optical mems for free-space communication by lixia zhou …pister/245/2005s/lectures/optical/... ·...

Optical MEMS for Free-Space Communication

by

Lixia Zhou

B.S. (Tsinghua University) 1996 M.S. (University of California, Berkeley) 2002

A dissertation submitted in partial satisfaction of the requirements for the degree of

Doctor of Philosophy

in

Engineering – Electrical Engineering and Computer Sciences

in the

GRADUATE DIVISION

of the

UNIVERSITY of CALIFORNIA, BERKELEY

Committee in charge:

Professor Kristofer S. J. Pister, Co-chair Professor Joseph M. Kahn, Co-chair

Professor Roger T. Howe Professor Alice M. Agogino

Fall 2004

The dissertation of Lixia Zhou is approved:

________________________________________________________________ Professor Kristofer S. J. Pister, co-chair Date

________________________________________________________________ Professor Joseph M. Kahn, co-chair Date

________________________________________________________________ Professor Roger T. Howe Date

________________________________________________________________ Professor Alice M. Agogino Date

University of California, Berkeley

Fall 2004


Copyright 2004

by

Lixia Zhou

Abstract


by

Lixia Zhou

Doctor of Philosophy in Engineering - Electrical Engineering and Computer Sciences

University of California, Berkeley

Kristofer S. J. Pister, Co-chair

Professor Joseph M. Kahn, Co-chair

The convergence of MEMS technology with communication and digital circuitry

makes high-speed, low power, free-space communication links over distances up to

several km possible. MEMS corner cube retroreflectors (CCRs) are proposed to work

as a passive optical transmitter, sending collected information back to an interrogating

center. MEMS scanning micromirrors are proposed to steer a modulated laser beam

in order to establish a secure optical link between rapidly moving platforms.

Sub-millimeter-sized quad CCRs are fabricated by assembling two side mirrors

onto an actuated bottom mirror. An angular alignment accuracy of < 0.06° is achieved

through locking the two side mirrors using spring flexures and protrusion-notch

structures. The quad CCR incorporates a gap-closing actuator to deflect a base mirror,

allowing their reflectivity to be modulated up to 7 kb/s by a drive voltage less than 5

V. A 180-m free-space optical communication link using a CCR as the transmitter is

demonstrated. CCRs have been integrated into miniature, autonomous “Smart Dust”

1

nodes that constitute a distributed wireless sensor network. A signal-to-noise ratio

analysis of CCR-based links is also presented, considering the impact of CCR

dimensions, link distance, and other factors.

An SOI/SOI wafer bonding process is developed to fabricate scanning

micromirrors using lateral actuation. The process is an extension of the SOI

technology and can be used to fabricate stacked high-aspect-ratio structures with

well-controlled thicknesses. The fabricated one-axis micromirror scans up to 21.8°

optically under a DC actuation voltage of 75.0 V and has a resonant frequency of 3.6

kHz. The fabricated two-axis micromirror scans up to 15.9° optically for the inner

axis at 71.8 V and 13.2° for the outer axis at 71.2 V. The micromirror is observed to

be quite durable and resistant to shocks.

Torsional beams with T-shaped cross sections are introduced to replace

rectangular torsional beams in two-axis MEMS micromirrors in order to reduce the

cross-coupling between the two axial rotations. The fabricated bi-directional two-axis

micromirror works up to ±7° for the outer-axis and from -3° to 7° for the inner-axis

under DC actuation.

Professor Kristofer S. J. Pister, Co-chair Date

Professor Joseph M. Kahn, Co-chair Date

2

I dedicate this thesis to my husband, Gang Wang.

i

TABLE OF CONTENTS

1. INTRODUCTION .......................................................................................................... 1

1.1. Free-Space Optical Communication Using CCRs and Scanning Micromirrors ...... 1

1.2. Background of Designing CCRs as 3D Devices...................................................... 3

1.3. Background of Designing Scanning Micromirrors .................................................. 4

1.4. Outline of Dissertation ............................................................................................. 6

2. MEMS CORNER CUBE RETROREFLECTORS (CCRs) ........................................... 7

2.1. Overview of SOI-Based CCRs................................................................................. 7

2.2. Design and Fabrication of CCRs.............................................................................. 8

2.2.1. Design of gap-closing actuator .......................................................................... 9

2.2.2. Design of structure-assisted assembly ............................................................. 11

2.2.3. Fabrication ....................................................................................................... 12

2.3. Performance of Fabricated CCRs........................................................................... 15

2.3.1. DC and AC actuation of fabricated CCRs....................................................... 15

2.3.2. Optical performance of fabricated CCRs ........................................................ 20

2.4. Signal-to-Noise Ratio Analysis of CCR-Based Links ........................................... 27

2.5. Integration into Sensor Nodes ................................................................................ 33

3. MEMS SCANNING MICROMIRRORS AND SOI/SOI WAFER BONDING

PROCESS ......................................................................................................................... 38

3.1. Design of Scanning Micromirrors Using Lateral Actuation .................................. 39

3.2. SOI/SOI Wafer Bonding Process ........................................................................... 40

3.2.1. Bonding mechanism ........................................................................................ 41

3.2.2. Minimizing bow for SOI wafers...................................................................... 42

3.2.3. Strategies to enhance bonding ......................................................................... 47

ii

3.2.4. Detailed process flow ...................................................................................... 48

3.3. Bond Characterization............................................................................................ 50

3.3.1. Diagnosis of bonded structures by SEM and infrared images......................... 50

3.3.2. Electrical interconnection realized by bonded structures ................................ 52

3.3.3. Shear stress test of bonded structures .............................................................. 56

3.3.4. Air sealing by bonded structures ..................................................................... 58

3.4. Mechanical Modeling and ANSYS Simulation of Micromirrors .......................... 62

3.4.1. Analytical simulation....................................................................................... 62

3.4.2. ANSYS simulation .......................................................................................... 71

3.5. Performance of Scanning Micromirrors................................................................. 73

3.5.1. DC and AC actuation of fabricated one-axis scanning micromirrors.............. 75

3.5.2. DC and AC actuation of fabricated two-axis scanning micromirrors ............. 80

3.6. Reliability and Robustness of Micromirrors .......................................................... 82

3.6.1. Reliability of micromirrors .............................................................................. 82

3.6.2. Shock resistance of micromirrors .................................................................... 85

4. MEMS SCANNING MICROMIRRORS WITH T-BAR TORSIONAL BEAMS ...... 89

4.1. Torsional Beams with T-Shaped Cross Section..................................................... 89

4.2. ANSYS FEM Simulation ....................................................................................... 91

4.3. DC and AC Actuation of Micromirrors with T-bar Torsional Beams ................... 93

4.4. Comb Drive Actuators for Large Displacements ................................................... 97

5. CONCLUSIONS AND DISCUSSIONS .................................................................... 101

5.1. Summary of Results over CCRs........................................................................... 101

5.2. Summary of Results over Scanning Micromirrors and SOI/SOI Wafer Bonding

Process......................................................................................................................... 102

5.3. Future Work ......................................................................................................... 104

REFFERENCE ............................................................................................................... 108

iii

APPENDIX A – MATLAB SCRIPTS TO MODEL FAR-FIELD IMAGE PATTERN

REFLECTED BY CCRS ................................................................................................ 116

APPENDIX B – MATLAB SCRIPTS TO MODEL DSCS RELATED WITH

MISALIGNMENT ANGLE OF CCRS.......................................................................... 118

APPENDIX C – SOI/SOI WAFER BONDING PROCESS FLOW.............................. 120

C1. Layout Features / Design Rules ........................................................................ 120

C2. Detailed Process Flow....................................................................................... 121

APPENDIX D – ANSYS SCRIPTS TO MODEL MECHANICS OF SCANNING

MICROMIRRORS ......................................................................................................... 126

APPENDIX E – MATLAB SCRIPTS TO CALCULATE THE CURVATURE OF A

MULTILEVEL WAFER ................................................................................................ 128

iv

ACKNOWLEDGMENTS

I have really enjoyed five years of graduate student life here at Berkeley, including

many sleepless nights, years of hard work, and most important of all, invaluable

experience of learning from mentors and colleagues. I would like to thank Professor

Joseph Kahn for taking me into his research group; as a result, I accidentally bumped into

MEMS area and beheld the beauty of this continuously-developing field. Professor Kris

Pister inspired me on many aspects due to his enthusiasm, sense of humor, and never-

dying confidence. I would also like to thank my two other committee members, Professor

Roger Howe and Professor Alice Agogino for their support and constructive advise on

the thesis.

Veljko Milanovic showed me what is hard-working; because of him, I learned how to

have fun when working in the Microlab. Thanks to Mathew Last for giving advice in

series of design review and contributing greatly to my research. I would also like to thank

Michael Cohn, Hongbing Liu, Daniel McCormick, Hyuck Choo, Sunghoon Kwon, Baris

Cagdaser, Robert Conant, Matthew Wasilik, Xiaofan Meng, Ning Chen, and Christopher

Keller, for sharing tricks in the Microlab and/or providing help in conducting research.

I thank other students and doctors in 471 Cory, Brian Leibowitz, Brett Warneke, Seth

Hollar, Anita Flynn, Sarah Bergbreiter, Michael Scott, Richard Yeh, Colby Bellew,

Lance Doherty, Chinwuba Ezekwe, and Steven Lanzisera, for broadening my view on

other fields, such as integrated circuits and robotics.

I would like to thank our grant administrator, Tom Parsons, for his patience in

arranging trips, paper submission, and many other routines.

v

Special thanks to my friend, Jinwen Xiao, for being a partner to our constantly-

changing hobbies, from tennis, table tennis, to swimming. I thank Jianyang Xu for

inviting me to so many trips and giving terrific breaks from the intense graduate student

life. I would also like to thank many of my friends, Xinyan Deng, Qiang Lu, Jin Wang,

Wei Mao, Xiaoming Zhu, and Roy You, for being together and earning Ph.D titles side

by side.

Many thanks to my conference buddies, Raffi Kamalian and Ye Wang, for having

good time together in IABs and MEMS conferences.

Thank Mehrdad Roosta from Iolon, Inc. for helping me to perform shock test. Thank

Bart Mathewson for helping me in drawing the cool 3D schematic layout.

Finally, I would like to thank my husband, Gang Wang, for his unlimited patience,

encouragement, and love throughout thick and thin.

vi

INTRODUCTION

1. INTRODUCTION

This dissertation describes the development of two Microelectromechanical Systems

(MEMS) devices, corner cube retroreflector (CCR) and scanning micromirror, which are

used for free-space optical communication.

1.1. Free-Space Optical Communication Using CCRs and Scanning Micromirrors

Free-space optical communication has attracted considerable attention for a variety of

applications where line-of-sight is applicable, such as metropolitan network extensions

[1], last-mile Internet access [2], inter-satellite communication [3], and earth-to-space

links [4]. Optical communication offers significant advantages over radio frequency (RF)

communication, including secure link, wide bandwidth, small terminals, low power

consumption, freedom from frequency allocation issues, and simultaneous multi-node

communication capabilities. Thus optical communication is favored when building a

compact, high transmission rate, and low power communication system where the line-

of-sight constraint is satisfied.

One of the key components in this two-way free space optical communication system

is a compact, reliable, and inexpensive laser beam steering device that provides a fast

scanning capability for pointing, acquisition, tracking, and data communication. A

scanning micromirror based on the technology of MEMS is introduced to fulfill this

requirement [5][6]. MEMS scanning micromirrors can be built with flat and reflective

mirror surfaces, high optical resolution, fast scanning capability, reliable actuating

mechanism, and large volume production.

1

INTRODUCTION

MEMS phased arrays composed of groups of relatively small micromirrors are also

proposed to scan the laser beam [7][8]. They can be actuated through large deflection

angles with substantially reduced response time. But they involve more complicated

actuator design, i.e., not only capable of rotations around the two axis, but also able to

move vertically to compensate the phase difference between mirrors. Also active

feedback controls over individual mirrors can be very complicated.

The emergence of distributed sensor network systems brings on a demand for a

communication platform with extremely small power consumption [9][10][11][12]. That

is when CCRs come into play. Zwirn proposed to use a microfabricated CCR as a free-

space optical transmitter [13]. An unactuated CCR consists of three mutually orthogonal

mirrors that form a concave corner, thus light incident on this ideal CCR (within an

appropriate range of angles) is reflected back to the source. By modulating the orientation

of one of the three mirrors, an on-off-keyed digital signal can be transmitted back to the

interrogating light source. Such a CCR has been termed a “passive optical transmitter”

because it can transmit without incorporating a light source. An electrostatically actuated

CCR transmitter offers the advantages of small sizes, relatively fast transmission rates,

low power consumption and convenient integration with solar cells, sensors and CMOS

control circuits. CCR transmitters have been employed in miniature, autonomous sensor

nodes (“dust motes”) in the Smart Dust project [14].

MEMS micromirrors are used for actively transmitting data when the system requires

a seeking and tracking ability, such as scanning the interrogating laser beam at the base

station of a distributed sensor network system or steering the coded laser beam between

two moving unmanned air vehicles. MEMS CCRs are intended to passively transmit

2

INTRODUCTION

digital signals for a platform with relatively low transmission rates and extremely small

power budget, such as in a Smart Dust sensor mote.

1.2. Background of Designing CCRs as 3D Devices

Fabrication of three-dimensional structures with precisely positioned out-of-plane

elements poses challenges to current MEMS technologies. One way to achieve three-

dimensional structures is to rotate parts out-of-plane on micro-hinges [15][16]. Previous

CCRs have been fabricated in the MUMPS process [17][18] and side mirrors were

rotated out-of-plane on hinges. However, these CCRs had non-flat mirror surfaces and

high actuation voltages. Most importantly, the hinges released from surface-

micromachined processes typically have gaps, permitting motion between linked parts.

Thus the out-of-plane structures attached to the substrate through this kind of hinges were

not able to obtain accurate vertical alignment and CCRs fabricated in this way had poor

retroreflective efficiency.

Using an elastic hinge instead of structural hinges composed of interdigitated layers

improves the alignment scenario tremendously. Structures can be bent out of plane by

utilizing either the large residual stress difference between two kinds of thin films

(bymetal hinges) [19], the thermal shrinkage of cured polyimide (polyimide hinges) [20],

or the surface tension forces of melting thick photoresist pads (photoresist hinges) [21].

Small radii of bending can be obtained through these methods and adding carefully-

designed interlocking braces allows a better control over the orientations of out-of-plane

structures. It is reported that photoresist hinges self assembly structures with a yield as

high as 75% and angle accuracy of 1.8 mrad [21].

3

INTRODUCTION

However, the elastic hinges have the drawback of occupying a large area on chip due

to the scheme of rotating structures out-of-plane from the chip surface and the existence

of those interlocking braces. Also the rotation actuator implemented in this process

displays an extremely high actuation voltage [22], which will become a problem to

design driving circuits on an autonomous sensor node.

Here we propose a new scheme, structure-assisted assembly, to fabricate and

assemble compact CCRs that achieve accurate alignment between three mirrors and

operate under a conveniently low actuation voltage [23]. The assembly-assisting

structures include V-grooves and spring clamps, which are widely used to align fibers

with other optical devices to achieve high coupling efficiency [24][25]. V-grooves can

guide the assembled structures into the desired position and spring clamps are employed

to maintain out-of-plane structures on accurate orientation.

1.3. Background of Designing Scanning Micromirrors

Scanning micromirrors have been developed for a wide range of applications in

addition to steering laser beams, such as optical crossbar switches [26], digital projectors

[27], barcode readers [28], adaptive optics [29], and tunable lasers [30]. However, the

purpose of laser beam steering for free space optical communication brings on different

requirements over scanning micromirrors, such as large mirror sizes (~1 mm in

diameter), rotation ability over two axis, large DC scan angles (±10° optical), fast

switching ability (transition time between positions < 100 µs), and strong shock

resistance (hundred Gs).

While surface micromachining generally does not offer considerable scanning range

for a large size mirror, MEMS micromirrors based on silicon-on-insulator (SOI) wafers

4

INTRODUCTION

and deep reactive ion etching (DRIE) technology overcome this problem by having an

etched cavity under the scanning micromirror. It also provides attractive features such as

perfect mirror flatness, high-aspect-ratio springs, and thus small cross-mode coupling.

Many strategies have been developed around these two technologies in order to make

scanning micromirrors with large size mirrors, wide steering angles, and fast responding

speed. Conant et al first presented a vertical comb drive actuator fabricated on the two

layers of a SOI wafer [31]. However, their process requires an accurate alignment

between two layers in different heights (~ 50 µm). Consequently, several self-alignment

fabrication processes were developed to enable precise alignment between vertically

stacked layers [32][33]. Another way to tackle this alignment problem is using a

photoresist hinge to rotate [34] or plastically displacing [35] a group of comb fingers out-

of-plane so that two groups of comb fingers remain to be perfectly spaced and form an

angular comb drive actuator.

Although vertical/angular comb drive actuators provide high force density, it has

difficulty in producing two-axis scanning micromirrors with comparable steering

performance on both axial rotations. Kwon et al used a backside island to provide

electrical isolation and mechanical coupling for a two-axis scanning micromirror [36],

but this device has a much lower resonance frequency in the outer axial rotation than that

of the inner axial rotation. Milanovic et al used mechanical rotation transformers to

produce a two-axis scanning micromirror with high resonant frequencies [37], but the

steering range is limited.

Scanning micromirrors realized by an off-axis lateral force overcome the alignment

issue in vertical comb drive actuators and its advantages also include small momentum of

5

INTRODUCTION

inertia, a large actuation force, and consequently a large scanning angle and fast response

[38]. We propose an SOI/SOI wafer bonding process to fabricate scanning micromirrors

actuated by a lateral comb drive actuator.

