Measurements of material properties using differential capacitive strain sensors

Abstract

This paper describes a laterally deflecting micromachined device that offers high sensitivity and wide dynamic range to electronically monitor the thermal expansion coefficient, tensile and compressive residual strain and Young's modulus of microstructural materials, as well as the temperature dependence of these properties. The device uses sidewall capacitance between interdigitated tines to sense displacement caused by the release of residual stress in a bent-beam suspension. Electrostatic force is used to obtain load-deflection profiles. The suspensions and tines are arranged such that output is a differential readout, immune to common mode parasitic capacitance. Analytical and numerical modeling results are presented and the device concept is verified by three different fabrication approaches using polysilicon and nickel as structural materials. Measured values of residual strain, thermal expansion and Young's modulus are very consistent with measurements taken by other approaches and those reported previously. For example, the residual strain in certain electrodeposited Ni structures was tracked from 68.5 microstrain at 23°C to -420 microstrain at 130°C, providing an expansion coefficient of 8.2 ppm/K; the best fit Young's modulus provided by the device was 115 GPa.

Full text

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002 489
Measurements of Material Properties Using
Differential Capacitive Strain Sensors
Larry L. Chu, Long Que, Member, IEEE, and Yogesh B. Gianchandani, Member, IEEE
Abstract—This paper describes a laterally deflecting micro-
machined device that offers high sensitivity and wide dynamic
range to electronically monitor the thermal expansion coefficient,
tensile and compressive residual strain and Young’s modulus of
microstructural materials, as well as the temperature dependence
of these properties. The device uses sidewall capacitance between
interdigitated tines to sense displacement caused by the release
of residual stress in bent-beam suspension. Electrostatic force is
used to obtain load-deflection profiles. The suspensions and tines
are arranged such that output is a differential readout, immune
to common mode parasitic capacitance. Analytical and numerical
modeling results are presented and the device concept is verified
by three different fabrication approaches using polysilicon and
nickel as structural materials. Measured values of residual strain,
thermal expansion and Young’s modulus are very consistent with
measurements taken by other approaches and those reported
previously. For example, the residual strain in certain electrode-
posited Ni structures was tracked from 68.5 microstrain at 23 C
to 420 microstrain at 130 C, providing an expansion coefficient
of 8.2 ppm/K; the best fit Young’s modulus provided by the device
was 115 GPa. [737]
Index Terms—Capacitive measurement, strain, temperature co-
efficient, Young’s modulus.
I. INTRODUCTION
MONITORING the mechanical properties of structural
materials is a critical challenge in MEMS research and
manufacturing. Device performance parameters are sensitive to
variations in Young’s modulus ( ), residual strain ( ), residual
stress ( ) and the thermal expansion coefficient ( ) of structural
materials, which can vary with manufacturing conditions. It is
particularly challenging to control these properties in additive
fabrication processes, in which the structural material is de-
posited onto a substrate wafer. For example, residual stress in a
thin film of polysilicon formed by low pressure chemical vapor
deposition (LPCVD) may vary with deposition temperature,
pressure, doping, as well as post-deposition anneal conditions
[1], [2]. Packaging variables such as the choice of packaging
Manuscript received August 3, 2001; revised March 24, 2002. This work was
performed at the University of Wisconsin, Madison, and supported in part by an
Industrial and Economic Development Research program award from the State
of Wisconsin and by Canopus Systems, Inc., through U.S. Army Aviation and
Missile Command (AMCOM) contract DAAH01-00-C-R104. Subject Editor
R. T. Howe.
L. L. Chu is with the Department of Electrical and Computer Engineering,
University of Wisconsin, Madison, 53706 WI USA.
L. Que is with OpticNet, Inc., Hayward, CA 94545 USA.
Y. B. Gianchandani was with the University of Wisconsin, Madison,
53706 WI USA. He is now with the Electrical Computer Science Depart-
ment, University of Michigan, Ann Arbor, MI 48109-2122 USA (e-mail:
yogesh@umich.edu).
Digital Object Identifier 10.1109/JMEMS.2002.803277.
and die attachment materials and deployment conditions
such as operating temperature and humidity can also have an
impact. The ability to directly monitor select properties would
allow accurate compensation of device response to changing
conditions. The properties of primary interest in this study are
strain and Young’s modulus, which are related by stress. In
addition, the coefficient of thermal expansion is studied for
cases in which thermal stresses are significant.
Average stress in a thin film can be monitored by commer-
cial tools from the change in curvature that it induces on sub-
strate wafer [3]. A number of micromachined strain sensors
complement this method, offering spatial resolution of a few
hundred microns. Although some of these require mechanical
actuation [4], [5], most involve passive structures that are de-
signed to deform measurably under the residual stress when
they are released from the substrate [6]–[12]. These deforma-
tions are measured visually, sometimes using a micromachined
vernier. Although useful in a laboratory setting, this method is
not necessarily convenient for high volume manufacturing. In
this context, an electrical readout better conforms to standard
integrated circuit (IC) test equipment and procedures. More im-
portantly, an optical or visual readout renders the strain sensor
useless upon packaging, eliminating many conceivable appli-
cations, whereas an electronic readout potentially permits the
strain sensor to be co-fabricated or co-packaged with another
device such as an accelerometer or gyroscope, improving the
system accuracy by offering real-time or test-mode calibration
over the lifetime of its deployment.
An electrostatic pull-in technique has been used in the past to
electronically monitor residual stress [13], [14]. In this method,
a clamped bridge or diaphragm is deflected by applying a
voltage bias to an electrode located under it, generally to the
point that it collapses, although this is not always necessary
because the capacitance between the actuation electrode and the
microstructure can be used to gauge displacement and obtain a
load line [15], [16]. This technique is better suited for tensile
materials because moderate compressive forces may buckle
the structure and render it unusable. In addition, the vertical
deflection of the bridge or diaphragm (perpendicular to the
substrate) may be less appealing for devices that are designed
to deflect laterally if the structural material is anisotropic (e.g.,
single crystal silicon or polysilicon with a preferential grain
orientation). When the pull-in technique is used, stiction forces
may prevent recovery from collapse, limiting the lifetime of a
device or the repeatability of a measurement. Furthermore, the
fabrication process must permit the inclusion of an electrode
under the microstructure.
1057-7157/02$17.00 © 2002 IEEE

