A Cavity-Less Micromachined Capacitive Pressure Sensor for Wireless Operation in Liquid Ambient,

A Cavity-Less Micromachined Capacitive Pressure Sensor for Wireless Operation in Liquid Ambient,
K. Takahata1 and Y.B. Gianchandani2
Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA
This paper reports a micromachined capacitive pressure sensor
that does not use the traditional cavity and diaphragm, and its use in
aqueous environment.
The device is fabricated with two
micromachined plates of stainless steel and an intermediate polymer
layer that is soft enough to deform in the target pressure range. A
polyurethane room-temperature-vulcanizing liquid rubber of 38-μm
thickness is used as the deformable material. For frequency-based
interrogation of the capacitance, a passive inductor-capacitor tank is
fabricated by combining the capacitive sensor with an inductive
coil, which is formed using an 80-μm-diameter copper wire.
Wireless sensing in liquid is demonstrated by monitoring the
variation in the resonant frequency of the tank via an external coil
that is magnetically coupled with the tank. The sensitivity at room
temperature is measured to be 23-33 ppm/KPa over a dynamic range
of 340 KPa, which is shown to match a theoretical estimate obtained
by a bonded elastomer model. The geometrical impact on the
frequency response is also evaluated.
Capacitive pressure sensors are favored for low-power and
telemetric applications since they draw no DC power, and
conveniently form passive inductor-capacitor (L-C) tank circuits for
frequency-based measurement of pressure [1-3]. Micromachined
capacitive pressure sensors typically use an elastic diaphragm with
fixed edges and a sealed cavity in between the diaphragm and the
substrate below [4, 5]. Since this configuration relies on the
deflection of a relatively thin diaphragm against a sealed cavity, in
some applications there is a concern of robustness of the diaphragm
and leaks in the cavity seal. For example, in implantable
applications, diaphragm or cavity failure is unacceptable.
Survivability with high over-pressures and mechanical robustness
are critical for certain military uses. Lead transfer for the sealed
electrode has also been a persistent challenge.
This research explores a capacitive pressure sensor that
consists of two micromachined metal plates with an intermediate
polymer layer, eliminating the need of diaphragms and cavities.
Use of polymeric material that is soft enough to deform over a target
pressure range allows thickness of the polymer, or capacitance of
the parallel plate capacitor, to be dependent on hydraulic pressure
that surrounds the device (Fig. 1). This capacitive change can be
interrogated by monitoring the resonant frequency of an L-C tank in
which the sensor serves as a capacitor of the tank. The tank can be
formed by coupling an inductor coil with the sensor separately, or it
can be done by winding an insulated wire directly on the sensor [6].
The wireless interrogation can be implemented using an external
antenna/inductor that is magnetically coupled with the L-C tank
device (Fig. 2). The simple sandwich configuration of the pressure
sensor provides not only mechanical robustness by eliminating the
risk of cavity/diaphragm failures but also more freedom in the
selection of structural materials. The latter feature will allow us to
use appropriate materials to achieve an inherent compatibility of the
device with target environments, e.g., those in corrosive liquid and
the human body, circumventing packaging-related limitations that
can negatively impact the cost and applicability of the device.
Figure 1: Cross sectional view of the cavity-less bulk-metal/
elastomer capacitive pressure sensor.
Figure 2: Electrical representation of the wireless measurement
set-up for the L-C tank device.
The capacitance of the device is determined by the thickness of
the intermediate elastomer that is varied with the ambient pressure.
For a rectangular layer of an incompressible, homogeneous
elastomer that is bonded with rigid plates on both sides, the
relationship between an applied pressure, P, on each of the plates
and the resultant strain, e, can be expressed as [7]:
⎡ 1 ⎛ Y 2 − W 2 ⎞2 ⎤
EA 2
⎟ ⎥ log(1 − e )
S − S 0 2 − E ⎢1 + ⎜⎜ 2
⎢ 3 ⎝ Y + W 2 ⎟⎠ ⎥
where E is the Young’s modulus of the elastomer, 2Y and 2W are the
length and width of the rectangle layer, respectively. A is a constant
given by
4 W⎛
+ ⎜2 −
3 Y ⎝
S is a geometric parameter called shape factor, which is
approximately represented for the structure by
S0 ,
2T (Y + W ) (1 − e )
where 2T is the resultant thickness of the layer upon the
compression and S0 is the original shape factor with the initial
thickness (2T0) before the compression. The strain can be expressed
as e=1-T/T0. The final thickness determines the capacitance of the
structure C = ε ( 4YW ) /( 2T ) , where ε is the permittivity of the
elastomer, and then the resonant frequency of the L-C tank,
f = 1 /( 2π LC ) , where L is the inductance of the tank. The
permittivity of polyurethane is reported to be stable over the
pressure range that is involved in this effort [8]. With these, the
ratio of the resonant frequency after the compression to the original
one and that for capacitance can be coupled with the strain as
⎛ f ⎞
⎜⎜ ⎟⎟ = 0 =
= 1− e
⎝ 0⎠
Figure 4:
Individual capacitive
plates fabricated by
μEDM of type-304
stainless steel foil.