1.4. Outline of Dissertation

The following chapters in this dissertation address in detail the design and fabrication

of CCRs and scanning micromirrors. Chapter 2 presents the design, fabrication,

assembly, testing over optical and electrical performance, and integration of CCRs with

other components of Smart Dust motes. Chapter 3 describes the design, fabrication,

mechanical modeling, and testing of scanning micromirrors manufactured by an SOI/SOI

wafer bonding process. In Chapter 4, torsion beams with T-shaped cross sections are

introduced to overcome the cross-coupling problem existing in the two-axis scanning

micromirrors with rectangular torsion beams. Chapter 5 concludes the dissertation by

reviewing the features of the SOI/SOI wafer bonding process and the possible

applications with this process. Outstanding issues and directions for future work,

including better design of comb drive suspension springs, are outlined.

6

MEMS CORNER CUBE RETROREFLECTORS

2. MEMS CORNER CUBE RETROREFLECTORS (CCRs)

The Smart Dust project aims to integrate a power source, multiple sensors, a micro

computer, and a communication platform, forming a miniature, autonomous sensor mote.

CCRs serve as a passive transmitter for the Smart Dust mote working under extremely

low power consumption to transmit signals collected by the sensors on the mote back to

an interrogating center.

CCRs modulate the reflected light intensity by modulating the orientation of one of

their three orthogonal mirrors. In order to achieve high signal to noise ratio at the

interrogating center which is several hundred meters away, CCRs must have mirror

surfaces which are extremely flat and highly reflective. Moreover, mirrors must maintain

strict orthogonality when CCRs are not actuated. As the data transmission rate depends

on how fast the orientation of the mirror in CCRs is modulated, it is desirable to have a

high resonance frequency over the rotation mode of the actuated mirror. Also the driving

voltage needs to be low in order to conveniently integrate with CCRs’ power source and

driving circuits.

2.1. Overview of SOI-Based CCRs

We introduce a new scheme, structure-assisted assembly, to fabricate and assemble

CCRs that achieve accurate alignment of out-of-plane parts. The optical and electrical

properties of CCRs produced through this method are superior to previous CCRs

fabricated in the MUMPS process. Improvements include a tenfold reduction in mirror

curvature, a threefold reduction in mirror misalignment, a fourfold reduction in drive

7


voltage, an eightfold increase in resonance frequency, and improved scalability due to the

quadruplet design.

Here we present detailed information about the design, fabrication, and performance

of these quad CCRs. We describe an experimental free-space optical link using a CCR

transmitter, and present an analysis of the signal-to-noise ratio (SNR) of CCR-based

optical links. Fabricated CCR is incorporated with other parts of Smart Dust mote and

transmits signals collected by the accelerometer and light-level sensor.

2.2. Design and Fabrication of CCRs

The layout of CCR side mirrors and bottom mirror is displayed in Figure 2-2 and the

SEM picture in Figure 2-2 shows a fabricated and assembled CCR. The two side mirrors

are assembled into the V-grooves on the chip, while the bottom mirror is designed to be

torsionally actuated so that it can modulate the light intensity of the retro-reflected light

beam.

Notch

Protrusion V-groove

Actuation Stop

Notch

Protrusion V-groove

Actuation Stop

Notch

Protrusion V-groove

Actuation Stop

V-groove

Actuation Stop

Figure 2-1. Layout of CCR side mirrors and bottom mirror.

8


Torsional Spring Beam

Side Mirror 1

Side Mirror 2

Actuated Bottom Mirror

Actuation Stop

Tether

Torsional Spring Beam

Side Mirror 1

Side Mirror 2

Actuated Bottom Mirror

Actuation Stop

Tether

Figure 2-2. SEM picture of assembled CCR quadruplet. Note the spring-locks

beside the V-grooves to grab the feet of the side mirrors and the notch-

protrusion clutch at the top of the side mirrors to achieve more accurate

positioning. The extended beams with triangular heads act as limit

stops for the gap-closing actuator, and land on electrically isolated

substrate islands after the moving mirror pulls-in.

9

2.2.1. Design of gap-closing actuator

We have chosen to fabricate CCRs on silicon-on-insulator (SOI) wafers to obtain flat

and smooth mirror surfaces. The chemical mechanical polishing gives SOI wafer surfaces

a RMS (root-mean-square) roughness on the order of nanometer. Also the total thickness

variation of the device layer across a 100 mm-diameter SOI wafer can be as small as 1

µm, producing a very flat mirror surface.


An electrostatic gap-closing actuator is an appropriate choice for modulating the

orientation of a CCR mirror. It provides a high actuation torque and thus low driving

voltage. The actuated mirror is fabricated in the device layer of the SOI wafer and

suspended by two torsional springs. The device layer and substrate layer of the SOI wafer

conveniently form the opposing electrodes of a gap-closing actuator. With half of the

substrate layer under the mirror etched away, the gap-closing actuator provides a pure

torsional moment when a voltage is applied between the mirror and the underlying

substrate. The narrow gap (the one we choose is 2 µm) between the device layer and

substrate layer provides an angular deflection of 5.7 mrad for a mirror plate with a side

length of 350 µm. This amount of angular deflection induces an enormous change over

the retro-reflected light intensity, giving an on-off signal ratio of over 20 dB, which is

sufficient for the purpose of modulating the signal level digitally. At the same time, the

narrow gap size enables high actuation moment with low drive voltage, as electrostatic

actuation force inversely depends on the square of the gap size between electrodes.

Another advantage of this gap-closing actuation design is that it decouples the sizing

of the actuated mirror from the sizing of the actuator. The substrate electrode lies under

the mirror plate, spanning from the center of the mirror plate to the root of two extended

beams on the device layer, whose position determines the size of the actuator. The

extended beams act as mechanical stops to prevent shorting between the two actuator

plates when the moving mirror reaches pull-in position. After pull-in, the triangular-

shaped stops make point contact with electrically isolated islands on the substrate,

minimizing stiction and allowing the release of the mirror when the actuation voltage is

removed. The amount of angular deflection and pull-in voltage depends on the position of

10


the extended beams while the mirror plate may be designed larger to reflect sufficient

light for the intended communication range.

The tethers between the moving mirror and the rest of the chip in Figure 2-2 hold the

actuated mirror in place, preventing it from sticking to the substrate when releasing. They

are broken by probes after the assembly.

2.2.2. Design of structure-assisted assembly

Two groups of V-grooves are patterned in the device layer to assist the insertion of

the two side mirrors. They are situated orthogonally around the actuated bottom mirror.

Each of the side mirrors has “feet” that can be easily inserted into the larger open end of

the V-grooves. Also the substrate under the V-grooves has been etched away to facilitate

this insertion. After the insertion, the side mirrors are pushed toward the smaller end of

the V-grooves, where the feet are anchored by springs next to the V-grooves which are

spaced apart by a distance slightly smaller than the thickness of the side mirror. One side

mirror has a notch at the top and the other side mirror has a spring-loaded protrusion at

the top; after assembly, the protrusion on one side mirror locks into the notch on the other

side mirror, maintaining accurate alignment between the two mirrors.

In this way, we can naturally fabricate four CCRs that share a common actuated

bottom mirror, although the performance of those four CCRs may differ because of the

asymmetrical positioning of the side mirrors and the presence of etching holes on part of

the actuated mirror plate. Compared to other single CCR designs, the quadruplet design

increases the probability of reflecting the light back to the base station without

significantly increasing die area or actuation energy.

11


2.2.3. Fabrication

As shown in Figure 2-3, the process starts with a double-side-polished SOI wafer

with a 50 µm device layer and a 2 µm buried oxide layer. First, a layer of thermal oxide

with 1 µm thickness is grown on both sides of wafer at 1100oC. We pattern the front-side

oxide with the device-layer mask. The main structures are on this layer, including the

bottom mirror, two torsional spring beams suspending the bottom mirror, gap-closing

actuation stops, and V-grooves for anchoring the side mirrors. Then we flip the wafer

over, deposit thick resist, and pattern the back-side oxide using the substrate-layer mask.

The substrate layer functions as the second electrode of the gap-closing actuator and

provides two electrically isolated islands as the pull-in stop for the actuator. We perform

DRIE etching from the back-side first. After etching through the substrate, we continue

the etching to remove the exposed buried oxide, reducing the residual stress between the

buried oxide and device layer that might otherwise destroy the structures after the front-

side etching. Then we DRIE etch the front-side trenches. After etching, the whole chip is

dipped into concentrated HF for about 10 min, to remove the sacrificial oxide film

between the bottom mirror and substrate. There is no need to employ critical-point drying

after release, because the tethers between the moving mirror and the rest of the chip hold

the actuated mirror in place, preventing it from sticking to the substrate.

12


SCS Wet oxide Thick resist

Pattern both sides

HF wet release

Frontside etch

Backside etch

Wet oxidation

SCS Wet oxide Thick resist

Pattern both sides

HF wet release

Frontside etch

Backside etch

Wet oxidation

Figure 2-3. Bottom mirror fabrication process.

The side mirrors can be fabricated in the same process or by another standard single-

mask process on a SOI wafer. A separate process provides more flexibility over choosing

the thicknesses of the device layer, i.e., the thickness of the side mirrors, bottom mirror,

and supported suspension beams. We patterned the device layer with the shape of side

mirrors, followed by a long-duration HF release.

13


(a) Before assembly:

Side mirror 2

Side mirror 1

Bottom mirror

(b) After inserting side mirror 1:

(c) Finally insert side mirror 2:

(a) Before assembly:

Side mirror 2

Side mirror 1

Bottom mirror

(b) After inserting side mirror 1:

(c) Finally insert side mirror 2:

Figure 2-4. Assembly sequence. Snap locks yield alignment accuracy better than 1

mrad.

14

When both the bottom mirror and side mirrors are ready, we mount the side mirrors

onto the bottom mirror manually to form a fully functional CCR. Figure 2-4 shows the

sequence of assembly. First, we pick up side mirror 1, using a pair of fine-tip tweezers.

We insert it into the large-opening end of the V-grooves around the bottom mirror and

push it into the slot, where the feet of side mirror 1 are grabbed by the springs beside the

V-grooves. Then we pick up side mirror 2 and insert into the perpendicular V-grooves.

When both mirrors are pushed to the end of V-grooves, the spring-loaded protrusion on

one side mirror is locked into the notch on the other side mirror and these spring-loaded

structures ensure that the side mirrors remain in correct alignment. This assembly process


can be completed within several minutes under a stereomicroscope. After assembly, we

use a probe to finely tune the position of side mirrors and use UV-curable epoxy to secure

the side mirrors to the chip. As silicon reflects only about 30% of visible light, we

evaporate a 50 nm-thick layer of gold either before or after assembly without masking, to

increase the optical reflectivity of the CCRs.

2.3. Performance of Fabricated CCRs

In the Smart Dust project, the CCR needs to operate with an actuation voltage less

than 5 V, to be compatible with solar cell power and low-voltage CMOS control signals.

The modulation speed of the CCR should be in the range of several kb/s. Most

importantly, the optical performance of CCR has to be good enough to transmit a signal

for several hundred meters with low bit-error probability.

2.3.1. DC and AC actuation of fabricated CCRs

x

gθ

(a) (b)

x

gθ

x

gθ

(a) (b)

Figure 2-5. A simple model of the gap-closing actuator in CCRs. (a) Mirror

suspended by two torsional beams; (b) Cross section of CCR bottom

mirror, switching from “1” state to “0” state.

The bottom mirror in CCRs can be modeled as a torsionally suspended mirror

actuated with a gap-closing electrostatic actuator, as shown in Figure 2-5. The deflection 15


of the actuated mirror takes place under the resultant of the electrostatic torque and spring

torque. This gap-closing actuator has a pull-in position and pull-in voltage different from

the simple cantilever case with a gap-closing actuator on the tip [39]:

m

inpull Wg4404.0=−θ (2-1)

2/1

0

3685.9⎟⎟⎠

⎞⎜⎜⎝

⎛= −

−m

inpullinpull L

KV

εθθ (2-2)

where g is the actuator gap, i.e., the thickness of buried oxide layer in the SOI wafer.

Here, Wm and Lm are the width and length of the actuator plate, and Kθ is the torsional

spring constant of two suspending beams.

Figure 2-6 shows experimental results of deflected angle versus applied voltage, as

well as the theoretical calculations. Experiments demonstrate a DC pull-in voltage as low

as 4.7 V and a pull-in angle of approximately 0.4·g/Wm, in good agreement with

theoretical predictions. Notice that the full angular travel of the actuator is g/Wm

theoretically, which is 6.7 mrad for a gap distance of 2 µm and an actuator width of 300

µm. In experiments, the actuated mirror of CCRs is deflected by 5.7 mrad at most

because the gap-closing stops prevent the moving mirror from crashing to the other

electrode node. This gives a difference in the deflected angles after pull-in between the

experimental and theoretical values.

16


0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

Actuation Voltage (V)

Ang

le D

ispla

cem

ent (

mra

d)

Experimental

Theoretical

Figure 2-6. Actuator angular displacement vs. applied DC actuation voltage.

The mechanical resonance frequency of the actuated plate is given by

2/1

21

⎟⎟⎠

⎞⎜⎜⎝

⎛=

mIkf θ

π (2-3)

where Im is the moment of inertia of the actuated plate.

The frequency response of one CCR, measured using a POLYTEC laser Doppler

vibrometer, is shown in Figure 2-7. A pure sinusoidal voltage source is applied to the

gap-closing actuator and a lock-in amplifier senses the output signal at twice the

frequency of the drive signal. Electrical resonance occurs at 2.2 kHz, corresponding to a

mechanical resonance frequency of 4.4 kHz. Because the actuation torque is proportional

to V2, the torque is applied at twice the frequency of the electrical drive signal. The

17


frequency at which the squared amplitude is half its DC value is around 3.5 kHz. This

corresponds to a mechanical cut-off frequency of about 7.0 kHz, implying that the CCR

can be digitally modulated up to about 7 kb/s. A much higher modulation speed could be

achieved by fabricating the bottom mirror on a SOI wafer having a decreased device-

layer thickness, with little or no impact on other performance characteristics of the CCR.

1.0E-08

1.0E-07

1.0E-06

1.0E-05

100 1000 10000

Electrical Drive Frequency (Hz)

Am

plitu

de o

f Vel

ocity

(a.u

.)

10-5

10-6

10-7

10-81.0E-08

1.0E-07

1.0E-06

1.0E-05

100 1000 10000

Electrical Drive Frequency (Hz)

Am

plitu

de o

f Vel

ocity

(a.u

.)

10-5

10-6

10-7

10-8

Figure 2-7. Frequency response of the actuated bottom mirror plate.

18

Figure 2-8 presents the step response of a CCR to a 250 Hz square wave. At t = 0.5

ms, the actuation voltage is turned off. The actuated mirror is restored to its relaxed

position under the restoring torque of the torsional springs, turning on the beam reflected

from the CCR. At t = 2.5 ms, the actuation voltage is turned on, pulling down the

actuated mirror, and turning off the beam reflected from the CCR. Both release and pull-

down exhibit transition times of about 55 µs. When the mirror is released, it exhibits


ringing for about 1 ms before settling to the relaxed position. The 1 ms settling time

implies a maximum modulation rate of about 1 kb/s. Fortunately in this process we can

add an isolated substrate area under the actuated plate to obtain increased squeeze-film

damping after release of the actuation voltage. We have demonstrated that this can

greatly reduce the settling time, permitting the maximum modulation speed to be limited

only by the resonance frequency.

-4

-2

0

2

4

6

8

0 1 2 3 4 5

Time (ms)

Ang

le D

ispl

acem

ent (

mra

d)

Plate pull-in

Plate released

-4

-2

0

2

4

6

8

0 1 2 3 4 5

Time (ms)

Ang

le D

ispl

acem

ent (

mra

d)

Plate pull-in

Plate released

Figure 2-8. Response of the actuated bottom mirror plate to a 250 Hz square wave.

A major goal of the Smart Dust project [40] is to minimize the energy per bit required

for transmission. The capacitance of the CCR changes from around 1.3 pF before pull-in

to 3 pF after pull-in. The actuation voltage is around 5 V. A rough estimate of the energy

expended during each pull-in action is CV2 ≈ 75 pJ (no energy is required to release the

CCR). Assuming non-return-to-zero encoding, energy is required only when the 19


transmitted bit transitions from ‘1’ to ‘0’, so that the average energy consumption is

about 19 pJ/bit. This compares quite favorably to other (RF) approaches such as

Bluetooth, which has a fundamental transmission cost of 1 nJ/bit over a communication

distance of a few 10s of meters.

2.3.2. Optical performance of fabricated CCRs

A useful parameter describing the optical performance of CCR is the differential

scattering cross section (DSCS). It is defined as [41]

i

ooi

o ILInn

dd 2

)ˆ,ˆ( =Ωσ (2-4)

where is the incident light direction, is the reflected light direction, Iin on i is the light

intensity incident on the CCR, Io is the reflected light intensity at the observation plane

and L is the distance between the CCR and the observation plane. Note that the DSCS has

dimensions of m2/sr. The DSCS depends on the mirror dimensions, mirror flatness,

mirror surface quality, mirror reflectivity, and relative alignment between the mirrors. In

addition, the DSCS depends on the directions of the incident and reflected beams. For a

CCR with three identical square mirrors, the DSCS is largest for incident and reflected

directions close to the body diagonal, i.e., and near in on )1,1,1(3

1 .