490 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002
This paper describes a micromachined strain sensor that pro-
vides an electronic readout from a laterally deflecting structure
1that combines the behavior of passively deformed and elec-
trostatically actuated structures to provide certain unique capa-
bilities. The readout is a differential capacitance, which is im-
mune to common mode parasitics. Moreover, a single device
is not only suitable for monitoring a wide range of tensile and
compressive strains, but also yields the Young’s modulus of the
structural material upon the execution of a simple capacitance
versus voltage (C–V) test such as that used routinely in charac-
terization of MOS transistors. It is a single-layer device and thus
simple to fabricate. Since the structure is never deflected to the
point of collapse, it is expected to provide a long deployment
lifetime and is potentially suitable for the postpackaging moni-
toring of material properties in real-time or test-mode operation.
In this effort, the operation of the differential capacitive strain
sensor is theoretically evaluated and experimentally verified.
Section II describes the operation and modeling of the capac-
itive strain sensor. The discussion also includes the effects of
nonidealities to the performance of the sensor. Section III out-
lines the three distinct fabrication sequences used to validate the
device. Section IV presents the measured results for three sets
of fabricated devices. It is demonstrated that these devices can
be used not only to measure the stated properties of both tensile
and compressive materials but also to provide the temperature
coefficient of these properties. Finally, Section V summarizes
the findings in this effort.
II. MODELING
This section presents analytical and numerical models re-
lated to both the strain measurement and the Young’s mod-
ulus measurement. The impact of structural nonidealities is also
evaluated.
A. Basic Operation
In the differential capacitive strain sensor [see Fig. 1(a)], a
series of ribs are suspended above the substrate by bent-beams.
Bent-beam suspensions relieve both tensile and compressive
residual stresses by inward and outward motions of the apex,
respectively. The ribs support interdigitated tines that function
as electrodes for the sidewall capacitors. The suspensions and
tines are arranged such that the capacitance on one side of a rib
increases as the other decreases. In other words, in response to
residual strain in the structural material, the structures labeled
A move in the opposite direction to those labeled B and C. This
permits a differential readout that is immune to common mode
parasitics. The residual strain in the structural material is de-
termined from the differential capacitance, defined as
, which is 0 in tension and 0 in compres-
sion. The Young’s modulus of the material is determined from
the curvature of the plot of (or conversely, ) versus an
applied bias voltage between elements A and B (or C). The bias
voltage causes an electrostatic force, resulting in a displacement
that is measured by the change in capacitance. The displacement
1Portions of this article have occurred in conference abstract form in [17],
[18], and [19].
(a)
(b)
Fig. 1. (a) Schematic of the differential capacitive strain sensor and
(b) definition of bent-beam dimensions.
is related to the stiffness of the suspension, which is proportional
to the Young’s modulus. The curves obtained are referred to as
C–V curves. The procedure for determining Young’s modulus
is, therefore, similar to the C–V test commonly used for MOS
transistors.
Bent-beams are excellent transducers for converting both ten-
sile and compressive residual strain to displacement [10]. The
sensitivity and range of the deformation in the bent beam sus-
pension are a function of its bending angle and can be cus-
tomized to address the needs of a particular application or fab-
rication process. In general, the devices have high sensitivity
and a wide dynamic range. A number of devices have been de-
signed by varying the structural design parameters, with target
sensitivities in the range of 0.1–1 fF/MPa and a range of about
300 MPa.
The displacement of the bent-beams in response to residual
stresses can be calculated analytically. Using variables defined
in Fig. 1(b), the governing equation is
(1)
with the boundary conditions
(2)
where is the flexural rigidity of the suspension, is the axial
force used to model the effects of stress and is the suspension

