cmos-mems high gee capacitive accelerometers · cmos-mems high gee capacitive accelerometers ......
TRANSCRIPT
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CMOS-MEMS High Gee Capacitive Accelerometers
Amy Wung
A report submitted in partial fulfillment of the requirements of the degree of:
MASTER of SCIENCE
in
ELECTRICAL AND COMPUTER ENGINEERING
at
CARNEGIE MELLON UNIVERSITY
Advisor: Prof. G. K. FedderReader: Tamal Mukherjee
December 23, 2007
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i
Dedicated to my parents, Edward and Bea Wung, and my brother Derek Wung for their encouragement and love.
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Abstract
This report describes the design and testing of a tri-axial high gee integrated CMOS-MEMS capac-
itive accelerometer. Military and industrial applications, such as vehicle crash and safety testing and
in-flight munitions testing, require inertial sensors capable of measuring accelerations up to 20,000
gee’s, where 1 gee = 9.8 m/s2. Commercial piezoresistive high gee MEMS are not integrated with the
sense electronics on a single chip. The CMOS-MEMS capacitive accelerometer design has the advan-
tage of smaller size, weight, and reduced parasitics due to single-chip integration.
The high gee accelerometer capacitive design is a new derivative of previous work at Carnegie
Mellon University on low gee capacitive accelerometers. The structure of this high gee accelerometer
departs from traditional low gee plate and comb drive capacitive sensing accelerometers, instead tak-
ing the form of an array of cantilever structures. The cantilever’s reduced mass and increased stiffness
increases the sensitivity range to the desired 20,000 gee’s. An array of cantilever structures is electri-
cally connected in parallel to obtain larger capacitive sensitivity.
The design methodology presented in this paper will demonstrate the theory and simulations used
to optimize the cantilever mechanical structures and capacitive sensing method. Preliminary electrical
and shock testing results in the 50-30,000 gee range will be presented to show functionality and linear-
ity of the sensor.
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Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Objective .....................................................................................................1Motivation ...................................................................................................1Previous work .............................................................................................2CMOS-MEMS process ...............................................................................3CMOS-MEMS high gee accelerometer design ..........................................4
Chapter 2: Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . 8Inertial sensor mechanical structures ..........................................................8Lateral high g-force accelerometer mechanical design issues ..................15Vertical accelerometer mechanical design issues .....................................19
Chapter 3: Capacitive Sensing . . . . . . . . . . . . . . . . . . . . . . 21Principle of capacitive sensing .................................................................21Lateral high-gee accelerometer capacitive sensing ..................................21Vertical high-gee accelerometer capacitive sensing .................................26Sense Circuitry ..........................................................................................29
Chapter 4: Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Zero input testing ......................................................................................32Shock Testing ...........................................................................................37.Future Work .............................................................................................41.Conclusions ..............................................................................................41Acknowledgments ....................................................................................42
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
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Chapter 1 Introduction
1.1 ObjectiveThis report details the accomplishments in the design and testing of a unique CMOS-MEMS high
gee accelerometer that is integrated with circuitry on a single chip. The design challenges of the accel-
erometer involve designing a mechanically robust structure that responds linearly to an input accelera-
tion, with a maximum detectable acceleration of 20,000 gees.
1.2 MotivationInertial sensors embedded within munitions allow in-flight measurement of performance metrics,
such as pitch, yaw, and thrust, during free-flight. There are stringent design requirements imposed on
inertial sensors used to measure munition movements in-flight. Foremost is the need to miniaturize,
since very little room in a munitions device is given over for sensing and metrics. Power consumption
is also limited. Further, the inertial sensors must be designed to sense accelerations as high as tens of
kilo gees, and be robust enough to withstand these same accelerations repeatedly. Cost is another
pressing design issue, as with any emerging technology. Finally, the inertial design seeks to be easily
customizable. The accelerometer design’s sensitivity should be easily adjustable to the desired testing
range. Similarly, the electronics should exist as a re-usable block for magnetometers, gyroscopes, and
other sensors.
1 Introduction
1
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Chapter 1 Introduction
The design goals for this high gee accelerometer is to achieve tri-axial sensing with integrated cir-
cuitry on a single die of volume less than 250 mm3, and weight less than 18 mg. The desired maximum
detectable acceleration in all three axes is 20,000 gees.
1.3 Previous workThe majority of commercially available inertial sensors are limited by a sensing range of plus or
minus 250 gees or less, where 1 gee = 9.8 m/s2. This sensing range is too limited for the high accelera-
tion and roll environment of in-flight munitions testing. The most common design for accelerometers
with a high sensing range utilizes piezoresistive sensing methods. Alberta Microelectronic Centre has
demonstrated silicon piezoresistive accelerometers that are capable of sensing accelerations up to
106 gee with operating voltages of 5 V, and are as small as 300 by 300 microns [5]. Endevco makes a
variety of commercially available silicon piezoresistive and piezoelectric accelerometers, with differ-
ent sensitivity ranges for different applications [6].
Piezoresistive accelerometer designs achieve many of the previously mentioned goals, most nota-
bly the size and sense range requirements. However tri-axial modules do not have the necessary sense
range. Endevco’s tri-axial piezoresistive accelerometer models are limited to 2000 gee’s, and weighs 8
grams [6],[7]. Another drawback is that the electronics associated with piezoresistive accelerometers
are not integrated on the same chip as the mechanical sensor. For the Alberta Microelectronic Centre’s
piezoresistive accelerometer, the piezoresistor deposition requires temperatures as high as 965 degrees
C, much too high for the deposition to be a post-CMOS process [5]. Endevco’s Model 7264A piezore-
sistive accelerometer is fabricated using silicon bulk micromachining processing, and housed between
two additional silicon layers, with exposed bonding pads to interface with external circuitry [8]. In
contrast, this project’s goal is to design a CMOS-MEMS sensor design with integrated circuitry. Inte-
grating the sensor and circuitry on a single chip allows for lower costs, smaller packaging, and
increased signal-to-noise ratio due to less parasitics. This report will describe the design methodology,
2
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Chapter 1 Introduction
including both theory and simulation, and conclude with preliminary shock testing results up to 200
gees.
1.4 CMOS-MEMS processThe CMOS-MEMS process for designing inertial sensors satisfies all the previously mentioned
requirements. The ability to fabricate the circuitry and mechanical sensor simultaneously allows for a
much smaller device. An additional advantage of the small size is the shorter interconnect distance,
thereby reducing the effects of parasitic resistances and capacitances. The fabrication technique is cost
effective, because it uses generic CMOS processing techniques, and also because the sensor and its
accompanying circuitry is fabricated on a single chip. There is some post-processing involved to
release the structures, but the additional cost of the post-processing is negligible compared to CMOS
processing, packaging, and testing costs. Finally the design is customizable, because its sensitivity
range can easily be adjusted by adjusting the dimensions of the device.
