High-resolution Micromachined Interferometric Accelerometer
by
Nin C. Loh
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2001
C 2001 Massachusetts Institute of Technology
All rights reserved.
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 16 2001
LIBRARIES
BRKER
Authored by ................
...........
Department of Mechanical Engineering
May 23, 2001
Certified by ......
...... .. ......................
Scott R. Manalis
ssistant Professor, Media Arts & Sciences and Bioengineering
-I
R ead by ..........
Accepted by ...........
Thesis Supervisor
.........
......
............................................
George Barbastathis
Assistant Professor, Mechanical Engineering
Thesis Reader
....
............................................
.
Ain Sonin
Chairman, Departmental Committee on Graduate Students
1
2
High-resolution Micromachined Interferometric Accelerometer
by
Nin C. Loh
Submitted to the Department of Mechanical Engineering
On May 23, 2001, in partial fulfillment of the requirements for the degree of
Master of Science
ABSTRACT
A miniature high-resolution accelerometer with a bulk-micromachined silicon proof mass and an
interferometric position sensor was developed. The interferometer consists of interdigitated
fingers that are alternately attached to the proof mass and support substrate. Illuminating the
fingers with coherent light generates a series of diffracted beams. The intensity of a given beam
depends on the out-of-plane separation between the proof mass fingers and support fingers.
Displacements of the proof mass can be detected with a resolution of 10-3 A/rt Hz over a range of
600 A. Structures with a mechanical resonance ranging from 80 Hz to 8.2 kHz were fabricated
with a two mask process involving two deep reactive ion etches, an oxide etch stop, and a
polyimide protective layer. The structures were packaged with a laser diode and photodiode into
8.6 cm 3 acrylic housings. The 1 kHz resonant structure detected 200 ng/rt Hz at 400 Hz with a
dynamic range 7x10 5 . Although the acceleration resolution of the 80 Hz resonant structure is
currently limited by the background seismic noise, we speculate that the ultimate limit is the
thermomechanical noise of 6.8 ng/rt Hz. The advantage of the interferometric sensor over
tunneling accelerometers is its simple fabrication process and large open-loop dynamic range.
Thesis Supervisor: Scott Manalis
Title: Assistant Professor, Media Arts & Sciences and Bioengineering
3
4
ACKNOWLEDGEMENTS
I wish to thank my adviser, Professor Scott Manalis, for his guidance and for leading a
group that fosters creativity, teamwork, enthusiasm, and hands-on research. My two years at
MIT have been most enjoyable, thanks to the members of the our group, Emily Cooper, Jirgen
Fritz, Cagri Savran, and Andrew Sparks. I also want to thank our administrative assistants,
Rosanne Kariadakis, Martha Lugo, and Alicia Peyrano for making my research more efficient.
Our UROP Peter Russo has helped with the packaging of the devices.
The interferometric accelerometer spawned from two project classes co-taught by Scott
and Professor Martin Schmidt. The class members, Emily Cooper, Saul Griffith, Jeremy Hui,
Jeremy Levitan, Ole Nielsen, Oluwamuyiwa Olubuyide, Rehmi Post, Cecily Ryan, and Jbrg
Scholvin, performed groundbreaking work on this sensor. I want to especially thank Emily for
documenting and transferring the technology from the first class, Professor Schmidt for his
technical insight, and J6rg for helping me to develop the fabrication process.
The fabrication of our accelerometer went smoother thanks to the expertise and help of
the MIT Microsystems Technology Laboratory staff and students, especially Vicky Diadiuk, Bill
Teynor, Tom Takacs, Kurt Borderick, Andy Fan, and Isaac Lauer. I also want to thank Saul
Griffith for showing me the marvels of the lasercutter, a tool that was essential to the packaging.
Funding for this research was provided by the MIT Media Laboratory's Things That
Think (TTT) consortium. During my last two semesters I was supported by a graduate research
fellowship from Motorola.
Finally, I am deeply grateful to my parents and older siblings for their support and
sacrifice in my academic journey.
5
CONTENTS
1 INTRODUCTION
1.1 Motivation: current accelerometers.................................................
1.2 High-resolution tunneling accelerometers.........................................
1.3 Optical interference accelerometers.................................................
1.4 Thesis overview ........................................................................
11
11
13
14
15
2 THEORY
2.1 Interdigital accelerometer.............................................................
2.2 Interdigital position sensing..........................................................
2.3 N oise analysis..........................................................................
16
16
17
20
3 DESIGN AND FABRICATION
3.1 Proof mass wafer......................................................................
3.1.1 D esign......................................................................
3.1.2 Fabrication process........................................................
3.1.3 Fabrication results.........................................................
3.2 Packaging.............................................................................
3.2.1 First generation design....................................................
3.2.2 Second generation design................................................
3.3 Photodiode wafer.....................................................................
3.3.1 D esign......................................................................
3.3.2 Fabrication process.......................................................
3.3.3 Electrical properties......................................................
24
24
24
28
31
33
33
36
38
38
39
41
4 RESULTS
4.1 Signal conditioning..................................................................
4.2 Mechanical drive stage.............................................................
4.3 Package assembly...................................................................
4.4 Sensor performance.................................................................
4.4.1 Sensitivity.................................................................
4.4.2 Noise spectrum............................................................
4.4.3 Linearity...................................................................
4.4.4 Cross-axis sensitivity and drift.........................................
42
42
42
43
46
46
49
51
54
5 CONCLUSION
57
6
APPENDICES
A MECHANICAL MODELS
A. 1 Folded pinwheel analytical model..................................................
A.2 Cantilever proof mass deflection...................................................
58
58
60
B MASK DESIGN
B.1 Proof mass wafer......................................................................
B.2 Photodiode wafer......................................................................
61
61
62
C FABRICATION DETAILS
C.1 Proof mass wafer.....................................................................
C.2 Photodiode wafer.....................................................................
C.3 Packaging.............................................................................
65
65
68
70
D FIRST GENERATION PACKAGE RESULTS
72
7
LIST OF FIGURES
1.1
1.2
1.3
2.1
2.2
2.3
2.4
2.5
2.6
2.7
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
Mechanical model of a typical accelerometer and useful parameters..................
Trade-off between volume and resolution at 100 Hz of commercial single-axis
accelerom eters.................................................................................
Simplified cross-section of typical micromachined tunneling accelerometer.........
Schematic of micromachined accelerometer using interdigitated fingers as a
.
position sensor................................................................................
Diagram of diffraction off (a) parallel and (b) vertically offset interdigitated
.....
fingers....................................................................................
wavelength
about
eight
intensity
of
sine
squared
intensity
in
linearizing
Error
offset............................................................................................
Position noise of interdigital cantilever for atomic force microscopes. (Reprinted
with permission from APL paper, [12]).....................................................
Thermomechanical noise as a function of resonant frequency for a 30 mg proof
mass w ith Q of 100 at 300 K .................................................................
Interdigital noise as a function of operating frequency for various resonant
frequencies.....................................................................................
Seismic noise in 4th floor laboratory.......................................................
Schematic of folded-pinwheel as an interdigital accelerometer proof mass...........
Layout and dimensions of folded pinwheel proof masses...............................
Folded pinwheel proof mass resonant frequencies versus spring length L............
Fabrication process sequence for interferometric accelerometer proof mass wafer.
a.) Thermal oxidation of SOI wafer. b.) Topside lithography and DRIE etch to
define fingers, springs, and mass. c.) Spin-on and cure polyimide. d.) Bottomside
lithography and DRIE etch to define mass. e.) BOE etch of box oxide. f.) Ash
polyim ide in oxygen plasm a.................................................................
5x micrograph of 10 kHz proof mass corner...............................................
1Ox backlit micrograph of 10 kHz interdigitated fingers showing release.............
Cross-section of first generation package..................................................
Actual size schematic of the first generation package pieces. (A) is the bottom
piece on which the proof mass rests. (B) is the bottom shim. (C) is the top shim
with rectangular holes for the wirebonds and electrical leads. (D) is the top piece
with a circular hole for the laser diode, a circular recess (red) for the plastic lens,
and a rectangular recess (yellow) for the bonding plates. The blue lines represent
shallow grooves to align the proof mass die (A) and photodiode die (D).............
Normalized signal-to-noise ratio versus incident power for 8.2 kHz sensor driven
at 4 kH z .........................................................................................
Cross-section of second generation package...............................................
Laser diode-lens system for generating a small beam....................................
8
11
12
14
16
17
19
20
21
22
23
24
26
27
30
31
31
33
34
35
36
37
3.12
3.13
3.14
3.15
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
A. 1
B. 1
B.2
B.3
C. 1
D.1
D.2
D.3
Actual size schematic of the second generation package pieces. (A) is the bottom
piece on which the proof mass rests. (B) is the bottom shim. (C) is the top shim
with rectangular holes for the wirebonds and electrical leads. (D) is the top piece
with a semicircular cut-out for the laser dio de and a rectangular recess (yellow)
for the bonding plates. The blue lines represent shallow grooves to align the
proof mass die (A) and photodiode die (D).................................................
Layout of photodiode die....................................................................
Fabrication process sequence for photodiode wafer. a.) Thermal oxidation. b.)
Topside lithography to open field oxide. c.) Implant dopants. d.) Dopant drivein/activation and reoxidation. e.) BOE etch to open contact holes. f.) Deposit
aluminum. g.) Pattern aluminum. h.) DRIE etch through-hole......................
Plot of custom photodiode output versus incident power...............................
Schematic of piezoshaker used to actuate the sensors...................................
Diagram of tabletop and packaging experimental set-ups..............................
Comparison of resolution of 8.2 kHz sensor in tabletop and package set-ups.......
Sensitivity of (a) 1020, (b) 432, and (c) 80 Hz packaged sensors......................
Noise spectrum of (a) 1020 and (b) 432 Hz packaged sensors..........................
Noise spectrum of 80 Hz packaged sensor................................................
Output versus acceleration of (a) 1020, (b) 432, and (c) 80 Hz packaged sensors...
Illustration of cross-axes......................................................................
Maximum cross-axis sensitivities of 432 Hz packaged sensor compared to z-axis
sensitivity .......................................................................................
Thirty-minute drift of 432 Hz packaged sensor...........................................
Diagram and definition of parameters of folded-pinwheel structure with springs
parallel to mass................................................................................
37
39
40
41
43
44
45
48
50
51
53
54
55
56
58
Frontside (a) and backside (b) mask for proof mass wafer..............................
Mask set for photodiode wafer. a.) Mask 1 defined photodiode active regions. b.)
Mask 2 opened contact holes. c.) Mask 3 pattern interconnects. d.) Mask 4
defined D RIE through-hole..................................................................
Sample dies from (a) Mask 1, (b) Mask 2, (c) Mask 3, and (d) Mask 4...............