If we illuminate an unactuated CCR with laser light, the far-field diffraction pattern

corresponds to the DSCS for reflected light directions close to . Since an

unactuated CCR reflects a laser beam back to the same direction as the incoming light, a

special optical setup has to be employed to separate the outgoing light from the incoming

light and allow the detection of its far-field diffraction pattern. As shown in Figure 2-9, a

on in−

20


linearly polarized laser beam is first oriented to fully pass through a polarized beam

splitter. The following quarter-waveplate changes its linear polarization to circular. After

three reflections off an unactuated CCR, the light returns with the opposite circular

polarization. As the beam passes through the same quarter-waveplate, it changes to

linearly polarized again, but with a direction orthogonal to the original laser beam. The

beam is then reflected by the polarized beam splitter and collected by an imaging

receiver. The distance from the CCR to the imaging lens has to be small enough to allow

the lens to collect the refraction beam within the interested range of angles, and long

enough to have the refraction pattern considered to be collected at the far field.

Laser

Lens

CCR

Imaging Receiver

¼ Waveplate

Polarized Beam Splitter

Laser

Lens

CCR

Imaging Receiver

¼ Waveplate

Polarized Beam Splitter

Figure 2-9. Optical setup designed to separate the incoming light and the outgoing

light retro-reflected by an unactuated CCR. The far-field diffraction

pattern of the CCR is collected by the imaging receiver.

Figure 2-10 (a) shows the measured far-field diffraction pattern of an unactuated

CCR, with illumination along the body diagonal direction, while Figure 2-10 (b) presents

the simulated diffraction pattern for a perfect CCR of the same size [41]. The wavelength

of the illumination light is 632.8 nm. Both measured and simulated patterns exhibit

similar “star” patterns, corresponding to an effective reflecting area that is a six-sided

21


polygon. The angular separation between nulls is 1.2 mrad in the experiment, and 1.0

mrad in the simulation, showing good agreement. The experimental results demonstrate

that any angular misalignment between the mirrors must be smaller than 1 mrad, or else

we would not be able to observe the diffraction pattern with null spacing on the order of 1

mrad.

1.2 mrad 1 mrad1.2 mrad 1 mrad

Figure 2-10. Far-field patterns of light reflected from CCR show good alignment

between the three mirrors of the CCR. Left: experimental result for a

fabricated device; Right: theoretical result for a perfect CCR of the

same size.

The collinear DSCS (CDSCS) is defined as the value of the DSCS when the

directions of illumination and observation are collinear, i.e., . The CDSCS is

relevant because in CCR-based links, the receiver is usually placed along the axis of

illumination. If the distance L is sufficiently large, then the receiver subtends a small

solid angle Ω

io nn ˆˆ −=

o, over which the DSCS is approximately equal to the CDSCS. Under these

assumptions, the received power Po can be computed approximately using

22


oiio

io nnddIP Ω⋅−Ω

⋅≈ )ˆ,ˆ(σ (2-5)

For example, if a CCR consists of three identical square mirrors having side length a and

reflectivity rm, and is illuminated along the body diagonal by light at wavelength λ, the

CDSCS is

2

343))1,1,1(

31),1,1,1(

31(

λ

σ m

o

radd

=−Ω

(2-6)

In (2-6), we see that the CDSCS is proportional to the power captured by the CCR (a

factor a2) and the power reflected in three bounces from the mirrors (a factor ), and is

inversely proportional to the solid angle into which light is diffracted from the CCR (a

factor λ

3mr

2/a2).

At a wavelength of 632.8 nm, uncoated silicon has a reflectivity of approximately 0.3,

whereas gold has a reflectivity of 0.99. For an ideal CCR with a 250 µm bottom mirror

and 450 µm side mirrors1 illuminated along the body diagonal, Fraunhofer diffraction

theory predicts CDSCS values of 1.2 × 10−3 m2/sr and 4.4× 10−2 m2/sr for uncoated and

gold-coated devices, respectively. We have experimentally measured CDSCS values of

9.3 × 10−4 m2/sr and 2.8× 10−2 m2/sr, for uncoated and gold-coated devices, respectively.

These measured values are close to the theoretical predictions, further confirming the

near-ideal optical quality of the fabricated CCRs.

We have realized free-space optical communication over a range of 180 m. As shown

in the optical setup of Figure 2-11, a continuous-wave laser (CW) beam with 632.8 nm

wavelength, 0.8 mW power and 0.1 mrad divergence (half-angle) is directed towards

23

1 In devices fabricated to date, the dimensions of the side mirror are slightly larger than those of the bottom mirror because the bottom mirror is minimized to minimize layout area.


CCR by a small mirror placed in front of the telescope. The telescope has an entrance

aperture of 8 cm diameter, subtending a half-angle of 0.22 mrad at the CCR. When the

CCR bottom mirror is not actuated, the beam reflected back to the telescope has a

divergence (half-angle) of 0.7 mrad; when the mirror is deflected by 5.7 mrad, this

reflected beam splits apart into two beams, each directed 11.4 mrad away from the optical

axis, well away from the telescope entrance aperture. As the size of the directing mirror

in front of the telescope is small compared to the aperture of the telescope, the amount of

light signal blocked by the directing mirror is minimal compared to the amount of signal

collected by the telescope. The CCR is driven by a pseudo-random, non-return-to-zero bit

sequence at 400 b/s. Light collected by the telescope passes through an optical bandpass

filter having 632.8 nm center wavelength and 10 nm bandwidth, and is imaged onto a

silicon photodiode with dimensions of 0.81 mm × 1.37 mm, which is coupled to a

transimpedance amplifier.

The detected optical signal matched with the transmitted bit pattern after a free space

transmission of 180 meters, as depicted in Figure 2-12. The modulated signal is received

with high SNR (> 22.3 dB), although its amplitude fluctuates slowly due to air turbulence

in the optical path.

24


Oscilloscope Laser

Photo DetectorCCR

Telescope Lens

Uplink DataInL

Bandpass Filter

Oscilloscope Laser

Photo DetectorCCR

Telescope Lens

Uplink DataInL

Bandpass Filter

Figure 2-11. Optical setup for uplink free-space optical communication using a CCR

as a passive transmitter.

Figure 2-12. Detected 400 b/s signal after free-space transmission over 180 m.

Waveform 1: CCR drive signal; Waveform 2: detected photocurrent,

which is proportional to the intensity reflected from CCR.

It is also interesting to see the detected optical signal after a free space transmission

of 180 meters over a longer time, as depicted in Figure 2-13. The pseudo-random

generated signal is propagated to the receiver with a large amplitude variation and the

25


SNR between the most intensified and weakest signals differs by about 10 dB. The

amplitude fluctuation of the received signal is due to the atmospheric turbulence when

the beam transmits from the laser to the CCR and from the CCR to the receiver.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5Time (sec)

Am

plitu

de o

f Sig

nal (

a.u.

6

)

Figure 2-13. Detected signal at 800 bit/s after free-space transmission over 180 m

for a longer period of time.

Studies over atmospheric turbulence show that turbulence-induced fading can be

reduced substantially by aperture averaging when the receiver aperture is larger than the

correlation length [42] (~ 1806328.0 ×=Lλ mm = 10.7 mm in our case). Therefore,

most of the detected signal variation is contributed from the limited size of the

transmitting CCR since the lens of the light receiver is much bigger than the correlation

length of intensity fluctuations. Besides making a compromise between the signal level

and the size of the Smart Dust mote for some extreme conditions, an alternative solution

26


is increasing the power of the interrogating laser beam so that the received signal

achieves the desired SNR.

2.4. Signal-to-Noise Ratio Analysis of CCR-Based Links

In this section, we present an analysis of the SNR of free-space optical links using

CCR transmitters, to identify critical design parameters and aid in design optimization.

Here, we neglect the effects of atmospheric turbulence. These effects may be negligible

for short-range indoor links. For outdoor links with ranges up to a few hundred meters,

turbulence-induced intensity fluctuations may often be overcome simply by an increase

in transmitted power, as in the example of Figure 2-12.

Our analysis considers a system design as in Figure 2-11. A CW laser beam with

power Pi and divergence half-angle θi, is incident on the CCR from a range L. The

intensity Ii, incident on the CCR is

i

ii

LP

Iθπ 22 tan

= (2-7)

The telescope has light collection area Ac. We assume that L is sufficiently large, and that

Ac is sufficiently small, that the intensity of light reflected from the CCR is constant over

the telescope aperture. Since the telescope subtends a solid angle Ωo = Ac /L2 at the CCR,

using (2-7), the telescope collects a signal power

)ˆ,ˆ(tan 24 ii

oi

cisig nn

dd

LAP

P −Ω

=σ

θπ (2-8)

when the CCR is not actuated (logical ‘1’). The telescope is assumed to collect negligible

signal power when the CCR is actuated (logical ‘0’). Assuming the photodetector has

responsivity R, when the CCR is not actuated (logical ‘1’), the signal photocurrent is

27


)ˆ,ˆ(tan 24 ii

oi

cisig nn

dd

LRAP

i −Ω

=σ

θπ (2-9)

Hereafter, for concreteness, we assume that the CCR consists of three identical square

mirrors having side length a and reflectivity rm, and is illuminated along the body

diagonal by light at wavelength λ. In this case, the CDSCS is given by Equation (2-6).

Thus, the signal photocurrent when the CCR is unactuated (logical ‘1’) is given by

i

cmisig

LRAraP

iθπλ 242

34

tan3

= (2-10)

Note that the signal photocurrent is proportional to the laser power Pi. Because the beam

is subject to diffractive spreading when propagating both to and from the CCR, the

photocurrent depends on the transmission range as L−4, instead of the L−2 dependence

usually observed in free-space optical links. The photocurrent depends on mirror size as

a4, mirror reflectivity as and on wavelength as λ3mr

−2, for reasons explained previously.

We now calculate the ambient light noise received by the photodetector. Suppose that

the photodetector has area Ad, and that the telescope has focal length f. The area in the

CCR plane “seen” by the photodetector is

2

2

fLA

A df = (2-11)

Assume that the region surrounding the CCR is illuminated by ambient light having

spectral density pbg (this quantity represents power per unit area per unit wavelength, and

has units of W/(m2⋅nm)), and that this region reflects ambient light with reflectivity rbg.

Suppose that the telescope employs an optical bandpass filter having bandwidth ∆λ.

28


Within the filter bandwidth, the total ambient light power reflected from the region

“seen” by the photodetector is

2

2

f

LArpARpP dbgbg

fbgbgbgλ

λ∆

=∆= (2 12)

Assuming that the region surrounding the CCR is a Lambertian reflector [43], the power

Pbg results in an irradiance at the telescope of

22 f

Arp

L

PI dbgbgbg

bgπ

λ

π

∆== (2-13)

Hence, the ambient light-induced photocurrent is

2f

RAArpRAIi cdbgbg

cbgbgπ

λ∆== (2-14)

Note that the ambient light photocurrent is independent of the transmission range L, but is

proportional to the photodetector area Ad and to the telescope light-collection area Ac. In

order to minimize ambient light noise, it is desirable to choose the photodetector to be

only as large as required to capture the entire CCR image.

We assume that a preamplifier is employed to amplify the received photocurrent, and

will refer all noises to the preamplifier input. The ambient light induces white shot noise,

which has a (one-sided) power spectral density (PSD) given by

bgbg qiS 2= (2-15)

Additional noises may be contributed by the preamplifier. A feedback or load resistance

RF will contribute white noise having PSD F

BR R

TkS

4= , where kB is Boltzmann’s constant

and T is absolute temperature. The preamplifier transistors are assumed to contribute

white noise with PSD Samp. Assume that the preamplifier (or a following lowpass filter)

29


limits the noise bandwidth to a (one-sided) bandwidth B, where B is approximately equal

to the bit rate. Then the total noise variance is given by

(2-16) BSSS ampRbgtot )(2 ++=σ

The peak electrical SNR is

2

2

tot

sigiSNR

σ= (2-17)

Assuming that all noise sources are Gaussian distributed, the bit-error probability is

given by

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2SNRQPb (2-18)

where ⎟⎟⎠

⎞⎜⎜⎝

⎛=

2erfc

21)( xxQ . Achieving a bit-error probability of 10−6 requires a peak SNR

of about 19.5 dB.

Table 2-1 summarizes the symbols used during the SNR analysis of CCR-based links

and lists their experimental values in the communication test over a range of 180 m. The

signal power reflected by CCRs is calculated through the measured DSCS, about 67% of

the one reflected by a perfect CCR with similar sizes. The noise is dominated by the

white noise from the loading resistor as the experiment is conducted indoor and the

ambient light is low in amplitude. The analysis gives a SNR of 24.3 dB, agreeing with the

experimental SNR of 22.3 dB.

Symbol Parameter Value

Pi Laser power 0.8 mW

θi Laser divergence half-angle 0.1 mrad

λ Laser wavelength 0.633 µm

30


L Communication range 180 m

Ii Light intensity incident on the CCR 7.86×10-3 W/m2

Ac Light collection area of the receiving telescope 5.03×10-3 m2

f Focal length of the telescope 0.4 m

DSCS Measured differential scattering cross section of the CCR with a 500 µm bottom mirror and 600 µm side mirrors

0.108 m2

Psig Signal power collected by the telescope when CCR is not actuated

1.32×10-10 W

R Responsivity of the photodetector at wavelength λ 0.3 A/W

isig Signal photocurrent when CCR is not actuated 3.96×10-11 A

Ad Receiving area of the photodetector 1.1×10-6 m2

Af Area of the field viewable by the photodetector 0.22 m2

pbg Spectral density of the ambient light ~10-5 W/m2/nm

rbg Reflectivity of the background which CCR is sitting on 0.3

∆λ Bandwidth of optical bandpass filter at the receiving end 10 nm

Pbg Ambient light power reflected from the region “seen” by the photodetector

6.6×10-6 W

Ibg Intensity of the ambient light collected by the telescope 6.48×10-11 W/m2

ibg Photocurrent induced by the ambient light 1.95×10-11 A

Sbg Power spectral density of the white shot noise induced by the ambient light and signal light

2.00×10-29 A2/Hz

SR Power spectral density of the white noise contributed by the load resistance RF (=20 MΩ)

5.62×10-27 A2/Hz

Samp Power spectral density of the white noise contributed by the preamplifier transistors

1.44×10-28 A2/Hz

B Bandwidth of the preamplifier or the following lowpass filter

1000 Hz

σtot Total noise variance 2.40×10-12 A

SNR Peak electrical signal-to-noise ratio 24.3 dB

Table 2-1. Symbols used during the SNR analysis of CCR-based links and their

experimental values in the communication test over a range of 180 m.

31


Figure 2-14 plots the relationship between the interrogating laser power Pi and the

maximum transmission range L, assuming a bit-error probability Pb = 10−6, for different

values of the CCR side length a. Here a perfect CCR with three equal-sized square

mirrors is assumed for the simplicity of the analysis. The transmitted bit rate is 1 kb/s. All

other important parameters, such as interrogating beam divergence, collecting lens

aperture, photodiode dimensions, bandwidth of the transimpedance amplifier, and

feedback resistance, are assumed to be the same as those in the free-space communication

experiment, listed in Table 2-1. One significant change over the analysis from the

experiment is that the communication link is assumed to be established under sun light

instead of indoors. Therefore the shot noise from the ambient light is no longer

negligible. It contributes approximately the same amount of noise as the thermal noise

from the feedback resistor, while amplifier noise is still small enough to be ignored

during the analysis. As illustrated in the Figure 2-14, the maximum transmission range L

depends on the laser power as 41−iP , and depends linearly on the CCR side length a.

Figure 2-14 demonstrates that a CCR-based link of several hundred meters range is

feasible.

32


0 2 4 6 8 100

500

1000

1500

2000

2500

Interrogating Laser Power Pi (mW)

Com

mun

icat

ion

Ran

ge L

(m)

0.25 mm

0.5 mm

0.75 mm

CCR Side Length: 1 mm

0 2 4 6 8 100

500

1000

1500

2000

2500

Interrogating Laser Power Pi (mW)

Com

mun

icat

ion

Ran

ge L

(m)

0.25 mm

0.5 mm

0.75 mm

CCR Side Length: 1 mm

Figure 2-14. Communication range L vs. interrogating laser power Pi required to

achieve a bit-error probability Pb of 10-6 for different CCR side lengths

(assuming that the CCR consists of three equal-sized square mirrors).

The communication link is assumed to be established under the

sunlight.

2.5. Integration into Sensor Nodes

Micromachined CCRs have been packaged with other components of Smart Dust

“motes”, i.e., solar cell, 1 Mb/s CMOS optical receiver, finite-state machine counter, low-

power ADC, accelerometer, and light-level sensor, to form a 16 mm3 autonomous solar-

powered sensor mote [14], as shown in Figure 2-15. Each mote consists of three dies, a

0.25 µm CMOS ASIC die, a 2.6 mm2 SOI solar cell array chip, and a MEMS four-

quadrant CCR die. The mote has successfully sampled photosensor data and transmitted

33


it over the optical link with the CCR under the illumination of one sun, or under

incandescent or LED illumination of equivalent intensity.

Solar Cell Array

CCRs

XLCMOS

IC

Solar Cell Array

CCRs

XLCMOS

IC

Figure 2-15. 16 mm3 solar-powered Smart Dust mote with bi-directional optical

communication. Components include a multi-junction solar power

array, 1 Mb/s optical receiver, CCR as an optical transmitter, 8-bit

ADC, digital controller, accelerometer and light-level sensor.