CHU et al.: MEASUREMENTS OF MATERIAL PROPERTIES USING DIFFERENTIAL CAPACITIVE STRAIN SENSORS 491
Fig. 2. Sensor response to residual strain for 200-

m long, 5-

m wide,
suspensions which are 4-

m in thickness; assuming 10 tines per side with an
overlap distance of 167

m and a nominal gap of 1

m.
length. In the absence of any externally applied forces the dis-
placement of the apex is given by (3) for tensile material and (4)
for compressive materials
-(3)
-(4)
where . The response of the sensor is plotted
as a function of residual strain in Fig. 2. The analytical model
closely matches finite element analysis results in this range of
dimensions [10].
B. Capacitance–Voltage (C–V)
Whereas strain is measured from the passive deformation of
the bent beams in response to the residual stress, the measure-
ment of Young’s modulus requires an applied electrostatic force.
This is provided by a voltage bias between two adjacent ribs.
The applied voltage changes the separation between the tines,
which is monitored capacitively. The slope of the C–V curve
can then be related to the Young’s Modulus since the device di-
mensions are known.
The C–V modeling approach was conceptually similar to
those described in [14], [15] and [16]. Capacitance between
tines was numerically modeled using FastCap™ [20]. It was
determined for a range of separations between tines and stored
in a look-up table. Starting with the zero-bias separation be-
tween the tines, separation was decremented in small intervals.
At each separation, the capacitance was determined from the
look-up table, while the corresponding bias voltage required
to cause the displacement was determined from force balance
by equating the electrostatic attractive force to the mechanical
restoring force:
(5)
where is the effective mechanical spring constant of each
structural unit including two bent-beam suspensions, one rib
and associated tines; is the in-plane displacement from the
zero-bias position. The spring constant has three components
Fig. 3. Definitions of dimensional parameters needed for modeling of
nonidealities.
Fig. 4. Theoretical C–V curves for
k
values representing Young’s moduli
of 40–220 GPa in 20 GPa increments assuming the bent-beam compliance
dominates.
which include the contributions from the displacement of bent-
beams, the bending of tines and the torsion of supporting ribs:
(6)
(7)
(8)
(9)
where is the compliance of one bent-beam, is the com-
pliance of one tine and is the compliance of one support rib.
The rest of the symbols are as defined in Fig. 3. Equations (6) to
(9) are verified to be within 17% agreement with the FEA results
obtained using ANSYS [21]. In the preferred implementation,
and ; the compliance of bent-beam
will dominate.
Fig. 4 shows calculated C–V curves obtained by this method
showing the effect of change in Young’s modulus assuming that
the compliance of the tines and rib is negligible (
and ). In effect, each of the curves shown in the figure
has a different spring constant; for a lower Young’s modulus,
the spring is softer, causing the response to veer up at a smaller
applied voltage. For these simulations, the suspension had the