63
64
Lasercutter drawings for (A) top piece, (B) top shim, (C) bottom shim, and (D)
bottom piece of first and second generation packages. Black lines represent
through cuts, yellow areas are 1 mm deep rasters, red areas are 4 mm deep, orange
lines are 2 mm clean-up lines, and cyan lines are shallow (<500 pim) alignment
lin es.............................................................................................
71
Sensitivity of 428 Hz first generation package............................................
Noise spectrum of 428 Hz first generation package......................................
Linearity of 428 Hz first generation package.............................................
72
73
73
9
61
LIST OF TABLES
3.1
3.2
4.1
4.2
4.3
C. 1
Gravitational deflection, higher resonant frequencies, and load at failure values
calculated by Mechanica for each proof mass design....................................
Design and measured resonant frequencies...............................................
28
32
Noise level of each package during the packaging process.............................
Parameters of fitted sensitivity transfer functions........................................
Acceleration and deflection linearity and dynamic range of packaged interdigital
accelerom eters.................................................................................
46
49
Lasercutter settings for fabricating packages.............................................
71
10
52
1
INTRODUCTION
1.1 Motivation: current accelerometers
reson ant frequen cy
b
k
2~
m
quality factor
Q
b
Figure (1.1). Mechanical model of a typical accelerometer and useful parameters.
Accelerometers are a vital part of inertial guidance, airbag deployment, and earthquake
detection systems. Figure (1.1) is a simple mechanical model of an accelerometer, in which a
inertial, or proof, mass of mass m is suspended by a spring of spring constant k and a dashpot of
damping constant b.
This class of sensors determines acceleration by measuring either the
position z of the proof mass relative to the rigid support (passive) or the force required to keep
the proof mass stationary (force-feedback).
Accelerometers can vary greatly in the way they
detect this lag, as well as in size and minimum detectable acceleration. Before the advent of
silicon micromachining, accelerometers were large electromechanical structures, sometimes
Starting at the end of the 1970's, bulk-
involving several discrete components [1].
micromachining (through-wafer etching) was used to fabricate silicon accelerometers with
piezoresistive, capacitive, or piezoelectric position sensing [2]. Although bulk-micromachining
offered a way to make smaller and more reliable sensors, its cost prevented such devices from
proliferating into low-cost markets such as the automotive industry.
In the early 1990's,
capacitive accelerometers batch-fabricated from thin films on silicon (surface micromachining)
provided a low cost alternative to traditional sensors in airbag deployment systems.
Today,
virtually all airbags are controlled by such sensors because of their size (DIP chip package
measuring less than 0.5 cm 3), cost (<$5), and accuracy (1%). While adequate for detecting 50 g
(fifty times the acceleration of gravity (g = 9.81 m/s 2 )) collisions, surface micromachined
capacitive sensors can only resolve disturbances around a milli-g.
Accelerometers that can detect accelerations less than a millionth that of gravity, or
micro-g, are necessary for measuring seismic disturbances as well as gravitational waves [3, 4].
11
Present-day sensors with such low noise are typically larger than the size of an egg and cost
several hundreds of dollars.
Figure (1.2) is a plot of the volume of various single-axis
commercial accelerometers as a function of their resolution at 100 Hz. The trade-off between
size and resolution is apparent.
Several research groups are currently developing
microfabricated sensors with sub-micro-g resolution and a package volume of less than 10 cm 3,
The goal of this thesis work is to develop a new approach for fabricating and packaging an
accelerometer with these characteristics.
1000
Piezoelectric sensing
Capacitive sensing
100
E
E
10
SA
Sx
0
SX
xe
1
0 .1 1 1 1 1111111 I
0.001
0.01
1111111
1111111
0.1
1
1
11111 1
10
1 111111
100
111 1111
1000
Resolution (ug/rt Hz)
Figure (1.2). Trade-off between volume and resolution at 100 Hz of commercial single-axis accelerometers.
12
Microfabricating sensors that resolve accelerations in the 10 to 100 nano-g range is a
major challenge [5]. The mass of the proof mass often decreases with sensor size, increasing the
resonant frequency f.. This reduces the displacement z of the proof mass resulting from small
accelerations because the static deflection of the proof mass (ignoring damping) is inversely
proportional to the square of its resonant frequency.
kz = ma => z =
a
a
-
O)g
4
2
(1.1)
f2
where a), is the angular resonant frequency.
For example, a bulk-micromachined capacitive
accelerometer with a 126 Hz resonant proof mass of 14.7 mg can resolved 0.1 micro-g at 1 Hz
[6].
This noise is over a thousand times less than that of surface-micromachined capacitive
accelerometers whose masses and resonant frequencies are typically 1 pg and 10 kHz,
respectively. In addition to large, compliant proof masses, high resolution accelerometers also
require highly sensitive displacement detection. However, some position detection schemes do
not scale well with size. For instance, the sensitivity of capacitive sensors decreases as the area
of the sensing capacitor is reduced. As the sensitivity goes down, parasitic capacitances can
become significant if the readout circuitry is not close enough to the sensor.
1.2 High-resolution tunneling accelerometers
Over the last decade, a major effort in microfabricating nano-g accelerometers has used
electron tunneling as the position detector of a bulk-micromachined proof mass.
Tunneling
transducers, which measure the tunneling current between proof mass and a reference electrode,
are ideal for microfabrication because of their insensitivity to miniaturization. The tunneling
current depends predominantly on the two closest atoms between the mass and reference.
Furthermore, because the tunneling current is exponentially dependent on the tunneling gap,
electron tunneling transducers can resolve displacements down to 10-4 A/rt Hz. However, to
achieve a significant tunneling current, the proof mass must be positioned several angstroms
away from the tip. This strict tolerance increases the likelihood of the proof mass crashing into
the tip during large accelerations. For this reason, tunneling accelerometers typically operate in
13
force-feedback where the tunneling current is used to control a deflection voltage that keeps the
proof mass stationary.
Deflection electrode
Tunneling tip
Silicon
Metal
Figure (1.3). Simplified cross-section of typical micromachined tunneling accelerometer.
Most high resolution tunneling accelerometers consist of a large proof mass (10 to 40
mg) with a conductive side that is brought within 10 angstroms of the reference tip as shown in
Figure (1.3). To keep a constant tunneling gap, deflection electrodes are placed around the proof
mass to limit its movement to about 1 A.
Sometimes the tunneling tip is also actuated,
electrostatically [7] or piezoelectrically [8], to achieve higher bandwidth. Recently, researchers
have microfabricated accelerometers based on electron tunneling transducers that resolve 30
ng/rt Hz between 7 Hz and 1.1 kHz [9].
The tunneling accelerometer has several drawbacks. Although feedback can extend the
bandwidth of a low resonant frequency, high
Q (low
damping) proof mass, such a mechanical
structure is difficult to constrain to within 1 A of movement. The microfabrication process is
complex and can involve up to seven masks and two or more bonded wafers. Furthermore,
process variations complicate the design of the controller. The performance of the tunneling
accelerometer is also highly sensitive to the cleanliness of the electrodes [10].
1.3 Optical interference accelerometers
Optical interference transducers are capable of achieving a position resolution equivalent
to electron tunneling transducers. Interferometric displacement sensors can take many forms,
including a Michelson interferometer [11] or a Fabry-Pdrot cavity [3]. In the mid-1990's, an
interferometer was developed to increase the resolution and decrease the alignment sensitivity of
atomic force microscope cantilevers [12]. This interferometer measured the intensity of a single
14
mode from the diffraction pattern reflected off interdigitated fingers on the cantilever. The offset
between two sets of fingers could be resolved to 5xl04A at 200 Hz and was linear up to a tenth
of the wavelength of the light source, or 600 A of motion. An accelerometer based on such a
position transducer can achieve a dynamic range of over 10
4
without the use of any force-
feedback. Moreover, such an optical interferometer is a good candidate for micromachining
because the dimensions of the interdigitated fingers must be on the order of the wavelength of
the light for significant separation of the diffraction modes.
In the fall of 1999, the first
accelerometer to use interdigitated fingers as a position detector was fabricated [13]. Although
the sensor resolved micro-g accelerations, the fabrication had low reproducibility and yield
(<10%), and the device lacked a package.
1.4 Thesis overview
We present the design, fabrication, packaging, and characterization of a miniature highresolution accelerometer based on an interferometric transducer. In Chapter 2, we discuss the
theory behind the sensor as well as analyze sources of noise. Chapter 3 describes the design and
fabrication of our sensor, which is composed of the proof mass, plastic housing, and photodiode.
In Section 3.1.1, we focused on improving the performance and robustness of the proof mass
from its previous design. For example, the mechanical structure was designed for high linearity
of motion in the sensitive axis and low sensitivity to external strains. Section 3.1.2 discusses the
microfabrication of the proof mass, including the steps taken to release low resonant frequency
structures with 100% yield and high reproducibility. The fabrication of the package and the
process of assembling an interdigital accelerometer are covered in Section 3.2.
Chapter 4
describes the testing apparatus and the measured performance of the sensor, including sensitivity,
linearity, and noise. Section 4.3 discussed how we ensured that resolution was not lost when
transferring the sensor from a tabletop set-up with well separated diffraction modes to a small
package with closely packed modes. Finally, Chapter 5 summarizes the work and discusses
future directions of research in and applications of interdigital accelerometers.
15
2
THEORY
2.1 Interdigital accelerometer
Laser
Source
Light
Detector
Di
ction
Aearn.
Support
Substrate
Proof Mass
Interdigitated
Figer
Figure (2.1). Schematic of micromachined accelerometer using interdigitated fingers as a position sensor.
A schematic of the first micromachined interdigital accelerometer is shown in Figure
(2.1). Like the tunneling accelerometer in Figure (1.3), there is a proof mass suspended by a
spring. However, instead of a tunneling tip and deflection electrode, the interferometric sensor
has flat fingers extending from the proof mass that interleave with fingers extending from the
support substrate. When the interdigited fingers are illuminated with coherent light, a diffraction
pattern is reflected. The movement of the proof mass is determined by measuring the intensity
of one of the diffraction beams which is a sensitive function of the offset between the two sets of
fingers. The theory behind this position sensing will be detailed in the next section.
16
2.2 Interdigital position sensing
Incident Beam
-2nd Mode
+2nd Mode
Oh Mode
d
a.)
Incident Beam
+1st Mode
-1st Mode
-- z=W/4
b.)
Figure (2.2). Diagram of diffraction off (a) parallel and (b) vertically offset interdigitated fingers.
