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INTERNAL ELECTROSTATIC TRANSDUCTION FOR BULK-MODE MEMS RESONATORS
INTERNAL ELECTROSTATIC TRANSDUCTION FOR
BULK-MODE MEMS RESONATORS

Sunil A. Bhave and Roger T. Howe
Berkeley Sensor & Actuator Center, 497 Cory Hall, University of California, Berkeley, CA 94720

ABSTRACT
This paper demonstrates a new approach to electrostatic drive and
detection of bulk acoustic resonators in which the electrode-gaps
are filled with a high dielectric constant material. Internal
electrostatic transduction
has much higher efficiency than air-gap
electrostatic transduction for bulk-mode resonators, which results
in improved electrical performance. As a proof-of-concept, we
demonstrate this phenomenon by electrostatic actuation of a
1.9GHz AlN ( ~ 9) film bulk acoustic resonator (FBAR).
INTRODUCTION
Surface micromachining technology supports fabrication of multi-
frequency, electrostatically transduced lateral bulk resonators. A
single mask can include multi-frequency filters, oscillators and
mixers. However, lateral bulk acoustic resonators have very large
motional resistance due to reduced transducer area [1] and
inefficient air-gap electrostatic transduction (compared to
piezoelectric transduction [2]). Creative approaches to increasing
transducer area include forming a coupled array of resonators [3]
and large diameter bulk annular ring resonators [4]. However, to
reach motional resistances on the order of 50 , we would need a
coupled array of 100 resonators or a 400 m diameter ring
resonator. The signal routing challenges for these structures will be
daunting at GHz frequencies and the chip area occupied by these
resonator designs will be larger than an FBAR (which has motional
resistance of 2 ).

The electrostatic force and motional current for a parallel-plate
electrostatic transducer are:
in
DC
v
g
A
V
f
2
0
;
x
g
A
V
i
DC
2
0

Both terms are proportional to the permittivity of capacitor
dielectric (
0
for air or vacuum). We propose to fill the electrode
gaps of the bulk acoustic resonators with a dielectric material
having much higher permittivity than air. The high- dielectric will
enhance both the force density of the electrostatic actuator as well
as the sense capacitance, thereby reducing the motional resistance
of these resonators by
2
.

Bouwstra et al demonstrated that audio-frequency cantilever
beams can be driven and sensed using silicon nitride dielectric
capacitors embedded in a silicon resonator [5]. The resonator made
use of Poissons ratio to convert applied strain perpendicular to the
beams thickness into strain along the beam, which coupled into
the fundamental bending mode. The approach was deemed
inefficient because air-gap capacitive transduction provided larger
displacement, the preferred performance metric at that time.
BULK-MODE INTERNAL ELECTROSTATIC
TRANSDUCTION
Bulk-mode resonators have significantly different design
requirements compared to flexural resonators. These resonators
typically have displacements on the order of a few nanometers. In
Travel support has been generously provided by the Transducers Research
Foundation and by the DARPA MEMS and DARPA BioFlips programs.
principle, we can enhance the transduction efficiency of bulk
resonators by filling the air-gaps with a low Youngs modulus,
high- dielectric material. A more practical approach would be to
find a dielectric with similar acoustic velocity as the resonator
material and build-in an internal electrostatic transducer at the
maximum strain anti-nodes rather than the maximum
displacement nodes. This approach would minimize bulk energy
losses due to acoustic velocity mismatch and optimize transduction
efficiency of the resonator. TiO
2
with relative permittivity ~ 80
and bulk acoustic velocity 7900m/s is an attractive material for this
purpose.

In order to benchmark the performance of the internal electrostatic
transducer, we evaluate its performance in a 3
rd
overtone lateral
bulk acoustic resonator. This class of resonators has been
demonstrated with air-gap electrostatic [1,4] and piezoelectric
transduction [2]. The 3
rd
overtone can be excited and detected by
introducing layers of TiO
2
at the two anti-nodal planes, as shown
in Figure 1.
Figure 1.
Schematic of electrostatically transduced 3
rd
overtone
bulk acoustic resonator

The motional resistance of this resonator is
L
A
E
Q
g
A
V
R
TiO
DC
tic
electrosta
4
2
2
0
2
2
2
1

By replacing the electrode-gap with TiO
2
at the antinodes, we can
reduce the motional resistance by
2
= 6,400.

A 14MHz bulk acoustic resonator with 1 m air-gap electrostatic
transducers has a motional resistance of 590k [1]. The 3
rd

harmonic of an identical resonator with TiO
2
dielectric
transduction would have a motional resistance of 275 . Similarly,
the motional resistance of the 1.2GHz 3
rd
harmonic ring resonator
[4] would scale down from 282k to 44 .