Researchers at Carnegie Mellon University have previously designed working CMOS-MEMS
accelerometers [1], resonators [2], and chemical sensors [3], all fabricated in generic CMOS foundries
and post-processed in the Carnegie Mellon University clean room. The MEMS devices described here
are fabricated in the Jazz Semiconductor SiGe BiCMOS process, which includes 4 metal layers. After
the chips are processed in the CMOS foundry, there remains some post processing for microstructural
release. Post processing involves a vertical oxide etch to define the mechanical structures, followed by
a timed vertical silicon etch and an isotropic silicon etch to release the mechanical structures. Metal
layers are used as a mask to define the structure [4]. The top metal layer is used to protect the circuitry
from being etched away during the post-processing. Figure 1.1 details each step of this process.
3
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Chapter 1 Introduction
Figure 1.1 (a) Cross-section of integrated CMOS-MEMS chip after foundry processing. (b) Cross-
section after vertical silicon dioxide etch. (c) Cross-section after vertical silicon etch. (d) Cross-section
after isotropic silicon undercut etch [4].
1.5 CMOS-MEMS high gee accelerometer designThe CMOS-MEMS high gee accelerometer design builds heavily on a CMOS-MEMS low gee
accelerometer designed in 2005. [1] The design, in contrast with other piezoresisitive high gee sensors,
uses capacitive sensing methods. The capacitive sensing design principle is detailed in Chapter 3. The
mechanical topology deviates from traditional capacitive sensing accelerometers, which use comb
drives attached to a large movable plate mass anchored by springs. In order to increase the sensitivity
range of the accelerometer, the high gee accelerometer design uses instead an array of separately
anchored comb fingers which are capable of bending under high gee forces.
4
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Chapter 1 Introduction
Figure 1.2 (a) Top-view finite-element simulation of CMOS-MEMS high gee lateral accelerometer
design under 1000 gees of acceleration in the y-axis. Color scale indicates lateral deflection. (b) Top-
view finite-element simulation of CMOS-MEMS high gee vertical accelerometer design under
1000 gees of acceleration in the z-axis. Color scale indicates out-of-plane deflection amplitude.
(a)
stator electrode
stator electrode
suspensionbeam
movingelectrode
movingelectrode
Max:7.70 nm
Min:0 nm
stator electrode
stator electrode
suspensionbeam
movingelectrode
movingelectrode
Max:7.70 nm
Min:0 nm
stator electrode
stator electrode
suspensionbeams
movingelectrode
movingelectrode
Max: 18.62 nm
Min: 0 nm
stator electrode
stator electrode
suspensionbeams
movingelectrode
movingelectrode
Max: 18.62 nm
Min: 0 nm(b)
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Chapter 1 Introduction
The lateral and vertical accelerometer comb finger structures are pictured in Figure 1.2. Scanning
electron microscope (SEM) photographs of the fabricated accelerometers are pictured in Figure 1.3.
The lateral comb finger structure has a center suspension beam, and electrodes on either side. The sus-
pension beam is narrower than the electrodes, so that the electrodes do not bend significantly com-
pared to the suspension beam. Similarly, the vertical comb finger structure has thin suspension beams
and thick electrodes. There are two sets of suspension beams on the vertical comb finger, for vertical
curl matching. The mechanical principle of operation for each device is further discussed in Chapter 2.
Figure 1.3 Scanning electron microscope (SEM) photographs of a section of the fabricated (a)
1.0 mm x 0.2 mm lateral accelerometer array and (b) 1.2 mm x 0.2 mm vertical accelerometer array.
This report will discuss the mechanical design challenges in creating a robust structure that
achieves a sense range of up to 20,000 gees. Another design obstacle evolved from imperfections in
the CMOS fabrication process and the post-processing, resulting in lateral curl in the rotor beams. The
electrical design challenges include an improved understanding of the capacitance between CMOS
metal-oxide stacks, and how the capacitance changes with changing gap and overlap area.
Tri-axial accelerometers with integrated circuitry have been fabricated and tested. The sense cir-
cuitry has been tested with zero input acceleration, and the integrated CMOS-MEMS lateral acceler-
ometer has been shock tested at accelerations below 200 gees. The integrated CMOS-MEMS vertical
(a) (b)
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Chapter 1 Introduction
accelerometer has been shock tested at accelerations below 30,000 gees. Initial shock testing has
shown functionality of the integrated CMOS-MEMS high-g accelerometers.
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Chapter 2 Mechanical Design
2.1 Inertial sensor mechanical structuresLow gee accelerometers
A common surface-machined low gee accelerometer structure is a plate mass, with comb capacitive
transducers on two opposite sides and anchored by springs on the other two sides. Figure 2.1 shows a
simplified picture of such an accelerometer structure, with only a portion of the comb drive pictured.
Figure 2.1 A simplified comb drive accelerometer model, where the movable comb fingers and
anchored comb fingers form a capacitive divider, and an external acceleration changes the capacitance.
Only one set of comb fingers are shown for simplicity.
The capacitive comb fingers that are attached to the plate interlace with the anchored comb fingers,
making up a differential capacitive divider. An external acceleration causes the plate and comb fingers
2 Mechanical Design
y
xdeflection
y
y
xdeflection
y
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Chapter 2 Mechanical Design
to move with respect to the anchored comb fingers. The change in gap results in a change in capaci-
tance, which can be measured to determine the direction and magnitude of the external acceleration.
This method of capacitive sensing is further discussed in Chapter 3.
Lateral high gee accelerometers
For the low gee accelerometer in Figure 2.1, the upper limit of the sensitivity range is determined
by the maximum free range of movement of the plate mass. Assuming the accelerometer is at rest, the
gap between comb fingers is go. The desired high gee accelerometer specification is to displace a dis-
tance less than go under a 20 kilo gee input acceleration.
The displacement sensitivity of the low gee accelerometer, to first order, is given by the following
equation:
. (2.1)
where Δx is the plate’s displacement due to an input acceleration a. The accelerometer displace-
ment in (2.1) is dependent on the structure’s mass m and the spring constant k. The maximum detect-
able acceleration is therefore:
. (2.2)
As an example, a CMOS-MEMS accelerometer with plate length of 260 µm and a plate width of
220 µm has a resonant frequency of 12.7 kHz. [1] The plate mass therefore moves approximately
1.5 nm per gee. The gap between comb fingers at rest is 1.5 µm, which means that the maximum
detectable acceleration for this sensor is 1,000 gees.