where C0 and f0 are the original capacitance and resonant frequency
prior to the compression, respectively. Therefore, the relationship
between the applied pressure and the ratio in the resonant frequency,
f/f0 =F, can be expressed using Eqs. (1) and (4) as
⎡ 1 ⎛ Y 2 −W 2 ⎞
EAS0 ⎛ 1
⎜ 4 − 1⎟ − E ⎢1 + ⎜⎜ 2
2 ⎝F
⎢ 3 ⎝ Y + W 2 ⎟⎠
( )
⎥ log F 2 . (5)
Figure 3 illustrates the fabrication process for the sensors. The
base and top plates with the indicated dimensions were cut from
type-304 stainless steel sheets with thickness of 100 µm and 50 µm,
respectively, using micro-electro-discharge machining (µEDM) [9]
(Fig. 4). The top plate was designed to be slightly smaller than the
base plate (50-μm offset from all sides of the base plate) to assist
with the self-alignment of the two plates in the assembly step
performed later. The base plate was still connected to the original
foil with two tethers after the machining as shown in Fig. 4. A
two-part polyurethane RTV liquid rubber (Poly 74-20, part-A:
polyurethane pre-polymer, part-B: polyol, Polytek Development
Co., PA, USA) with the softener (part-C: plasticizer) was used to
form very soft (<20 Shore A) and robust rubber. This effort used the
formulation of parts A:B:C=1:1:1, which provides rubber with the
Young’s modulus of 67 KPa [6]. After applying the mixed solution
to the upper surface of the base plate, the top plate was placed on it.
The top plate was self-aligned to the base due to surface tension of
the solution. After curing, the device was released from the original
foil (Fig. 5a). The cured polyurethane had ~38-μm thickness (Fig.
5b), providing the nominal capacitance of 6.0 pF. An inductive coil
Figure 5: (a: upper) Fabricated device with the cured polyurethane
being released from the original stainless-steel foil by breaking the
tethers; (b: lower) sidewalls of the capacitive device showing
stainless-steel/polyurethane layers.
(5-mm diameter, 5 turns) of 80-μm-thick enamelled copper lead was
coupled with the device to form an L-C tank by bonding the
terminals of the coil to the capacitive plates with conductive
adhesive. The oxide layers of the stainless steel were mechanically
removed prior to the bonding to lower the contact resistance, i.e.,
increase the quality factor of the tank. The resonant frequency of
the fabricated L-C tank was measured to be 95 MHz in air, which is
close to the theoretical value (~80 MHz) obtained with the measured
capacitance and inductance of the tank.
Figure 6 illustrates the set-up used for the wireless sensing
tests. The fabricated L-C tank devices were placed within a sealed
plastic chamber, and magnetically coupled with an external coil
through the chamber walls. The resonant frequency of the tank was
monitored by tracking the frequency of the characteristic peak,
which was reflected by the resonance of the tank, in an s-parameter
(s11) of the external coil that was connected to a network-spectrum
analyzer while changing pressure inside the chamber. The chamber
was filled with deionized water to demonstrate operation in liquid.
The devices provided a distinct resonant peak, even without
packaging/coating for electrical protection. With the same set-up,
the frequency dependence on temperature was also evaluated at
atmosphere pressure. Temperature of the chamber was controlled
Figure 3: Fabrication process flow.
Figure 6: Set-up for wireless testing.
by changing the distance between the device and a source of heat
located outside of the chamber as shown in Fig. 6.
Figure 7 shows a typical measured response with the wireless
set-up at room temperature in DI water. Compared to the 95 MHz
resonant frequency in air, the reduced resonant frequency was
expected with the increased parasitic capacitance due to the
operation in water. The sensitivity is calculated to be 23-33
ppm/KPa for the pressure range up to 340 KPa. The same
measurement at 40 °C also plotted in Fig. 7 exhibits a similar curve
with an offset of about +0.4 MHz from that at room temperature.
The resonant frequency measured with varying temperature at
atmosphere pressure is plotted in Fig. 8, indicating a linear
dependence with its coefficient of +783 ppm/°C. The increase of
the resonant frequency suggests the decrease of the capacitance,
which can be due to the thermal expansion of the polyurethane.
(The dielectric constant of polyurethane elastomer was reported to
be stable at the temperature range used in this experiment [10].)
Figure 7: Typical frequency response of the fabricated device vs.
pressure measured with the wireless set-up in Fig. 6 at room and
elevated temperatures.
It is worth evaluating the measurement results obtained and
their consistency with the theoretical estimation. To simplify the
task for this initial analysis using Eq. (5), the following calculation
assumes that the capacitive structure has a simple rectangular shape
with 4×1-mm2 area, which corresponds to the largest rectangular
portion of the actual design (Fig. 3). It further assumes that the
dimensions of the top and base plates as well as the intermediate
elastomer layer are all identical.