492 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002
Fig. 5. FEA displacement plot of two tine pairs under applied voltage.
Fig. 6. Calculated curves showing the impact of variation ofthe initial gap on
the C–V response.
following dimensions: m, m, rad,
4.4 m thickness. Ten pairs of tines were assumed with 167 m
interdigitated overlap length. The sidewalls of the tines were as-
sumed to have a reentrant profile that was 22 off vertical (with
a68 angle to the substrate) due to fabrication. The zero-bias
gap between the upper edges of adjacent tines (where the tines
were closest) was 1.85 m. The tines were assumed to be 2.2 m
above the substrate.
In order to generate curves shown in Fig. 4, the following pro-
cedure was followed. First the zero-bias capacitance of the tine
structure was determined. This capacitance corresponds to the
initial tine separation and was found by reading off the position
in the numerically simulated capacitance table that was previ-
ously generated. The assumed separation between the opposing
tines was then decremented infinitesimally. At each step, the ca-
pacitance was determined from the table and was found by
solving (5). The iterations were terminated when electrostatic
pull-in occurred. An FEA simulation was also performed using
commercially available CoventorWare software [22]. This con-
firmed the overall operation of the device. It also showed that
even in situations that the tines are compliant, for small deflec-
tions the pairs of opposing tines remain roughly parallel even as
they are deflected toward each other (see Fig. 5).
C. Modeling of Nonidealities
In order to better understand the impact of structural nonide-
alities upon the sensor behavior, several additional simulations
were performed. In particular, variations in initial tine separa-
tion, tine sidewall angle and out-of-plane displacement of the
tines were investigated. Such variations could conceivably be
caused by poor process control. In all of these simulations, the
nominal dimensions were as for Fig. 4 and the Young’s modulus
Fig. 7. Calculated C–V curves showing the impact of varying the sidewall
angles of tines.
Fig. 8. Calculated C–V curves showing the impact of out-of-plane deflection
of tines.
was 100 GPa, unless specified otherwise. Fig. 6 shows varia-
tions in the C–V curve caused by changing the initial gap be-
tween the upper edges of the tines from 1.65 m to 2.05 m
in 0.1 m increments. It is clear that the zero-bias capacitance
changes as expected, but the slopes of the C–V curves remain
roughly unchanged for bias values almost up to 150 V. Fig. 7
shows the impact of changing the sidewall angles of the tines
on the C–V curves from 60 to 80 while keeping unchanged
the mid-height spacing at the zero-bias value. Evidently, this
can have a significant impact on both the intercepts and curva-
tures. This dimensional parameter should be tightly controlled.
Fig. 8 shows how the total capacitance of a single tine varies as
a neighboring tine is raised or lowered. Although the C–V curve
is shifted along the -axis, the curvature is not significantly af-
fected up to 150 V. The out-of-plane deformation is minimal if
the thickness-to-width aspect ratio is high. Typically, high-as-
pect ratio processes also provide exceptional control over side-
wall angle, offering a suitable test implementation of such a
device.
III. FABRICATION
Differential capacitive strain sensors were realized using
three approaches. Set A used electroplated Ni as structural
material with molds formed by standard UV lithography; set

CHU et al.: MEASUREMENTS OF MATERIAL PROPERTIES USING DIFFERENTIAL CAPACITIVE STRAIN SENSORS 493
(a) (c)
(b) (d)
Fig. 9. Images of fabricated capacitive strain sensors: (a) set A, optical micrograph of a Ni structure, (b) SEM image of the set A variant denoted A0, (c) set B,
LIGA Ni structure, and (d) set C poly Si structure.
B, also using Ni, was implemented with LIGA technology,
with molds formed by collimated X-ray exposure; set C used
LPCVD polysilicon in a surface micromachining process.
Set A was fabricated on silicon wafers insulated with 1 m
thick thermal oxide and 0.5 m thick LPCVD nitride. A 2 m
thick sputtered Ti sacrificial layer was patterned and covered
with a Cr/Ni seed layer. The devices were electroplated into a
photoresist mold from a nickel sulphamate solution. At 54 C
temperature, using 5–10 mA/cm current density, a thickness
of 4.4 m was achieved in 9.5 min. The electroplating was
performed using a nickel anode in a 1500 mL Pyrex beaker
with 1000 mL of plating solution agitated with a motor. The
sidewalls of the plated structures were 68 to the substrate due
to resist reflow during the hard bake. (This can be determined
from the thickness of the mold and the difference between
the line widths at the bottom and the top of the feature.) The
photoresist mold was subsequently stripped and the sacrificial
material etched away. Following this, the sample was coated
with a self-assembled monolayer using octyltriethoxysilane
(ODS, CH CH Si OC H ) [17]. Octyltriethoxysilane is
preferred over other alternatives, such as octadecyltrichlorosi-
lane (OTS) and perfluorodecyltrichlorosilane (FTDS), because
ODS is less sensitive to moisture contamination and yields an
advancing contact angle of 93 for water on an oxidized Si
wafer. It was found that the ODS solution remained effective
in excess of 24 h after the preparation of the chemical under
normal laboratory conditions. An optical image of a fabricated
structure is shown in Fig. 9(a).
In a variant of set A denoted set A0, the current density and
temperature used for the electroplating step were modified, pro-
ducing tensile Ni which had 192–264 strain at room tempera-
ture. A structure from this set is shown in Fig. 9(b).
Set B was fabricated on (#7740) glass substrates using LIGA
technology [23]. These devices were plated on a 2- m-thick