In order to modify this design to function under input accelerations of over 20 kilo-gees, the ratio of
stiffness to mass must be increased. The mass of the device is dominated by the large plate, and the
Δxa
------ mk---- 1
ωr2------= =
amax g0 ωr( )2×=
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Chapter 2 Mechanical Design
mechanical stiffness is determined by the springs. The simple solution would be to increase the stiff-
ness of the springs, and decrease the size of the plate mass. However, decreasing the size of the plate
mass would decrease the number of comb fingers that can fit on the side of the plate, thus decreasing
the total sense capacitance. This has an adverse effect on the sensitivity, as described further in Chapter
3. Increasing the stiffness of the springs is possible by changing the geometry of the springs. However
the springs should not be designed such that the nonlinearities from extensional stress become signifi-
cant, as the plate movement would no longer be linear with acceleration. Thus there are limits to
changing the plate and spring dimensions without having adverse effects of the sensor performance.
Another idea is to take the goal of a stiff, less massive structure, to the practical limit - which would
be a single cantilever beam. The design concept chosen is to create a sensor from an array of anchored
cantilevers. The effective mass of the cantilever and its stiffness then determines the resonant fre-
quency and displacement sensitivity.
Figure 2.2 Top view finite element simulation of a 60 μm long, 2 μm wide free-end cantilever
bending under a 1000 gee input acceleration, next to two stator structures. The color scale indicates lat-
eral deflection.
stator electrode
stator electrode
Max: 2.0 nm
Min: 0 nm
stator electrode
stator electrode
Max: 2.0 nm
Min: 0 nm
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Chapter 2 Mechanical Design
A simple free-end cantilever exhibits design problems, however. Under an external acceleration,
the free end will deflect, while the anchored end remains in place. Thus the sidewall of the rotor canti-
lever will no longer be parallel to the stator, as seen in Figure 2.2. It would not be correct to assume
parallel-plate operation between the rotor and stator electrodes in Figure 2.2. In parallel-plate opera-
tion, the capacitance for the capacitance between electrodes is given by:
(2.3)
where t and L are the dimensions of the plate, and g is the distance between the plates. It will be shown
in Chapter 3 that for small changes in g, the parallel-plate capacitance changes nearly linearly. The
capacitance for a tilted-plate capacitor is given by:
(2.4)
where g is the average distance between the plates, and θ is the angle formed by the plates. Even for
small values of θ, the capacitance does not change linearly with θ [9]. Therefore, without parallel plate
operation, the output will not be linearly proportional to the input acceleration.
The free-end cantilever design, then, must be modified to ensure that the sidewall of the rotor will
remain parallel to the stator, even under a large input acceleration. The first generation of modified
cantilever structures for a lateral high gee accelerometer was discussed briefly in a previous paper
from Carnegie Mellon University [1]. The lateral high gee accelerometer design is made up of an array
of 80 rotor fingers, where a single comb finger structure is pictured in Figure 1.2(a). The cantilever
structure’s suspension beam is narrow, while the side electrodes are wider and do not bend signifi-
cantly. The most significant deflection comes from bending in the center beam. The shape of the elec-
trodes are designed with the intent to balance the moments on both ends of the center beam, creating a
C εLtg
--------=
C εtLθ
-------- 2g Lθ+2g Lθ–-------------------⎝ ⎠
⎛ ⎞ln≈
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Chapter 2 Mechanical Design
guided-end condition on the beam. With the center beam deflecting under guided-end conditions, the
side electrodes will move laterally, parallel to the stators. Thus the design preserves the parallel-plate
operation.
The FEMLAB simulations shown in Figure 2.3 illustrates the mechanical design principle. The dis-
placement plot of the bending beam in Figure 2.3(a) shows the guided-end bending caused by the bal-
ancing of moments. The displacement plot of the electrode in Figure 2.3(b) shows that the side
electrodes have approximately the same displacement along its entire length. The displacement is not
exactly uniform over the length of the electrode, but the difference in displacement is within 5% of the
total deflection. From these simulations, the displacement sensitivity of the accelerometer is approxi-
mately 6.4 pm/gee.
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Chapter 2 Mechanical Design
Figure 2.3 Finite element results for lateral accelerometer cantilever structure bending under
1000 gees input acceleration. a) Plot of lateral displacement of the side electrode. b) Plot of lateral dis-
placement of the center suspension beam.
Vertical high gee accelerometer
The vertical high gee accelerometer’s design was initiated by Tsai [1]. It operates on much the same
principle as the lateral high gee accelerometer. The accelerometer is an array of 112 rotors, where a
single set of fingers are pictured in Figure 1.2(b). The side electrodes are much thicker in the z-axis
than the suspension beams, which ensures that the electrodes do not bend significantly. The mass of
6.0
5.0
4.0
3.0
2.0
1.0
0
y-di
spla
cem
ent [
nm]
0 10 20 30 40 50 60 x-position [μm]
6.0
5.0
4.0
3.0
2.0
1.0
0
y-di
spla
cem
ent [
nm]
0 10 20 30 40 50 60 x-position [μm]
6.55
6.5
6.45
6.4
6.35
6.3
6.25
y-di
spla
cem
ent [
nm]
0 10 20 30 40 50 60 x-position [μm]
6.55
6.5
6.45
6.4
6.35
6.3
6.25
y-di
spla
cem
ent [
nm]
0 10 20 30 40 50 60 x-position [μm]
(a)
(b)
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Chapter 2 Mechanical Design
the side electrodes are designed to create balancing moments on the suspension beams, to satisfy the
guided-end condition, as demonstrated in the simulation results pictured in Figure 2.4(b). The elec-
trode displacement shown in Figure 2.4(c) is nearly equal along the length of the electrode, within 2%
of the total displacement. The displacement sensitivity is approximately 18.5 pm/gee from the finite
element simulation.
Figure 2.4 Finite element results for vertical accelerometer cantilever structure bending under
1000 gees input acceleration. a) Plot of out-of-plane displacement of the side electrode. b) Plot of out-
of-plane displacement of the center suspension beam.
y-di
spla
cem
ent [
nm]
0 10 20 30 40 50x-position [μm]
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0
y-di
spla
cem
ent [
nm]
0 10 20 30 40 50x-position [μm]
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0
y-di
spla
cem
ent [
nm]
18.6
0 10 20 30 40 50x-position [μm]
18.5
18.5
18.5
18.5
18.5
y-di
spla
cem
ent [
nm]
18.6
0 10 20 30 40 50x-position [μm]
18.5
18.5
18.5
18.5
18.5
(a)
(b)
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Chapter 2 Mechanical Design
2.2 Lateral high g-force accelerometer mechanical design issuesAn undesirable effect of process variation on the high gee CMOS-MEMS accelerometers is the
presence of lateral curl in the lateral accelerometers. In the first generation design of the lateral acceler-
ometer, the suspension beam has a length of 60 µm. The CMOS-MEMS beam includes metal 1, 2, and
3 layers, where metal 1 is 1.2 µm wide, metal 2 is 1.0 µm wide, and metal 1 is 0.8 µm wide, as illus-
trated in Figure 2.5 (a). Significant lateral curl has been observed for these dimensions, as pictured in
Figure 2.5.