17
Imagine a row of reflective fingers all in the same plane as shown in Figure (2.1 a). If the
fingers are illuminated with coherent light, a series of diffracted beams, or modes, will be
reflected. The spacing between the modes depends on the illumination wavelength, A, and the
finger pitch d. The angle 0,n between the nth mode beam and the specular (0th order) mode
beam off fingers with pitch d is
O,
= sin-
(2.1)
2d
When all the fingers are in the same plane, all the even modes will be bright while all the odd
modes will be dark. If the distance h from the fingers to an observation plane is large compared
to distance of the nth beam from specular beam at the same plane, the latter is approximately
xn
=
nhX
2d
(2.2)
for the lower order modes.
If one were to gradually displace every other finger in the vertical direction, the intensity
of each mode will change. As the offset approaches A/4, the even modes will vanish while the
odd modes will appear. The intensity of each mode is a sine squared function of this offset z.
For example, the intensity of the first mode is proportional to
I1MODE
sin
(2.3)
Therefore, by measuring the intensity of any of the modes, the offset between the fingers can be
determined.
Because only the intensity and not the position of these modes changes, the
photodiode alignment is not critical. Moreover, the relationship between the offset and intensity
can be well approximated as linear relationship.
Figure (2.2) shows that the relative error
between a linearization of a sine squared intensity about a finger offset of an eighth wavelength
18
and the actual intensity is less than 5% within a deflection range of a tenth wavelength. When
red light is used, this linear range is over 600 A.
0.1
0.05
CU
0|
Zi
a:
-0.05 I
I
-U. 1~ I
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Finger Offset per Wavelength
Figure (2.3). Error in linearizing sine squared intensity about eight wavelength offset
The use of interdigitated fingers as a position detector was first applied to measuring the
deflection of cantilevers for the atomic force microscope [12].
One set of the fingers was
attached to the base of the cantilever while the other was attached to the tip. The noise of this
position detector was found to be 0.02 A in a 10 Hz to 1 kHz bandwidth. Figure (2.3) is the
position noise spectrum obtained by Manalis et al. This noise, dominated by the wavelength and
phase noise of the laser at frequencies up to 1 kHz [14], is comparable to what is achievable with
electron tunneling position detectors.
19
10'2
z
10*4.
10
100
1000
Frequency (Hz)
Figure (2.4). Position noise of interdigital cantilever for atomic force microscopes. (Reprinted with permission
from APL paper, 1996 [12])
2.3 Noise analysis
The resolution of all accelerometers is ultimately limited by thermomechanical noise, a
white noise given by
a
_
aTM
8lkBfO =3.2lX10'J" 2
mQQ
at room temperature (T
(2.10)
300 K) where kB is Boltzman's constant and
Q is
the quality factor.
Figure (2.4) shows the thermomechanical acceleration noise for a 30 mg proof mass with a
100 (typical of ambient conditions) at room temperature as a function of resonant frequency.
20
Q of
0.1
C
0.0
8
CU
0.01
-
a>
10
1000
100
104
Resonant Frequency (Hz)
Figure (2.5). Thermomechanical noise as a function of resonant frequency for a 3 0 mg proof mass with
Q of 100 at
300 K.
As mentioned Section 2.4, the dominant noise at frequencies under I kHz of the
interdigital AFM cantilever is most likely caused by wavelength and phase fluctuations of the
laser. This noise changes the intensity of the diffraction modes in the same way as changing the
finger offset. The translation of this laser fluctuation to position noise increases linearly with the
finger offset [11, 15].
For this reason, the wavelength/phase noise can be minimized by using
lower order modes as well as operating with the fingers near the zero offset bias. Figure (2.5) is
a plot of the equivalent acceleration of the interdigital cantilever position noise as a function of
operating frequency for structures with various resonant frequencies.
The equivalent
acceleration was found by multiplying the position noise values in Figure (2.3) with the square of
the proof mass angular resonant frequency. Recall from Equation (1. 1) that the acceleration of a
proof mass is the product of its deflection and the square of its angular resonant frequency.
Therefore, the equivalent acceleration of the interdigital position noise decreases with the
resonant frequency of the proof mass. For example, a 30 mg, 100 Hz proof mass should have a
wavelength/phase noise of 4 ng at 50 Hz which is lower than the thermomechanical noise of 6
21
........
. . . ......
ng.
Building a sensor that is limited purely by the thermomechanical noise would be
extraordinary because the noise of most accelerometers is dominated by other sources such as the
measurement circuit [16, 17].
I
I
I
I
I
I
I
I
I
I
I
I
I
I1
100
1-.
10
C)
CU)
1
Resonant Frequency
0.1
100 Hz
500 Hz
1 kHz
10 kHz
CU
03
CT
0.01
I
I
I
I
11111
,
,
,
1000
100
10
, ,
I
1 1
1
104
Operating Frequency (Hz)
Figure (2.6). Interdigital noise as a function of operating frequency for various resonant frequencies.
Above 1 kHz, the noise of the interdigital cantilever noise is dominated by shot noise.
Shot noise is caused by a fluctuating current due to the random arrival of electrons across the pn
junction in the photodiode. It is a white noise proportional to the root of the DC current iDC
across the diode.
iSHOT =
2 qioc
(2.12)
[A/rt Hz]
where q is an electron charge.
There are other sources of noise present in the interdigital accelerometer that are usually
lower than the laser wavelength/phase and shot noise. These sources include the intensity,
22
pointing, and flicker noise in the laser noise and the flicker, Johnson noise, and input noise in the
amplifier [15].
A crucial noise source not inherent to the sensor is the background seismic noise. This
low frequency noise ranges between 1 pg to 0.1 ng depending on the geographic location [18].
Figure (2.6) shows the background noise of a floated optics table measured in our 4th floor
laboratory in Cambridge, MA.
10
I
I
1
C
0
.10
L.
Ca)
0.1
U
CI)
0.01
100
10
Frequency (Hz)
Figure (2.7). Seismic noise in 4th floor laboratory.
23
3
DESIGN AND FABRICATION
3.1 Proof mass wafer
3.1.1 Design
Laser
Source
Figure (3.1). Schematic of folded-pinwheel as an interdigital accelerometer proof mass.
We choose to suspend the proof mass with diagonal, "folded pinwheel" springs as shown
in Figure (3.1). A variation of this structure, in which the springs run parallel to the mass, has
been previously studied and modeled [19] and is shown in Figure (A. 1). For motion normal to
the plane of the device, the folded pinwheel is over two orders of magnitude more linear than
straight tethers. Because the folded springs allow the mass to rotate slightly, it is less sensitive to
24
external strains. This makes it more robust than a straight tether design. Furthermore, the folded
springs allow the fabrication of long, highly compliant springs without significantly increasing
the size of the device. We choose to move the springs to 45 degrees to allow an area to attach
the fingers as well as to reduce the nonlinearity of motion in the sensitive axis.
The dimensions of the proof mass and springs were determined by the desired resonant
frequency. As mentioned in Section 2.3, to obtain nano-g acceleration resolution that is limited
only by thermomechanical noise, it was necessary to have a 30 mg, 100 Hz resonant frequency
proof mass. Because these low resonant structures have narrow operating bandwidth and a
slower response, we also designed for 500 Hz, 1 kHz, and 10 kHz resonant proof masses. For
reasons that will be explained in Section 3.1.2, we chose to fabricate our devices with backetched silicon on insulator wafers (BESOI). The springs and fingers would be composed of only
the thin device layer while the mass would be composed of all three layers. Through a generous
donation from the Schmidt Group at MIT, we obtained BESOI substrates with a 20 ptm device
layer, a 1 ptm buried oxide layer, and a 381.5 pm handle layer. Given the density of silicon, we
calculated that we needed a 5.6 mm square to obtain a 30 mg proof mass. We then chose
sensible values for the open space around the proof mass (140 pm) and springs (200 pm) and the
width of the springs (140 pm).
Figure (3.2) shows the layout of the proof mass dimensions. We entered the dimensions
into the analytical model and ProEngineer to determine the length of the springs that would give
us the desired resonant frequencies. Figure (3.3) is a plot of the length of the springs versus the
resonant frequency obtained by Mechanica finite-element modeling (FEM) and the analytical
model of the folded pinwheel with springs running parallel to the mass. The simulation and
model agree well up to about 1 kHz resonant frequency. Near this resonant frequency, the extra
length in the springs due to its 45-degree slant becomes significant, and the spring is actually less
stiff than the model. For this reason, we choose to use the FEM lengths, given in Figure (3.2) for
our design. The equations for the analytical model can be found in Appendix A.
25
Figure (3.2). Layout and dimensions of folded pinwheel proof masses.
It is clear from the plot that achieving a resonant frequency above 4 kHz would be
difficult given the size of our proof mass. For this reason we shrunk the proof mass to a 1.4 mm
square and shortened the spring widths and gaps for the 10 kHz device. We then used FEM to
obtain the required spring length given in Figure (3.2).
26
4000
I I
I
I
I
I
I I
I
I
I
I
I
I
I
I
I
II I I I I I I
3500 -
I
I
mecnanic FENv
Analytical Model
3000 -c
2500
2000
U-
CU
C
1500
0
1000 500 0
0
500
1000
1500
2000
2500
3000
3500
Spring Length L (urn)
Figure (3.3). Calculated folded pinwheel proof mass resonant frequencies versus spring length L
Our FEM also allowed us to predict the maximum deflection due to gravity, higher
resonant frequencies, and maximum load before failure. The second and third resonant modes
compose of rotations about the diagonal of the proof mass. In theory, they occur at a factor of
N-
from the first resonant mode [19]. In Section 3.1.3, we will present the actual resonant
frequencies.
The failure of the proof mass was assumed to occur when the maximum stress
(located where the tethers join the support substrate) reaches the yield stress of silicon, 2 GPa.
Table (3.1) lists these three values for each of the proof masses.
In the center of one side of the proof mass are fifty 175 pm x 6 pm x 20 pm interdigitated
fingers as shown in Figure (3.2). Although the location of the fingers guarantees that their outof-plane separation will always change during rotation about a diagonal, it also ensures that the
maximum separation change will be less than if the fingers were located near a set of springs
orthogonal to the diagonal axis of rotation. The fingers are twice as wide and half as long as the
ones on the original interdigital accelerometer to eliminate breakage and stiction. The fingers on
the proof mass overlap with the fingers on the support substrate for 125 pm, giving an area of
27
450 pm x 125 pm in which to focus the laser. This area was an ample target for the 75 pm
focused laser diode spot sizes we could achieve.
1st Resonant
Max Deflection in
2nd & 3rd Resonant
Frequency
Gravity (um)
Frequency
100
31
200Hz
27
500
1.2
900 Hz
67
1.0 kHz
0.37
1.7 kHz
100
10 kHz
0.25
16 kHz
227
Load at Failure (g)
Table (3.1). Gravitational deflection, higher resonant frequencies, and load at failure values calculated by
Mechanica for each proof mass design.