494 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002
sacrificial layer using a Ni sulphamate solution which had Ni
concentration of 82 g/L. At 56 C temperature and 32 mA/cm
current density, a thickness of 55 m was achieved in 95 min
[see Fig. 9(c)]. The electroplating was performed with a nickel
anode in a 400 mL tank with a pump and a filter. The increased
thickness provides large sidewall capacitance, which improves
sensitivity and reduces measurement uncertainty. Thick struc-
tures also eliminate out-of-plane deformation and resist buck-
ling even when highly compressive forces are encountered. The
LIGA devices also benefit from precise dimensional control and
from vertical sidewalls.
Set C, the polysilicon devices, were fabricated on a Si sub-
strate with a 2- m oxide isolation layer capped by a 1-k -thick
LPCVD nitride layer. The sacrificial layer was 2.5 m thick
PECVD oxide, while the structural layer was 2.5 m LPCVD
polysilicon deposited at 600 C in two layers, between which
a phosphorus implant of 1 10 cm was performed. The
polysilicon was annealed at 1000 C for 30 min and patterned
by an SF and O reactive ion etch (RIE). The sacrificial layer
was etched in buffered HF acid. A device is shown in Fig. 9(d).
IV. EXPERIMENTAL RESULTS
This section describes measurements of fabricated samples.
Residual strain measurements and the extraction of thermal ex-
pansion coefficients are described first followed by C–V mea-
surements of Young’s modulus. The performance of the capac-
itive strain sensors was verifiedin both tensile and compressive
material.
A. Thermal Expansion Coefficient and Residual Strain
Measurements
Passive bent beam strain sensors [10] were located adjacent
to the capacitive devices in the layout. Vernier readings from
these devices were used to determine the local residual strain
and using this information the expected values of differential ca-
pacitance were calculated by the analytical approach described
in the modeling section. In addition, samples were heated and
strains were measured as a function of temperature.
The for Ni deposited in set A was first measured by passive
bent-beam strain sensors, with m, m and
rad. Strain was measured as a function of temperature
by visually monitoring their deformations and compensating for
of Si, which changes from 2.5 ppm/K at 23 C to 4 ppm/K at
500 C [24]
(10)
where is the strain observed by the strain sensor. The
residual strain changed from 1.1 10 at 23 Cto 880
microstrain at 100 C. The for Ni used in set A increased
from 13.5 ppm/K at 50 Cto 16.5 ppm/K at 150 C (see
Fig. 10). This compares well with previously published results.
One report indicates that for Ni increases from 10.2 ppm/K
at 20 C to 16.3 ppm/K at 300 C and holds the latter value
at 400 C as well [25]. Another report indicates that for Ni
electroplated under particular conditions may increase from
8.5 ppm/K averaged over the temperature range from 25 to
Fig. 10. The thermal expansion coefficient of the structural metal as measured
by passive bent-beam strain sensors.
Fig. 11. The thermal expansion coefficient of the structural metal as measured
by four adjacent differential capacitive strain sensors. The support ribs buckled
near 60 C.
50 C to 15.1 ppm/K averaged over the temperature range of
25–367 C [26].
The capacitive strain sensors were then used to monitor the
Ni residual strain in set A as a function of temperature. Mea-
surements from four adjacent devices showed a linear increase
in differential capacitance from 20 Cto60C (see Fig. 11).
Measurements were taken with 0.5 fF precision using a de-
vice with 10 tine pairs with 168 m overlap length and 5 m
nominal gap, suspensions with m, m and
rad. and ribs with m and m. The
device response to increasing temperature was theoretically es-
timated using FastCap™, assuming that the average for Ni
exceeds that for Si by 10 ppm/K. This result is superimposed
on the measured data in Fig. 11. Based on the passive strain
sensor measurements (see Fig. 10) and previously published re-
sults, the expansion mismatch between nickel and silicon over
20–60 C was 6–11 ppm/K, consistent with the differential ca-
pacitance measurements. At temperatures 60 C, however, the
4.4- m thick devices were affected by out-of-plane buckling of
the support ribs. This suggests dimensional constraints for de-
vice designs.
In the variant of set A denoted A0, a device with dimensions
of m, m and rad. with 18 tine
pairs at 1.3 m separation and 91 m overlap, was expected to