Figure 2.5 (a) Cross-section illustration of suspension beam, showing the stepped metal widths.
(b) SEM photograph of first generation lateral high g-force CMOS-MEMS accelerometer design,
showing significant lateral curl. (c) SEM photograph of the same structure, with greater magnification,
illustrating the unequal gaps between the rotor and stators.
Lateral curl can be the result of several causes, including electrostatic forces from dielectric charg-
ing, and fabrication misalignment of the metal layers. The observed curl is consistent in direction and
deflection for all released devices from the same processing run. This evidence suggests that the cause
of the lateral curl in the lateral high g-force accelerometers is due to variation during processing, possi-
bly due to metal layer misalignment and stress gradients.
M etal3
M etal2
M etal1
0.1 μm
0.1 μm
M etal3
M etal2
M etal1
M etal3
M etal2
M etal1
0.1 μm
0.1 μm
(a) (b) (c)
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Chapter 2 Mechanical Design
Figure 2.6 (a) SEM photographs of test structures with the same dimension as those pictured in
Figure 2.5, processed at the same foundry but in a later processing run. (b) Greater magnification of
the vernier fingers attached to the pictured structures in (a). The vernier fingers are 1 μm wide.
Figure 2.7 a) Top view SEM photograph of a second generation of test structures. b) Greater mag-
nification of the vernier fingers attached to the pictured structures in (a). The vernier fingers are 1 µm
wide at the base, and taper to 0.5 µm wide at the tip.
There is notable variation between processing runs, which also indicates the problem is in metal
layer misalignment or stress gradients. Figure 2.6 and Figure 2.7 both show SEM photographs of sim-
ilar structures from two different processing runs. The devices in Figure 2.6 show approximately
0.8 μm deflection at the tip. In comparison, the devices in Figure 2.7 show less than 0.1 μm deflection
at the tip, although the structures in Figure 2.6 have equivalent dimensions.
(a) (b)
(a) (b)
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Chapter 2 Mechanical Design
Metal layer misalignment, material stress gradients, and other processing variation in the CMOS-
MEMS process will always be present. The designer does have options however to mitigate the effects
of process variation. One option, which all the structures above already take advantage of, is to make
each metal layer slightly narrower than the metal layer below it. In the accelerometer designs, the
metal 1 layer is 0.2 µm wider than the metal 2 layer, which is in turn wider than 0.2 µm wider than the
metal 3 layer. This cross-section is pictured in Figure 2.5 (a). Assuming that the metal offset between
layers due to process variation is not greater than 0.1 µm, the edges of each metal layer are uncon-
strained allowing the relaxation of axial stress without significant lateral curl. The first generation
accelerometer design already makes use of this design trick, however there is still significant curl, even
when the cross section in Figure 2.8 shows that the misalignment between metal layers is not greater
than 0.1 µm.
The cross-section shown in Figure 2.8 was taken using a focused ion-beam to slice through the sus-
pension beam of a lateral high g-force accelerometer. Although the cross-section shows that the metal
layer misalignment is less than 0.1 µm, several other process non idealities can be observed from cross
section. There is a visible sidewall on the left side of the structure, of approximately 0.1 µm thickness.
The sidewall is either polymer redeposited during the release process, or is an artifact of the FIB cross
section. Due to charging from the nearby structure, it is unclear from the photo if the sidewall is sym-
metrical on both sides. Additionally, the bottom metal in the stack does not have a clear cut vertical
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Chapter 2 Mechanical Design
sidewall. The top and bottom Ti/W metal barrier layers are wider than the aluminum metal layer. Fur-
thermore, there is a dark area to the left of the bottom metal layer, which could possibly be oxide.
Figure 2.8 Cross-section of a lateral high gee accelerometer. The shadow on the right side is the
unanchored section of the accelerometer that has been cut off, but did not fall into the silicon etch pit
below.
Because the exact cause of the lateral curl is still unknown, the simplest solution to prevent lateral
curl is to widen the suspension beam of the accelerometer. The design of the second-generation lateral
accelerometer suspension beam has a 2.0 µm-wide metal 1 layer, a 1.8 µm-wide metal 2 layer, and a
1.6 µm-wide metal 3 layer. The new design is extremely conservative, with the suspension beam being
almost twice as wide as its predecessor. Since this design change, the offset of the released high gee
lateral accelerometers has been reduced to less than 0.1 µm. The wider structures have been verified to
release using the standard post-CMOS MEMS processing.
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Chapter 2 Mechanical Design
2.3 Vertical accelerometer mechanical design issuesIn the case of the vertical accelerometer, the 1.2 μm wide, 60 μm long, suspension beams are
expected to curl significantly out of plane of the chip. The curl is due to differing residual and thermal
expansion stress in the metal and oxide layers that compose the beam. Since those beams only contain
one metal layer and one oxide layer, the stress gradient is sufficient to produce a relatively large
amount of vertical curl. For this reason, there are two sets of bending beams in series to provide curl-
matching. Because the curl-matching beams are all the same dimensions, they will curl equally, and
the side electrodes will remain parallel to the substrate after releasing. This design implementation of
curl matching does come at the sacrifice of extra layout area. A perspective view of the released canti-
lever structure is shown in Figure 2.9.
Figure 2.9 Perspective view of high-gee vertical accelerometer cantilever structures.
These structures have been verified to release using the standard post-CMOS MEMS processing.
Figure 2.10(a) shows the measured topology of a released high-gee vertical accelerometer. The mea-
surement equipment has an x-y resolution of approximately 1 µm, which is why the topology image is
not clearly defined. The structures on the right side of the image are the most clearly in focus, which is
where displacement was measured along the curl-matching beams. The displacement of the curl-
matching beams is shown in Figure 2.10(b) and (c) to be approximately equal, so that the electrodes
remain in the same plane as the stators.
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Chapter 2 Mechanical Design
Figure 2.10 (a) Measured vertical displacement of a released high-gee vertical accelerometer using
a Veeco NT 3300 white light interferometer. (b) Measured displacement of the curl-matching beams
located at cross-section A-A’. (c) Measured displacement of the curl-matching beams located at cross-
section B-B’.