With the measured polyurethane thickness 2T0=38 μm and the
lateral dimensions of the selected rectangle, i.e., 2Y=4 mm and
2W=1 mm, the constant A and the shape factor S0 are calculated to
be 1.76 and 10.5, respectively. Using Eq. (5) with these values and
E=67 KPa, the normalized resonant frequency, F, as a function of
hydrostatic pressure, P, is numerically solved and plotted in Fig. 9.
The “band” shown in the graph represents the possible range of the
theoretical response with an assumption of ±5% variations in the
thickness and Young’s modulus of the polyurethane layer. The
measurement result in Fig. 7 at room temperature is also plotted in
the graph for comparison. It is clearly seen that the theoretical
estimation matches well with the measured response at lower
pressure. It can also be seen that the measured response deviates
from the theoretical response as the pressure is increased.
Figure 10 shows calculated frequency change (F) with pressure
as a function of the width-to-thickness ratio (W/T) of the rectangular
Figure 9: Comparison of relative frequency changes (F) between
the measured result from Fig. 7 and the theoretical response of the
device with the simplified 4×1-mm2 rectangular shape.
Figure 10:
Calculated F vs.
pressure as a
function of the W/T
ratio of the
elastomer layer.
The result indicates
higher sensitivity
with lower W/T.
Figure 8: Typical frequency dependence on temperature measured
at atmosphere pressure.
elastomer layer. The calculation assumes the length-to-width ratio
(Y/W) of 4 as in the simplified shape of the fabricated device used
for the analysis in Fig. 9. The plot for W/T=26.3 corresponds to the
actual device and identical to the theoretical plot in Fig 9. The result
indicates the strong dependence of the sensor response on the W/T
The slightly lower response and deviation from the theoretical
estimation seen in Fig. 9 could be partially because of the presence
of the extra portions (four 0.8×0.7-mm2 rectangles) in the actual
device that were excluded in the analysis − these portions partially
increase the width (W), i.e., the W/T ratio of the device, leading to a
reduced response as predicted in Fig. 10. Another hypothesis may
be related to the deformation of the capacitive plates especially in
the thinner top plate. The compressive strain of the polymer layer
depends on the lateral location on the structure under a uniform
applied pressure [11]. Hence the upper plate can bend if it is not
completely rigid, which is the real case. This deformation, i.e.,
non-uniform displacement of the plate, may also be a partial source
of the deviation. Non-ideal factors attributed to thin layer of the
polyurethane material including inhomogeneity of the material and
inclusion of particles while mixing the liquid components of the
material can be a potential contributor as well. Nevertheless, it is
noteworthy that the theoretical model for the bonded elastomer,
which was originally developed for macro-scale blocks, is useful to
find an approximate response, within a limited pressure range (up to
300 KPa), of a micromachined device with an elastomer layer
whose thickness is only a few tens of microns.
The device construction will need some optimization for
improved performance and practicality of the device. The analytical
result in Fig. 10 suggests a path to achieving higher sensitivity with
modified designs of the device. The high temperature coefficient of
this device may limit its applications. One of potential options to
address the issue would be the use of composite rubbers that
incorporate inorganic negative thermal expansion (NTE)
nanoparticles [12]. The device will need to be coated with a
dielectric layer for electrical insulation when the device is
surrounded by a conductive medium. This will be important
especially for biomedical and implant applications where the device
makes direct contact with polarizable liquids such as body fluid and
blood. These electrical and biological insulations can be easily
achieved by the use of Parylene materials − the flexible, stretchable
feature of the material is expected to minimize the impact of coating
on the mechanical behavior of the device.
This research has explored a micromachined capacitive pressure
sensor that eliminated both a diaphragm and a sealed cavity from its
construction. The sensor consists of two metal plates and an
intermediate polymer, which is expected to offer high mechanical
robustness and reliability. The device was constructed with
stainless-steel plates fabricated by a μEDM technique and
polyurethane liquid rubber as the polymer layer that permitted
self-aligning of the micromachined plates in the assembly process.
This material combination can offer good corrosion resistance and
fracture toughness, potentially reducing the difficulties associated
with packaging for selected applications. The sensor and a
5-mm-diameter copper coil were combined to form an L-C tank,
which was successfully used to implement wireless frequency
readout for pressure monitoring up to 340 KPa gauge pressure in
liquid. The maximum sensitivity was observed to be 33 ppm/KPa.
The comparison between the measured result and theoretical
response obtained with a bonded elastomer model revealed the
effectiveness of the model in predicting the sensor response.
The authors would like to thank TRIUMF, Vancouver, B.C.,
Canada, for providing access to their measurement equipment and
Mr. Mark Richardson at the University of Michigan, Ann Arbor, for
his assistance in the micromachining work. Y. Gianchandani
acknowledges partial support from the IR/D program of the
National Science Foundation (NSF), USA. The findings do not
necessarily reflect the views of the NSF.
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