Simulation and fabrication of piezoresistive membrane type MEMS strain sensors
Li Caoa, Tae Song Kimb*, Susan C. Mantella** and Dennis L. Pollab
a
Dept. of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455
Dept. of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455
b
Abstract
Two piezoresistive (n-polysilicon) strain sensors on a thin Si3N4/SiO2 membrane with
improved sensitivity were successfully fabricated by using MEMS technology.
The
primary difference between the two designs was the number of strips of the polysilicon
patterns. For each design, a doped n-polysilicon sensing element was patterned over a thin
3 m Si3N4/SiO2 membrane. A 1000 m x 1000 m window in the silicon wafer was etched
to free the thin membrane from the silicon wafer. The intent of this design was to fabricate
a flexible MEMS strain sensor similar in function to a commercial metal foil strain gage. A
finite element model of this geometry indicates that strains in the membrane will be higher
than strains in the surrounding silicon. The values of nominal resistance of the single strip
sensor and the multi-strip sensor were 4.6 k and 8.6 k, respectively. To evaluate
thermal stability and sensing characteristics, the temperature coefficient of resistance [TCR
= (R/Ro)/T] and the gage factor [GF = (R/Ro)/] for each design were evaluated. The
sensors were heated on a hot plate to measure the TCR. The sensors were embedded in a
vinyl ester epoxy plate to determine the sensor sensitivity. The TCR was 7.5x10-4 and
9.5x10-4 /oC for the single strip and the multi-strip pattern sensors. The gage factor was as
high as 15 (bending) and 13 (tension) for the single strip sensor, and 4 (bending) and 21
(tension) for the multi-strip sensor. The sensitivity of these MEMS sensors is much higher
than the sensitivity of commercial metal foil strain gages and strain gage alloys.
Keywords: Polysilicon; MEMS; Strain sensors; Finite element method
1. Introduction
*
Current address : Thin Film Technology Research Center, KIST, 39-1 Haweolgog-dong, Seongbuk-gu,
Seoul 136-791, Korea
**
Corresponding author
1
In measuring the strain, among the physical principles that have been employed, the
piezoresistive property of electronic materials is often utilized in strain sensor applications.
Since piezoresistive materials for strain measurements were developed by Mason et al.[1],
many efforts have concentrated on fabricating piezoresistive strain sensors. Many metal and
metal alloys thin films have been studied for strain measurements, such as Au[2], Cu[3],
Mn[4], Bi-Sb[5], Ni-Cu[6], Ni-Cr[7,8], Pd-Cr[8]. RuO2 based thick film was studied for
piezoresistive strain sensors [9]. Polysilicon is another well-known piezoresistive material.
French et al. showed that even when the polysilicon sensitivity is poor, strain measurements
are possible because the resistivity of polysilicon has a low temperature dependence [10].
One potential approach of MEMS strain sensors is in structural health monitoring. For
example, Hautamaki et al. [11] studied silicon based n-polysilicon strain sensors that were
fabricated using MEMS technology.
These sensors were embedded in a polymer
composite structure and used to evaluate the strain in the structure. MEMS strain sensors
hold a distinct advantage over conventional metal foil based strain gages in that the overall
sensor system (consisting of a strain sensor, signal conditioning and telemetry circuit, and
antenna) does not require a wire connection. These completely integrated devices are well
suited for composite aircraft components, bridge and ship structures.
Detection of
excessive loads can help avoid catastrophic failure of these structures. Critical to this
application are the sensor characteristics. A monofilament strain sensor was fabricated by
depositing a single filament of piezoresistive material onto a 500 µm thick silicon wafer.
As the silicon wafer base is strained, the sensor filament is also strained. Hautamaki et al.
[11] found that the strain transfer from the polymer composite to the monofilament sensor
was on the order of 30-50%. For example, a 1000  load on the structure produced only
300-500  in the sensor. These researchers concluded that MEMS strain sensor response
must be sensitive so as to produce the desired resolution for subsequent signal processing.
The monofilament sensor also performed inconsistently: gage factors when the sensor was
loaded in bending were nearly 47% higher than for uniaxial loads.