(a)
(b)
(c)
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Chapter 3 Capacitive Sensing
3.1 Principle of capacitive sensingCapacitive sensing is commonly used in the design of MEMS sensors as a low-power method of
converting mechanical movement to electronic signals. It is especially useful for inertial sensors
because the resulting voltage change will be, to first-order approximation, proportional to the external
acceleration. The high-gee accelerometers described in this paper use the same electrical connections
to form the capacitive bridge as the low-gee accelerometers designed by Tsai [1].
3.2 Lateral high-gee accelerometer capacitive sensingFor the lateral high-gee accelerometer, the design principle is to sense the change in capacitance
caused by an increase or decrease in the gap between comb fingers. Figure 3.1 shows the electric con-
nections in the comb fingers that create the capacitive bridge in the lateral accelerometer. In the cross
section in Figure 3.1(b), capacitance C1 decreases and capacitance C2 increases as the rotor moves to
the left.
For the purposes of calculating the accelerometer’s sensitivity, it is necessary to know the rest
capacitance of each node in the capacitive bridge, and the parasitic capacitance of the output node, Vo,
to ground. The magnitude of the rest capacitance is difficult to calculate by hand accurately, because of
the alternating layers of conducting metal and insulating silicon dioxide, as well as the different widths
between layers. Finite element simulation is used to determine capacitance between the electrodes.
3 Capacitive Sensing
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Chapter 3 Capacitive Sensing
Figure 3.1 (a) Top-view of a single cantilever in the lateral accelerometer array, with cross-section
marked. (b) Cross-section of one rotor finger between two stators which form the comb drive capaci-
tive bridge used to sense acceleration along the y-axis. Vo represents the sense output voltage, and Vm
is the modulation voltage which powers the capacitive bridge.
The 2-dimensional electrostatic simulation results, pictured in Figure 3.2, give the effective capaci-
tance between a single stator and rotor sidewall to be 2.4 fF, taking into account the stepped metal
widths. In comparison, the parallel-plate approximation, using the minimum gap of 1.0 μm, estimates
the capacitance to be 2.6 fF. Using the maximum gap of 1.4 μm, the parallel-plate approximation esti-
mates the capacitance to be 1.9 fF. For one side of the differential output, there are 40 total cantilever
structures electrically connected in parallel in a single lateral high gee accelerometer. Each capacitor in
the capacitive bridge in Figure 3.3 represents a total capacitance of 40 cantilever structures with elec-
z
y
z
y
(b)
y
x
y
x
A
A’
A
A’(a)
deflection y
C2C1
+Vm +Vm
-Vm-Vm
Vo Vo VoA A’
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Chapter 3 Capacitive Sensing
trodes connected in parallel. For the differential output, the two capacitors C1A and C1B are matched
and behave identically under an input acceleration. The two capacitors C2A and C2B are matched as
well. At rest, the capacitors each have capacitance Co = 97 fF.
Figure 3.2 Two-dimensional electrostatics simulation of a single rotor between two stator fingers.
The color scale indicates the electric potential.
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Chapter 3 Capacitive Sensing
Figure 3.3 Schematic representation of capacitive bridge formed by two sets of 40 parallel cantile-
ver structures having parallel electrodes in the lateral high gee accelerometer.
The accelerometer’s sensitivity also depends on how that capacitance changes with the input accel-
eration. This design achieves first-order linear changes in capacitance in response to acceleration. By
approximating the metal stacks as a parallel-plate capacitor, its capacitance is given by (2.3).
When the electrode displaces by a distance , the capacitance change is,
(3.1)
assuming that . This is a reasonable assumption. For example, the FEA simulations discussed in
Chapter 2 give the displacement sensitivity of the rotor to be 6.4 pm/gee for the lateral accelerometer.
For a 20,000 gee input acceleration, the displacement will be 128 nm, which is much less than the
1.5 μm at rest gap. Substituting (2.1), the change in capacitance is, to first order, proportional to accel-
eration:
. (3.2)
V m
-V m
V o +
V o -
C 1 A
C 1 BC 2 A
C 2 B
4 0 c a n ti lev e rs tru c tu resh a v in gp a ra lle le le c tro d e s
4 0 c a n ti le v e r s tru c tu re sh a v in gp a ra lle le le c tro d es
V m
-V m
V o +
V o -
C 1 A
C 1 BC 2 A
C 2 B
4 0 c a n ti lev e rs tru c tu resh a v in gp a ra lle le le c tro d e s
4 0 c a n ti le v e r s tru c tu re sh a v in gp a ra lle le le c tro d es
Δx
ΔC εAg Δx–--------------- εA
g------– εA Δx⋅
g g Δx–( )----------------------- εA Δx⋅
g2-----------------≈ CoΔxg
------= = =
Δx g«
ΔC εAg2------ a
ωr2------⋅=
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Chapter 3 Capacitive Sensing
Repeating the 2-d finite element simulation in Figure 3.2 while changing the gap between the metal
stack cross-sections gives the change in sidewall capacitance per length over input accelerations. Mul-
tiplying the capacitance per length by the length of the electrode and by the number of cells in the array
gives the data in Figure 3.4, where the capacitance of C1A and C2A is plotted over input accelerations
of gees. The correlation coefficient of both curves in Figure 3.4 are 0.998.
Figure 3.4 Capacitance of C1A and C2A in the lateral accelerometer capacitive bridge, with respect
to input acceleration.
The output voltage of the capacitive bridge will also change linearly. Due to charge conservation on
the high impedance output node, the voltages on the capacitors are constrained by the following rela-
tion:
. (3.3)
where Vo is the one-sided voltage output of the differential capacitive bridge, Vm is the signal powering
the capacitive bridge, Co is the capacitance of C1 and C2 at rest, and ΔC is the change in capacitance
20 000,±
90.092.094.096.098.0
100.0102.0104.0106.0
-20.0 -10.0 0.0 10.0 20.0input acceleration (kilo-g's)
Cap
acita
nce
(fF)
C1AC2A
Vm Vo–( ) Co ΔC+( ) Vo Vm+( ) Co ΔC–( )=
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Chapter 3 Capacitive Sensing
due to an input acceleration. Including the effect of parasitic capacitance Cp between the output node
Vo and ground gives:
. (3.4)
Substituting (3.1), Vo reduces to:
(3.5)
From Chapter 2, it is known that each rotor in the lateral accelerometer will displace by 6.4 pm/gee.
