A Micromachined Capacitive Pressure Sensor Using a Cavity-Less Structure with Bulk

A Micromachined Capacitive Pressure Sensor Using a Cavity-Less Structure with Bulk
Sensors 2008, 8, 2317-2330
ISSN 1424-8220
© 2008 by MDPI
Full Research Paper
A Micromachined Capacitive Pressure Sensor Using a
Cavity-Less Structure with Bulk-Metal/Elastomer Layers and
Its Wireless Telemetry Application
Kenichi Takahata 1,* and Yogesh B. Gianchandani 2
Department of Electrical and Computer Engineering, University of British Columbia, 2332 Main
Mall, Vancouver, BC V6T 1Z4, Canada; E-mail: [email protected]
Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal
Ave., Ann Arbor, MI 48109-2122, USA; E-mail: [email protected]
* Author to whom correspondence should be addressed.
Received: 31 December 2007 / Accepted: 31 March 2008 / Published: 2 April 2008
Abstract: This paper reports a micromachined capacitive pressure sensor intended for
applications that require mechanical robustness. The device is constructed with two
micromachined metal plates and an intermediate polymer layer that is soft enough to
deform in a target pressure range. The plates are formed of micromachined stainless steel
fabricated by batch-compatible micro-electro-discharge machining. A polyurethane roomtemperature-vulcanizing liquid rubber of 38-μm thickness is used as the deformable
material. This structure eliminates both the vacuum cavity and the associated lead transfer
challenges common to micromachined capacitive pressure sensors. For frequency-based
interrogation of the capacitance, passive inductor-capacitor tanks are fabricated by
combining the capacitive sensor with an inductive coil. The coil has 40 turns of a 127-μmdiameter copper wire. Wireless sensing is demonstrated in liquid 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
estimation. Temperature dependence of the tank is experimentally evaluated.
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Keywords: pressure sensor, wireless, stainless steel, polyurethane, micro-electro-discharge
1. Introduction
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 frequencybased measurement of pressure [1-3]. Micromachined capacitive pressure sensors have typically used
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. Lead transfer for the sealed electrode has also been a persistent challenge. This has
motivated the development of innovative fabrication methods that involve multilayer deposition,
planarization, and other remedies, but require relatively high mask counts [6, 7]. Another approach to
deal with this has been to move the sense gap outside the cavity [8].
This research explores a capacitive pressure sensor that consists of two micromachined metal plates
with an intermediate polymer layer. Sandwich-type constructions with deformable intermediate layers
have been used in some micromachined sensors [9, 10] as well as commercial pressure mapping
systems (for, e.g., seat pressure monitoring) [11]. The selected configuration aims to eliminate the
need of diaphragms and cavities from the micromachined capacitive sensors. 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. This capacitive change can be interrogated by either a hard-wired interface or a wireless set-up
in which the sensor serves as a capacitor of an L-C tank. The inductor coil can be separately coupled
with the sensor (Figure 1a), or it can be formed by winding an insulated wire directly on the sensor to
minimize the device size (Figure 1b). The wireless interrogation is performed by an external
antenna/inductor that is magnetically coupled with the L-C tank device (Figure 2). Proper choice of
materials compatible with particular environments will offer broader opportunities such as in
automobile and biomedical applications that respectively include air pressure monitoring in the tires
[12] and bowel pressure detection [13]. The inherent environmental compatibility is a significant
advantage because it allows us to circumvent constraints and problems associated with the packaging
[14] that in general degrades device performance and cost effectiveness in the device manufacturing
This paper is constituted as follows. Section 2 describes the working principle and design of the
sensor. The details of the fabrication process for the L-C tank device and the results are presented in
Section 3. Section 4 reports the results of experimental characterization for the elastomer material used
in this effort as well as the developed L-C tank device and the demonstration of wireless sensing with
the device. These experimental results are evaluated in conjunction with the theoretical analysis in
Section 5, followed by discussion in Section 6. Section 7 concludes the overall effort. Portions of this
paper have appeared in conference abstract form in [16, 17].
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Figure 1. Bulk-metal/elastomer capacitive pressure sensor in the form of the L-C tank
for frequency-based pressure monitoring: (a: left) Cross sectional view of the sensor
coupled with a separate inductor, and (b: right) a device with an inductor wound on the
Figure 2. Electrical representation of the wireless measurement set-up with the L-C tank device.