2
In this paper, a new strain sensor designed for improved performance, greater sensitivity
and less variation between bending and uniaxial response, is described. The sensing
material is patterned over a thin membrane.
The thin membrane provides a flexible
backing for the sensing element. Subsequently, the sensor response for this new design
should be better than the designs in [11]. Novel fabrication methods are required for this
design to be manufactured. These methods include: developing a repeatable method for
fabricating the thin membrane, and developing a technique for uniformly etching the silicon
wafer beneath the thin membrane. Two different sensor designs were fabricated and tested.
The primary difference between the two designs was the number of strips of the doped npolysilicon pattern. Two measures were used for sensitivity evaluation: the temperature
coefficient of resistance [TCR = (R/Ro)/T], and the gage factor [GF = (R/Ro)/]. Ro is
the nominal resistance, R is the resistance change, T is the temperature change, and  is
the strain at the sensor. To evaluate the thermal stability, the TCR was measured by
heating the sensors on a hot plate. To obtain the strain transfer effect of embedding, the
gage factor (sensitivity) for each sensor design was found by embedding the sensor in a
vinyl ester epoxy plate and loading the plate.
2. Experimentation
2.1 General description of sensors
In the two sensor designs (single strip and multi-strip), the sensing element was patterned
over a thin Si3N4/SiO2 layer (Figure 1). Doped n-polysilicon was used to sense the strain
changes. The silicon beneath the Si3N4/SiO2 layer was etched to form a membrane with a
cross sectional area 1000 m x 1000 m. The overall cross sectional area of the sensor was
10 mm x 10 mm.
2.2 Fabrication of sensors
3
The general steps required to fabricate a thin membrane backed device are:
1. Grow 1.5 m silicon dioxide SiO2 onto a silicon wafer using wet thermal oxidation and
deposit 1.5 m silicon nitride Si3N4 using a low-pressure chemical vapor deposition
(LPCVD);
2. Etch Si3N4 using Reactive Ion Etching (RIE) and SiO2 with Buffered Oxide Etch (BOE)
solution (10:1) in order to form a 1000 m x 1000 m window at the back side;
3. Deposit 0.3-0.4 m phosphorus doped polysilicon using LPCVD and anneal the
polysilicon layer at 850C temperature for 1 hour;
4. Partially etch the back side of the wafer using deep trench RIE (DRIE) and form a 1000
m x 1000 m window;
5. Pattern polysilicon strips onto the membrane by using RIE;
6. Consecutively deposit a 0.03 m Ti and 0.12 m Ag electrode by E-beam process and
pattern it using lift-off process;
7. Completely etch the silicon opening away by using DRIE (Plasma Therm SLR series)
to form a 1000 m x 1000 m Si3N4/SiO2 membrane. The etching gases were C4F8 and
SF6; and
8. Coat a 40-60 m thick polymer SU-8 on the top of the wafer and pattern.
A schematic diagram of the fabrication process is shown in Figure 2. The annealing step
was included in this fabrication to stabilize the electrical property of the sensors. Before
depositing the Ti/Ag electrode layer, the wafer was slightly etched in a BOE solution for
removing the possible oxide layer on the polysilicon patterns. This step enhanced the
ohmic contact between electrode and polysilicon. An SU-8 polymer film was spun onto the
silicon wafer in order to protect the thin membrane and thin polysilicon patterns.
2.3 Measurement of sensing characteristics
4
Two types of sensors, a single strip and a multi-strip sensor, were embedded in a vinyl ester
epoxy specimen to evaluate the gage factors. Three specimens were constructed: i) a
specimen with an embedded commercial strain gage (EA-00-125AD-120E) mounted on a
blank 10 mm x 10 mm x 0.5 mm silicon wafer; ii) a specimen with an embedded MEMS
single strip sensor having a 1000 m x 1000 m membrane window; iii) a specimen with
an embedded MEMS multi-strip sensor having a 1000 m x 1000 m membrane window.