In the Smart Dust communication architecture, a single base station transmits

commands and queries to a collection of motes via a broadcast free-space optical

downlink at bit rate up to 1 Mb/s. The base station also illuminates the CCRs and uses a

telescope and photodiode to receive messages transmitted via the CCR-based uplink at a

bit rate approximately 180 b/s. If the base station is equipped with an imaging receiver

incorporating multiple pixels, it can decode uplink messages transmitted simultaneously

and without synchronization by multiple dust motes, a form of space-division

multiplexing.

Figure 2-16 shows a signal transmitted by a CCR and received by a base-station

receiver. The 8-bit data packets alternately transmit data sensed by the accelerometer and

34


light-level sensor. Data packets are separated by a stop bit ‘0’ and a start bit ‘1’. The

asynchronous transmission data rate is approximately 182 bit/s, and is determined by the

clock frequency of the internal oscillator in the ASIC chip.

Figure 2-16. Detected data packets transmitted at 182 bit/s by the modulation of the

CCR on a Smart Dust mote and received by a photodiode detector.

Start (‘1’) and stop (‘0’) bits from each packet are highlighted.

35

A more compact version of Smart Dust mote is displayed in Figure 2-17. It consists

of only two chips, one ASIC chip and one ICARUS die with CCRs, solar cells and an

accelerometer fabricated through a single process, ICARUS process [44]. ICARUS

process fabricates CMOS circuits and DRIE structures on an SOI wafer with filled

trenches isolating structures electrically [44]. The CCRs fabricated in ICARUS process

contains the same assembled side mirrors, except that there is no backside holes under the

actuated bottom mirror. The mirror is electrically divided into two parts by an isolation

trench close to the center of the mirror. One side of the mirror is connected to an

actuation voltage while the other side is electrically grounded, sharing the same voltage


potential as the substrate. As the actuation voltage is applied, an electrostatic force is

generated on the side which the actuation voltage is applied on while there is no force

acting on the other side. Therefore a torque is created and rotates the micromirror.

Figure 2-17. SEM of the 6.6 mm3 Smart Dust mote, a two-chip assembly. CCRs are

fabricated in ICARUS process which also fabricates solar cells,

accelerometers, and NMOS buffers.

One advantage of ICARUS CCRs is that the settling time during which the actuated

mirror is released from its snap-in position to its resting position is found to be

significantly shorter, compared to CCRs fabricated from the previous process. This

improvement is attributed to the presence of squeeze film damping when the mirror is

released from its snap-in position. In the earlier process, the substrate wafer was removed

from underneath one half of the mirror so that no significant film damping is present

during the release of the mirror. However, for ICARUS CCRs, the handle wafer is

present underneath the entire mirror, so there is a significant amount of damping during

36


both the snap-in and release of the mirror. A shorter settling time means a faster

modulating rate of the mirror and therefore CCRs can transmit a signal at approximately

its resonance frequency without adding complicated feedback control.

37

MEMS SCANNING MICROMIRRORS AND SOI/SOI WAFER BONDING PROCESS

3. MEMS SCANNING MICROMIRRORS AND SOI/SOI WAFER

BONDING PROCESS

Scanning micromirrors are proposed to steer the laser beam in order to establish free-

space optical communication links between two small unmanned aerial vehicles for the

Steered Agile Laser Transmitter project [6]. Micromirrors are responsible for pointing,

tracking, and transmitting the modulated laser beam.

Two 1.5 m wingspan MLB Bats [45] serve as the aerial platform for the

communication system. They fly with a pre-designed spiral pattern, or in other words,

they know roughly the relative position of the other airplane. But an onboard micromirror

is needed to cancel the angular vibrations present on each airplane and steer the laser

beam within a range of angles in order to achieve the precise location of the other

airplane. The angular vibration of the small airplane can be as large as ± 5° and an extra ±

5° margin is provided in the design of the beam steering mirror to accommodate the

acquisition of optical links. A closed-loop control of the micromirror will be employed to

improve its switching ability, making a transition time between positions around the

order of 100 µs. Also the micromirror needs to have strong shock resistance since the

landing acceleration for a UAV is approximately 10 ~ 15 g.

Electrostatic comb drive actuator is the preferred scheme for actuating scanning

micromirrors over other methods, such as electromagnetic, thermal, or piezoelectric

actuators, because electrostatic actuators offer faster transition capability and lower

power consumption. These properties are essential for the micromirrors to maintain the

38


optical link with the target and operate on a UAV where miniaturizing and fuel saving are

aggressively pursued. Moreover, the required feedback signal for controlling a

micromirror can be implemented by just including a group of sensing fingers directly on

the electrostatic comb drive actuator.

3.1. Design of Scanning Micromirrors Using Lateral Actuation

Our group introduced the method of realizing scanning micromirrors by utilizing a

lateral comb drive actuator [38]. As shown in Figure 3-1, the bi-directional force

generated by a lateral comb drive actuator is transferred as an off-axis torque over two

torsional beams by two transfer arms.

Lateral Force

Low-Mass Mirror

Transfer Arm

Two Anchored Torsional Beams

Lateral Force

Low-Mass Mirror

Transfer Arm

Two Anchored Torsional Beams

Figure 3-1. Torsional movement of scanning micromirrors is realized by an off-

axis lateral force generated from a lateral comb drive actuator.

An obvious benefit of this scheme is the separation of the micromirror and the

actuator which provides more flexibility to the design. A large actuator can be designed

to extend to both in-plane directions of the layout and all comb fingers always add equal

amount of moment of inertia to the device. The DC scanning range of a lateral actuated

39


micromirror can be very large since it is limited only by the maximum stress that the

material of the device can sustain while the range of a micromirror with a vertical/angular

actuator is limited by the height-to-length ratio of the comb drive finger which is often

compromised by having long fingers to provide enough torque. The lateral actuation

design offers more shock resistance, too. The lateral movement of the device is resisted

both by the torsional beams and actuator suspension beams, in contrast to single torsional

beam suspension when using a vertical comb drive actuator.

3.2. SOI/SOI Wafer Bonding Process

This multilevel design was formerly fabricated on an SOI wafer using a combination

of timed DRIE etching and DRIE etching with etch stops. However, timed etching does

not produce uniform structures across the wafer and therefore needs careful monitoring.

A new approach, SOI/SOI wafer fusion bonding, is introduced to attain multilevel

structures with well-controlled thickness.

In the proposed new process a patterned third layer is aligned and bonded onto a

patterned SOI wafer, producing 3D devices or stacked high-aspect-ratio structures. The

third layer comes from the device layer of another SOI wafer [46][47][48], with a choice

of thickness as small as 2 µm and a thickness uniformity of ± 0.5 µm, whereas structures

fabricated by the timed etching counterpart can have a thickness variation of 5 µm across

a wafer. The sacrificial handle wafer of the bonded SOI wafer can be disposed of by

either plasma blank etching or mechanical grinding. When the handle wafer is left with

the desired thickness, a subsequent polishing step can provide another layer to the stack.

Then more layers can continue to be added on by wafer fusion bonding, constructing

multi-layer structures. One drawback of this layer stacking strategy is that bonding gets

40


more difficult as the stresses in the stacked layers induce more bow and warpage over the

wafer. Besides stacking several levels of high-aspect-ratio structures, silicon fusion

bonding introduces little or no thermal stress because of the well-matched thermal

expansion between the bonded layers and the fabricated monolithic single crystal

structures are completely compatible with subsequent high-temperature process steps,

such as oxidation and diffusion.

In addition to allowing tighter control over the thicknesses of the critical layers, the

improvement of fabricating scanning micromirrors using this new bonding process

includes producing at a higher yield, obtaining a functional two-axis scanning

micromirror, and scanning at a larger angle with a smaller actuation voltage.

3.2.1. Bonding mechanism

When two mirror-polished and cleaned silicon wafers are brought closely, they are

immediately bonded with each other [49]. After the bonded pair is brought into a furnace

and annealed for a certain time, the bonds across the interface are strengthened and two

silicon wafers are fusion-bonded with each other. The proposed SOI/SOI wafer bonding

process is to employ this adhesion property between silicon, creating a monolithic multi-

level device, whose thickness is strictly controlled.

Understanding the bonding mechanism helps us in optimizing the process flow and

choosing the recipe parameters. The following is a compendium of research results

regarding to the bonding procedure and its chemistry [50][51][52]. Prior to bonding,

polished silicon wafers are chemically treated so that the wafer surface is terminated with

a high density of silanol groups (Si-OH). These groups are covered with several mono-

layers of water. When the two wafers are brought into intimate contact, an immediate

41


weak bond occurs due to the hydrogen bonding between the OH groups on the two wafer

surfaces. The bonded wafer pair is then annealed in a furnace. First at a temperature

below approximately 300°C, silanol bonds are converted to siloxane bonds (Si-O-Si):

Si-OH + OH-Si -> Si-O-Si + H2O (3-1)

The resulting water diffuses into the silicon crystal to form silicon dioxide:

Si + 2 H2O -> SiO2 + 2 H2 (3-2)

When temperature exceeds 800°C, silicon oxide begins to flow, fill up the interface

micro-gaps, and form strong siloxane bonds all over the wafer.

Therefore, the primary condition to achieve the bonding between two silicon wafers

is a clean and flat wafer surface, making the contact area as large as possible. An

annealing temperature higher than 800°C is also preferred since at that temperature the

glass layer on the bonding interface starts to reflow and the achieved bond strength is

comparable to that of single crystal silicon. In practice, a conservative annealing

temperature of 1150°C is used to ensure that the process works. Methods, such as oxygen

plasma activation and/or tetramethoxysilane (TMOS) solution dip [50], can be adopted

later to decrease the annealing temperature (≤ 500°C) while still achieving bonding

energies that are sufficiently high for a micromechanical device.

3.2.2. Minimizing bow for SOI wafers

It has been experimentally observed that in order to achieve a secure silicon-silicon

bonding, the roughness of wafer surface has to be less than 1 nm and the bow of a 4-inch

wafer is no greater than 5 µm [53]. Our experiments show that two wafers with a bow as

large as 25 µm can be bonded without problems. However, an SOI wafer from our

42


vendor, BCO Technologies, has a typical bow of 75 µm, preventing an adequate bonding

between SOI wafers. Strategies are needed to flatten wafers and increase the yield of

bonding.

The bow of an SOI wafer is mainly induced by the mismatch of thermal expansion

coefficient between silicon and oxide, causing excess mechanical stresses in the SOI

wafer after annealing at elevated temperatures and subsequent cooling. At high annealing

temperature, there is no internal stress between the silicon and oxide layers due to the

reflow ability of the oxide layer. As temperature drops, oxide contracts but silicon shrinks

more. Therefore, the thermal mismatch between silicon and oxide builds up internal

stress and cause the wafer to bend, as shown in Figure 3-2. A simple model to calculate

the bending caused by the thermal stress is presented in [54] and described in the

following. From the basic principle of mechanics, the stress in the films must obey the

following conditions:

(1) Force balance:

(3-3) ∑=

=N

iiF

10

where Fi is the normal force acted on layer i and N is the number of layers.

(2) Moment balance:

0212

'1

1

11

3

=⎟⎟⎠

⎞⎜⎜⎝

⎛++∑ ∑∑

=

−

==

N

i

i

j

iji

N

i

ii ttFtEρ

(3-4)

where Ei’ is the planar modulus for layer i, ti is the thickness of layer i, and ρ is the radius

of wafer curvature.

(3) Interface strain continuity for any two adjacent layers:

43


ρ

αρ

α2'2'

1

11

11

+

++

++ −+∆=++∆ i

ii

ii

i

ii

ii

ttE

FTttE

FT (3-5)

where αi is the thermal expansion coefficient of layer i and ∆T is the temperature

difference between the annealing temperature and room temperature.

F1, t1, α1F2, t2, α2

Fi, ti, αi

SCS Wet oxide

F1, t1, α1F2, t2, α2

Fi, ti, αi

F1, t1, α1F2, t2, α2

Fi, ti, αi

SCS Wet oxide Figure 3-2. An SOI wafer is curved by residual stresses. Fi, ti, and αi are the normal

force, thickness, and thermal expansion coefficient of layer i.

According to this simple model, there are several ways to reduce the bow in an SOI

wafer:

(1) Reduce the thickness of the buried oxide layer. This idea is not practical because a

certain thickness of oxide layer (preferably 2 µm) is required in order to keep the

parasitic capacitance of the bonding pads and inter-connection wires small for the

feedback control of mirror positions. However, a step of timed-etching the exposed oxide

to a thinner thickness can be added between the DRIE etching of the device layer and the

bonding of the two wafers in order to reduce the wafer stress. 10:1 HF should be used for

this purpose because compared to 49% HF, its etching speed is slow enough to strictly

control the remaining oxide to be thick enough for acting as the etching stop for the later

DRIE etching. In this way, a thinner oxide film is left in the exposed area to reduce the

stress while a 2 µm-thick oxide layer is remained under the bonding pads and inter-

connection wires to maintain the low parasitic capacitance.

44


(2) Increase the thickness of the handle wafer. This is not a good solution, either,

since a thicker wafer presents more difficulty in accommodating the bending and makes

the bonding harder to achieve.

Figure 3-3. Add an oxide layer onto the back of the handle wafer of SOI wafers

to balance the stress and obtain a flatter surface.

SCS Wet oxideSCS Wet oxide

(3) Retain an oxide layer on the backside of the handle wafer. The sandwiched

structures, as shown in Figure 3-3, are able to balance the stress and obtain a flatter

surface. One thing to be noted is that any non-uniformity in the stress distribution might

introduce warpage to the multi-layered wafer. But the device layer of the SOI wafer is

etched by repeating the same pattern and the thickness of the added oxide layer is

uniform across the wafer. As a result, the local residual stress is expected to be minimal

to produce any significant warpage to the wafer.

45


Bow

of W

afer

(µm

)

0 0.5 1 1.5 2

-100

0

100

200

300

Thickness of Oxide on the Backside of the Wafer (µm)

Bow = 0

Bow

of W

afer

(µm

)

0 0.5 1 1.5 2

-100

0

100

200

300

Thickness of Oxide on the Backside of the Wafer (µm)

Bow = 0

Figure 3-4. The bow of the multilayer wafer is varied with the thickness of the

oxide layer added on the backside of a 50 µm/2 µm/350 µm SOI wafer.

Simulation shows a 1.5 µm-thick oxide layer optimizes the wafer

flatness.

The previously described stress-flatness model is used to find the proper oxide

thickness in order to obtain the flattest wafer. As illustrated in Figure 3-4, the bow of the

SOI wafer (with a 50 µm-thick device layer, a 2 µm-thick buried oxide layer, and a 350

µm-thick handle layer) is varied with the oxide thickness added on the backside of the

wafer. The simulation shows that a 1.5 µm-thick oxide layer makes the bow of the SOI

wafer zero and optimizes the flatness of the wafer. In experiment, an unprocessed SOI

wafer with the same thickness configurations has a bow of 76.3 µm initially. After

thermally growing a 1.5 µm-thick oxide layer on both sides of the SOI wafer and

46


removing the front side oxide layer, the bow of the SOI wafer became 17.8 µm, which is

small enough to allow a successful bonding with other SOI wafers.

3.2.3. Strategies to enhance bonding

Surface cleanness is another significant condition for successful wafer fusion bonding.

The initial hydrogen bonding that pre-bonds two wafers are weak and operates over a

short range, only when the two wafers are very close together. Therefore, having wafers

flat and free with particles are critical prior to bonding.

Several steps were practiced to ensure a strong adhesion force between the two

patterned SOI wafers. First, the design of the layout allocated about 50% of the wafer

surface as contact area to guarantee adequate force. Second, wafers were handled

carefully in the clean room. For example, a vacuum pen was used to grab a wafer on its

backside whenever applicable, as particles or scratches that can destroy a bond might be

introduced to the bonding surface of the wafer if using metal tweezers. Third, a layer of

thermal oxide was grown on the wafers as the first step of the process and was stripped

off just before cleaning and bonding occurred. This thermal oxide layer provides

protection throughout the wafer handling and is a common practice to be added in the

bonding process by researchers. Fourth, as suggested in the previous section, an oxide

layer was retained on the backside of the SOI wafers to balance the stress introduced by

the buried oxide layer in an SOI wafer. These sandwiched layers produce flatter wafers,

making bonding easier. Lastly, a series of chemical cleaning steps were carried out

during which a layer of hydrous thin oxide grew on the wafer surface. The hydrous oxide

is highly reactive and wafers with this hydrophilic surface are ready to bond at room

temperature.

47


It is also suggested by colleagues that the residual polymer film from the passivation

cycles during DRIE etching degrades the bonding surface and thus its complete removal

is important. Since this polymer film is stubborn and HF, piranha and RCA cleaning are

not sufficient, O2 plasma ashing for over 1 hour is recommended to completely remove

the film.

3.2.4. Detailed process flow

As shown in Figure 3-5, the process started with two SOI wafers, one with a 50 µm

thick device layer (we refer to it as the 50 µm SOI wafer) and the other with a 2 µm thick

device layer (we refer to it as the 2 µm SOI wafer). First, the device layers of the two SOI

wafers were patterned individually. After growing a thermal oxide layer with a thickness

of 3000 Å, the device layer of the 2 µm SOI wafer was patterned with DRIE etching. For

the 50 µm SOI wafer, a 1.5 µm-thick oxide layer was grown. The front side oxide is used

as a mask during the later DRIE etching while the backside oxide balances the stress in

the SOI wafer to achieve a flatter bonding surface. Then a timed DRIE etching step was

employed to obtain a layer including non-thickness-critical structures only, such as the

pushing/pulling arms for scanning micromirrors. This was done by patterning the front

side oxide layer first, depositing a layer of photoresist, patterning the deposited

photoresist, DRIE etching to a depth of 30 µm, peeling off the photoresist, and DRIE

etching until the exposed silicon structures were 6 µm high. Keeping an oxide layer on

top of the device layer during the DRIE etching is critical for protecting the bonding

surface since it is experimentally observed that the silicon surface exposed to DRIE

etching does not bond. Also note that two alignment marks were patterned on the

48


backside oxide layer of the 50 µm SOI wafer before the first DRIE etching. They are

bonding alignment marks as well as the lithography alignment marks for the substrate

patterning.