2. Device Principle and Design
The capacitance of the device is determined by the thickness of the intermediate elastomer that is
varied with the ambient pressure. An elastomer layer sandwiched between two rigid plates exhibits
higher compression stiffness than the same layer without the plates in the direction perpendicular to
the layer plane. 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 [18]:
⎡ 1 ⎛ Y 2 −W 2
EA 2
S − S 0 2 − E ⎢1 + ⎜⎜ 2
⎢ 3⎝Y +W 2
⎥ log(1 − e )
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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
3 Y
⎜2 −
and S is a geometric parameter called shape factor, which is approximately represented for the
structure by
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 [19]. 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 ,
C T0
⎝ f0 ⎠
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 Equations (1) and (4) as
⎡ 1 ⎛ Y 2 −W 2
EAS 0 2 ⎛ 1
⎜ 4 − 1⎟ − E ⎢1 + ⎜⎜ 2
2 ⎝F
⎢ 3⎝Y +W 2
( )
⎥ log F 2 .
For the configuration illustrated in Figure 1b, the two capacitive parallel plates with the indicated
dimensions were microfabricated from stainless-steel sheets by micro-electro-discharge machining
(μEDM) in this effort. μEDM is an electrothermal micromachining technique that can be used to cut
any type of electrical conductors including all kinds of metals and alloys [20]. The machining typically
uses cylindrical tungsten electrodes that are precisely shaped to have diameter ranging between 5 and
300 μm. Since these plates potentially have burrs at the edges as characteristic defects of the
machining technique, the top plate was designed to be slightly smaller than the base plate (50-μm
offset from all sides of the base plate) to minimize probability of physical/electrical contact between
the two plates at the edges. Having the offset also assists with the self-alignment of the two plates in
the assembly step described in the subsequent section.
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3. Fabrication
In this effort, room-temperature-vulcanizing (RTV) liquid rubber of polyurethane was selected to
form the elastomeric layer. This material offers mechanical robustness such as high tear and abrasive
resistances, chemical resistance, and controllability of its softness over a wide range. It has been
extensively used in medical implant applications [21] and was also used to fabricate
micro/nanostructures for MEMS applications [22-24]. Other rubber materials such as
polydimethylsiloxane (PDMS) that are formed with low-viscosity liquids are also potential candidates
for the elastomer layer. Of course, mechanical properties such as plasticity limit, thermal expansion
coefficient, would play a role in the final selection, as would considerations about manufacturing and
The fabrication process is illustrated in Figure 3. As mentioned earlier, two capacitive plates were
patterned with μEDM using a PanasonicTM MG-ED72W system (step 1). The base and top plates were
cut from type-304 stainless-steel sheets with thickness of 200 µm and 50 µm, respectively, using
cylindrical electrodes with 190-µm diameter (Figure 4a). The base plate was still connected to the
original sheet through two tethers after the machining as shown in Figure 4a. 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), which is vulcanized to very soft
(<20 Shore A) and robust rubber, was used to form the intermediate polymer layer. The softness of the
rubber can be adjusted by changing the proportion of the softener to be mixed. This effort used a
formulation of part A:B:C=1:1:1. The mixed solution was applied to the upper surface of the base plate
(step 2), and then the top plate was placed on it (step 3). In this step, the top plate is self-aligned to the
base due to surface tension of the solution. After curing, the device was released as shown in Figure 4b
by mechanically breaking the tethers (step 4). The measured thickness of the cured polyurethane layer
was approximately 38 μm. The thickness of the layer can be adjusted by controlling the amount of the
solution to be applied. (In large scale production, many of the kinds of parameters that are used to
control the thickness of photoresist in photolithography – polymer viscosity, substrate spin speed, etc.
– can be used in this context as well.) Finally, the device was coupled with an inductive coil: For the
device in Figure 1b, the coil was formed by winding an enamel-coated copper wire (AWG 36, 40
turns) directly on the sensor and bonding the terminals on separate stainless-steel plates with
conductive adhesive (step 5). The fabricated L-C tank shown in Figure 4c was measured to have
nominal capacitance of 6.3 pF and inductance of 640 nH. Measured resonant frequency and quality
factor of the tank, which were probed via test leads shown in Figure 4c, were 106 MHz and 1.9
respectively. The measured resonant frequency of the tank is close to the theoretical frequency of
about 80 MHz that is obtained from the measured capacitance and inductance of the tank.