CHU et al.: MEASUREMENTS OF MATERIAL PROPERTIES USING DIFFERENTIAL CAPACITIVE STRAIN SENSORS 495
Fig. 12. Capacitance change referenced to the neutral position for a LIGA
device.
produce a fF. In comparison, the measured value
was 4.8 fF.
The measurements of a set B device indicated that the
residual strain was 68.5 microstrain at 23 C and 236 mi-
crostrain at 85 C. These values were determined by fitting the
measured to calculated values using the procedure outlined
in the Section II. This device had 24 tines in each of four banks,
with 900 m overlap length, 1040 m total length, 29 m width
and 10 m nominal gap; suspensions with m,
m width and rad.; and ribs with
m and m. The for Ni was calculated for set
B devices by using (10) and the capacitively measured values
of strain. After accounting for the for #7740 glass which is
3.25 ppm/K [24], these measurements indicate that for Ni that
was plated for set B devices was 8.2 ppm/K when averaged over
23–85 C, which falls within the range previously reported [26].
Further confirmation of the expansion coefficient was obtained
by using the change in alone as a function of temperature.
The calculated and measured capacitances were referenced to
the at 37 C, which was the interpolated zero-stress tem-
perature (Fig. 12). The close fit indicates that for Ni was
7.9 ppm/K. At 130 C the calculated increase in the gap between
the tines (with respect to the zero-stress position) was 3.95 m,
corresponding to a residual strain of 420 microstrain. This
matched with the calibrated visual measurement of 3.7 m.
In the set C devices, the residual stress measured by the pas-
sive strain sensors was compressive, at 250–260 strain. For a
device with suspension length of 100 m, width of 4 m, thick-
ness of 2.5 m and a bending angle of 0.2 rad with 22 tine pairs
at a separation 3 m and overlap of 112 m, this suggests a
reading of fF. In comparison, the measured value
was 5.0 fF.
B. C–V Measurements, Young’s Modulus, and Residual Stress
Although the Young’s modulus of bulk nickel is 208 GPa,
electroplated nickel demonstrates significant variability de-
pending on deposition conditions such as current density and
can have a substantially lower modulus [27]. This underscores
the need for in situ material property measurements. For Ni
electroplated under particular conditions, a value of 150 GPa
Fig. 13. Measured C–V as a function of temperature for surface
micromachined Ni structure. The buckling temperature for this device
was
>
70 C.
Fig. 14. Comparison of a measured C–V curve from Fig. 13 to a fitted
theoretical curve.
T
=
60
C.
was reported in [28] using a resonant beam technique. Another
study based on precision tensile machine tests reported 158 GPa
and 181 GPa for two separate runs done at the same foundry
[5], [29]. Another study concluded that the modulus decreased
from 156 GPa to 131 GPa when the electroplating current
density was increased from 20 to 70 mA/cm when using a
nickel sulfate-based bath [27]. Yet another study reported a
Young’s modulus of 231 GPa using a technique similar to the
tensile machine method [31].
Fig. 13 shows CV curves that were measured at various tem-
peratures for set A devices with dimensions as noted previously,
except rad. Numerically simulated curves were fitted to
measurements using the zero bias capacitance and the Young’s
modulus as fitting parameters. A comparison of a measured and
fitted curve pair is shown in Fig. 14. The best fit of corre-
sponded to a Young’s modulus of 135 15 GPa at 23 C for the
electroplated metal.
Measurements for the set B device are plotted in
Fig. 15 as fractional changes in measured capacitance,
i.e., , against . In this represen-
tation, the -axis is proportional to the fractional change in
the gap between the tines, while the -axis is proportional to
the electrostatic force. At 23 C the best fit corresponds to a