Another advantage of the folded-pinwheel design over the cantilever structure in Figure
(2.1) is the reduced deflection and tilt of the fingers due to gravity. This deflection causes
premature breakage, increases the effect of laser wavelength/phase noise, and limits the angle of
tilt of the sensor. In Appendix A.2, we calculate that the static deflection of a 100 Hz cantilever
proof mass is 46 um, or about 33% more than a folded pinwheel proof mass of equal resonant
frequency. More importantly, the tilt of the cantilever proof mass with respect to the substrate
would be almost half a degree. Any angle between one set of fingers and the other degrades the
diffraction pattern off the array. On the other hand, the folded-pinwheel proof mass will always
be parallel to the substrate in the absence of higher-order rotations about the diagonal.
3.1.2 Fabrication Process
The first interdigital accelerometer proof mass was fabricated in a two mask, CMOS
compatible process that had low reproducibility and yield.
It consisted of two timed deep
reactive ion etches (DRIE) in a plain silicon wafer and an acetone release. We used the same
process with two improvements. First, a buried oxide layer in the substrate was used to provide
a consistent etch stop for the DRIE, which is 100 times more selective for silicon than for oxide.
This decreases the sensitivity of the final spring dimension to variations in etch rate across the
wafer and on different wafers. The second improvement was a polyimide film to serve as a
support for the delicate springs and fingers during the subsequent DRIE etch through the handle
28
silicon to define the proof mass. The low pressure in the DRIE chamber can create a destructive
pressure differential across the thin springs.
The polyimide also allows the structures to be
released dry, without the breakage and stiction problems accompanying the previous acetone
release. Figure (3.4) shows the process cross-sections.
See Appendix B.1 for mask design
details.
The proof mass wafer process started with a 100 mm, single-side polished BESOI wafer
with a 20 ± 1 pim device layer, a 1 + 0.05 jim buried oxide layer, and a 381.5
±
0.5 im Si handle
layer. First, 0.56 pm of thermal oxide was grown as shown in Figure (3.4a). This oxide was
then patterned with Mask 1. After developing the resist, the exposed oxide was plasma etched to
clear all the oxide features to the silicon. The resist was then removed. Next the exposed device
layer silicon was then attached to a 150 mm quartz carrier wafer because the DRIE etcher only
accepts 150 mm wafers. The exposed device layer silicon then was deep reactive ion etched all
the way to the buried oxide layer as shown in Figure (3.4b).
After the DRIE etch, we released the wafer from the carrier in acetone and stripped the
resist in piranha. We then coated 20 pm of polyimide on the device layer side as shown in
Figure (3.4c). Next we patterned the backside of the wafer with Mask 2 and attached (with the
backside exposed) the wafer to a 150 mm quartz handle wafer. The handle silicon layer was then
deep reactive ion etched until the only the buried oxide layer was exposed under all the features.
At this point, shown in Figure (3.4d), the springs and fingers on the other side are visible through
the oxide. The wafer was then separated from the carrier in acetone.
We then removed the I pm of buried oxide in an 18-minute buffered oxide etch (BOE) as
shown in Figure (3.4e). The wafer was then mounted with the polyimide side up on a 100 mm
silicon carrier using a 5 mm ring of 10 jim-thick resist on the wafer edge. Finally, we etched
away the polyimide in an oxygen plasma. This last step, shown in Figure (3.4f), releases the
proof mass and allows the dies to be removed by only breaking the twelve 200 jm x 100 pm x
20 pm tabs. Appendix C. 1 lists the proof mass process steps in greater detail.
29
d.)
a.)
a.)
d.)
Li
___M
b.)
e.)
C.)
f.)
El
Li
Silicon
Silicon Dioxide
Cross-section on proof mass
Polyimide
Figure (3.4). Fabrication process sequence for interferometric accelerometer proof mass wafer. a.) Thermal
oxidation of SOI wafer. b.) Topside lithography and DRIE etch to define fingers, springs, and mass. c.) Spin-on
and cure polyimide. d.) Bottomside lithography and DRIE etch to define mass. e.) BOE etch of box oxide. f.) Ash
polyimide in oxygen plasma.
30
3.1.3 Fabrication results
Figure (3.5). 5x micrograph of 10 kHz proof mass corner.
Figure (3.6). 1 Ox backlit micrograph of interdigitated fingers showing release.
31
Using the process outlined above, we released proof masses with 100% yield. Figure
(3.5) shows a 5x micrograph of the corner of a 10 kHz proof mass. Figure (3.6) is a backlit lOx
magnification of the 6 um interdigitated fingers showing all fifty fingers perfectly intact and
released.
In Section 3.1, we used FEM to predict the resonant frequencies of the proof masses. We
measured the resonances by looking at the peaks in the frequency spectrum of the first
diffraction mode intensity in the tabletop set-up.
See Section 4.3 for details on tabletop
experimental set-up. Table (3.2) compares the measured resonant frequencies to their design
values. The measured frequencies deviated from the design values due to deviations between the
actual and expected mask and wafer dimensions. Process variations had less effect since the
variation in resonant frequencies from wafer to wafer was about 5%. As predicted by theory, the
rotational resonances occurred near a factor of
V[
from the natural frequency.
More
importantly, these higher order resonances occurred well beyond our frequency range of interest
for each proof mass.
Design 1st Resonant
Actual 1st Resonant
Design 2nd & 3rd
Actual 2nd & 3rd
Frequency
Frequency
Resonant Frequency
Resonant Frequency
100 Hz
80 ±4 Hz
200 Hz
150 Hz
500 Hz
430 + 10 Hz
900 Hz
780 Hz
1.0 kHz
1020 1 50 Hz
1.7 kHz
1.6 kHz
10 kHz
8.2+0.1 kHz
16 kHz
14 kHz
Table (3.2). Design and measured resonant frequencies
32
3.2 Packaging
3.2.1 First generation package
Laser diode
Figure (3.7). Cross-section of first generation package
We designed a plastic housing to hold the interdigital accelerometer with a laser diode
and photodetector.
Figure (3.7) shows a cross-section of this package. The first generation
package consisted of four acrylic pieces cut with a CO 2 lasercutter as shown in Figure (3.8).
With the exception of the top piece, which is 1/4-inch thick, all the pieces are cut from 1/8-inch
thick cast black (for light exclusion) acrylic. The bottom piece holds the device die and has a
hole under the proof mass to allow it to oscillate. The top piece has a hole to hold a plastic
collimating lens (Thorlabs CAY033) and a 670 nm, 5mW, laser diode (Sanyo DL3149-056)
whose source is placed at the focal length of the lens. The red laser was chosen to maximize
diffracted mode spacing (See Equation (2.2)) and allow visual alignment. Attached to this piece
is a silicon die with pn junction diodes located around a 125-pm diameter DRIE through-hole.
This photodiode wafer is discussed in Section 3.3. The diodes are wire-bonded to two alumina
plates (Thermomicroscope 30-600-0110) nearby. Electrical leads carrying the output signal are
33
soldered to these plates. The middle two pieces form a 1/4-inch (6.7 mm) shim to allow the
diffraction modes to spread and be differentiated from each other. There is one shim attached to
both the top and bottom pieces. The separation of 6.7 mm corresponds to a mode of spacing of
250 pim.
A
C
B
D
Figure (3.8). Actual size schematic of the first generation package pieces. (A) is the bottom piece on which the
proof mass rests. (B) is the bottom shim. (C) is the top shim with rectangular holes for the wirebonds and electrical
leads. (D) is the top piece with a circular hole for the laser diode, a circular recess (red) for the plastic lens, and a
rectangular recess (yellow) for the bonding plates. The blue lines represent shallow grooves to align the proof mass
die (A) and photodiode die (D).
The assembly of this package involves three alignments after the necessary components
have been fixed onto their corresponding piece. First, the two halves are aligned parallel and as
close together as possible without touching (<0.5 mm). Second, the laser diode is positioned into
the hole in the top piece such that its reflection off the accelerometer is directed back into the
hole in the photodiode die. Lastly, the bottom piece is moved until the laser spot is illuminating
the interdigitated fingers, and the diffraction modes are incident on the correct photodiodes.
Then the two halves are cemented together. The completed package is 2.33 cm x 1.84 cm x 1.67
cm (7.2 cm 3 ) and weighs about 8 g. It has five necessary leads: three for the laser diode and two
for the photodiode.
After testing the first package, we found that the noise was two to three orders of
magnitude greater than the interdigital cantilever noise in Figure (2.3). We discovered that there
was not enough light getting through the hole in the photodiode wafer. Figure (3.9) shows how
the sensor signal-to-noise ratio of an 8 kHz proof mass driven at constant, 4 kHz acceleration
diminishes with incident power due to the low sensitivity.
34
0.8
E
C14
Ce)
E
v
0.6
N
E
0
0.4--
z
00
iT
0.4
0
0.01
1
0.1
Incident Power (mW)
Figure (3.9). Normalized signal-to-noise ratio versus incident power for 8.2 kHz sensor driven at 4 kHz
The focal lengthf of the collimating lens and angular divergence of the laser diode beam
0,s, gave a collimated beam radius of
r,,, = ftan,, = 3.33mm- tan80 = 468pm
(3.1)
This width is 56 times the area of the 125 pm hole in the photodiode. This agrees with our
finding that the power on the other side of the hole was diminished by a factor of 30. For this
reason we abandoned the first generation package. Results from a 428 Hz sensor packaged in
this manner are shown in Appendix D.
35
FN
I
- _-E
iR-
-
,-
-
-
-
-
-
-
3.2.2 Second generation Dackane
Output
Epoxy
Laser diode
hotodiodesW
wire
Wirebond
Accelerometer
f ingers
Side view
Front view
Figure (3.10). Second generation package.
The second generation package used a similar four-piece housing that aligned the proof
mass die parallel to the photodiode wafer. However, instead of bringing the light through the
hole we directed it in from the side at a small angle (about 250) as shown in Figure (3.10). This
time we used a faster (shorter focal length) glass lens (Thorlabs 350140-B) with a focal length of
1.45 mm. When attached directly to the can of the laser diode, the lens brought the light to a
focus around 15 mm away from the lens. This meant that the laser source was
s =x+f -WD =x+1.45mm-0.88mm
=
(f
-
=(
I--
S")
1.45mm
I
,= 1.6mm =>x = I.mm(32
15mm
away from the tip of the can, agreeing with the laser diode manufacturer's value of 0.93 + 0.05
mm. The distances in Equation (3.2) are shown in diagram of the laser diode-lens system in
Figure (3.11). More importantly, this diode-lens system gave us a pre-focus beam width of less
than 220 pm.
r,,,,
s tan0,,, =1.55mm -tan8 0 = 218gm
36
(3.3).
This meant that we could fit the entire beam in the 450 pm width of the finger region. If the
beam were to exceed the width of the fingers, the specular reflection would overlap into the 1st
mode, increasing the noise. With this new package design we can deliver over 3 mW to the laser
diode, increasing our signal-to-noise ratio compared to the first generation package.