ELECTROSTATIC EXCITATION OF AN FBAR

We used Agilent Technologies AlN FBAR [6] to demonstrate
internal electrostatic transduction. AlN has a relative permittivity
of ~ 9

and the resonator has a mechanical quality factor Q ~ 1350
4
2
Nodal
Plane
Dielectric
Drive
Dielectric
Sense
g
v
in
i
out
V
dc
L
E =
Youngs modulus
A =
Cross-section area
Q =
Quality factor
=
Resonant frequency
L =
Half wavelength
g =
Length of transducer element
V
DC
=
Bias voltage
= Permittivity of TiO
2
0
2
2
TiO
TiO
Anti-node
4
2
Nodal
Plane
Dielectric
Drive
Dielectric
Sense
g
v
in
i
out
V
dc
L
E =
Youngs modulus
A =
Cross-section area
Q =
Quality factor
=
Resonant frequency
L =
Half wavelength
g =
Length of transducer element
V
DC
=
Bias voltage
= Permittivity of TiO
2
0
2
2
TiO
TiO
Anti-node
Solid-State Sensor, Actuator and Microsystems Workshop
0-9640024-5-0
59
Hilton Head Island, South Carolina, June 6-10, 2004
at a resonant frequency of f
0
=
1.92GHz. Electrostatic force is
quadratic; therefore we can actuate the FBAR with an input signal
at half the resonant frequency (Figure 2). This ensures that there is
no piezoelectric actuation of the resonator. A low-pass-filter was
added to prevent any harmonics from the RF synthesizer from
reaching the input electrode.
Figure 2. Test equipment setup for half-frequency measurement.
The Spectrum Analyzer is set to MAX_HOLD as the synthesizer
frequency is swept near half-resonance frequency.

Electrostatic actuation will generate stress in the resonator at the
resonant frequency:
2
2
0
0
4
1
)
(
t
v
f
T
in
AlN
tic
electrosta

This electrostatic stress generates dielectric displacement and
results in piezoelectric displacement current:
2
2
0
33
0
0
,
4
1
)
(
t
v
d
Q
A
f
i
in
AlN
piezo
out

The output current also has an electrostatic component due to the
quadratic electrostatic force. However, this component is
extremely small compared to the piezo component due to the
relatively large resonator thickness.

By sweeping the RF synthesizer frequency from 958MHz to
964MHz and using the MAX_HOLD function [7] on the 8562EC
Spectrum Analyzer, we were able to construct the mechanical
transfer function and extract Q of the FBAR (Figure 3).
Figure 3. FBAR transmission spectrum obtained using half-
resonance electrostatic actuation. Q ~ 1400 was extracted from the
shape of the transfer function.
Figure 4. Output power is proportional to the square of the input
power, verifying internal electrostatic actuation of the FBAR.

While the output current is due to piezoelectric effect, the
mechanical motion of the FBAR is due to electrostatic stress.
Hence, both the mechanical motion and output power are
proportional to square of the input power (Figure 4).

The FBAR is a one-port device and hence is not suitable for
electrostatic transduction. However, these two measurements
provide preliminary experimental verification of internal
electrostatic drive for bulk-mode resonators.
CONCLUSION
Internal electrostatic transducers using high- dielectrics can
achieve
2

higher efficiency than conventional air-gap transducers.
This new approach will enable us to fabricate arrays of small foot-
print lateral bulk acoustic resonators with motional resistances
<1k . It will also open up the opportunity to design microwave
frequency resonators with reasonable motional resistances. As a
proof-of-concept, we excited an FBAR at 1.92GHz with internal
electrostatic actuation.
ACKNOWLEDGMENT
The authors wish to thank Dr. Dan Radack and the DARPA
NMASP program, whose generous grant (#N66001-00-1-8955)
has made this research possible.
REFERENCES
1. T. Mattila, et al, Micromechanical Bulk Acoustic Wave
Resonator, 2002 Ultrasonics Symposium, pp. 945-948.
2. S. Humad, et al, High Frequency Micromechanical Piezo-on-
Silicon Block Resonators, IEDM 2003, pp. 957-960.
3. M. Demirci, et al, Mechanically Corner-Coupled Square
Microresonator Array for Reduced Series Motional Resistance,
Transducers 2003
, pp. 955-958.
4. S.-S. Li, et al, Micromechanical Hollow-Disk Ring
Resonators, MEMS 2004, pp. 821-824.
5. S. Bouwstra, et al, Excitation and Detection of Vibrations of
Micromechanical Structures using a Dielectric Thin Film,
Sensors and Actuators
, 17 (1989), pp. 219-223.
6. R. Ruby, et al, Ultra-Miniature High-Q Filters and Duplexers
using FBAR Technology, ISSCC 2001, pp. 120-121.
7. J. Wang, et al, 1.14-GHz Self-Aligned Vibrating
Micromechanical Disk Resonator, RFI