The specimen material (vinyl ester) and geometry (160 mm x 30 mm x 6.0 mm) are
identical. The overall MEMS sensor size was 10 mm x 10 mm x 0.5 mm thick. The strain
gage mounted on a blank silicon wafer in the strain gage specimen had the same size and
geometry as the MEMS strain sensor. For each specimen, the embedded device was placed
at a height one quarter the overall thickness and at one end of the specimen, as shown in
Figure 3. This location was selected to ensure good sensor response in bending. Two
different loadings were applied, bending and uniaxial tension. A cantilever beam method
was used to apply the bending load [12]. The specimen was held rigid at one end. A
bending load, ranging from 0 to 11.8 kN, was applied to the free end of the specimen.
Bending tests were run in both compression and tension bending by turning over the
specimen. The same specimen was loaded in tension on a MTS Test-QT/10 machine. A
(uniaxial) tension load, ranging from 0 to 1.6 kN, was applied.
2.4 Overall calibration technique of sensors
Sensor calibration entails developing a repeatable relationship between the change in sensor
resistance and the strain measured at the sensor. The strain gage on a silicon wafer
embedded in vinyl ester (the strain gage specimen) provides a standard for measuring strain
at the sensor. Identical tests are conducted on the strain gage specimen and the MEMS
specimens.
The strain gage data are used to obtain the MEMS sensor strain when
embedded in the vinyl ester epoxy specimen. Sensor calibration follows the standard
methodology applied to commercial metal foil strain gage calibration.
The sensor
calibration procedure is detailed in [14].
5
3. Simulation
A finite element model (ANSYS software, Swanson Associates) of the sensor structure was
constructed to verify the effect of the membrane on sensor strain. The silicon wafer was
modeled using 2181 three dimensional linear tetrahedral elements (ANSYS element
solid73) and the membrane was modeled using 8 shell elements (ANSYS element shell63).
The mesh was refined to ensure a stable solution. To take advantage of the symmetry of
the sensor geometry, only half of the sensor was modeled (Figure 4). Along the edges of
the silicon at x =  5.0 mm, the boundary was simply supported. Bending or tension loads
were prescribed at the both edges, at x =  5.0 mm. The tension load consisted of applying
a constant displacement (ux = 2.2 x 10-6 m) at the edges. The bending load consisted of
applying a constant moment (My = -0.24 x 10-3 Nm) at the edges. These two loads were
applied because they will produce a constant strain field at the top surface of a silicon wafer
that has no membrane. The discontinuity at the membrane causes the strain field to change
in and near the membrane. However far from the discontinuity, the strain field converges
to a constant value near the edges of the wafer for both load conditions. For the purpose of
comparing bending and tension strains, all strains were normalized with respect to the strain
at the edge of the wafer. To validate the model, strains at the edges of the silicon wafer
with membrane model were compared with strains in a silicon only model. Edge strains in
the wafer/membrane model were consistent with strains in the silicon only model when
uniform bending or tension loads were applied at the edges.
Model predictions of the bending and tension strains along y = 0 mm (x = 0 to 5 mm) and x
= 0.25 mm (y = 0 to 5 mm) are shown in Figures 5 and 6 respectively. In both figures, the
strains are normalized with respect to the strains at the edges of the wafer. The sensing
element is oriented such that the length of the element is parallel to the y = 0 mm axis
(Figure 4). Strains along x = 0.25 mm, then, are strains at the midpoint of each strip of the
sensing element. Strains along y = 0 mm are strains along the center strip of the multi-strip
6
sensor or along the single strip of the single strip sensor. Both figures clearly indicate that
strain in the membrane is higher than strain in the surrounding wafer. Higher strain in the
membrane will improve the sensor sensitivity. It is interesting to note that bending strain is
consistently higher than tensile strain. The figures also provide insight as to how a multistrip sensor will behave compared to a single strip sensor. In the single strip sensor, the
sensing element lies along the y = 0 mm axis. The average strain along this axis is
measured (Figure 5). The multi-strip sensor, however, spans across the width of the
membrane. Bending and tension strains vary along the length of a turn as well as between
turns (Figure 6). The model, then, indicates that the multi-strip sensor having 5 sensing
strips (Figure 4) will average both strains within each turn and over all the turns, leading to
increased variation over the single strip sensor.