Lens Center
s"t
Laser Diode
r7:'
source
'
Lens f= focal length
-
f-WD
S
Figure (3.11). Laser diode-lens system for generating a small beam.
The four acrylic package pieces are shown in Figure (3.12).
Like the first generation
package, all the pieces are 1/8-inch thick except for the 1/4-inch thick top piece. Because the
3
dies are offset from each other and the laser diode is outside, the total volume, 8.6 cm (2.33 cm
x 2.20 cm x 1.67), is larger than its predecessor. This new package still weighs about 9 g.
A
C
B
D
Figure (3.12). Actual size schematic of the second generation package pieces. (A) is the bottom piece on which the
proof mass rests. (B) is the bottom shim. (C) is the top shim with rectangular holes for the wirebonds and electrical
leads. (D) is the top piece with a semicircular cut-out for the laser diode and a rectangular recess (yellow) for the
bonding plates. The blue lines represent shallow grooves to align the proof mass die (A) and photodiode die (D).
Although the hole in the photodiode wafer was no longer needed, we kept with our
custom photodiodes because the exposed active areas were easier to align to and had better
37
signal-to-noise ratios than a glass-covered commercial photodiode of equal area (United Detector
Technology HRO08).
The assembly of the second generation package followed the same
procedure as the first generation except that the laser diode was glued to the outside of the
package instead of behind the through-hole in the photodiode die. The results in Section 4 are
taken from sensors in second generation packages.
3.3 Photodiode wafer
3.3.1 Design
The photodiode wafer was designed around the first generation plastic housing. Figure
(3.13) shows the layout of the photodiode die. We placed four pn junction diodes around a 125pm through-hole in the positions of the -1st, +2nd, -3rd, and +4th modes when placed 6.7 mm
away from the fingers (giving a 250 pm mode separation). The rationale behind the multiple
photodiodes was the ability to test multiple modes at once and to perform a subtraction of two
adjacent photodiode signals to lower the laser intensity noise [12]. We found the first mode from
specular to be the most sensitive, and hence all the results in Chapter 4 are from the measurement
of this mode. Furthermore, subtraction of the signal from two adjacent modes did not increase
the signal-to-noise ratio because the laser intensity noise was not the dominant noise source. The
area of each photodiode was 200 pm wide and 150 pm long plus trapezoids on the top and
bottom to extend the active area to cover a 540 arc around the hole, allowing for theta
misalignment with the fingers. Each photodiode has an anode contact that extends along 200 pm
wide traces to a 1.6 mm square bond pad.
38
__
-
M IN
_
_ __
-
- __
- -
I
Figure (3.13). Layout of photodiode die
3.3.2 Fabrication Process
The photodiode wafer fabrication was a four mask CMOS compatible process. See
Appendix B.2 for mask design details. Figure (3.14) shows cross-sections of the wafer during
various steps in the process. The process to create the pn junction diode was borrowed from the
Microelectronics Processing Technology class (6.152J) at MIT.
The diodes are formed by
implanting boron dopants into an n-type substrate. The starting material was a 100 mm, 525 pmthick, single-side polished (100) n-type (phosphorus doped) silicon wafer with resistivity of 1.0
ohm-cm. The process began with growing 560 nm of oxide and pattering with Mask 1 to expose
the diode regions (Figure (3.14a)). The wafers were then sent to Implant Sciences (Wakefield,
MA) to have boron implanted (Figure (3.14b)). When they returned, we annealed the wafers to
drive-in and activate the dopants (Figure (3.14c)). The oxide over the contacts were then etched
away (Mask 2) leaving only the lines on which the anode interconnects would run (Figure
(3.14d)). Then 1 gm of aluminum (1%
Si) was deposited (Figure (3.14e)), patterned with Mask
3, and sintered (Figure (3.14f)). Finally, the through-holes were patterned on the backside with
Mask 4 and etched with the DRIE (Figure (3.14g)). Appendix C.2 lists the photodiode process
steps in greater detail.
39
d.)
a.)
e.)
C.)
g.)
n-type Silicon
Silicon Dioxide
p-type Silicon
Aluminum
Figure (3.14). Fabrication process sequence for photodiode wafer. a.) Topside lithography on thermal oxidation to
open field oxide. b.) Implant dopants. c.) Dopant drive-in/activation and reoxidation. d.) BOE etch to open contact
holes. e.) Deposit aluminum. f.) Pattern aluminum. g.) DRIE etch through-hole.
40
3.3.3 Electrical properties
We measured the sensitivity of our custom photodiode by focusing a 670 nm laser diode
on the active area and measuring the output through a current amplifier (106 V/A gain) while
varying the incident power. The intensity was varied by using neutral density filters and by
adjusting the laser current and calibrated using a power meter (Coherent LM+). Figure (4.6) is a
plot of the output versus the incident power. The slope gives a sensitivity of 0.33 A/W which is
comparable to commercial photodiodes.
1.4
I
-
I
I
-I
I.I
I
1.2
-
-
1
E
-
-
0.8
4-a
0.
0.6
-
-
0.4
-
0.2
-S
0'
0
0
I
0.5
1
1.5
2
2.5
3
3.5
Incident Power (mW)
Figure (3.15). Plot of custom photodiode output versus incident power
41
4
4
RESULTS
4.1. Signal conditioning
The output of the photodiode used to detect changes in diffraction beam intensity was
amplifier with a commercial low noise current amplifier (Keithley 428). Previously we dropped
the photocurrent across a large resistor but we found that the voltage across the resistor saturated
around 0.4 V.
This is because resistors have a limited voltage compliance [20].
The
transimpedance amplifier, on the other hand, faithfully converts the photocurrent in a signal as
well as allows bandpass filters and voltage biases. We operated our photodiodes with zero bias
because we did not need responsivities greater than 100 ps (10 kHz) and the negative bias would
increase the dark current. The gain was set between 104 and 105 V/A, which was adequate for
amplification above the noise of the devices down the line such as an FFT spectrum analyzer
(Stanford Research Systems SR760) and a DSP lock-in amplifier (Stanford Research Systems
SR830). Furthermore, the 10 MQ resistance of the photodiodes restricted the gain to less than
107 V/A since the propagation of voltage error across the current amplifier increases with the
feedback resistance or gain.
Voieu
= V110gi 1+
Rfedbak
Rsource)
(4.1)
The laser diodes were driven by an ultra low noise driver (ILX Lightwaver LDX-3620)
set in constant power mode. The laser current was set around 55 mA, which gave a laser output
of about 3.3 mW.
4.2 Mechanical drive stage
In order to test our accelerometer, we needed a system to impart known accelerations.
First we tried a permanent magnet, electro-dynamic shaker (LDS V456 driven by LDS PA1000)
but we found that voltage or frequency changes in the signal generator could cause the shaker to
impart large acceleration impulses that could destroy a low frequency device. For this reason,
we built a piezoelectrically actuated shaker like the one in Figure (4.1) using five piezoelectric
42
stacks (Thorlabs AE0505D16). The stacks were mounted horizontally between a 2 mm-thick
aluminum plate with 10-32 tapped holes and right angle plate (Thorlabs AP90). The piezostacks
were connected electrically in parallel and driven by a function generator (Stanford Research
Systems DS345). On the aluminum plate, we mounted our test sensor along with an Analog
Devices ADXL105JQC capacitive accelerometer as a reference. This latter device measures
accelerations up to 12 kHz with a 250 mV/g sensitivity and a noise density of 225 pg/rt Hz. Off
to the side of the stage we mounted a Wilcoxon 731 seismic piezoelectric accelerometer to
measure seismic disturbances down to 3 ng between 0.05 and 400 Hz with a sensitivity of 10
V/g. All sensors were mounted with their sensitive axes in the direction of stage actuation. Both
reference signals were filtered and amplified with a low noise voltage amplifier (Stanford
Research Systems SR560).
Direction of
actuation
10-32
tapped holes
Outline of
piezostack
behind plate
Aluminum plate
Piezostack
Front View
Side View
Figure (4.1). Schematic of piezoshaker used to actuate the accelerometers.
4.3 Package assembly
Before we packaged an accelerometer, we had to verify that it was released and obtain a
benchmark resolution. To do this, we tested the performance of the proof mass in a large
tabletop set-up, repeating the experiments performed by Cooper et al. We attached the proof
mass into the two bottom pieces of the package and mounted the half-package to the shaker,
oriented such that the fingers point horizontally. On the fingers we focused a 3.3 mW laser beam
with a 15.36 mm focal length aspheric lens (Thorlabs C260TM-B). The intensity of the first
mode was measured from a distance of 14 cm away from the interdigitated fingers with a 3.6 mm
43
x 3.6 mm silicon photodiode (Thorlabs FDS 100). The tabletop set-up is shown in Figure (4.2).
This put the modes at a well-separated distance of 5.2 mm from each other. An increased
sensitivity represented by the presence of a large voltage peak near the expected resonant
frequency on the spectrum analyzer indicated that the device was released. We then drove the
sensor with sine waves from function generator and measured the signal-to-noise ratio at various
frequencies.
mass package
Commercial Proof
Photodiode
Laser diode
Tabletop set-up
=
XYZ positioner
Photodiode package
Packaging set-up
Figure (4.2). Diagram of tabletop and packaging experimental set-ups.
After obtaining the best case resolution of the sensor, we assembled the package. We
attached a photodiode wafer to the top package piece and made the necessary gold wire bonds
and solder connections. After attaching the top shim, we positioned the optics half-package less
than half a millimeter away from the proof mass half-package. We then attached a focusing lens
to a laser and positioned the two by the open side of the package piece as shown in Figure (4.2).
The pieces were aligned until the laser illuminated the fingers and the -1st mode was incident on
a photodiode. Then we repeated the resolution measurements, using the reference accelerometer
44
to ensure equal drive acceleration. At this point we could adjust the position of the laser and
photodiodes to maximize the signal-to-noise ratio.
While packaging the sensor, we learned how to handle the trade-off between the focus of
the incident beam and of the diffraction modes. High sensor sensitivity requires high laser power
incident on both the fingers and the photodiodes. Maximizing incident power on the fingers
means placing them near the focus.
However, a focused beam on the fingers results in a
defocused beam at the photodiodes. We solved this problem by moving the fingers away from
the focus toward the laser until the spot size was fully contained in the interdigitated region.
Then we aligned the largest photodiode on the die to measure the defocused -1st mode. The
maximum signal-to-noise ratio was achieved in this configuration.
60
Tabletop
x
50
-.
N
Package
ID Limit
-
0e
40
x
cn
0
30
x
-
20
10 '
20 0
300
500
400
600
700
800
Frequency (Hz)
Figure (4.3). Comparison of resolution of 8.2 kHz sensor in tabletop and package set-ups.