The capacitive structure was also coupled with and centered in a larger circular coil (5-mm
diameter, 5 turns) formed using AWG 40 (φ 80 μm) enamelled copper lead. This configuration was
selected for preliminary wireless testing to enlarge the magnetic coupling coefficient [25] between the
device and the external antenna/coil while reducing the negative impact of eddy current generated in
the stainless-steel plates. The use of conducting adhesive between the stainless-steel plates (without
surface preparation) and copper leads of the coil with a conductive adhesive provided high contact
resistance between them. This caused the low quality factor mentioned earlier, which limits the
Sensors 2008, 8
frequency-based measurement including wireless implementations. The high resistance at the contact
was believed to be due to the protective oxide layer of stainless steel. One simple method to
circumvent this is to roughen the surfaces of the steel using various physical methods such as lapping
and grit blasting to remove the oxide layer. The devices used for the wireless tests were constructed
with top (50-μm thick) and base (100-μm thick) plates whose outer surfaces were mechanically
roughened prior to bonding of the copper coils. The bonding was performed using a silver-filled
conductive adhesive with low-resistivity (<2×10-4 Ω⋅cm), improving the electrical connection between
Figure 3. Fabrication process flow to fabricate the capacitive pressure sensor (steps 14) and the L-C tank (step 5).
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Figure 4. (a: upper left) Base and top plates for the capacitive sensor fabricated by
μEDM (step 1 in Figure 3), (b: upper right) device released from the original sheet of
the base plate (step 4 in Figure 3), and (c: lower) fabricated L-C tank with a coil wound
using AWG-36 (φ 127 μm) enamelled copper wire (step 5 in Figure 3). The tank is
connected with the test leads for electrical characterization.
4. Experimental Results
4.1. Measurement of Young’s Modulus of Polyurethane Elastomer
To characterize the Young’s modulus, E, of the polyurethane elastomer used for the fabrication, a
compression test was performed using a 3-mm-cubic sample of the material without any plates
attached to it. The measurement was performed with a digital force gauge (DPS-1, Imada Inc., IL,
USA) that provided 1-mN resolution. Figure 5 plots measured pressure with varying strain up to 0.33
in the test, showing the initial compression modulus of 67 KPa, which is 15 % of the modulus reported
in [22]. It also shows that the apparent modulus (corresponding to dP/de in Equation (1) for a sample
bonded with the rigid plates) is effectively increased with strain, which is a common behavior of an
elastomer associated with increase of the shape factor, S [18].
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Figure 5. Pressure vs. strain measured with a 3-mm-cubic polyurethane rubber sample.
4.2. Characterization of the L-C tanks and Wireless Sensing Tests
The fabricated devices were tested with both hard-wired and wireless set-ups. In the wired set-up,
the tank with the directly wound coil shown in Figure 4c was placed in a pressurized chamber with air,
and the variation of its reactance peak with applied pressure was monitored by an HP4195 spectrum
analyzer using the test leads transferred through the chamber wall. This reactance is an output that
assumes a series capacitor-resistor model of the analyzer. This model exhibits the most distinct shift in
the set-up.
Figure 6 illustrates the set-up used for the wireless sensing tests. The L-C tank device, which was
coupled with the 5-mm-diameter coil, was placed within another sealed chamber with thin plastic
walls, and magnetically coupled with an external coil (φ ~10 mm, 185 nH) 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 RF power
fed from the analyzer to the external coil was 100 mW in this test. The chamber was filled with
deionized (DI) water for this wireless experiment to demonstrate operation in liquid; the device
provided a distinct resonant peak 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 by changing the distance between the device and a source
of heat located outside of the chamber as shown in Figure 6.
Figure 7 shows the shifts of the reactance peaks measured with the wired set-up due to gauge
pressure change in 69 KPa steps up to 345 KPa at room temperature (20 °C). The result is plotted in
Figure 8a, indicating the response of 2.6-9.6 Hz/Pa and sensitivity of 11-39 ppm/KPa in this pressure
range. The nonlinear behavior observed in the plot is consistent with the measured response in the
compression modulus of the polyurethane rubber, i.e., the layer becomes stiffer as it is squeezed,
resulting in the reduced response.