Sensor gage factor data will be
qualitatively compared to these model predictions in the following section.
4. Results and discussion
4.1 Sensor structure
Single strip and multi-strip n-polysilicon patterns were formed on a 3 m thin Si3N4/SiO2
membrane. A top view of each pattern is shown in Figure 7. The width of a sensing strip
was 20 m for the single strip and 30 m for the multi-strip pattern. The overall sizes of the
single strip and the multi-strip patterns were 400 m x 100 m and 400 m x 760 m,
respectively. The Si3N4/SiO2 membrane window was transparent and flat. The thick SU-8
coating on the membrane does not affect the shape of the membrane as shown in Figures
7(a) and (b).
Figures 8 shows the bulk micromachined deep trench of the back side of the sensors.
Vertical side wall was achieved in these sensors, but the surfaces of the side walls were not
smooth. The prominence and depression patterns of the side walls are continuous from the
top to the bottom. From this continuous shape, it is presumed that the initial patterned line
7
shape of the mask material, SiO2 layer, might affect the entire surface shape of the etched
side walls.
4.2 Electrical properties
In order to check the electrical contact between Ti/Ag and n-polysilicon, current-voltage
characteristics were measured with a HP 4284A Precision LCR meter. The current-voltage
curve is nearly linear regardless of the n-polysilicon pattern styles. The linear relationship
indicates good ohmic contact between the Ti/Ag electrode and the n-polysilicon thin films.
The nominal resistance for the single strip sensor was 4.6 k while that of the multi-strip
sensor was 8.6 k. There was little variation in sensor resistance for sensors fabricated on
the same wafer. This consistent initial resistance can be attributed to the annealing step. In
addition, temperature coefficients of resistance (TCR) for the single strip and multi-strip
sensors were evaluated over a temperature range of 25oC to 130oC. Figure 9 shows a
typical TCR plot for a multi-strip sensor. The normalized resistance change with the
temperature was linear for each design. The TCR is the slope of the data. A TCR close to
zero is desirable. Low TCR indicates that variations in the ambient temperature do not
have a significant effect on the resistance of the sensor. The TCR was as low as 7.5x10-4
/oC for the single strip and 9.5 x 10-4 /oC for the multi-strip sensors.
4.3 Sensing characteristics
The bending and tension test results for the two sensor designs are shown in Figures 10 and
11, respectively. The sensor strain was determined from the strain gage specimen test data
collected under similar loading condition [14]. The normalized resistance change with the
sensor strain was linear for each design. The normalized resistance change increased
linearly with the sensor strain as a compression bending load was applied. Similarly, the
normalized resistance change decreased as a tension bending load or a tension load was
8
applied. Gage factors are the slopes of the data shown in Figures 10 and 11. The gage
factors (sensitivity) were 15 (bending) and 13 (tension) for the single strip sensor, and 4
(bending) and 21 (tension) for the multi-strip sensor as shown in Figure 12.
The ideal sensor would have a gage factor that is consistent regardless of the loading. Of
the two windowed strip sensors, the single strip sensor performs most consistently. The
gage factors for the single strip sensor vary by 15% between bending and tension tests. The
gage factors for the multi-strip sensor vary considerably between bending and tension tests.
The multi-strip sensor covers a large area of the membrane surface and will be more
sensitive (than the single strip sensor) to variations in the strain across the membrane.
Thus, the large variation in gage factors for the multi-strip sensor (as compared to the single
strip sensor) implies that the strain distribution across the membrane is not uniform. These
data are supported by the finite element results. The finite element predictions of strain
across the membrane (Figure 6) also show that the strain will not be uniform in the region
where the multi-strip sensor is patterned.