Once the resolution of the package was near that of the tabletop set-up, we gently applied
quick setting epoxy around the package and allowed it to cure. Figure (4.3) shows a comparison
45
of the resolution of the 8.2 Hz sensor in both the tabletop and package set-up as well as the
interdigital detection limit set by the laser wavelength/phase noise extracted from Figure (2.3). It
is evident that the accelerometer did not lose much resolution going from the tabletop to our
package.
Furthermore, the noise of the package is only about a factor of 3 greater than the
interdigital limit. This is the procedure with which we packaged a 1020 kHz, 432 Hz, and 80 Hz
sensor in the second generation housing. Table (4.1) shows the resolution of each sensor in each
stage of the packaging process. The resolution would often increase by a factor of 2 to 3 after
the package was sealed because the laser diode, proof mass, and photodiode would be fixed with
respect to each other.
Resonant
Drive
Tabletop Noise
Prepackage
Postpackage
Frequency (Hz)
Frequency (Hz)
(ptg/rt Hz)
Noise (pg/rt Hz)
Noise (pg/rt Hz)
1020
400
0.7
0.7
0.2
432
160
0.8
0.6
0.2
80
40
0.1
0.1
0.1
Table (4.1). Noise level of each package during the packaging process
4.4 Sensor Performance
4.4.1 Sensitivity
Like most accelerometers, the interdigital sensor can be modeled by the mass suspended
by a spring and damper in Figure (1.1).
The second order transfer function between the
acceleration A(l) and the proof mass position Z(1) is
Z(f)
A(f)
(4.2)
1
4_
2
2
f _f
2
)+j(ff
0 /Q)]
Movement of the proof mass due to acceleration changes the intensity of the diffracted beams.
The intensity change is proportional to the photocurrent from the photodetector which in turn is
proportional to the voltage V(1) at the output of the current amplifier (to the frequency roll-off of
the amplifier). Assuming the relationship between the proof mass position and mode intensity is
46
linear, we can use a constant, G, to account for this constant of proportionality as well as the gain
of the current amplifer. Then the transfer function between output voltage and acceleration is
V(f)
GZ(f)
A(f)
A(f)
G
4
2[(f 2f
2
)+ j(ff
0 /Q)]
The real magnitude of the transfer function is then
A(f)
44
G
V(f)
47t2f4+(1/Q2
2)f2f2+f
4]
Equation (4.4) is the transfer function that defines the sensitivity of the interdigital
accelerometer.
We measured the sensitivity of the packaged interdigital accelerometers using a
LabVIEW program which controlled the function generator to drive the sensor at incremental
frequencies. At each frequency, the stage is driven at two different accelerations and a lock-in
amplifier extracts the component of both the test and reference accelerometer signals at that
frequency. The sensitivity was calculated by taking the ratio of the change in sensor signal to the
change in acceleration. We then fit a function with the form of Equation (4.4) to the sensitivity
data points to obtain the
Q of the device.
Figure (4.4) shows the sensitivity of the 1020, 432, and
80 Hz resonant frequency packages assuming current amplifier gains of 105 V/A (we measured
the highly-sensitive 80 Hz device with a gain of 104 V/A). Table (4.2) lists the parameters in the
second-order transfer function.
The comparable values for the gain G demonstrate that the
intensity of the modes in each package is of equal magnitude. This is also evident in the fact that
the low frequency sensitivities scale with the inverse of the square of the resonant frequency.
This result suggests that the packaging is highly reproducible.
47
SI
1000
Measured
Fit (Q=1 10)
-
c,)
100
%
S
C,)
C
ci)
Co
10
- -
1
a
-- -
-
5005
w
0 V 4 0 W-19
*
*
>4
1000
100
(a)
Frequency (Hz)
Measured
Fit (Q=185)
_
1000
C
C
-
100
-
10 1
1
*
1
(b)
400
300
200
70 80 90100
---.
500 600
Frequency (Hz)
I
II
I
Measured
Fit (Q=68)
C)
104
C
1000
-
30
(c)
40
I
II-
70
60
50
Frequency (Hz)
80
I-
90 100
Figure (4.4). Sensitivity of (a) 1020, (b) 432, and (c) 80 Hz packaged sensors.
48
Resonant Frequency
Quality Factor
Low Frequency
(Hz)
G (V/m)
Sensitivity (V/g)
1020
110
7
1.4x10 8
432
185
30
2.4x10 8
80
68
1300
2.2x10 8
Table (4.2). Parameters of fitted sensitivity transfer functions.
4.4.2 Noise spectrum
The noise spectrum of the sensor was measured by taking the FFT of the signal when the
sensor was not being actuated. For this measurement, we move the shaker onto a small platform
mechanically isolated by bubblewrap which has slightly lower seismic noise than the floated
table alone.
The voltage noise was converted to an equivalent acceleration by dividing the
spectrum by the fitted sensitivity function.
Figure (4.5) shows the noise equivalent acceleration of the 1020 kHz and 432 Hz sensors
including the measured seismic and shot noises and the theoretical interdigital detection and
thermomechanical noises.
The interdigital detection noise in these sub-kHz frequencies is
dominated laser wavelength/phase noise. Not shown is the measured photodiode/amplifier noise
which is usually 1 to 2 orders of magnitude below the thermomechanical noise.
The
photodiode/amplifier noise is the noise from the sensor when the laser diode is off. The noise of
the 1020 Hz sensor is limited up to 50 Hz by the seismic disturbance. At higher frequencies, this
sensor appears to be limited by the theoretical laser wavelength/phase noise. This suggests that
the interdigital deflection noise in our package is similar to that of the interdigital AFM
cantilever. The 432 Hz accelerometer, whose laser noise has a lower equivalent acceleration, is
completely limited by the seismic disturbance. To determine its true self noise, one would have
to obtain two similar 432 Hz packages and determine the coherence of their noise signals when
mounted next to each other. Correlated noise points to the seismic noise while uncorrelated
noise corresponds to the self noise of each sensor [4]. The use of this technique is beyond the
scope of this thesis.
49
W-
I
0.1
I A-
I
I
;0-
-Sensor
-- Seismic
I I I II
--------- ID Limit
-------- ThermomEechanical
Shot
E
0)
0,29111"
0.01
0.001
w
-
A
-
v v W
0.0001
z
i
10
i
I
I
I
I
I
I
Frequency (Hz)
Sensor
--Seismic
--------- ID Lim it
-. .-----Thermomechanical
Shot
N
0.01
E
C
0
0.001
Cu
L.
a)
CD)
.)
I
100
10
(a)
i
0.0001
(b)
105
L------- ------ - ----- --M-------- -------- ----------- -
100
10
Frequency (Hz)
Figure (4.5). Noise spectrum of (a) 1020 and (b) 432 Hz packaged sensors
50
=MM
Figure (4.6) is the noise spectrum of the 80 Hz sensor. The noise of this sensor, is limited
by seismic disturbances. Like the 432 Hz sensor, a coherence measurement on the 80 Hz sensor
will also be needed to determine its self noise limit. The 80 Hz noise spectrum shows that we
may be able to measure the thermomechanical noise of the proof mass because it is greater than
the laser phase noise above 10 Hz. At 40 Hz, the thermomechanical noise is 6.8 ng while the
interdigital noise is 2.8 ng.
0.1
N
r
0)
E
0.01
C
0
0.001
Sensor
Seismic
0.0001
ID Limit
--------- Thermomechanical
Shot
10-5 _---------------------------
z
10 6
'
'
'
I
'
10
1
Frequency (Hz)
Figure (4.6). Noise spectrum of 80 Hz packaged sensor.
4.4.3 Linearity
The linear range of the accelerometer was tested by driving the shaker at a set frequency
with increasing amplitude and measuring the output on the FFT. Recall that the intensity of each
diffraction mode is a sine squared relationship with the finger offset. At a high enough drive
acceleration, the output signal no longer resembles the sine wave drive signal because of this
nonlinear relationship. Figure (4.7) shows the output linearity of the 1020, 432, and 80 Hz
51
packaged accelerometers while Table (4.3) summarizes their linearity in acceleration and
equivalent deflection calculated using Equation (1.1). The linear deflection ranges agrees with
our analysis in Section 2.2 that the interdigital sensor is only linear to about a tenth of the
wavelength of the light source, or 67 nm. We can determine the open loop dynamic range of the
1020 Hz device by taking the ratio of the linear range to the resolution. At 400 Hz, the dynamic
range of the 1020 Hz sensor is over 7x 05. Because we cannot determine the true self noise of
432 Hz and 80 Hz sensors with the use of coherence techniques, we can only put a lower limit on
their dynamic range. The sensor dynamic ranges are also listed in Table (4.3).
Device Resonant
Drive
Linear Acceleration
Linear Deflection
Dynamic
Frequency (Hz)
Frequency (Hz)
Range (g)
Range (nm)
Range
1020
400
0.15
36
7x105
432
160
0.04
54
>2x10'
80
40
0.001
39
>Ix104
Table (4.3). Acceleration and deflection linearity and dynamic rnage of packaged interdigital accelerometers.
52
700
600 - 400 Hz Drive
500 -
C.
M
400 -
300
0
200 100 -
(a)
0.15
0.1
0.05
0
Drive Acceleration Amplitude (g)
800
.
.
,
,
700 - 160 Hz Drive
600
600 --500 -400 o
300 200 -
100 0.02
0.01
Drive Acceleration Amplitude (g)
0
(b)0
I I I
35
0.03
I
40 Hz Drive
30
25
20
3
o
15
10
5
*
0
(c)
0
0.0008
0.0004
Drive Acceleration Amplitude (g)
0.0012
Figure (4.7). Output versus acceleration of (a) 1020, (b) 432, and (c) 80 Hz packaged sensors.
53
4.4.4 Cross-axis sensitivity and drift
Figure (4.8). Illustration of cross axes.
Input accelerations with components in directions other than the sensitivity z-axis can
cause the finger offset to change due to proof mass rotations about its diagonal. As mentioned in
Section 3.1.1, the two rotational resonant frequencies occur at a factor of V3 from the first
resonant frequency. We measured the sensitivity of the accelerometer due to inputs in the axis
across the finger length (transverse) and along the finger length (longitudinal) by mounting the
sensor in different orientations on the shaker. The transverse and longitudinal axes are illustrated
in Figure (4.8). Because we did not, use another reference accelerometer to ensure that the test
sensor was not being accelerated in its sensitive axis, the actual cross-axis sensitivity may
actually be lower that our result. Figure (4.9) shows the upper limit on the low frequency crossaxis sensitivity of the 432 Hz packaged accelerometer compared to the z-axis sensitivity. The
plot shows that the folded pinwheel proof mass is at least 50 and 250 times more sensitivity in
the z-axis than the transverse or longitudinal axes, respectively.