496 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002
Fig. 15. Measured
C
for set B sensors at various temperatures.
C
is the
measured
C
at
V
=
0
.
Fig. 16. Measured
1
C
for set B strain sensors at two temperatures.
Young’s modulus of 115 10 GPa. Some of the uncertainty is
attributable to the calculation of fringing fields and the impact
of parasitics in measurements. These were eliminated from the
strain measurements because was used instead of .
Consequently, it may be possible to reduce the uncertainty by
using measurements (Fig. 16). A set of curves such as this
may be useful as a process control standard even if not used to
extract the material properties.
Both the set A and set B devices showed that the Young’s
modulus of electroplated Ni decreased with increasing temper-
ature. This is also evident from the trend in Fig. 15. The temper-
ature coefficient of the Young’s modulus, which is the same as
that of , was estimated as 1590 ppm/K. There is significant
uncertainty in this value because measurement and fitting er-
rors are compounded. This parameter is also strongly dependent
on fabrication conditions and values ranging from 550 ppm/K
[28] to 952 ppm/K [24] have been reported previously.
To verify the measurements obtained using the differential
capacitive strain sensor, a load-deflection test was done to mea-
sure the Young’s modulus. Nickel specimens from set B with
mm, m and mm were used
in the test. The deflection specimen was mounted on a holder
such that it was cantilevered with the boundary conditions of a
fixed-free beam (see Fig. 17). Using a Chatillon TCD200 uni-
versal tensile tester (which can also provide compressive loads)
which has a force resolution of 0.01 N, a blade edge was low-
ered with precise motion control to exert a line force at a spe-
Fig. 17. A typical set of data obtained with the load-deflection measurement.
cific location. The force-displacement measurement yielded the
effective spring constant of the cantilever and this spring con-
stant was used to calculate the Young’s modulus of the mate-
rial. Using this method, 40 load-displacement curves were gath-
ered with a loading force applied 7.6 mm from the clamped
point. A typical load-deflection curve is shown in Fig. 17; for
this particular measurement, the spring constant is 27.6 gram
force per mm deflection. This spring constant translates into
GPa. The average of 40 such measurements yield
a Young’s modulus of 115.5 GPa with a standard deviation of
4.3 GPa. These measurements agree well with the strain sensor
reading of 115 10 GPa.
Using the measured values of strain and Young’s modulus the
thermal stress in the metal microstructures can be calculated in a
piecewise linear manner. For the plating solution and conditions
used in the set A devices, at 23 C the stress is essentially zero
and at 100 C it is approximately 105 MPa. The residual stress
for the set B structure was 7.88 MPa at 23 C and 27.1 MPa
at 85 C using GPa. For set C, in which the structural
material was expansion matched to the substrate, the Young’s
modulus was not measured. However, using the widely used
value of 160 GPa, the stress was 40 MPa to 42 MPa at room
temperature.
Trace levels of contamination and variations in plating
conditions can significantly affect the mechanical properties of
electroplated materials. An X-ray energy-dispersive spectrum
(XEDS) plot of the set A Ni plating sample indicated very
minute contamination from Cu only.
V. CONCLUSION
In summary, the differential capacitive strain sensor is
demonstrated to measure strain, Young’s modulus and thermal
expansion coefficient for both compressive and tensile mate-
rials. As a result, temperature dependency of these mechanical
properties can be determined. For polysilicon, the stress is
measured to be between 40 MPa and 42 MPa. Also, it was
found that the for electroplated Ni was 8–16 ppm/K over
23–150 C; the residual strain changed from neutral to 880
microstrain over 23–100 C in one case and 68.5 microstrain
to 420 microstrain over 23–130 C in another case; and the
Young’s modulus ranged from 115–135 GPa at room tempera-