SOI wafer 1: 50 µm/2 µm/350 µmSOI wafer 2: 2 µm/1 µm/350 µm

Pattern two wafers individually

Alignment pre-bond by Karl Suss bonder, followed by 9 hours of annealing at 1150°C

STS DRIE etch handle wafers and release in HF

SCS Wet oxide









SCS Wet oxideSCS Wet oxide Figure 3-5. Process flow of fabricating scanning micromirrors using the

SOI/SOI wafer bonding process.

The next step was pre-bonding the two patterned SOI wafers with alignment and then

annealing the bonded wafer pair in a furnace. After stripping off the oxide layer on the

front side of the wafers in 10:1 HF, both patterned SOI wafers were cleaned in piranha,

modified RCA1, RCA2 with de-ionized water rinsing in between. Then the two cleaned

SOI wafers were aligned and pre-bonded by a Karl Suss BA6 bond aligner, followed by 9

49


hours of annealing at 1150°C in a furnace. An inspection using an IR microscope showed

a fully bonded wafer pair.

DRIE etching was then used to dispose of the top handle wafer partially and pattern

the substrate layer of the bonded wafer. With a protective layer of the top handle wafer

left, the bonded wafer pair was diced into several dies. The individual dies or group of

dies were DRIE etched to fully dispose of the top handle wafer afterwards. The dies were

then cleaned in Piranha and released in 5:1 buffered HF. It is extremely important to

clean first and release later as the HF dip before photoresist cleaning leaves polymer

residues on the chip, which are extremely difficult to get rid of and often causes the

electrical actuation of the micromirror to become non-functional. Finally the released

individual chip was wire-bonded and packaged.

3.3. Bond Characterization

3.3.1. Diagnosis of bonded structures by SEM and infrared images

The cross section of two bonded wafers can be seen using SEM after intentionally

broken into pieces, as shown in Figure 3-6. There is no discontinuity between two bonded

layers, indicating a solid bonding.

50


bonding interface bonding

interface

bonding interface bonding

interface

Figure 3-6. The cross section of bonded Si wafers with pre-patterned structures

shows continuity at bonded areas, indicating a solid bonding.

The bonding quality and alignment accuracy can also be monitored with an infrared

camera during the process. Since infrared light transmits through silicon, the well-bonded

area appears bright in the IR camera while areas with voids or etched patterns appear

dark. Two typical images of bonded wafers without voids and with one void are shown in

Figure 3-7. The dark circle in both images is a shadow in the optical path of the camera

and does not move with the wafers, so the dark circle does not represent the variation of

the bonding quality.

51


(a)

(b)

Figure 3-7. Infrared transmission images of bonded Si wafers without voids (a) and

with one void (b).

3.3.2. Electrical interconnection realized by bonded structures

The interface of bonded silicon wafers is generally not perfect at the atomic level, not

only in that the crystal orientations of two wafers are not strictly aligned, but also in that

52


species other than silicon atoms, such as siloxane bonds (Si-O-Si) and H2 molecules, are

often present on the interface. The electronic property of the bonding interfaces is

important for interconnecting two bonded layers electrically.

As shown in Figure 3-8, a group of bridge structures is fabricated to characterize the

electronic property between two bonded layers. It consists of a 2 µm-thick bridge

connecting two pads that are made of the 50 µm-thick layer. The resistivity of the bonded

2 µm-thick layer is 0.1~0.3 Ω-cm and the resistivity of the underlying 50 µm-thick layer

is 0.005~0.02 Ω-cm. Both the 2 µm-thick layer and the 50 µm-thick layer are p doped.

Two probes are pressed upon the two 50 µm-thick pads individually to measure the

electrical property of the bridge structure. Since the resistivity of the underlying 50 µm-

thick layer is much lower than that of the bonded 2 µm-thick layer, the current-voltage

relationship between two pads mainly depends on the dimensions of the 2 µm-thick

bridges and the two bonding interfaces at the two ends of the bridge.

53


Figure 3-8. Testing structures to characterize the electronic property of the bonding

interfaces. A 2 µm-thick bridge connects two pads that are made of the

50 µm-thick layer. Note that there is a misalignment of 7 µm along the

horizontal direction between two bonded layers while no

misalignement along the vertical direction for this run.

Two typical current-voltage (IV) curves of the bonded bridge structures are shown in

Figure 3-9. The resistances for the short and long bridge structures, derived from the

slope of the IV curves, are 4.57 kΩ and 13.28 kΩ. It shows that two bonded structures

have an ohmic connection. The resistance ratio between the long bridge and short bridge,

2.90 in this case, corresponds to their length ratio, 3.0.

54


-2.5

-2

-1.5

-1

-0.50

0.5

1

1.5

2

2.5

-10 -5 0 5 10Voltage (V)

Cur

rent

(mA

)

short bridge 1

long bridge 1

Figure 3-9. Current-voltage curve of bonded bridges shows an ohmic inter-

connection between two bonded layers that are both p-doped.

Many other bonded bridges display a current-voltage relationship similar to the

curves in Figure 3-10. It is not strictly linear, although the resistance ratio between the

short bridge (resistance: 2.45 kΩ, derived from the slope of the curve) and long bridge

(resistance: 6.32 kΩ, derived from the slope of the curve) is 2.58, close to 3.0. It seems

that a potential barrier exists between the two bonded layers, possibly due to the lattice

defects and contaminants in the interface region. However, electrical interconnection is

still possible to be made through bonded layers, although it might present difficulty in

realizing the high-resolution control of the charge distributions since the magnitude of the

potential barrier varies from device to device. A closed-loop feedback control is a

possible solution to overcome the effect of this barrier voltage variance associated with

the bonded interface.

55


-2

-1

0

1

2

-10 -5 0 5 10Voltage (V)

Cur

rent

(mA

)

short bridge 2

long bridge 2

Figure 3-10. Current-voltage curve of bonded bridges shows an inter-connection

between two bonded layers that are both p-doped.

3.3.3. Shear stress test of bonded structures

A shear stress test is carried out to measure the bonding strength between two bonded

layers. As shown in Figure 3-11, a 2 µm-thick plate is bonded to an underlying 50 µm-

thick trunk. The size of the bonding area in the middle is about 100 µm × 40 µm. The

bonded structures are then suspended by four 2 µm-thick, 10 µm-wide, and 200 µm-long

suspension beams. The spring stiffness of these suspension beams can be easily

calculated through their dimensions. An in-plane force is exerted at the tip of the 50 µm-

thick plate in the direction perpendicular to the length of the suspension beams. The

displacement of the bonded structures under the applied probe force can be viewed

through the nearby ruler under a microscope.

56


50 µm-thick plate

2 µm-thick suspension beams

probe force

ruler

100 µm

50 µm-thick plate

2 µm-thick suspension beams

probe force

ruler

100 µm

Figure 3-11. A testing structure is designed to measure the bonding strength of two

bonded layers. Note that there is a misalignment of 13 µm along the

horizontal direction between two bonded layers while about 2 µm along

the vertical direction for this run.

As the probe force increases, two bonded layers are expected to show de-bonding

from each other as the shear stress acted on the bonded interface exceeds the ultimate

stress. Therefore the ultimate shear stress of the bonded layers can be obtained by

multiplying the spring constant of the suspension beams by the displacement of the

bonded layers at the de-bonding point. However, the strength test shows that when a

pushing force of about 1.0 mN is exerted, the structure breaks at the root of its suspension

beam, before the bonding fails. Thus only the lower limit of the ultimate shear stress,

which is approximately 0.25 MPa in this case, is obtained. Another testing structure gives

a lower limit of 1.01 MPa. Compared with the ultimate tensile stress of 9.0 ± 3.9 MPa

measured by a pulling test over two structured wafers bonded in another paper [55], our

numbers are low. But it is high enough to function as the linkage between the

57


micromirror and the transfer arms since the shear stress sustained by the bonded interface

is less than 1 MPa. In addition, the bonded wafers were found to withstand the post-

bonding steps, such as de-ionised water rinsing, spin drying, photo-lithography handling,

and chemical-mechanical polishing.

3.3.4. Air sealing by bonded structures

Circular cavities clamped on the edges are fabricated to test the sealing quality held

by bonded structures. The wafer bonding is carried out in a vacuum, leaving the pressure

inside the cavity lower than the ambient atmosphere. When the handle wafer of the

bonded wafer pair is released and the sealed cavity is exposed to the atmosphere, the

pressure difference between the inside air and the outside atmosphere displaces the

capping layer inward, as shown in Figure 3-12. Therefore a measurement over the

displacement profile of the capped layer can reveal the sealing and bonding quality held

by bonded structures.

If the maximum downward deflection, w, of the center of the edge-clamped circular

plate is bigger than the thickness of the capping layer, the large deflection theory is used

to calculate w. It is related to the pressure difference between the cavity and the

atmosphere, q, as the following expression [56]:

3/1

662.0 ⎟⎠⎞

⎜⎝⎛=

Etqaaw (3-6)

where a is the radius of the circular plate and t is the thickness of the capping plate, i.e.

the bonded layer. The pressure difference between the sealed cavity and the ambient

environment can thus be determined by measuring the deflection at the center of the

edge-clamped circular plate:

58


4

3

29.0 atEwq = (3-7)

Figure 3-12. Profile of a circular cavity clamped on the edges, measured by a Wyko

NT3300 interferometer.

If the maximum deflection is less than half the thickness of the capping layer, the

center deflection is reached under the assumption of small deflections as the following

equation:

( ) 3

421

163

Etqaw ν−= (3-8)

Then the pressure difference between the sealed cavity and the ambient environment

can thus be determined by:

( ) 42

3

1316

aEwtqν−

= (3-9)

59


Figure 3-13. Deflection of a capping layer clamped on the edges, simulated by FEM

analysis.

The small deflection and large deflection assumptions give different relationships

between the center deflection, the thickness of the capping plate and the pressure if

comparing Equation (3-7) and Equation (3-9). Unfortunately the deflections of most

testing cavities are measured to be right on the boundary condition, i.e. the maximum

deflection is about half of the thickness of the capping layer. Therefore, a numerical

method using the large-displacement nonlinear analysis is employed to estimate the

pressure difference between the sealed cavity and the ambient atmosphere according to

the measured deflection and capping layer thickness. Figure 3-13 shows the deflection of

a capping plate that is simulated by Pro-mechanica, a commercial FEM program, using

the large-displacement nonlinear analysis.

60


Table 3-1 shows the pressure inside the sealed cavity for several devices, numerically

calculated through Pro-mechanica. The average pressure calculated through the

deflection of the capping membrane is about 74.5 kPa with a standard deviation of 3.4

kPa. The variations in the calculated pressure come from the estimation of the thickness

of the capping plate. Since measuring the thickness right on the cavity is difficult, the

thickness is obtained by measuring the height of a nearby step formed by a bonded

structure, which is slightly different than the thickness of the capping plate.

Device

#

Thickness

of capping plate

t (µm)

Radius

of cavity

a (µm)

Displacement

at center

w (µm)

Pressure

in the cavity

pc (kPa)

1 2.24 100 0.28 69.4

2 2.24 150 1.17 71.2

3 2.24 200 2.37 74.6

4 2.34 100 0.23 71.1

5 2.34 150 0.98 74.1

6 2.34 200 2.12 77.0

7 2.39 100 0.17 77.4

8 2.39 150 0.80 78.2

9 2.39 200 2.03 77.4

Table 3-1. Numerically calculated pressure inside the sealed cavity.

The chamber vacuum of Karl SUSS bond aligner during the bonding is about 80 kPa,

according to the chamber pressure gauge on the front panel of the machine. Since the

chamber is flushed with N2 before bonding happens, the air enclosed by the sealed cavity

consists of N2 only and does not react with silicon. Therefore, the vacuum pressure given

by the pressure gauge agrees with the number calculated through the deflection of the

capping membrane.

61


3.4. Mechanical Modeling and ANSYS Simulation of Micromirrors

A mechanical model is established to show the bending of the pushing/pulling arm

and the rotation of the suspension beams under a lateral actuation force. First a

relationship between the actuation force and the actuated angle is obtained. Then the

working range of micromirrors under a static loading is calculated based on the

maximum principal stress criterion. Finally, the analytical result predicted by the model is

compared with the result calculated by ANSYS FEM simulation.

3.4.1. Analytical simulation

Unlike many other straightforward MEMS actuation mechanism, the analysis of

scanning micromirrors actuated by a lateral comb drive actuator is complicated by its

transfer mechanism. As a lateral force is exerted on the pushing/pulling arms, the arms

bend and the torsional beams rotate. The angle of rotation for the micromirror depends

not only on the strength of the actuation force, but also on the dimensions of the

pushing/pulling arms.

The case of pushing actuation is discussed first. As shown in Figure 3-14, two

pushing arms are combined into one and a linkage beam connects the pushing arm and

the torsional beams which are not shown in the figure. When applying a pushing force Fx

generated by a comb drive actuator on the left side, the pushing arm bends and the

torsional beams rotate around their central axis. The dashed lines represent the original

positions of the structures, while the solid lines stand for the displaced structures under

the comb-drive lateral force. The left side of the pushing arm is undergoing guided lateral

movement since the attached comb drive suspension beams are compliant to translation

along the pushing direction while opposed to the orthogonal movements. The top side of

62


the linkage beam is free to rotate, but resistant to any lateral movement. This is to assume

that the torsional beams, to which the linkage beam is attached, are robust to lateral

movements but compliant to rotation.

y

x

Fx

FyFx

MBMA

y

θFyt

Pushing Arm

Linkage Beam

Torsional Beam

y

x

Fx

FyFx

MBMA

y

θFyt

Pushing Arm

Linkage Beam

Torsional Beam

Figure 3-14. The cross section of the pushing arm and the rigid linkage beam under

the pushing force Fx generated by a lateral comb drive actuator. The

dashed lines represent the original position of the structures, while the

solid lines stand for the displaced structures under the comb-drive

lateral force.

The pushing arm is designed to be compliant whereas the linkage beam is rigid. As

the lateral force is loaded on the left side of the pushing arm, the arm bends and exerts Fx,

Fy, and MB on the linkage beam. In addition to the usual transverse load, the pushing

beam carries an axial compressive force. Axial compression increases the deflection and

bending moment produced by a transverse load. However, we cannot superpose the effect

of the axial load on the state produced by the transverse load alone. Instead, axial and

transverse loads must be considered simultaneously [57]. Universal beam theory still

applies to this problem since all the conditions that are assumed in the universal beam

theory are still satisfied, i.e., the deflection in the pushing arm is small compared with the

length of the arm, the plane section remains plane in the pushing arm, and no shear stress

63


is involved. The only difference between this case and the simple cantilever deflection is

that the bending moment induced by the axial load has to be taken into account besides

the moment caused by the transverse load.

Consider the bending moment induced by the axial force Fx in Figure 3-14. When the

lateral deflection y is zero, Fx is directed through the centroid of the cross section and

poses no moment to the pushing arm. When the pushing arm is deflected, Fx has a

moment arm of y about a point on the beam axis and produces a bending moment -Fxy.

Therefore, the standard moment-curvature relation of universal beam theory,

Mdx

ydEI =2

2

, becomes

yFxLFMdx

ydEI xyB −−+= )(2

2

(3-10)

where E is the modulus of silicon, I is the bending momentum of the pushing arm, MB is

the moment exerted by the linkage beam, Fy is the transverse force, L is the length of the

pushing beam, and x is the distance from the point to the left end of the pushing beam. Fx

is generated by the comb drive actuator and is constant throughout the beam. Fy and MB

are the only unknown parameters that need to be determined through the boundary

conditions.

The linkage beam is considered to be rigid and balanced by the forces and moments

from the pushing arm below and the torsional beams above, as shown in Figure 3-15.

Define MA’ to be the moment exerted by the torsional beams and MB’ by the pushing arm,

then we have

(3-11) 0)cos('' =−−− θθ tFtFMM yxBA

64


MB’

MA’Fx

Fy

Fx

Fyt θ

MB’

MA’Fx

Fy

Fx

Fyt θ

Figure 3-15. Rigid linkage beam balanced by the forces and moments from the

pushing beam below and the torsional beams above.

The counter moment of MA’ is the one that rotates the torsional beams, so we have

θθkM A =' (3-12)

where kθ is the rotational spring constant of the suspended torsional beams and θ is the

angle of rotation, which we are interested in solving. The torsional stiffness of the

torsional beams with a rectangular cross section can be expressed by a general equation

θ

θkT

KGTLt ==

2 (3-13)

where T is the applied torque, Lt is the length of the torsional beam, K is a factor

depending on the cross-section dimensions of the torsional beam, G is the shear modulus

of the material, and ‘2’ in the equation indicates two torsional beams suspending the

micromirror. Unlike torsional beams with a circular section, K of the torsional beams

with a rectangular cross section is a value less than the polar moment of inertia, J. The

approximated formula (error within 4%) of K for the torsional beams with a rectangular

cross section can be obtained through Saint-Venant’s method and is found to be [58]

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−= 4

43

12136.3

316

ab

ababK (3-14)

where 2a and 2b are the width and thickness of the rectangular section and satisfy a≥b.