54
1 0 im Im A - - 10 4_--
- --
- -
10K
Z-axis
*
x
Transverse
Longitudinal
o
1
4-I
x
(~)
C
ci)
x
x
(I)
x
x
xx
00
0.1
00
70
80
90
100
Frequency (Hz)
Figure (4.9). Maximum cross-axis sensitivity of 432 Hz packaged sensor compared to z-axis sensitivity.
Low drift is an important characteristic of accelerometers used for inertial guidance. To
measured the drift of the sensor, we recorded the zero-g bias for 30 minutes in a closed room.
Figure (4.10) is a plot of the drift of the 432 Hz packaged accelerometer. This plot shows a
maximum drift rate of 7 ptg/min and an overall drift of less than 30 pg. Commercial inertialgrade accelerometers have drifts on the order of + 1 mg over the span of one year. Longer tests
in a temperature-controlled environment will have to be performed to fully characterize the drift
of our sensor.
55
I.,RNIIIJIgN
I
'
'
'
' I ' I I
I
II I
I
I
I I
I
I
I I
I
I
4 10~
CD
.0
C
2 10~
E
0
0
+4-
C:
0
-2 10~
~ IP ' '!j F
r
1 ~~
-4 10~
I
0
I
I
5
I
I
I
I
i
i
10
i
I
I
15
L
-
20
25
Time (min)
Figure (4.10). Thirty-minute drift of 432 Hz packaged sensor.
56
30
5 CONCLUSION
The motivation for this thesis was to explore the use of an interferometric position
detector in a low-volume, high-resolution accelerometer. Current efforts to fill this commercial
void involve using electron tunneling to make very sensitive measurements of low resonant
frequency proof masses.
We designed and micromachined accelerometers based on optical
interference off interdigital fingers because this transducer has the advantages of a larger open
loop dynamic range and simpler fabrication process than tunneling.
After developing a
technique for releasing fragile structures, we released 80 Hz, 430 Hz, 1.0 kHz, 8.2 kHz
interdigital proof masses with less than 5% variation in the resonant frequency due to processing.
We lasercut acrylic 8.6 cm3 packages that integrate a proof mass with a laser diode and a
photodiode. Packages with 80 Hz, 432 Hz, and 1020 Hz proof masses demonstrated sensitivities
that scaled with the inverse square of the resonant frequency, a result that supports the
reproducibility of the packaging process.
The 1020 Hz package achieved a resolution that
equaled the position resolution of the interdigital AFM cantilevers and an open loop dynamic
range of over 105 . Analysis of the coherence of two sensors would be needed to determine the
true self noise and dynamic range of the 432 Hz and 80 Hz packages, sensors which are both
limited by the background seismic noise.
Future work on this accelerometer would involve a more extensive study of the cross-axis
sensitivity and the drift. The package volume can be further reduced by using a vertical cavity
surface emitting laser (VSCEL) fabricated into a smaller photodiode die. A fabrication process
that aligns and bonds an entire wafer of such dies to the proof mass wafer could reduce the cost
of and time to assemble one package. In this scenario, the packaging would only involve making
the electrical connections and sealing out the environment.
The existing application of our accelerometer would be to quantify seismic disturbances,
a measurement useful for vibration sensitive experiments.
Other applications would be in
triangulation, or the use of a network of three accelerometers to pinpoint a seismic disturbance
such as a finger tap on a board or a person moving in a room.
57
MECHANICAL MODELS
A
A.1 Folded pinwheel analytical model
connecting tether
main tether
E = modulus of elasticity
L
G = shear modulus
g = acceleration of gravity
Is
WI
d = displacement for 1 g z-axis input
main tether moment of inertia
I=
when bent in z direction
I'
=
main tether moment of inertia
when bent in sideways
main tether polar moment of inertia
J=
12
A
T
-
=
connecting tether moment of inertia
when bent in z direction
IUI t
12'
=
connecting tether moment of inertia
when bent sideways
z-axis
Figure (A. 1). Diagram and definition of parameters of folded-pinwheel structure with springs parallel to mass.
The following analytical model can be found in detail in Mitchell Novack's Master of
Science thesis [19]. Figure (A. 1) is a diagram of the folded pinwheel design with all its relevant
dimensions and parameters. We used this model to calculated the resonant frequency of the
oscillation in the z-direction. The resonant frequency is found by looking at the deflection due to
a 1 g input in the z-direction.
-
k
g
(2irf0)2
_igiff,
"2
(A.1)
58
The total displacement is the sum of three displacements that result from separate effects. The
first is due to the bending of the main tethers and is equal to
MgL3
24EII
r
8GJ 2L+4EIs+6GJL
2GJ 2 L +EIs
(I A.2)
The second deflection is created by the torsion of the main tether and is equal to
d2
Mgs2 L
A.3)
8GJ,
Lastly, the third deflection is caused by the bending of the connecting tether and is equal to
( k.4)
d3 = Mgs
48EI2
For completeness, the moment of inertia formulae are given below.
.tb3
1 = 12
bt3
12
il = I, +II
wt3
12 =
12
.
tw3
12
J2 = 12 + I2
(A.5)
(A.6)
Knowing the three deflections, the resonant frequency can be calculated.
27c
(A.7)
d,+d
2 +d 3
Using this model, one can obtain resonant frequencies that agree with a well-built simulation to
better than 5%.
59
A.2 Cantilever proof mass deflection
We will determine the deflection of a 100 Hz silicon cantilever proof mass like the one in
Figure (2.1). The structure can be modeled as a massless cantilever with a bending moment at
the end equal to the product of the weight of the mass mg and the beam length L. If the proof
mass is a 1000 pm square that is 525 tm thick and weights 1.2 mg, the length of a 1000 gm-wide
(W), 20 gm-thick (H) supporting cantilever would have to be
EWH_
1/3
1/3
L =EWH
(160x109N/m2
2
167
f
)
X3
(A .8)
1/3
-1x10-3 m -(20 x10 6
-(100/s)2
.1.2x10-6
kg
where E is the modulus of elasticity of silicon, 160 GPa, and k is the spring constant of the
cantilever. The static deflection at the end of the cantilever due to gravity would then be [21].
6mgL 3
3
EWH
A*
6.1.2 x 106 kg- 9.8m/s 2 _(8.8 x 10160x10
9 N/m
2
i)
3
-1x10-'m.(20x10-6 M)
-
38gm
(A.9)
3
Moreover, the tilt of the proof mass fingers with respect to the substrate fingers would be
-
12mgL 2
EWH 3
12-1.2 x10-6 kg. 9.8m/s
2 _(8.8
x10-3 m)
160 x10 9 N/m 2 -1x10-3 m. (20 x106 m)
2
3
-OOO85rad=0.49'
(A.10)
Because the fingers are at the end of the deflected 1000 pm long proof mass, the total deflection
of the fingers is
6 FINGERS =
X
+ 1000gm -sin4m = 38gm + 8.5gm = 46.5gm
60
(A. 11)
B
MASK DESIGN
B.1 Proof mass wafer
breakout tabs
I
(b.)
(a.)
Figure (B. 1) Frontside (a) and backside (b) mask for proof mass wafer.
61
The proof mass wafer required two darkfield, contact masks. The first mask defined the
fingers and springs as well as the top of the proof mass while the second mask defined the
bottom of the proof mass as well as the openings under the springs and fingers. Both mask
designs were created in Cadence and outsourced to be etched into chrome on 5" x 5" quartz
using 0.5 ptm spot-size e-beam. Figure (B.1) shows the layout of each mask.
The masks were designed allow the proof mass dies to be removed by breaking twelve
200 pim x 100 ptm tabs in the device layer holding it to the wafer at the end of the process.
Although this would reduce the number of structures we could fit on one wafer because a frame
would have to be left surrounding each die, it was absolutely necessary because the delicate
structures would not survive being diced with a saw. We made each of the low frequency (100,
500, and 1 kHz) proof mass dies the same size and placed the interdigitated fingers at the same
position (8 mm across and 4.5 mm down from the top left corner) so that they would require only
one package size. These dies were made intentionally large, 16 mm x 16 mm, to allow handling
with a vacuum pen during packaging. For the small 10 kHz proof mass, the die was shrunk to 16
mm x 8 mm to save wafer space. However, its finger position from the 16 mm edge is similar to
the lower frequency proof mass dies. We made the supporting frame around each die 3.6 mm
wide. On one 100 mm wafer, there are four 100 Hz, 500 Hz, and 1 kHz and two 10 kHz proof
masses.
B.2 Photodiode wafer
The photodiode wafer required one clearfield and three darkfield contact masks. The first
mask was a darkfield mask that defined the active regions of the photodiode to be implanted.
The second mask was a clearfield mask that opens up the oxide for the electrical contacts. The
third mask was a darkfield mask that defined the interconnects and bond pads. Lastly, the fourth
mask was a darkfield mask that defined the DRIE through holes. As in the case of the proof
mass wafer, all mask designs were created in Cadence and outsourced to be etched into chrome
on 5" x 5" quartz using 0.5 pim spot-size e-beam. Figure (B.2) shows the layout of each mask.
62
- -----------
4~
44
.4
44
4*
a.)
b.)
C.)
d.)
Figure (B.2). Mask set for photodiode wafer. a.) Mask
1 defined photodiode active regions. b.) Mask 2 opened
contact holes. c.) Mask 3 pattern interconnects. d.) Mask 4 defined DRIE through-hole.
Just as in the case of the proof mass wafer, we used the DRIE to release the dies. Each of the
thirty dies, measuring 16 mm x 8 mm is held to the frame by six 200 pm x 100 ptm x 525 pm
breakout tabs. Figure (B.3) shows an enlarged view of the same die on each mask.
63
a.)
alignment marks
b.)
C.)
breakout tabs
d.)
Figure (B.3). Sample dies from (a) Mask 1, (b) Mask 2, (c) Mask 3, and (d) Mask 4.
64
C
FABRICATION DETAILS
Microfabrication of the proof mass and photodiode wafers was performed in the MIT
Microsystems Technology Laboratory (MTL). This interdepartmental laboratory includes the
Integrated Circuits Laboratory (ICL) class 10 cleanroom, and the Technology Research
Laboratory (TRL) class 100 cleanroom.
C.1 Proof mass wafer
The proof mass wafer was a two mask CMOS compatible process. The starting material
was a 100 mm, single-side polished BESOI wafer with a 20 1 1 pim device layer, a 1 1 0.05 pm
oxide box layer, and a 381.5 + 0.5 pm Si handle layer.