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Figure 6. Set-up used for the wireless testing of the device with the 5-mm-diameter coil
in liquid. The heat source is used to evaluate the sensor response at elevated
Figure 7. Frequency response of the reactance peak of the L-C tank measured with the
wired set-up due to gauge pressure change from zero to 345 KPa in air at room
Figure 8b shows a typical measured response with the wireless set-up at room temperature. The
reduced resonant frequency (of ~39 MHz) was expected with the increased parasitic capacitance due to
the operation in water. The frequency plot indicates a mildly saturating curve as similarly observed in
the wired test in air (Figure 8a). 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 Figure 8b exhibits a similar
saturating curve with an offset of about +0.4 MHz from that at room temperature. The slight difference
in the responses with pressure shown in Fig. 8b may be due to the temperature dependence of
mechanical properties of the particular polyurethane material used. The resonant frequency measured
with varying temperature at atmosphere pressure is plotted in Figure 9, indicating a linear dependence
with its coefficient of +783 ppm/°C. The increase of the resonant frequency suggests the decrease of
the capacitance, which is expected to 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 [26].)
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Figure 8. (a: left) Frequency response vs. gauge pressure plotted from the result in
Figure 7 measured with the wired set-up in air at room temperature, and (b: right)
similar measurement results with the wireless set-up in DI water at room and elevated
Figure 9. Resonant frequency of the tank vs. temperature measured with the wireless set-up.
5. Theoretical Analysis of the Experimental Results
It is worth evaluating the measurement results obtained and their consistency with the theoretical
estimation. To simplify the task for this initial analysis using Equation (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 (Figure 1b). It further assumes that
the top and base plates as well as the intermediate elastomer layer have exactly the same dimensions of
4×1 mm2.
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. The measured Young’s modulus, E, of the particular polyurethane is 67
KPa as observed in Figure 5. Using Equation (5) with these values, the normalized resonant frequency,
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F, as a function of hydrostatic pressure, P, is numerically solved and plotted in Figure 10. 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 Figure 8b 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. Comparison of relative frequency changes between the measured result from
Figure 8b and the theoretical estimation based on the model in Equation (5).
6. Discussion
The slightly lower response and deviation from the theoretical estimation seen in Figure 10 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 additional areas of the bonded elastomer layer can
contribute to increased compression stiffness of the layer. Another hypothesis may be related to the
deformation of the capacitive plates especially in the thinner top plate. The compressive strain of the
elastomer layer depends on the lateral location on the structure under a uniform applied pressure [27].
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 sandwiched
elastomer, which was originally developed for macro-scale blocks, is useful to find an approximate
response, within a limited pressure range (up to 200-300 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 temperature coefficient of this device (783 ppm/°C) is higher than typical values of the
vacuum-cavity pressure sensors (<100 ppm/°C [28]), but is comparable to that of piezoresistive
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devices. (The sensitivities in frequency and capacitance are on the orders of 1-10 ppm/Torr and 10-100
ppm/Torr, respectively, which are lower than the typical 100-1000 ppm/Torr available from
diaphragm-based sensors [28].) This may be addressed by tailoring the choice of the elastomer
material: One of potential options would be the use of composite rubbers that incorporate inorganic
negative thermal expansion (NTE) nanoparticles [29]. In addition, although the device was functional
without packaging in DI water with high resistivity used for the wireless tests, it 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. One of the simplest and most
effective methods would be to coat the entire device with Parylene materials, which are dielectric,
biocompatible polymers that have been used for a variety of products in electronic and biomedical
fields [30] − the flexible, stretchable feature of the material is expected to minimize the impact of
coating on the mechanical behavior of the device. The coating will also minimize the potential
diffusion of liquid into the polymer from the sides not protected by the metal plates..
In this initial effort, the capacitive plates were micromachined using the traditional serial μEDM
technique and were manually assembled (using a self-assembly technique). To increase the throughput
of the production, these processes can potentially be performed in a batch manner by a combinational
use of batch-mode μEDM [31] for cutting the plates and screen printing or spray coating for the liquid
rubber layer formation. Use of planar spiral coils with bonding pads, possibly fabricated on flexible
substrates, may be an effective approach to physical/electrical coupling with the capacitive sensor for
the L-C tank assembly.
7. Conclusions
This research has explored a micromachined capacitive pressure sensor that eliminated both a
diaphragm and a 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 micromachined stainless-steel plates fabricated by batch-compatible
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 robustness, potentially reducing the difficulties associated with packaging for selected
applications. The sensor and 40-turn copper coils were combined to form L-C tanks, which were
successfully used to implement frequency readout for pressure monitoring with the maximum
sensitivity of ~40 ppm/KPa and extended to the wireless telemetry measurement. The sensing was
demonstrated in both air and liquid environments with up to 340 KPa gauge pressure. Future work will
encompass structural and material optimization, as well as reliability testing.
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
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program of the National Science Foundation (NSF), USA. The findings do not necessarily reflect the
views of the NSF.
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