High-resolution Micromachined Interferometric ... - DSpace@MIT

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

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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

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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.

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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

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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

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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................................................................................

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40 41 43 44 45 48 50 51 53 54 55 56

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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 (

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

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........ . . . ......

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

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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,

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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.

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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

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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.

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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).

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4000

I I

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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

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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.

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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.

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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.

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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

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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

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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 (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.

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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.

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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 (