The comb finger gap at rest is 1.5 m. Assuming Vm is a 1 V amplitude sinusoid and zero parasitic
capacitance to ground, Vo+ and Vo- will be sinusoids whose amplitude sensitivity is 4 V/gee. The dif-
ferential output will be a sinusoid with an amplitude sensitivity of 8 μV/gee.
3.3 Vertical high-gee accelerometer capacitive sensingThe vertical accelerometer senses acceleration through changing the overlap between comb fingers,
rather than the gap distance. The electrical connections in the comb drive capacitive bridge are also
different, as shown in Figure 3.5(b). Approximating the metal-oxide stacks as parallel-plate capacitors,
the change in capacitance is calculated by
(3.6)
where Lo indicates overlap distance, t indicates the comb finger thickness, and represents the verti-
cal displacement. The change in capacitance is shown to be proportional to the vertical displacement.
Vm Vo–( ) Co ΔC+( ) Vo Vm+( ) Co ΔC–( ) VoCp+=
Vo
VmΔxg
------⋅
1 Cp 2Co( )⁄+----------------------------------=
μ
μ
ΔCε Lo t⋅( )
g-------------------
ε t Δz+( ) Lo⋅g
--------------------------------–εLo Δz⋅
g-------------------–= =
Δz
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Chapter 3 Capacitive Sensing
Replacing Δx with Δz, (3.4) and (3.5) hold true for the vertical accelerometer, so that the one-sided
output voltage of the differential capacitive bridge is given by
(3.7)
For one side of the differential output, there are 112 total cantilever structures electrically connected in
parallel in a single vertical high gee accelerometer. Again, the capacitors C1A and C2A in the capacitive
bridge in Figure 3.6 each represent the total capacitance of the 56 electrode capacitances in parallel.
The two cross-sections in Figure 3.5(b) and (c) are designed such that the total capacitance of C1A and
C2A will be matched.
Repeated 2-d finite element simulations while varying the overlap area between cross-sections
gives the change in sidewall capacitance per length over input accelerations. Multiplying the capaci-
tance per length by the length of the electrode and by the number of cells in the array gives the data in
Figure 3.6, where the capacitance of C1A and C2A is plotted over input accelerations of gees.
The plot has a correlation coefficient of 0.998 for both curves.
Vo
VmΔzg
------⋅
1 Cp 2Co( )⁄+----------------------------------=
20 000,±
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Chapter 3 Capacitive Sensing
Figure 3.5. (a) Top-view of a two cantilevers in the vertical accelerometer array, with cross-sec-
tions marked. (b) Cross-section of the comb drive capacitive bridge used to sense acceleration along
the z-axis. Again, Vo represents the sense output voltage, and Vm is the differential modulation voltage
which powers the capacitive bridge. (c) Cross-section of a different cell in the cantilever array, show-
ing different electrical connections.
A
A’
A
A’(a)
y
x
y
x
z
y
z
y
(b) (c)
z
y
z
y
+Vm
-Vm
Vo
C1
C1
C2
C2
+Vm
-Vm
Vo
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Chapter 3 Capacitive Sensing
Figure 3.6 Capacitance of C1A and C2A in the vertical accelerometer capacitive bridge, with respect to
input acceleration.
From the finite element simulations described in Chapter 2, it is known that each rotor in the verti-
cal accelerometer will displace by 18.5 pm/gee. The comb finger thickness if 4.8 μm. Assuming Vm is
a 1 V amplitude sinusoid and no parasitic capacitance to ground, Vo+ and Vo- will be sinusoids whose
amplitude sensitivity equals 3.75 μV/gee. The differential output will be a sinusoid with an amplitude
sensitivity of 7.5 μV/gee.
3.4 Sense CircuitryAs shown in Figure 3.3, the accelerometer capacitive bridge is driven by the modulation signal Vm,
which is generated on-chip. A block diagram of the described on-chip circuitry is shown in Figure 3.7.
The circuitry was designed specifically for this application by Rudolph Park at John Hopkins Applied
Physics Lab. A ring oscillator generates a 1.6 V amplitude, 10 MHz clock, and a clock divider allows
the user to tune the frequency of the modulation signal to be 10 MHz or less. For testing, the modula-
tion frequency was set at 1.7 MHz, to decrease the impact of 1/f noise. This frequency is higher than
94.096.098.0
100.0102.0104.0106.0108.0110.0
-20.0 -10.0 0.0 10.0 20.0input acceleration (kilo-g's)
Cap
acita
nce
(fF)
C1AC2A
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Chapter 3 Capacitive Sensing
the flicker noise corner frequency, so that only thermal effects generate noise in the transistors [1]. The
capacitive bridge output, therefore, should be a square wave at the modulation frequency, with ampli-
tude that varies with input acceleration.
The common-mode control circuitry periodically switches the capacitive bridge outputs to a bias
voltage, to control drift due to charging. The frequency of the common-mode switches is also select-
able by the user.
The capacitive bridge output is amplified by an on-chip amplifier with a gain of 3.6 for the lateral
accelerometer, and gain 23 for the vertical accelerometer. The difference in gain is due to the initial
expectation that the vertical accelerometer capacitive bridge output would be less than the lateral
accelerometer capacitive bridge output. The finite element simulations in Sections 3.2 and 3.3 which
show the vertical accelerometer gain is higher were not performed until later. The preamp output is
routed to a mixer, where the signal is demodulated. The mixer output contains a dc frequency compo-
nent, and a second component at twice the modulation frequency. A low pass filter, with gain of 2 and
bandwidth of 65 kHz, removes the second frequency component, leaving only the dc component,
which varies with input acceleration. The low pass filter provides the final output of the chip. The out-
put of each block is routed to a bondpad and available for testing. All the on-chip circuitry share a
power supply of 3.3 V.
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Chapter 3 Capacitive Sensing
Figure 3.7 Block-level diagram of complete on-chip circuitry.
Using the values of capacitance of C1A and C2A from Figures 3.4 and 3.6, Cadence extraction and
circuit simulation is performed to determine the differential output of the sense circuitry. The simula-
tion includes the effects of parasitic capacitance.
The differential output of the low pass filter from Cadence extraction and circuit simulation is
33.2 μV/gee and 130 μV/gee for the lateral and vertical accelerometers, respectively. These simulated
sensitivity values will be compared to the measured sensitivity values in Chapter 4.