65


Using Equation (3-12) to rewrite Equation (3-11), we obtain

θθθθ tFtFkM yxB +−= )cos(' (3-15)

The first term is proportional to the angle of rotation, θ. Fx is the lateral force that

induces θ, so it is proportional to θ, too. As we count the first order of θ only, the second

term can be simplified to Fxt. As Fy is the transverse force induced by the rotation, it is

also a term proportional to the first order of θ. Thus the third term is a second order of θ

and can be neglected. Rewriting Equation (3-11), we get

tFkM xB −≈ θθ' (3-16)

As MB is the counter moment of MB’, combining this expression with Equation (3-10),

we get the equation that determines the displacement of the pushing arm:

)(2

2

xLFtFkyFdx

ydEI yxx −+−=+ θθ (3-17)

This is a second order differential equation and its solution consists of two parts. One

part is a general solution and the other part is a particular solution associated with the

right side of Equation (3-17):

)()cos()sin( 21 xLFF

FtFkkxckxcy

x

y

x

x −+−

+−=θθ (3-18)

where c1 and c2 are unknown constants and EIFk x= . As the left side of the pushing arm

is undergoing guided lateral movement and the linkage beam is only free to rotate, the

boundary conditions become

0)0( ==xy (3-19)

(3-20) 0)0(' ==xy x

66


0)( ≈= Lxy (3-21)

θ−== )(' Lxy x (3-22)

With four boundary conditions and four unknown parameters (θ, Fy, c1, and c2), we

can solve the angle of rotation to be

(( )

))sin(2)cos(2

)sin()cos(

2

kLkLkLkLkLkLkEIk

EItk

+−−

+=

θ

θ (3-23)

The relationship between the lateral force, Fx, and the angle of rotation, θ, is

apparently nonlinear. However for a small actuation force, we can simplify Equation (3-

23) into

LEIk

tFLEIk

EItk x

/4/4

2

+=

+≈

θθ

θ (3-24)

Or rewrite it in this way,

θθ ⎟⎠⎞

⎜⎝⎛ +≈

LEIktFx

4 (3-25)

The off-axis lateral actuation of a micromirror is simplified to a simple model in

which a torque is applied on a torsional spring, whose spring constant is contributed by

not only the torsional beams, but also the transfer arms.

The next step is to find out the maximum stress occurring on the pushing arm and the

torsional beams. According to Equation (3-17), the bending moment on the pushing arm

is

yFxLFtFkM xyx −−+−= )(θθ (3-26)

The last two terms vary with x, while the rest of the terms are fixed throughout the

beam. A plot of the bending moment vs. x shows that the maximum bending moment

67


happens at the right end of the pushing arm, i.e., at x=L. For a small actuation force,

combine this expression with Equation (3-25), then the maximum bending moment on

the pushing arm becomes

θθθ LEItFkM x

4−≈−= (3-27)

The maximum stress experienced by the pushing arm satisfies

( )

θθ

σ θ

LEh

IhtFk

IMh x 2

22≈

−== (3-28)

where h is the thickness of the pushing arm. We can see that the maximum tensile stress

experienced by the pushing arm is only determined by the ratio of thickness and length of

the pushing arm, i.e., h/L, in addition to the angle of rotation.

For the rectangular torsional beams, the maximum shear stress happens at the

midpoint of each longer side of the rectangular section with a value of

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛++=

432

2max 9100.08023.18865.06095.0116

3ab

ab

ab

ab

abTτ (3-29)

where T is the applied torque on the rectangular torsional beams.

As noncircular beams are twisted, their cross sections do not remain plane but warp.

When one or both ends of the torsional beam are fixed as in case of the micromirror,

warping is prevented and the stresses and the angle of rotation produced by a given

torque are affected. Here for the purpose of finding the maximum principle stress, we

ignore this effect to get an easier solution, i.e., the tensile stress associated with warping

is neglected. Therefore, the principle stresses related to a pure rotation in the torsional

beams are

(3-30) 02 =σmax31 τσσ =−=

68


Single crystal silicon is a brittle material with a similar value of ultimate tensile

strength and ultimate compressive strength [59]. Therefore the best criterion to predict its

static-loading fracture condition is the maximum principal stress hypothesis, i.e. failure

occurs whenever one of the three principal stresses equals to or exceeds the yield tensile

strength. In order to determine the failure condition for static loading, the maximum

principal stress occurred on the pushing arm, described by Equation (3-28), and the

maximum principal stress occurred on the torsional beam, described by Equation (3-29),

is compared.

According to the maximum principal stress criterion, the safety factor for static

loading applied on a micromirror is

maxσuSn = (3-31)

where Su is the ultimate tensile stress, or yield stress of single crystal silicon, and σmax is

the maximum principal stress experienced by the pushing arm or the torsional beams.

69


Symbol Parameters Value

Su yield stress of silicon (GPa) 3

E Young's modulus of silicon (GPa) 160

G shear modulus of silicon (GPa) 67

θ mechanically rotated angle (deg) 10.0

a half width of torsional beams (µm) 8

b half thickness of torsional beams (µm) 3

Lt length of torsional beams (µm) 150

kθ rotational spring constant of torsional beams (N⋅m) 7.9×10-7

σmax,t maximum principal stress in torsional beams (GPa) 0.46

w width of pushing arm (µm) 14

h thickness of pushing arm (µm) 6

L length of pushing arm (µm) 500

4EI/L rotational spring constant contributed by pushing arms (N⋅m) 3.2×10-7

σmax,p maximum principal stress in pushing arms (GPa) 0.67

n safety factor 4. 5

Table 3-2. Safety factor of a micromirror with nominal parameters for rectangular

cross-section torsional beams, pushing arms, and rotated angles.

Table 3-2 shows the calculated safety factor for an example of the micromirror design.

The failure for static loading happens on the pushing arm instead of on the torsional

beams. If setting the desired mechanical tilting angle, θ, to be ± 10° (optical scanning

angle: ± 20°) and taking a typical value of the pushing arm, h = 6 µm and L = 500 µm,

the maximum tensile stress experienced by the pushing arm is 0.67 GPa with a safety

factor of 4.48, while the maximum principal stress on the torsional beams is only 0.46

GPa, about two-thirds of the stress experienced by the pushing arm. The table also

70


indicates that the pushing arms contribute to a substantial part of the total rotational

spring constant, which is not desired as the process has no strict control over the

thickness of the pushing arms.

The most of uncertainty on the parameters that affect the safety factor in Table 3-2

falls on the thickness of the pushing arms. In the current process, they are fabricated

through a timed DRIE etch. The non-uniformity of etching speed across the wafer usually

brings a variance of 2~4 µm to the thickness of the pushing arms. As a result, the safety

factor might vary from 4.5 to 2.7, which still falls in the range of common safety factor

design.

In the case of a pulling lateral force, define the parameters in the opposite direction

and the same analytical results as Equations (3-23) - (3-25) are reached.

3.4.2. ANSYS simulation

The analytical results obtained from the mechanical modeling are compared with

numerical values obtained through ANSYS simulation. The ANSYS script simulating the

rotation of a micromirror under a static loading is attached in Appendix D. Main

structures, including micromirror, rigid linkages, pushing arms, and two torsional beams,

are included in the program. The appropriate boundary conditions are imposed on the

ends of torsional beams and pushing arms. The structures are meshed using solid92

elements and calculations are performed using the large-displacement nonlinear option.

Three points derived from ANSYS simulation are plotted in Figure 3-16, along with

the analytical result calculated from the previously-described beam model and its linear

approximation at small forces. We can see from Figure 3-16 that theoretical calculation

agrees with ANSYS simulation results especially in the small-force region. As the

71


actuation force, Fx, becomes larger, the displacement of the pushing arm, y, is larger and

the bending moment produced by the axial force on the pushing arm, -Fxy, is increased by

the second order of Fx. Thus nonlinearity appears and the angle of rotation is bigger than

the linear relationship predicted by the small actuation force region. However, ANSYS

result does not show a similar trend. One possible reason is that the nonlinear analysis in

ANSYS takes into account of beam stiffening at large displacement and this effect

cancels the nonlinearity brought by the bending moment of the pushing arm. In practical,

as the working range of the micromirror typically rests within ± 20° optically, assuming a

linear relationship between the angle of rotation and the actuation force is usually valid.

0

10

20

30

40

50

60

70

0.000 0.001 0.002 0.003 0.004 0.005 0.006Driving Force (N)

Act

uate

d O

ptic

al A

ngle

(deg

ree)

Beam Theory ResultLinearization of Beam TheoryANSYS Result

Figure 3-16. Relationship between the driving lateral force and the actuated rotation

angle of a micromirror, calculated by theoretical analysis and ANSYS

simulation.

72


In the case of non-ideal rotational beams, such as the one with thin, wide rectangular

cross sections, the boundary conditions assumed in the model, i.e., Equations (3-19) - (3-

22), are not true. For example, the 2 µm-thick torsional beams, which are used in the

initial design of the micromirrors, are not only susceptible to rotation motion, but also the

up-down lateral motion (using the axes defined in Figure 3-14). Therefore, the right side

of the pushing arm moves up and down along with the torsional beams as a

pushing/pulling lateral force is applied to its left end, instead of keeping at a fixed

position as assumed in the analytical model. Consequently, the results described in

Equations (3-23) - (3-25) are not valid for this case. In order to get a more accurate

analytical result, the lateral translation of the torsional beams must be taken into account

and this leads to a too complicated problem to be solved analytically. However ANSYS

FEM simulation is still able to provide a numerical prediction to the actuation of a

micromirror with thin, wide rectangular torsional beams. We observed that the

experimental DC actuation of one-axis scanning micromirror agrees with the ANSYS

simulation result within 15%.

3.5. Performance of Scanning Micromirrors

A fabricated two-axis scanning micromirror is shown in Figure 3-17. The

micromirror is 800 µm in length and 2 µm in thickness, with 50 µm-height ribs below to

stiffen the mirror. It is suspended by two 2 µm-thick, 50 µm-wide, and 200 µm-long

inner torsional beams and rests over a rigid surrounding frame made up by the two

bonded layers. The whole frame is then supported by two outer torsional beams that have

similar dimensions as the inner torsional beams.

73


2 µm-thick mirror

6 µm-thick arm

Lateral comb drive actuator

2 µm-thick layer

50 µm-thick layer

6 µm-thick decoupling beam

2 µm-thick mirror

Frame

2 µm-thick mirror

6 µm-thick arm

2 µm-thick mirror

6 µm-thick arm

Lateral comb drive actuator

2 µm-thick layer

50 µm-thick layer


2 µm-thick layer

50 µm-thick layer


2 µm-thick mirror

Frame

Figure 3-17. A two-axis scanning micromirror fabricated by the SOI/SOI wafer

bonding process. The central mirror is suspended by two inner

rectangular torsional beams and therefore rests over a rigid surrounding

frame which is supported by two outer rectangular torsional beams.

74


For both axes, there are two pushing arms connecting the torsional beams and the

lateral actuator. The inner pushing arms are 6 µm in thickness, 15 µm in width, and 400

µm in length while the outer pushing arms are 6 µm in thickness, 11 µm in width, and

830 µm in length. The 6 µm-thick, 10 µm-wide, and 310 µm-long decoupling beam

connecting the inner pushing arms and the inner comb drive actuator shields the actuator

from rotating around the outer axis. It can be seen that the edges of 6 µm-thick beams

have small silicon spikes. They are frequently seen on the structures formed by the timed

DRIE etching due to the micromasking [60]. However, these grass-like defects should not

affect the mechanical function of the structures since they are small in size and quantities.

Figure 3-17 shows only part of the two lateral comb drive actuators with tapered fingers

and two of the four crab leg flexures suspending the actuator. The tapered comb fingers

are designed to achieve a certain DC scanning angle at a lower actuation voltage than the

one of using parallel comb fingers. As the comb fingers move in, the effective gap

distance between the two groups of tapered comb fingers decreases in contrast to the

constant gap distance when using parallel comb fingers. Therefore the electrostatic

actuation force increases as it inversely depends on the gap distance.

3.5.1. DC and AC actuation of fabricated one-axis scanning micromirrors

The static (DC) response of scanning micromirrors is captured by detecting the shifts

of the laser beam reflected by actuated micromirrors. Figure 3-18 shows the angle

displacement of a one-axis pulling-mode scanning micromirror under DC actuation. A

scanning angle of 21.8° is achieved at 75.0 V with the comb drive actuator pulling in

afterwards as a result of the combined effect of the side instability and rotation instability.

In order to attain a larger DC actuation range, a more stable design of the suspension

75


beams for the comb drive actuator is required, both in terms of the side stiffness and

rotating stiffness. The deviation from a linear relationship between the displaced angle

and the actuation voltage is mainly due to the tapered comb fingers in the comb drive

actuator. As the comb fingers are pulled closer, the gap distance between them decreases

and the electrostatic force increases, inducing a larger rotation angle on the micromirror.

0

5

10

15

20

25

0 1000 2000 3000 4000 5000 6000Actuation Voltage ^2 (V^2)

Opt

ical

Sca

nnin

g A

ngle

(deg

ree

Opt

ical

Sca

nnin

g A

ngle

(deg

ree)

0

5

10

15

20

25


Opt

ical

Sca

nnin

g A

ngle

(deg

ree

Opt

ical

Sca

nnin

g A

ngle

(deg

ree)

Figure 3-18. DC actuation of a one-axis pulling scanning micromirror.

Compared to the previous results reported in [61], the maximum DC scanning angle

of the one-axis scanning micromirror is increased from 11.0° to 21.8°. This enhanced

performance is benefited from changing the electrical connection of the substrate on the

device from floating to grounding. Leaving the substrate floating brings an uncertainty to

the charge leakage and induces instability to the charge distribution on the comb drive

actuator. This induces the micromirror vibrating when the actuation voltage is high.

76


Grounding the substrate eliminates the instability of the charge distribution and the

micromirror is able to work under a larger actuation voltage.

The experimental data agrees with the ANSYS analysis result. The lateral comb drive

actuator is calculated to generate a pulling force of 0.97 mN at 75.0 V. The force is

applied to a one-axis micromirror with similar dimensions in ANSYS and the simulation

shows that the micromirror scans the laser beam up to 18.4° optically. Compared to 21.8°

in experiments, the simulation result agrees with the experimental observation to be

within 15%. The difference between them comes from the estimation over the thickness

of the pushing arm, which is somewhat difficult to measure after the substrate is etched

away.

A modal analysis of the one-axis pulling mirror is carried out and calculates the first

four modes of the micromirror, whose mode shapes and frequencies are shown in Figure

3-19. Since the simulation only takes the mirror plate, the torsional beams, and the

pulling arms into account and leaves the comb drive actuator and its suspension beams

out, only the mode shapes accurately describe the situation while their frequencies are off,

especially for the modes which involve large displacements of the comb drive actuator.

The first mode, sitting on the left, top corner of the picture, corresponds to the out-of-

plane lateral movement of the micromirror; The second one, sitting on the right, top

corner of the picture, describes the rotation of the micromirror; the left, bottom one

displays the left-right twisting motion of the micromirror; and the right, bottom one

shows the dynamic deformation mode of the mirror plate. Since the out-of-plane lateral

and torsion modes of the micromirror involve large displacements of the comb drive

actuator in Y direction, their frequencies are not able to be obtained accurately through

77


simulations without including the actuator part while the frequencies of the twisting and

dynamic deformation modes can be accurately predicted by the simulations, given an

accurate input of the device dimensions.

Displacement in ZMode 2. 6.04 kHz








Figure 3-19. The four lowest resonant mode of a one-axis pulling micromirror.

Mode 1: out-of-plane lateral mode; Mode 2: rotation mode; Mode 3:

left-right twisting mode; Mode 4: mirror plate deformation mode.

The AC response of the one-axis micromirror is characterized using a laser Doppler

vibrometor (LDV) as the micromirror is actuated by an AC voltage source with a large

DC bias. Two groups of data were taken when the laser beam from the LDV was

positioned individually on the two opposite edges of the mirror, each about 400 µm from

the axis of rotation. The location of the detected points is chosen in this way so that the

78


signal corresponding to the rotation mode of the micromirror is strongest. The amplitude

and phase of the mirror movement in the out-of-plane direction are displayed in Figure 3-

20. Figure 3-20 (a) is measured on the spot where the rotation and the lateral out-of-plane

mode is co-phase under low frequency actuation while (b) is taken on the opposite side of

the mirror, where the rotation and the lateral out-of-plane mode is out-of-phase. The

phase difference between two groups of data is 180° at most frequencies since the

rotation mode dominates the movement of the mirror, except at the resonant frequencies

of the out-of-plane lateral mode and left-right twisting mode. According to their phase

differences, we were able to distinguish the rotational mode from the other modes. The

result shows that the one-axis device has a rotational resonant frequency of 3.6 kHz with

a quality factor of 12. The second mode at 4.1 kHz corresponds to the lateral out-of-plane

motion of torsional beams while the additional mode at 6.8 kHz is related to the left-right

twisting mode of the micromirror. Compared to the FEM simulation results of 2.67 kHz

(lateral out-of-plane mode), 6.04 kHz (rotational mode), and 8.41 kHz (left-right twisting

mode), the differences arise from the fact that the model does not take into account of the

comb drive array and its suspension beams. Furthermore, the analysis inputs several

estimated dimensions, such as the thickness of the transfer arms.

79


-500

-400

-300

-200

-100

0

1000 10000Frequency (Hz)

Phas

e (d

egre

e)

0

0

1

10


Vel

ocity

^2

(a.u

.)