The gage factors of MEMS fabricated piezoresistive sensors on the thin membrane, which
were obtained from bending and tension tests, are relatively larger than those of common
strain gage alloys (Table 1). Gage factors for MEMS strain sensors are more than double
those for common strain gage alloys [13]. The larger sensitivity value of MEMS based
membrane type piezoresistive micro-strain sensors shows the possibility of the usage as a
strain sensor. The high gage factor indicates high sensitivity to changes in strain.
Moreover, the high gage factor reduces the signal processing requirements and is
compatible with lower power electronics.
The gage factors found for the strip on membrane sensors (described herein) are
comparable to those found for the monofilament sensors fabricated directly on the wafer
(described in [11]). The single strip membrane design, however, has more consistent
performance between bending and tension loads. The monofilament sensor had gage
9
factors that ranged from 22 (bending) to 15 (tension), a variation of nearly 47%. The
consistent response to tension and bending loads exhibited by the single strip sensor on the
membrane is a significant improvement.
5. Conclusions
Two designs for the MEMS piezoresistive (doped n-polysilicon) strain sensors on a 3 m
thin Si3N4/SiO2 membrane were successfully fabricated and tested. The primary difference
between the two designs was the number of strips of the polysilicon patterns. Both a single
strip sensor and a multi-strip sensor were fabricated. The sensors, because they have been
annealed, showed little variation in nominal resistance. The thermal sensitivity (TCR) of
each sensor was very low. The TCR ranged from 7.5x10-4 to 9.5x10-4 /oC.
The gage factor for each sensor design was measured under tension and bending loads. The
single strip sensor gage factors in tension and bending were comparable (within 15%).
However, the gage factors for the multi-strip sensor varied considerably. The bending gage
factor for the multi-strip sensor was well below the tension gage factor.
This low
sensitivity in bending may be caused by the boundary effect of the membrane and side wall.
With the exception of the bending gage factor for the multi-strip sensor, the gage factors for
the membrane designs are comparable to those for the MEMS strain sensors designed by
Hautamaki et al [11]. The single strip sensor design, however, has the most consistent
response to bending and tension loads.
These findings are supported by finite element modeling of the strains in the membrane.
The membrane serves to amplify the strain in the wafer. Strains are greatest at the center of
the wafer and diminish significantly at the boundary between the membrane and wafer.
6. Acknowledgment
10
This research is funded by the US Naval Research Laboratory (NRL), contract number
N00014-94-C-2231.
7. References
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MEMS strain sensors embedded in composites, Journal of Microelectromechanical
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Table
12
Table 1
Gage factors [(R/R)/] for MEMS and common strain-gage materials
Figures
Figure 1.
Schematic top view of the single strip (left) and the multi-strip (right)
sensors.
Figure 2.
Schematic view of the fabrication process.
Figure 3.
Schematic drawings of strain measuring specimen.
Figure 4.
Schematic of the geometry and boundary conditions used in the finite
element model.
Figure 5.
Strains along the center of the sensor at y = 0 mm.
Figure 6.
Strains through the membrane along the line x = 0.25 mm.
Figure 7.
Micrographs of the patterned polysilicon in (a) a single strip sensor and
(b) a multi-strip sensor.
Figure 8.
SEM image of the magnified vertical side wall shape of the DRIE etched
back side silicon wafer.
Figure 9.
Change in resistance of sensors as a function of temperature (TCR value
of n-polysilicon).
Figure 10.
Normalized resistance change of (a) the single strip sensor and (b) the
multi-strip sensor in bending.
Figure 11.
Normalized resistance change of the single strip sensor and the multi-strip
sensor in uniaxial tension.
Figure 12.
Gage factor of the single strip sensor and the multi-strip sensor.
13
Table 1. Gage factors [(R/R)/] for MEMS and common strain-gage materials
Sensing material
Gage factor
n-polysilicon membrane single strip strain sensor (MEMS)
13-15
n-polysilicon monofilament strain sensor (MEMS) [11]
15-22
45%Ni-55%Cu alloy strain gage [13]
2.1
36%Ni-8%Cr-0.5%Mo-55.5%Fe alloy strain gage [13]
3.6
92%Pt-8%W alloy strain gage [13]
4.1
14