CHU et al.: MEASUREMENTS OF MATERIAL PROPERTIES USING DIFFERENTIAL CAPACITIVE STRAIN SENSORS 497
ture. Theoretical calculations indicate that C–V measurements
can be affected by variations in device dimensions. However,
when these are known a priori, the measurements of material
properties provided by differential capacitive strain sensors
are consistent with expectations. This device is suitable for
monitoring fabrication and packaging process variables and
may also be used to compensate other sensors over extended
periods of deployment for drifts in material properties.
ACKNOWLEDGMENT
The authors gratefully acknowledge the late Prof. H. Guckel
and Dr. B. Chaudhuri for helpful discussions. The authors also
acknowledge Prof. P. Nealey and Dr. T. Kim for help with the
self-assembled monolayer coating process, Prof. D. Stone for
assistance in hardness testing and R. Noll for the XEDS results.
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Larry L. Chu received the B.S. and M.S. degrees
from the University of Wisconsin—Madison in 1998
and 2001, respectively, both in electrical and com-
puter engineering. He is currently pursuing the Ph.D.
degree in the same department and expects to com-
plete the program in summer 2002.
From 1998 to present, he holds a research assist-
antship with the Microsystems Lab at the University
of Wisconsin—Madison. Since 1998, he has worked
on various aspects of micromachined structures for
sensing and actuation and completed several projects
from conceptualization to final device. He has been working on the design, op-
timization and application of electrothermal actuators and actuators in conjunc-
tion with compliant micro structures such as displacement amplifiers. He also
worked on the characterization of materials using micro structures and various
techniques for actuator fabrication. His current research interests include: the
design and fabrication of microsystems that use actuators and the use of these
microsystems in RF, optical, fluidic and microscopy applications.

498 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 11, NO. 5, OCTOBER 2002
Long Que (S’98–M’01) received the B.S. degree
in physics and the M.S.E.E. degree in optical com-
munication from Peking University, Beijing, P. R.
China, in 1990 and 1994, respectively. He received
the M.S. and Ph.D. degree from University of
Wisconsin–Madison in 1996 and 2000, respectively,
all in electrical engineering.
From 1990 to 1993, he was a Research Engineer at
the National Key Lab of Microfabrication on Optical
Technology, Institute of Optics and Electronics, Chi-
nese Academy of Sciences. From 1993 to 1994, he
was a Research Assistant in the National Laboratory on Local Fiber-Optic Com-
munication Networks & Advanced Optical Communication Systems, Peking
University. From January 1995 to June 2000, he was a Research Assistant at
Center for Nanotechnology, ECE Microsystems Lab at University of Wisconsin
at Madison. Since September, 2000, he joined asa R&D Engineer, then Principal
Engineer at OpticNet, Inc., Campbell, CA, where he has been developing optical
components using MEMS techniques for WDM and DWDM optical communi-
cation networks.
Dr. Que received a national research award in the development of submi-
cron and deep submicron IC technology from Chinese Academy of Sciences in
1997. He received the Vilas development fellowship from University of Wis-
consin—Madison in 2000 for his dissertation research work. He has published
more than a dozen papers in journals and conferences in optics, nanotechnology
and MEMS areas. He has six patents pending. He is a Member of SPIE.
Yogesh B. Gianchandani (S’83–M’95) received
the B.S., M.S., and Ph.D. degrees in electrical
engineering from University of California, Irvine,
University of California, Los Angeles, and Univer-
sity of Michigan, Ann Arbor, in 1984, 1986, and
1994, respectively.
From 1985 to 1989, he held industry positions with
Xerox Corporation and Microchip Technology, Inc.,
working in the area of integrated circuit design. From
1994 to 2001, he held various positions first at the
University of Michigan and then at the University of
Wisconsin–Madison. In 2002, he returned to the University of Michigan, where
he is currently an Associate Professor in the Electrical Engineering and Com-
puter Science Department. His research interests include all aspects of design,
fabrication and packaging of micromachined sensors and actuators and their in-
terface circuits.
Prof. Gianchandani received the National Science Foundation Career
Award in 2000. He serves on the editorial boards of the IOP Journal of
Micromechanics,Journal of Semiconductor Science and Technology, and
Microengineering and Sensors and Actuators. He also serves on the steering
and technical program committees for the IEEE International Conference
on Micro Electro Mechanical Systems (MEMS) and served as the General
Co-Chair for this meeting in January 2002.