VoltageReference
CurrentReference
CommonMode Ctrl
ClockDivider
Clock10 MHz
MEMSCapacitive
Accelerometer
Amplifiergain = 3.6 (lateral)gain = 23 (vertical)
Demodulator
Low Pass FilterBW = 65 kHzgain = 2
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Chapter 4 Testing
4.1 Zero input testingThree high-g CMOS-MEMS accelerometers and the corresponding sense circuitry have been fabri-
cated on a single CMOS chip of area 2.4 × 2.4 mm. The accelerometer chip was first tested with zero
input acceleration to measure bias offset. Due to processing mismatch between metal layers, there is a
slight mechanical offset in the capacitive bridge. The effect of this mechanical offset on the output is
the same as a constant input acceleration. The zero input differential output of the on-chip amplifier,
demodulator, and low pass filter for the lateral high-gee accelerometer are shown in Figures 4.1, 4.2,
and 4.3.
The amplifier outputs in Figure 4.1(a) and (c) show significant common-mode noise, which is
removed in the differential output in Figure 4.1(e). Figure 4.1(b), (d), and (f) show the spectre simula-
tions of the preamp for a constant input acceleration of 100 gees. In the spectre simulations, the differ-
ential output is expected to be a square wave, but the measured signal shows a slower time constant
than expected. Simulations show that the slower time constant is not due to capacitive loading from the
oscilloscope probe, so the cause is still unknown.
4 Testing
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Chapter 4 Testing
Figure 4.1 Lateral high gee accelerometer amplifier output results. (a) Positive side of measured
amplifier output and (b) simulated amplifier output. (c) Negative side of measured amplifier output
and (d) simulated amplifier output. (e) Measured differential amplifier output and (f) simulated differ-
ential amplifier output. Simulated outputs are for 100 gee input acceleration.
The mixer outputs in Figure 4.2(a) and (c) also show significant common-mode noise, which are
removed in the differential output in Figure 4.2(e).
(a) (b)
(c) (d)
(e) (f)
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Chapter 4 Testing
Figure 4.2 Lateral high gee accelerometer mixer output results. (a) Positive side of measured mixer
output and (b) simulated mixer output. (c) Negative side of measured mixer output and (d) simulated
mixer output. (e) Measured differential mixer output and (f) simulated differential mixer output. The
simulation output has acceleration input of 100 gees.
(a) (b)
(c) (d)
(e) (f)
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Chapter 4 Testing
Figure 4.3 Lateral high gee accelerometer filter output results. (a) Positive side of measured filter
output and (b) simulated filter output. (c) Negative side of measured filter output and (d) simulated fil-
ter output. (e) Measured differential filter output and (f) simulated differential filter output.
The filter outputs in Figure 4.3(a) and (c), as expected, show the same common-mode disturbance
that is removed in the differential output shown in Figure 4.3(e). The filter output is biased at 175 mV.
Due to parasitic coupling to clocked signals on-chip, there is some measurement noise even in the filter
differential output, as is easily seen in the simulations in Figure 4.3 (f).
The common mode of the preamp, mixer, and filter outputs are compared in Figure 4.4. Although
there is a great deal of common mode disturbance generated, it is removed in the differential outputs.
(a)(b)
(c) (d)
(e) (f)
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Chapter 4 Testing
The bias voltages and signal frequencies match simulation. While this testing does not prove function-
ality of the sensor, it does indicate that the electrical circuit design is performing as intended.
Figure 4.4 Lateral high gee accelerometer plots of measured common mode signals for the
(a) amplifier output, (b) mixer output, and (c) filter output.
(a)
(b)
(c)
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Chapter 4 Testing
4.2 Shock TestingA drop tower mechanism was constructed at Carnegie Mellon University which allows shock test-
ing for both vertical and lateral high-gee accelerometers. The calibration accelerometer used for the
drop tower was an ADXL 8131, which has a maximum range of 250 gees.
Preliminary testing has been limited to maximum deceleration less than 200 gee’s. Because the
expected outputs are in the mV range, a differential amplifier with a gain of 100 was used to amplify
the differential output of the filter. For each drop test, a time response was recorded for both the
CMOS-MEMS high-gee accelerometer and the calibration accelerometer, as shown in Figures 4.5 and
4.6. The gain of 100 due to the off-chip differential amplifier was removed from the data shown in Fig-
ures 4.5 and 4.6. While the two accelerometers are mounted on different printed circuit boards on
opposite sides of the drop tower, the shock deceleration they both experience should be equivalent, to
first order. Since the sensitivity of the calibration accelerometer is known, the maximum deceleration
from a single drop test can be extracted from the output of the calibration accelerometer.
Figure 4.5 Time response of lateral high-gee CMOS-MEMS accelerometer differential output and
calibration accelerometer output for a single shock test with maximum deceleration of 191 gees.
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.000 0.005 0.010 0.015 0.020time (s)
CM
OS-
MEM
S hi
gh-g
ac
cele
rom
eter
out
put (
mV)
0.00
0.50
1.00
1.50
2.00
2.50
3.00
calib
ratio
n ac
cele
rom
eter
ou
tput
(V)
HighG Y-axis Differential Output (μV) Calibration Accelerometer Output (V)
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Chapter 4 Testing
Figure 4.6 Time response of vertical high-gee CMOS-MEMS accelerometer differential output and
calibration accelerometer output for a single shock test with maximum deceleration of 179 gees.
The CMOS-MEMS accelerometer outputs with respect to input acceleration are plotted over sev-
eral drop tests in Figure 4.7. Using a linear fit, the accelerometer sensitivity is extracted from the slope
of the data. The linear fit for the measurement results in Figure 4.7 gives the correlation coefficient as
0.94 and 0.99 for the lateral and vertical accelerometers, respectively. The response of the lateral accel-
erometer includes increased measurement error, compared to the vertical accelerometer, due to added
noise from on-chip parasitic coupling between the differential output and other on-chip clocked sig-
nals. Both correlation coefficients are quite close to 1.0, and thus the sensors have shown linear behav-
ior below 200 gee’s.
The measured sensitivity of the lateral accelerometer is 3.0 μV/gee, compared to the simulated sen-
sitivity of 33.4 μV/gee, discussed in the previous chapter. The measured sensitivity of the vertical
accelerometer is 9.9 μV/gee, compared to the simulated sensitivity of 130 μV/gee. For both sensors,
there is about an order of magnitude difference between the measured and simulated sensitivity. The
cause of this discrepancy has not been determined.
-2.00-1.75-1.50-1.25-1.00-0.75-0.50-0.250.000.25
0.000 0.005 0.010 0.015 0.020time (s)
CM
OS-
MEM
S hi
gh-g
ac
cele
rom
eter
out
put (
mV)
0.00
0.50
1.00
1.50
2.00
2.50
3.00
calib
ratio
n ac
cele
rom
eter
ou
tput
(V)
HighG Z-axis Differential Output (mV) Calibration Accelerometer Output (V)
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Chapter 4 Testing
Figure 4.7 Measured CMOS-MEMS high-gee accelerometer output with respect to maximum
deceleration over several drop tests for (a) lateral and (b) vertical accelerometers, with modulation fre-
quency of 1.7 MHz.
