtain the nonlinear coupling parameter
G
e,2
in
a similar fashion to that used to determine the linear parameter
G
e,1
.
Before proceeding to measurements of the nonlinear electromechanical coupling, it is in-
structive to consider again the capacitor force expression. If a voltage signal with mixed AC
and DC components is fed to the capacitor an additional resonant term appears:
F
cap
V
2
=
V
2
DC
+
V
2
AC
+
2
V
DC
V
AC
.
(7)
The third, mixed term, explicitly given by 2
V
DC
V
0
cos
(
ω
AC
t
)
, has a maximum mechanical re-
sponse at
ω
AC
=
ω
m
and can be suppressed or enhanced by controlling the DC bias. This
is a useful and well known property, which allows control of electromechanical nonlineari-
ties [37, 38]. The resonant nature of this mixed term is also useful to perform homodyne de-
tection of the coherent mechanical oscillations induced by an AC drive. To this end, we use a
network analyzer (NA) of which port 1 is connected to the capacitor electrodes while port 2 is
connected to the optical photodetector used to read-out the mechanical motion (see Fig. 2(a)).
The S-parameter
S
21
in such a scheme will therefore carry the amplitude and phase response of
the mechanical resonator to the electrical driving force.
Measurements of the nonlinear electromechanical response were performed on device B,
whose fundamental in-plane mechanical mode has a resonance frequency of
ω
m
/
2
π
49 MHz,
intrinsic mechanical
Q
-factor
Q
m
=
344, and spring constant
k
eff
=
1
.
09 kN/m. In order to
avoid spurious transduction of large amplitude mechanical motion in these measurements, a
fixed probe laser wavelength detuned
50 nm from the optical resonance of device B is used.
Measurement of the electrostatic modification to the mechanical frequency is first measured,
using a weak AC drive voltage of
V
0
<
1 mV
rms
and DC voltages varying from 0
.
2 to 6 V. The
frequency of
V
AC
is swept using port 1 of the NA and the photodetected signal of the mechani-
cal response is measured on port 2. For these drive levels (
V
DC

V
0
), the mechanical frequency
shift in eq. (6) is dominated by the
V
2
DC
term. As can be seen in the waterfall plot of Fig. 4(a),
the mechanical resonance frequency of device B red-shifts with applied DC voltage, corre-
sponding to electrostatic softening. The extracted resonance frequency scales quadratically with
the applied DC bias, yielding a mechanical tunability parameter of
β
/
2
π
=
3
.
989 kHz/V
2
.
#228907 - $15.00 USD
Received 3 Dec 2014; revised 28 Jan 2015; accepted 29 Jan 2015; published 3 Feb 2015
©
2015
OSA
9 Feb
2015
| Vol.
23,
No.
3 | DOI:10.1364/OE.23.003196
| OPTICS
EXPRESS
3205