-300

-200

-100

0

100

200


Phas

e (d

egre

e)

0

0

1


Vel

ocity

(a.u

.)

Phas

e of

Vel

ocity

(d

egre

e)

103 104

Am

plitu

de o

f V

eloc

ity (a

.u.)

101

100

10-1

10-2

103 104

3.6 kHz4.1 kHz

6.8 kHz

103 104

Phas

e of

Vel

ocity

(d

egre

e)A

mpl

itude

of

Vel

ocity

(a.u

.)

100

10-1

10-2

103 104

3.6 kHz 6.6 kHz(a) (b)

-500

-400

-300

-200

-100

0


Phas

e (d

egre

e)

0

0

1

10


Vel

ocity

^2

(a.u

.)

-300

-200

-100

0

100

200


Phas

e (d

egre

e)

0

0

1


Vel

ocity

(a.u

.)

Phas

e of

Vel

ocity

(d

egre

e)

103 104

Am

plitu

de o

f V

eloc

ity (a

.u.)

101

100

10-1

10-2

103 104

3.6 kHz4.1 kHz

6.8 kHz

103 104

Phas

e of

Vel

ocity

(d

egre

e)A

mpl

itude

of

Vel

ocity

(a.u

.)

100

10-1

10-2

103 104

3.6 kHz 6.6 kHz(a) (b)

Figure 3-20. Frequency response of a one-axis pulling scanning micromirror. (a):

measured on the spot where the rotation and the lateral out-of-plane

mode is co-phase when actuated at low frequencies; (b) measured on

the opposite side of the mirror, where the rotation and the lateral out-of-

plane mode is out-of-phase.

3.5.2. DC and AC actuation of fabricated two-axis scanning micromirrors

Figure 3-21 shows the laser beam reflected by a two-axis scanning micromirror under

DC and AC actuation. For DC actuation, the comb drive actuator pulls in afterwards as

happened in the case of one-axis scanning micromirror, resulting from the combined

effect of the side instability and the rotation instability. There is slight cross-axis coupling

between the inner and outer rotation of the two-axis micromirror. When driving the inner-

axis actuator, the mirror rotates not only around the inner axis, but also the outer axis.

80


This problem is addressed later in the thesis. For AC actuation, the micromirror is able to

scan Lissajous curves as shown in the right picture of Figure 3-21.

reflected from the

frame

reflected from the nearby chip

reflected from the scanning

mirror Scattered by the nearby probe

reflected from the

frame

reflected from the nearby chip

reflected from the scanning

mirror Scattered by the nearby probe

Figure 3-21. Reflected laser beam by a two-axis scanning micromirror under DC

and AC actuation (each minor grid element represents 1° of optical

deflection.) Left: Vvert. = 60.2 V, Vhorz. = 79.9 V; Right: Vvert. = 45.1 +

10 × sin(2π×300×t), Vhorz. = 45.4 + 10 × sin(2π×100×t).

The two-axis micromirror scans up to 15.9° optically for the inner axis and 13.2° for

the outer axis under a static actuation, as shown in Figure 3-22. A further increase of its

dc scanning range needs to design the suspension beams of the comb drive actuators with

higher stability to work under large displacements. This is addressed in the later part of

the thesis.

81


0

2

4

6

8

10

12

14

16

18


Opt

ical

Sca

nnin

g A

ngle

(deg

ree Scanning over the inner axis

Scanning over the outer axis

Opt

ical

Sca

nnin

g A

ngle

(deg

ree)

0

2

4

6

8

10

12

14

16

18


Opt

ical

Sca

nnin

g A

ngle

(deg

ree Scanning over the inner axis

Scanning over the outer axis

Opt

ical

Sca

nnin

g A

ngle

(deg

ree)

Figure 3-22. DC actuation of a two-axis scanning micromirror.

The resonant frequency of the rotation mode over the inner axis for this two-axis

micromirror is 2.2 kHz while the one over the outer axis is 1.3 kHz. Compared to the

analytical results of 2.5 kHz for the inner axis and 1.2 kHz for the outer axis, they agree

within 15%.

3.6. Reliability and Robustness of Micromirrors

3.6.1. Reliability of micromirrors

The micromirror fabricated by the SOI/SOI wafer bonding process is expected to be

exceedingly reliable because of its monolithic single crystal silicon design. Single crystal

silicon is intrinsically resistant to fatigue and the all-suspension design eliminates the

frictional wear associated with contacting surfaces. Moreover, the bonding formed by

82


surface chemical activated pre-bonding and high temperature annealing have a strong

strength to hold two layers together.

However, a defective bonding interface may set off the propagation of a fatigue crack

and thus the device may fail because of delamination or fracture. Also the initiation of a

fatigue crack frequently occurs at the point of highest strain in the device. Therefore the

transfer arm, formed by a timed DRIE etch, may break at its linkage to the mirror plate

since that point experiences the maximum stress in a whole device.

A test was carried out to assess the long-term reliability of micromirrors. A one-axis

scanning micromirror was actuated for 34 days at 6.4 kHz, a frequency around its

rotational resonant frequency, with scanning amplitude of 17.8° optically. By measuring

the resonant frequency and scanning amplitude under a constant AC and DC driving

voltage, we were able to detect small changes in the mirror that could be indicative of

material fatigue. For example, a monotonic decrease in the resonant frequency or a

monotonic increase in the scanning amplitude might indicate fatigue and crack growth in

the device.

The scanning micromirror turns out to be quite durable. The resonant frequency and

amplitude were measured periodically and are displayed in Figure 3-23 and Figure 3-24.

We found that the change over its resonant frequency for 18.9 billion cycles is less than

1.2 % and the change over the amplitude is within 2.2 %. The device is still functional

after operated for 18.9 billion cycles. The small and irregular change over the resonant

frequency and amplitude indicates that no obvious fatigue is developed through the long-

term operation of the micromirror.

83


6.18

6.20

6.22

6.24

6.26

6.28

0.0 5.0 10.0 15.0 20.0Cycles (Billion)

Freq

uenc

y (k

Hz)

Figure 3-23. Measured resonant frequency of a one-axis scanning micromirror,

running at 6.4 kHz with scanning amplitude of around 17.8° for 18.9

billion cycles. The variation of resonant frequency is less than 1.2 %.

17.6

17.7

17.8

17.9

18.0

18.1

0.0 5.0 10.0 15.0 20.0Cycles (Billion)

Scan

ning

Ang

le (d

egre

e)

Figure 3-24. Measured scanning angles of a one-axis scanning micromirror, running

at 6.4 kHz with scanning amplitude of around 17.8° for 18.9 billion

cycles. The variation of scanning amplitude is less than 2.2 %.

84


3.6.2. Shock resistance of micromirrors

The multi suspension beams with high stiffness enable the lateral-actuated

micromirror to be quite resistant to shock and vibration. The acceleration of the mirror is

resisted both by the torsional beams and actuator suspension beams in contrast to the

single torsional beams as in the case of micromirrors with vertical/angular comb drive

actuators. The high-stiffness spring design of the lateral-actuated micromirror also helps

preventing the fracture or stiction of the structures under large shock loads.

Two major failure modes associated with the shock loads are dynamic fracture and

quasistatic fracture. Assume the device has a lowest resonant frequency fres. When the

pulse duration τ is smaller than 2.5/fres, the device is excited resonantly and its

acceleration of the mass can exceed the applied maximum acceleration. When the pulse

duration τ is bigger than 2.5/fres, the device behaves quasistatically and its acceleration of

the mass is equal to the applied maximum acceleration [62]. The reported values of the

pulse duration for the applied shock loads are in the range 50 µs – 6 ms [62]. We pick 1

ms, a typical number for many shock tests. The fabricated two-axis micromirror has a

lowest resonant frequency of 1.3 kHz and the pulse duration τ of 1 ms is smaller than

2.5/fres (1.9 ms). Therefore the mirror plate of the two-axis device is expected to be

excited resonantly during the shock test. However, for most one-axis micromirrors, the

lowest resonant frequency is around 3.5 kHz and the pulse duration τ of 1 ms is bigger

than 2.5/fres (0.71 ms). So the one-axis mirror is expected to be excited quasistatically

during the shock test.

For the quasistatic case, the maximum lateral force, F, induced by the loading shock

is m·amax, where m is the mass of the comb drive actuator, about 5×10-8 kg, and amax is the

85


peak acceleration during a shock test, which is chosen to be 500 g in our shock test.

Therefore the lateral force applied to the micromirror is about 0.25 mN. According to

Table 3-2, the maximum static lateral force a typical micromirror can survive is about 6.9

mN. Therefore the device should be able to survive through this kind of shock without

any problem when excited quasistatically.

For the resonant case, assume that the device has a quality factor of 20 for its lowest

resonant mode, the maximum lateral force generated by the loading acceleration is about

20·0.25 mN, or 5 mN. It is less than the quasistatic toughness, 6.9 mN. Moreover, the

dynamic fracture toughness of brittle materials is usually greater than, or equal to, the

corresponding quasistatic fracture toughness [63]. Therefore the two-axis micromirror

should be able to survive through the shock test.

A non-operational shock test was carried out to assess the robustness of the

micromirror. A 1cm × 1cm chip, which has one functional two-axis micromirror and two

functional one-axis micromirrors, is glued onto a ceramic package using a very thin layer

of silver epoxy. The package is then securely clamped on the table of a linear shake

machine from GHI systems, as shown in Figure 3-25. We assume that this attachment

mechanism does not significantly alter the shape or intensity of the shock pulse

experienced by the devices.

86


Packaged chipPackaged chip

Figure 3-25. The packaged chip is securely clamped on a shake table, ready for the

shock test.

The micromirror chip was subjected to four shocks each along the directions of the x,

y, and z-axis. Each shock, whose pulse shape was recorded by an accelerometer on the

shake table, has a peak acceleration of 500 g and pulse duration of 1 ms, as displayed in

Figure 3-26. The devices were examined with an optical microscope as well as

electrically actuated after the shock test. All three devices, including a two-axis

micromirror, a pulling one-axis micromirror and a push one-axis micromirror, are still

functional after the shock test. The observed reliability of the devices was found to be in

agreement with the predictions of the analyses.

87


-200

-100

0

100

200

300

400

500

600

0 1 2 3 4Time (msec)

Acc

eler

atio

n (g

)

Figure 3-26. Representative example of an acceleration pulse during the shock test.

Duration: 1 ms; Peak acceleration: 500 g.

88

MEMS SCANNING MICROMIRRORS WITH T-BAR TORSIONAL BEAMS

4. MEMS SCANNING MICROMIRRORS WITH T-BAR

TORSIONAL BEAMS

4.1. Torsional Beams with T-Shaped Cross Section

The previous gimbaled two-axis micromirror exhibits a cross-coupling between the

two axial rotations. When a voltage is applied over the outer-axis comb drive actuator,

the resulting rotation is purely around the outer axis. However, when driving the inner-

axis actuator, the mirror rotates not only around the inner axis, but also the outer axis. As

the voltage is increased and the mirror rotates more around the inner axis, the rotation

over outer axis increases, too.

The reason for the cross-coupling lies in the thin torsional beams of the outer gimbal

with rectangular cross sections. When a lateral force is pushing against the inner-axis

torsional beams, the inner transfer arm bends and generates an upward force on the frame

and therefore on the outer-axis torsional beams. Consequently, those two outer-axis

beams bend upwards since the 2 µm-thick torsional beams are not only susceptible to

rotational motion, but also compliant to out-of-plane lateral motion. The two transfer

arms attached to the outer-axis torsional beams follow the bending and produce a

rotational torque onto the outer torsional beams. As a result, the mirror rotates around the

outer axis.

The solution for the cross-axis coupling in the two-axis micromirror is using torsional

beams that are compliant to rotational movement but robust to both in- and out-of-plane

89


lateral movements. Torsional springs using open, thin-walled cross sections, such as T-

shaped cross sections, provide such an optimal combination of spring stiffnesses [64].

y

x

tf

b

h

tw

tfy

x

y

x

tf

b

h

tw

tf

Figure 4-1. T-shaped cross section torsional beams.

The bending stiffness kx and ky of T-bar torsional beams are calculated to be

(4−1) 33333 /2/)(2 ltEblhttbEk wwx f≈+≈

(4−2) 33333 /2/)(2 lhEtlhtbtEk ffwy ≈+≈

where E is the Young’s modulus of the material, b and tw is the width and thickness of the

web, tf and h is the width and thickness of the flange (see Figure 4-1), and l is the length

of torsional beams. The torsional stiffness kθ is described to be

lhtbtGk fw /)(32 33 +=θ (4−3)

where G is the shear modulus.

Compared with a rectangular-shaped torsional beam, spring constants of T-bar

torsional beams are strengthened in both lateral directions by several hundred times

(depending on the dimensions of the structure) whereas the torsional stiffness is only

90


doubled. Thus, micromirrors with T-bar torsional beams not only keep high transmission

efficiency, but also have less cross-coupling between the two axial rotations.

The use of T-bar torsional beams is compatible with our current process. The web

structure of the T-bar is fabricated on the 2 µm bonding layer while the flange part is

made of the underlying 50 µm layer. A schematic of the micromirror suspended by two

T-bar torsional beams is shown in Figure 4-2.

Lateral force

Low-mass mirror

Transfer arm

T-shaped cross-section torsional beams

Lateral force

Low-mass mirror

Transfer arm

T-shaped cross-section torsional beams

Figure 4-2. A mirror is suspended by two T-bar torsional beams.

4.2. ANSYS FEM Simulation

FEM simulation confirms this analysis, as shown in Figure 4-3. Figure 4-3 (a) shows

that for a scanner with rectangular torsional beams, the torsional beams of the outer axis

bend upwards and the mirror tilts around both the inner and outer axis as a pushing force,

Fx, is exerted on the inner-axis transfer arm. On the contrary, in Figure 4-3 (b), the two-

axis scanner with T-bar torsional beams shows no tilt over its outer axis and thus no

cross-coupling effect between its inner and outer axes.

91


(a)

Rectangular Cross Section

FxOuter-axis torsional beams bend upwards, and mirror tilts around both inner and outer axis.

Rectangular Cross Section

FxOuter-axis torsional beams bend upwards, and mirror tilts around both inner and outer axis.

(b)

T-shaped Cross Section

FxOuter-axis torsional beams do not bend, and mirror rotates around inner axis only.

T-shaped Cross Section

FxOuter-axis torsional beams do not bend, and mirror rotates around inner axis only.

Figure 4-3. (a) ANSYS simulation shows cross-coupling for two-axis scanner with

rectangular shaped cross section torsional beams; (b) ANSYS

simulation shows no cross-coupling for two-axis scanner with T-shaped

cross section torsional beams.

92


4.3. DC and AC Actuation of Micromirrors with T-bar Torsional Beams

A fabricated two-axis scanning mirror with T-shaped cross-section torsional beams is

shown in Figure 4-4. The image is taken from an optical microscope with a spatial high-

pass filter to show the edges clearly. As visible light is partially transmitted through a 2-

µm silicon layer, we can see the underlying 50-µm structures. The mirror is 800 µm in

diameter and 2 µm in thickness, with 50 µm-height ribs below to stiffen the mirror. The

T-bar torsional beams consist of two parts, the 80 µm-wide web structure in the 2 µm-

thick bonding layer and the 3 µm-wide flange part in the 50 µm-thick layer.

Comb drive actuator

Com

b dr

ive

actu

ator

Transfer arm

T cross-section torsional beams

2 µm-thick mirror with underlying 50 µm ribs


Comb drive actuator

Com

b dr

ive

actu

ator

Transfer arm


2 µm-thick mirror with underlying 50 µm ribs


Figure 4-4. A gimbaled two-axis scanner by the SOI/SOI bonding process.

As stated in Figure 4-5, the bi-directional two-axis micromirror works up to ±7° for

the outer-axis and from -3° to 7° for the inner-axis under DC actuation. The scanner pulls

in afterwards due to the same lateral and rotational instabilities in the comb drive array.

93


The limited scanning range over the inner axis is due to a small defect on its pulling

comb drive array. As predicted, there is no observed cross-coupling between two axial

rotations when a two-axis micromirror rotates around its inner axis up to 15°, actuated

manually with a probe.

-8

-6

-4

-2

0

2

4

6

8

0 1000 2000 3000 4000

Actuation Voltage ^2 (V2)

Opt

ical

Ang

le (d

egre

e)

Inner PushInner PullOuter PushOuter Pull

Figure 4-5. DC actuation of a bi-directional two-axis scanner with T-shaped cross-

section torsional beams.

Figure 4-6 shows the simulated modal shape and frequencies for the lowest four

modes in a one-axis micromirror using Pro-mechanica. As we can see, the resonant

frequency of the second mode is 40 kHz higher than that of the first mode.

94










Figure 4-6. Modal shapes and frequencies of a one-axis scanner with T-shaped

cross-section torsional beams. Mode 1: torsion mode; Mode 2: transfer

arm bending mode; Mode 3: out-of-plane lateral mode; Mode 4: in-

plane lateral mode.

The measured frequency response of a one-axis mirror with T-bar torsional beams

using a laser Doppler vibrometer is shown in Figure 4-7. It has a torsional resonance

frequency at 6.4 kHz, higher than that of a one-axis mirror with rectangular torsional

beams (3.6 kHz). The second mode at 25.3 kHz is far away from the first mode, as the

analytical simulation predicts.

95


(a)

0.001

0.010

0.100

1000 10000 100000Frequency (Hz)

Am

plitu

de o

f Vel

ocity

(a.u

.)