One possible cause is approximations made in the mechanical simulation, such as not including the
Ti/W metal barrier layers and not using the exact metal and oxide layer thicknesses, which were not
immediately available. The mechanical simulations were modified to include the average Ti/W, metal,
y = 3.0228x + 46.052R2 = 0.9377
0
100
200
300
400
500
600
700
0 50 100 150 200 250acceleration (g)
high
-g o
utpu
t (μV
)
y = 9.9141x + 105.38R2 = 0.9917
0
500
1000
1500
2000
2500
0 50 100 150 200acceleration (g)
high
-g o
utpu
t (μV
)
(a)
(b)
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Chapter 4 Testing
and oxide layer thicknesses measured from past processing runs. The lateral accelerometer displace-
ment sensitivity in the modified simulation was 7.7 pm/gee, compared to 6.4 pm/gee from the simula-
tions in Chapter 2. The vertical accelerometer displacement sensitivity in the modified simulation was
16.5 pm/gee, compared to 18.5 pm/gee from the simulations in Chapter 2. The modified simulations
do not show an order of magnitude increase in displacement sensitivity, so it is unlikely that this is the
cause of the lowered measured sensitivity.
Another possible cause is that the amplifier gain is reduced from circuit simulations. Because the
amplifier inputs are not routed to bondpads, to minimize parasitic capacitance, the gain of the on-chip
amplifier has not been measured currently to verify this theory. To test this theory, additional drop tests
were conducted at a lower modulation frequency of 200 kHz, as opposed to 1.7 MHz. These drop tests
were conducted at the Army Research Laboratory on a full-suite drop tower with higher impact capa-
bilities. The drop test results, shown in Figure 4.8, show a measured sensitivity of 49.8 μV/gee for the
vertical accelerometer. This is still much lower than the simulated sensitivity of 130 μV/gee, but higher
than the sensitivity obtained with modulation frequency of 1.7 MHz. This indicates that the gain in the
electronics did contribute to the lower measured sensitivity in earlier drop tests. However it does not
fully explain the lower measured sensitivity for the vertical accelerometer. The vertical accelerometer
sensitivity remains to be investigated further.
The correlation coefficient for the measurement results in Figure 4.8 is 0.994. These results show
that the vertical accelerometer is functioning under shock accelerations beyond 30,000 gees.
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Chapter 4 Testing
Figure 4.8 Measured CMOS-MEMS high-gee vertical accelerometer output with respect to maxi-
mum deceleration over several drop tests, with modulation frequency of 200 kHz.
4.3 .Future WorkTo investigate the discrepancy between simulated sensitivity and measured sensitivity, the resonant
frequency of the devices will be measured in the future. Amplifier gain will also be measured and
investigated as a possible source of reduced sensor sensitivity. The drop tower tests will be repeated
with an off-chip differential amplifier with a gain of 1000, to improve signal-to-noise ratio and obtain
more accurate sensitivity measurements. Performance reliability over time and temperature should be
investigated. Noise and cross-axis sensitivity should be characterized.
4.4 .ConclusionsA lateral and vertical high gee accelerometer capable of sensing accelerations has been designed
and shown to be functional at low input accelerations. The accelerometer design uses CMOS-MEMS
(a)
y = 0.0498x - 44.168R2 = 0.9938
0200400600800
10001200140016001800
0 10000 20000 30000 40000acceleration (g)
high
-g o
utpu
t (m
V)
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Chapter 4 Testing
fabrication to be fully integrated with sense circuitry on a single chip, making the sensor sufficiently
small and lightweight for in-flight munitions testing. The tri-axial integrated sensor and circuitry have
been fabricated on a single 2.4 mm x 2.4 mm chip.
The work described here has been shown through hand calculation and FEA simulations to produce
an output signal whose voltage is linear to the external acceleration, up to 20,000 gees. Mechanical
curl due to processing variations has been reduced. Structural release has been achieved. Preliminary
testing indicates that the sense circuitry is functioning as expected, and that the accelerometer responds
linearly under input accelerations below 30,000 gee’s.
4.5 AcknowledgmentsThe work presented has been funded by the Test Resource Management Center (TRMC) Test and
Evaluation/Science and Technology (T&E/S&T) Program through the Naval Undersea Warfare Cen-
ter, Newport, Rhode Island, under the Army Research Laboratory. It has also been funded by a
National Science Foundation Graduate Fellowship. The author thanks Suresh Santhanam and the staff
of the Carnegie Mellon Nanofabrication Facility for processing assistance, and Rudolph Park and
Johns Hopkins University Applied Physics Laboratory for circuit design.
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References
43
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[2] C. Lo, F. Chen and G. Fedder, “Integrated HF CMOS-MEMS Square-Frame Resonators with On-Chip Electronics and Electrothermal Narrow Gap Mechanism,” in Technical Digest of the 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005, pp. 2074-2077.
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[4] G. Fedder, S. Santhanam, M. L. Reed, S. C. Eagle, D. F. Guillou, M. S. Lu and R. Carley, “Laminated High-Aspect-Ratio Microstructures in a Conventional CMOS Process,” in Techni-cal Digest of the 9th IEEE International Workshop on Micro Electro Mechanical Systems, 1996, pp. 13-18.
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[7] Endevco Corporation, Piezoresistive Accelerometer Model 7268C Datasheet.
[8] J. Suminto, “A Wide Frequency Range, Rugged Silicon Micro Accelerometer with Overrange Stops,” in Technical Digest of the 9th IEEE International Conference on Microelectromechan-ical Systems,1996, pp.180-185.
[9] "Capacitive Sensing," class notes for ECE 18-614, Department of Electrical and Computer Engineering, Carnegie Mellon University, Fall 2004.
[10] H. Luo, G. Zhang, R. Carley and G. Fedder, “A Post-CMOS Micromachined Lateral Acceler-ometer,” IEEE/ASME Journal of Microelectromechanical Systems, vol. 11, pp. 188-195, June 2002.
[11] H. Xie and G. Fedder, “A CMOS Z-axis capacitive accelerometer with comb-finger sensing,” in Proceedings of the 13th IEEE International Conference on Micro Electro Mechanical Sys-tems, 2000, pp. 496-501.
[12] B. Razavi, Design of Analog CMOS Integrated Circuits, pp. 215-217. Boston: McGraw Hilll, 2001.
[13] S. D. Senturia, Microsystem Design. Boston: Kluwer Academic Publishers, 2001.