Step
1
Description
RCA clean (ICL)
10 min organic clean (5:1:1 H 2 0 : H2 0 2 : NH40H)
Rinse
15 s 50:1 H 2 0 : HF dip
Rinse
15 min inorganic clean (6:1:1 H 2 0 : H2 0 2 : HCl)
Rinse, spin dry
2
3
560 nm thermal oxidation (ICL)
Time (min)
10
30
20
TubeA3 recipe G224
Temp (*C)
800
1100
1100
10
10
1100
1100
70
20
20
60
1100
1100
1100
800
Measure oxide (ICL)
KLA Tencor UV1280 Ellipsometer
Measurement type: SiO 2 on Silicon
Thickness = 560 nm
65
Gas
N2
N2
N2
02
02
H2/02
02
N2
N2
4
Pattern frontside with Mask 1 (TRL)
HMDS
Spin cast 1 gm OGC825 positive resist (3000 rpm, 30 s)
30 min bake, 90 "C
Expose 2.5 s, soft contact, 365 nm, 9 mW/cm 2 intensity
Develop in OGC934 1:1
Rinse, spin dry
30 min bake, 120 C
5
Plasma etch thermal oxide on both sides (ICL)
Applied Materials Precision 5000 Etcher
AME5000 recipe Isabella LTO
Time (s)
Gas
10
10
320
02
CHF 3
CHF3
Rate
RF (W)
(scem)
20
15
10
100
0
350
Pressure
Magnetic Field
(mTorr)
(Gauss)
200
200
200
50
50
50
6
Mount to 150 mm quartz carrier (TRL)
Spin cast 10 pm AZ4620 positive resist rings (1500 rpm) on carrier
Press on wafer with device layer up
15 min bake, 90 "C
7
DRIE etch 20 pm device layer silicon (TRL)
STS Multiplex ICP etcher
sts2 recipe Shallow, 12 min
APC Manual 75%
Base Pres = 0 mT
Time (s) Overrun C4F8 Flow SF 6 Flow
Cycle
(s)
(sccm)
(sccm)
Pass
11.0
0
0
35
Etch
12.5
0
140
0
8
Trip Pres = 95 mT
Plate RF Coil RF
(W)
(W)
60
600
80
600
Dismount wafer and remove resist (TRL)
10 minute piranha clean (1:3 H2 0 2 : H 2 SO4 )
Rinse, spin dry
9
Spin cast 20 pm polyimide (TRL)
Spin cast VM652 adhesion promoter (1000 rpm, 30 s)
60 s hot plate bake, 120 C
Spin cast P12600 polyimide resin (500 rpm, 120 s)
5 min hot plate bake, 90 0C
30 min cure at 350 C in 40% N2 (load wafer horizontally at 150 C, 4 0C/min ramp)
66
10
Measure polyimide thickness (TRL)
Nanospec Thin Film Thickness Measurement System
Film Type: Thick Films (13)
Index of refraction = 1.50
Thickness = 20 um.
11
Pattern backside with Mask 2 (TRL)
HMDS
Spin cast 1 ptm OGC825 positive resist on frontside (3000 rpm, 30 s)
30 min bake, 120 C
Spin cast 10 ptm AZ4620 positive resist on backside (1500 rpm, 60 s)
60 min bake, 90 0C
Expose 25 s, soft contact, 365 nm, 9 mW/cm2 intensity
Develop in AZ440 MIF
Rinse, spin dry
15 min bake, 90 0C
12
Mount to 150 mm quartz carrier (TRL)
Spin cast 10 pm AZ4620 positive resist rings (1500 rpm) on carrier
Press on wafer with device layer down
15 min bake, 90 0C
13
DRIE etch 381.5 ptm handle layer silicon (TRL)
STS Multiplex ICP etcher
sts2 reci e MIT 37b a, 110 min
APC Manual 75%
Cycle
Time (s) Overrun
(s)
Pass
11.0
0
Etch
15.0
0.5
Base Pres = 0 mT
C4F8 Flow SF 6 Flow
(sccm)
(sccm)
0
95
70
0
Trip Pres 95 mT
Plate RF Coil RF
(W)
(W)
60
600
120
600
14
Dismount wafer and remove resist (TRL)
24 hour acetone dip
Rinse, drip dry
15
Wet etch 1 pm buried oxide (TRL)
18 min buffered oxide etch (BOE) dip
Rinse, drip dry
16
Mount to 100 mm silicon wafer (TRL)
Spin cast 10 pm AZ4620 positive resist ring (1500 rpm) on carrier perimeter
Press on wafer with device layer up
15 min bake, 90 C
67
17
Ash polyimide (ICL)
Matrix Systems 106 Stripper
Asher recipe Std, 12 min
C.2 Photodiode wafer
The photodiode wafer was a four mask CMOS compatible process. The starting
material was a 100 mm, 525 pim-thick, single-sided polished (100) n-type (phosphorus doped)
silicon wafer with resistivity of 1.0 ohm-cm.
Step
1
Description
RCA clean (ICL)
See C.1 Step 1
2
560 nm thermal oxidation (ICL)
See C.1 Step 2
3
Measure oxide (ICL)
See C.1 Step 3
4
Pattern frontside Mask 1 (TRL)
See C.1 Step 3
5
Plasma etch thermal oxide on both sides (ICL)
See C.I Step 4
6
Ash resist (ICL)
Matrix Systems 106 Stripper
Asher recipe Std, 1 min
7
Boron ion implantation (outsourced)
40 keV, 5E15 cm 2 dose, minimal tilt (<8')
8
RCA clean (ICL)
See C.1 Step 1
68
9
Dopant drive-in/activation and 57 nm reoxidation (ICL)
ICL tubeA3 recipe G123
10
Time (min)
10
20
Temp ("C)
800
950
5
10
7
950
950
950
15
950
10
950
35
800
Measure resistivity
Prometrix Omnimap 111 B Four Point Probe
Sheet resistance = 40 ohms/sq.
11
Pattern frontside with Mask 2 (TRL)
See C.1 Step 3
12
Wet etch thermal oxide on both sides (TRL)
8 min buffered oxide etch (BOE) dip
13
Pre-metal clean (ICL)
10 minute piranha clean (1:3 H 2 0 2 : H2 SO4 )
Rinse
10 minute piranha clean (1:3 H2 02 : H2 SO 4 )
Rinse
15 s 50:1 H 20: HF dip
Rinse, spin dry
14
Deposit 1 pIm aluminum/silicon (ICL)
Applied Materials Endura 5500
Endura recipe Al-Si, 1 um
15
Pattern frontside with Mask 3 (TRL)
See C.I Step 3
16
Etch aluminum (TRL)
4 min PAN etch, 45 0C
Rinse, spin dry
17
Sinter aluminum (TRL)
Load wafers in 51% N 2
30 min N 2/H 2 sinter at 400 0C
69
Gas
N2
N2
02
02
H2 /0 2
02
N2
N2
18
Pattern backside with Mask 4 (TRL)
HMDS
Spin cast 1 pm OGC825 positive resist on frontside (3000 rpm, 30 s)
30 min bake, 120 C
Spin cast 8 pm AZ4620 positive resist on backside (3000 rpm, 60 s)
10 min bake, 90 0 C
Spin cast 8 pm AZ4620 positive resist on backside (3000 rpm, 60 s)
60 min bake, 90 0 C
Expose 100 s (ten 10 s intervals w/ 10 s delay), soft contact,
365 nm, 9mW/cm 2intensity
Develop in AZ440 MIF
Rinse, spin dry
15 min bake, 90 OC
19
Mount to 150 mm quartz carrier (TRL)
Spin cast 10 pm AZ4620 positive resist rings (1500 rpm) on carrier
Press on wafer with device side down
15 min bake, 90 C
20
DRIE etch through wafer (TRL)
STS Multiplex ICP etcher
sts2 recipe MIT_37ba 200 min
See C.1 Step 11
21
Dismount wafer and remove resist (ICL)
24 hour acetone dip
Rinse, drip dry
C.3 Packaging
We used a Universal Laser Systems X-100 lasercutter with a 100 watt CO 2 laser. The
cutter takes a drawing, like a CorelDraw file, and traces the lines and rasters the solid areas like a
printer. The intensity and the speed of the laser can be set to different values for each color in
the drawing. The CorelDraw drawings for the plastic housings are shown in Figure (C. 1). Table
(C. 1) shows the laser settings for each of the colors. The cutter works well on acrylic (Plexiglas)
pieces thinner than 10 mm. Multiple passes are usually preferred because cutting more than 1
mm during a pass can cause melting of surrounding areas, leading to sloped sidewalls. The laser
lens we used had a focal length of 2 inches.
70
A_ I
A
B
C
D
First Generation
0
A
D
C
B
Second Generation
Figure (C. 1) Lasercutter drawings for (A) top piece, (B) top shim, (C) bottom shim, and (D) bottom piece of first
1 mm deep rasters, red areas
and second generation packages. Black lines represent through cuts, yellow areas are
are 4 mm deep, orange lines are 2 mm clean-up lines, and cyan lines are shallow (<500
sm) alignment lines.
Color
Setting
Power (%)
Speed (%)
Depth (mm)
Passes
Black
Vector
70
10
3.2
4
Red
Raster/Vector
40
20
3
3
Yellow
Raster/Vector
20
40
1
3
Orange
Vector
50
30
2
3
Cyan
Vector
30
30
<0.5
4
Table (C. 1). Lasercutter settings for fabricating packages.
71
-M-4-1 ;6"
D
FIRST GENERATION PACKAGE RESULTS
We packaged a 428 Hz sensor in the first generation package before realizing the low
sensitivity of the housing. Figure (D.1) is the sensitivity of the 428 Hz first generation package
which shows similar damping (Q=140) but a low frequency sensitivity (0.1 V/g) than is 400
times less than that of the 432 Hz second generation package. This lower sensitivity translates to
a noise spectrum that is more limited by the noise of the photodiode and amplifier than by the
background or laser wavelength/phase noise as shown in Figure (D.2).
The shot noise, not
shown, contributes about 0.7 pg/rt Hz of noise. Although the sensitivity and resolution are low,
Figure (D.3) shows that the linearity of the sensor is the same as in the second generation
package, as expected.
10
Measured
Fit (Q=140)
CD
C
C0
0.1
200
70 80 90100
300
400
Frequency (Hz)
Figure (D. 1). Sensitivity of 428 Hz first generation package.
72
500 600
Sensor
Seismic
Photodiode/Amplifier
-N
1
E
0.1
--------- ID Lim it
--------- Thermomechanical
0
o
0.01
0.001
CO
01
100
Frequency (Hz)
10
Figure (D.2). Noise spectrum of first generation 428 Hz package.
I
I I I I I I I I II I I III
2.5
I I I I
I
I
I
I
I
I
I
I
I
I
I
T-
160 Hz Drive
2
t;
o
1.5
1
0.5
0
-
0
'
0.03
0.02
0.01
Drive Acceleration Amplitude (g)
Figure (D.3). Linearity of first generation 428 Hz package.
73
0.04
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