6.4 kHz

25.3 kHz

10-1

10-2

10-3

103 104 105

0.001

0.010

0.100

1000 10000 100000Frequency (Hz)

Am

plitu

de o

f Vel

ocity

(a.u

.)

6.4 kHz

25.3 kHz

10-1

10-2

10-3

103 104 105

(b)

-600.0

-400.0

-200.0

0.0

1.0E+03 1.0E+04 1.0E+05Frequency (Hz)

Phas

e (d

egre

e)

103 104 105

Phas

e of

Vel

ocity

(deg

ree)

-600.0

-400.0

-200.0

0.0

1.0E+03 1.0E+04 1.0E+05Frequency (Hz)

Phas

e (d

egre

e)

103 104 105

Phas

e of

Vel

ocity

(deg

ree)

Figure 4-7. Measured frequency responses of a one-axis scanner with rectangular

cross-section torsional beams and one with T-shaped cross-section

torsional beams.

96


4.4. Comb Drive Actuators for Large Displacements

Most micromirrors fail with the comb drive actuator pulled_in due to its lateral and

rotational instabilities under large static displacements. An ideal suspension is compliant

in the direction of desired displacement and stiff in the orthogonal directions and

rotations. A crab-leg flexure is used as the suspension beam of the comb drive actuator,

as shown in Figure 4-8, due to its large linear deflection region.

y

x

g

∆g

g

∆g

Fy +_

(L2, I2) (L1, I1)

y

x

g

∆g

g

∆g

Fy +_

(L2, I2) (L1, I1)

Figure 4-8. A comb drive actuator suspended by a crag leg flexure.

The forward and side stiffness of the crab suspension beam, kx and ky, at zero

deflection are given by:

⎥⎦⎤

⎢⎣⎡

++

=υυ

4148

32

2

LEIkx (4−4)

⎥⎦⎤

⎢⎣⎡

++

=υ

υ41

14831

1

LEIky (4−5)

with 12

21

LILI

=υ , while E is the Young’s modulus of silicon, I1 and I2 are the momentum of

the inertia for the shin and thigh of the crab leg flexure, L1 and L2 are the length of the

shin and thigh. The side-to-forward stiffness ratio (ky/kx) at zero displacement is high

(around 10000 for a crab leg flexure with L1 = 50 µm, W1 = 11.4 µm, L2 = 650 µm, W2 =

97


4.5 µm, t = 50 µm.) However, the side stiffness, ky, decreases with increasing lateral

deflections and the comb drive actuator becomes more vulnerable to side pull_in.

A suspension flexure is also susceptible to rotation z axis, the out-of-plane direction.

As shown in Figure 4-9, the torque that restores the rotation of the comb drive actuator

comes from the lateral spring force. Therefore, the rotation stiffness kθ of the crab

suspension beam is related with the lateral stiffness, kx and ky, by the following equation:

xykyxkk yx ⋅∆⋅+⋅∆⋅=∆⋅ θθ (4−6)

where ∆θ, ∆x, and ∆y are the angle and lateral displacement of the joint from its original

position.

Comb Drive

ky

kx

(x,y)

(0,0)

Comb DriveComb Drive

ky

kx

(x,y)

(0,0)

Comb Drive

Figure 4-9. The rotation restoring force on a comb drive actuator is provided by the

lateral spring forces.

∆x and ∆y are related with ∆θ by the following equations:

θθ∆⋅−

∆−≈−=∆ yxxxx

2'

2

(4−7)

θθ∆⋅+

∆−≈−=∆ xyyyy

2'

2

(4−8)

98


Then we have a simpler expression of kθ:

(4−9) θθθθ ∆⋅⋅+∆⋅⋅=∆⋅ 22 xkykk yx

(4−10) 22 xkykk yx ⋅+⋅=⇒ θ

Assume that kx << ky since the design of the crab leg flexure makes a high stiffness

ratio between kx and ky. kθ is related with ky only:

(4−11) 2xkk y ⋅≈θ

Therefore the problem of designing a crab leg flexure with high rotation stiffness is

combined to the problem of designing one with high side stiffness. In addition, placing

the suspension on the upper and bottom position of the combs, i.e. maximizing x

according to Equation 4-11, also helps increasing rotational stiffness.

At large deflections, the side stiffness contributed from the thigh of the crab leg

flexure, ky, decreases to [65]

22

2

3100

xLEIky ∆

= (4−12)

From this expression, we can see that the side stiffness decreases with increasing

deflection in the x direction.

In order to increase the range of DC deflections, several strategies can be applied.

(1) Increase the forward stiffness of the suspension beams by increasing the width of

the flexure or decreasing the length of the flexure. Increasing the width of the flexure is

more effective since the side stiffness at large deflections is proportional to the cube of

the width according to Equation 4-12. Compared to the stiffness of the pushing arm and

torsional beams, the stiffness of the suspension beams contribute less than 1% to the total

99


stiffness. Therefore increasing the forward stiffness of the suspension beams will not

significantly affect the performance of micromirrors.

(2) Maximize the gap spacing of the comb drive actuator if a higher actuation voltage

is allowed since the comb drive actuator with small gap spacings are more susceptible to

side instabilities. The electrostatic force in the side direction is proportional to the cube of

the gap while the actuation force in the forwarding direction is only linearly proportional

to the gap. As the gap size increases by a factor of α, the voltage required to reach a

certain displacement increases by a factor of α , while the side stability is increased by

a factor of α.

(3) Employ pre-bent suspension beams [66] for the devices that work unidirectionally.

With pre-bent suspension beams, the side stiffness will be low initially and increase as

the suspension beams straighten. Therefore the side stiffness is low when the side

electrostatic force is low and increases as the side electrostatic force increases. It is

estimated that the use of pre-bent suspension beams increase the range of the deflection

by a factor of two [66].

100

MEMS SCANNING MICROMIRROR

5. CONCLUSIONS AND DISCUSSIONS

The focus of this dissertation is the development of two optical MEMS devices,

CCRs and scanning micromirrors, for free-space communication.

5.1. Summary of Results over CCRs

Sub-millimeter-sized CCRs are fabricated by assembling two side mirrors onto an

actuated bottom mirror. Assembled CCRs exhibit mirror non-flatness less than 50 nm,

mirror roughness less than 2 nm, and mirror angular misalignment less than 1 mrad

(0.06°), leading to near-ideal optical performance. The angular alignment accuracy is

achieved through locking the positions of the two side mirrors using spring flexures and

protrusion-notch structures. The quad CCR incorporates an electrostatic gap-closing

actuator, formed between the device layer and the substrate of the fabricated SOI wafer,

allowing their reflectivity to be modulated up to 7 kb/s. The actuation voltage is as small

as 4.7 V, compatible with the driving solar cell power and CMOS control switches. The

energy consumption, which averages 19 pJ per bit, is consistent with the power

requirements of a millimeter-scale autonomous sensor node. A 180-m free-space optical

communication link using a CCR as a passive optical transmitter has been demonstrated.

Quad CCRs have been integrated with other parts of Smart Dust mote, formulating

miniature, autonomous nodes that constitute a distributed wireless sensor network. An

analysis of the signal-to-noise ratio of CCR-based links, considering the impact of CCR

dimensions, ambient light noise, and other factors, has been presented.

101


5.2. Summary of Results over Scanning Micromirrors and SOI/SOI Wafer Bonding

Process

An SOI/SOI wafer bonding process is developed to fabricate scanning mirrors

actuated by lateral comb drive actuators. The process is an extension of SOI technology

and can be used to fabricate stacked high-aspect-ratio structures with well-controlled

thicknesses. Strategies, such as retaining an oxide layer on the back of the SOI wafer to

decrease the bow of the wafer and allocating more than 50% of the wafer surface as

bonding area to guarantee adequate bonding force, are employed to increase the yield of

the process. The bonding interface is characterized by SEM and infrared images,

indicating solid bonding between wafers. The I-V curves of bonded structures suggest

that electrical interconnection can be made through bonded layers, providing flexibility to

the interconnection design. A shear stress test is carried out and measures the lower limit

of the ultimate shear stress to be 1.01 MPa. The bonded structures show an excellent air

sealing property since the pressure inside the sealed cavities capped by a bonded layer

agrees with the read-out of the pressure gauge on the bond aligner during bonding.

An analytical simulation is established to analyze the scanning micromirrors by

employing the universal beam theory, considering the axial force acted on the transfer

arms, and assuming proper boundary conditions. It is best for predicting the rotation

angle and maximum stress of the scanning micromirrors having torsional beams with

high stiffness ratio between the lateral stiffness and the torsional stiffness such as T-bar

torsional beams, while not accurate for the case with thin, wide rectangular cross-section

since the latter case does not satisfy the assumed boundary conditions.

102


The fabricated one-axis micromirror with rectangular cross-section torsional beams

has the capability of scanning 21.8° under a DC actuation voltage of 75.0 V. It agrees

with the ANSYS FEM result within 15 %. The frequency response of the one-axis

micromirror shows that the mirror has a rotational mode at 3.6 kHz, an out-of-plane

lateral mode at 4.1 kHz, and a left-right twisting mode at 6.8 kHz. The fabricated two-

axis micromirror scans up to 15.9° optically under a DC actuation voltage of 71.8 V for

the inner axis and 13.2° at 71.2 V for the outer axis. The resonant frequency of the

rotation mode over the inner axis for this two-axis micromirror is 2.2 kHz while the one

over the outer axis is 1.3 kHz.

Torsional beams with T-shaped cross sections are introduced to replace rectangular

torsional beams in the two-axis MEMS micromirror in order to reduce the cross-coupling

between the two axial rotations. T-bar torsional beams have a high lateral stiffness in

both in- and out-of-plane directions while keeping a low torsional compliance. Also the

use of T-bar torsional beams is compatible with the SOI/SOI wafer bonding process that

is used to fabricate micromirrors. The two-axis micromirror with T-shaped cross-section

torsional beams shows no cross-coupling between two axial rotations within a large range

of scanning angles. The fabricated bi-directional two-axis micromirror works up to ±7°

for the outer-axis and from -3° to 7° for the inner-axis under DC actuation. The measured

frequency response of a one-axis mirror with T-bar torsional beams shows a torsional

resonance frequency at 6.4 kHz, higher than that of a one-axis mirror with rectangular

torsional beams.

The micromirror was observed to be quite durable with no obvious frequency and

scanning angle shifts after running at 6.4 kHz with scanning amplitude of around 17.8°

103


for 18.9 billion cycles. The micromirrors were tested on a shake table, subjected to

shocks with a peak acceleration of 500 g and pulse duration of 1 ms along the directions

of all three axes. All three devices were functional after the shock tests.

5.3. Future Work

Both CCRs and scanning micromirrors are developed to facilitate free-space optical

communication, establishing optical link among sensor nodes or between sensor nodes

and interrogating center. Future research directions should concentrate on the integration

and further development of the system.

Here is a list of possible research directions.

(1) Automated assembly of CCRs. Although the assembled CCRs display near-ideal

optical quality and excellent actuation performance, manual assembly of CCR mirrors is

a drawback of the current process. The automation of assembly can be realized by using

vacuum tips to handle small objects. The outer diameter of commercially available tips

can be as small as 200 µm, able to grab the side mirrors without blocking its pathway.

The ‘on’ and ‘off’ of the vacuum makes grabbing and releasing of the small objects

convenient. The placement of side mirrors can be controlled by programming micro-

positioners with six degrees of freedom.

(2) Optimization of scanning micromirror design. The comb drive actuator of

scanning micromirrors needs to be redesigned, as suggested in the previous chapter, so

that micromirrors have a larger DC scanning range. This can be done by increasing the

forward stiffness of the suspension beams, maximizing the gap spacing of the comb drive

actuator, or employing pre-bent suspension beams. The mirror surface needs to be metal

coated. Either gold or aluminum coating is able to bring up the reflection of a mirror

104


surface from 30 % to more than 90 %. However, coating the mirror with metal introduces

stresses to the 2 µm-thick surface, inducing curvature to the mirror. Putting 50 µm-thick

stiffening ribs behind the mirror surface helps keeping the mirror flat while the position

and shape of the stiffening ribs need to be optimized so that it contributes minimum

amount of momentum of inertia to the mirror. There is no lower limit to the size of the

stiffening ribs as the previous experiments show structures as narrow as 3 µm can be

bonded to another layer.

(3) Integration of scanning micromirrors with other parts of the communication

platform. A feedback control system for MEMS micromirrors is implemented by

measuring the mirror position electronically with the sense capacitors [67]. However,

beam-steering using gyro-stabilized MEMS scanning micromirrors still needs to be

implemented and integrated with imaging receiver to realize the beam acquisition and

link maintenance between two micro air vehicles.

(4) Application of scanning micromirrors in other areas. Besides free space optical

communication, there are a number of applications in which scanning micromirrors are

used. Having two-axis scanning capability and large scanning range, our scanning

micromirrors can be used for laser printer, projection video displayer, and other fiber

optic equipment, such as tunable lasers and fiber-optic switches.

(5) Improvement of the SOI/SOI wafer bonding process. More bonding layers can be

added in the process to eliminate the timed etching step completely. Realizing low

temperature silicon direct bonding between SOI wafers will give much flexibility to the

process such as fabricating bonded transducers and sensors over existing CMOS devices.

Methods such as oxygen plasma activation and/or tetramethoxysilane (TMOS) solution

105


dip can decrease the annealing temperature (≤ 500°C) while achieving bonding energies

that are sufficiently high for a micromechanical device.

(6) Application of the SOI/SOI wafer bonding process to other transducers and

sensors. MEMS micro engines and pressure sensors are two devices under active

investigation that employ silicon direct bonding. Wafer packaging realized by silicon

wafer bonding is the key enabling micromachining technology for the high-volume

production of low-cost MEMS components and systems. The SOI/SOI wafer bonding

process may play a role when several bonding layers with strict control over their

thicknesses are required.

Proof Mass

g

Anchor

Torsional Beam

Torsional Beam

Gap-Closing Sensing Comb Fingers

Proof Mass

g

Anchor

Torsional Beam

Torsional Beam

Gap-Closing Sensing Comb Fingers

Figure 5-1. Schematic of proposed accelerometer over the out-of-plane axis with

high sensitivity and resolution.

An accelerometer with high sensitivity and resolution over the out-of-plane axis can

be realized by the SOI/SOI wafer bonding process, as proposed in Figure 5-1. The out-of-

106


plane acceleration of the proof mass, which consists of both the device layer and the

substrate of the SOI wafer, is translated into the in-plane movement of gap-closing comb

fingers. Gap-closing capacitive sensing can be employed for the purpose of maximizing

sensitivity while lateral comb sensing is a better choice to achieve larger range and higher

linearity. Combining with accelerometers sensing two other axis’ movement, this makes

a single-chip monolithic three-axis accelerometer with equally high sensitivity over all

axes.

107

REFERENCE

REFERENCE:

[1] C. DeCusatis, “Optical data communication: fundamentals and future directions,”

Optical Engineering, vol. 37, no. 12, P3082-99, 1998.

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115

APPENDIX

APPENDIX A – MATLAB SCRIPTS TO MODEL FAR-FIELD

IMAGE PATTERN REFLECTED BY CCRS

% This MATLAB program calculates the far field image pattern reflected by a CCR.

% (theta, fai) is the direction of the incident light.

% (x0, y0), (x1, z1), (y2, z2) represent the size of three side mirror planes.

% Effarea(x, y) represents the effective area of CCR reflection.

% I(u,v) is proportional to the light intensity reflected by the CCR along direction (u,v).

clear;

lamda = 0.6328; klamda = 2*pi/lamda; % define the wavelength of the incident light.

% define the direction of the incident light. In this case, it’s the body diagonal direction.

theta = acos(1/sqrt(3)); fai = pi/4;

a = sin(theta)*cos(fai); b = sin(theta)*sin(fai); c = cos(theta);

% define the size of three side mirror planes with unit of um.

x0 = 640; y0 = 450; x1 = 750; z1 = 600; y2 = 750; z2 = 600;

size_max = max([x0,y0,x1,z1,y2,z2]);

% define the size of the far field image plane.

angle_size = 0.01; angle_step = 0.0001;

u = -angle_size:angle_step:angle_size;

v = -angle_size:angle_step:angle_size;

[u,v] = meshgrid(u,v); U = zeros(size(u));

% calculate the effective area (Effarea) of the CCR reflection.

plane_size = 2*size_max; plane_step = 10;

plane_num = plane_size/plane_step;

Effarea = zeros(plane_num+1, plane_num+1);

116

APPENDIX

xmin = sqrt(1-b^2)*min([y0; z1*b/c; y2+z2*b/c]);

ymin = sqrt(1-a^2)*min([x0; x1+z1*a/c; z2*a/c]);

zmin = sqrt(1-c^2)*min([x0*b/a+y0; x1*b/a; y2]);

c1 = b/a*sqrt(1-b^2)/sqrt(1-a^2);

c2 = c/sqrt(1-b^2)/sqrt(1-a^2);

c3 = a*b/sqrt(1-b^2)/sqrt(1-a^2);

for j = -plane_num/2:plane_num/2

x = j*plane_step;

xfactor1 = c1*x;

xfactor2 = c3*x;

x_orth = c2*x;

for k = -plane_num/2:plane_num/2

y = k*plane_step;

z = y-xfactor1;

y_orth = y-xfactor2;

if abs(y) < xmin

if abs(x) < ymin

if abs(z) < zmin

Effarea(j+plane_num/2+1,k+plane_num/2+1) = 1;

U = U+exp(-i*klamda*(x_orth.*u+y_orth.*v));

end;

end;

end;

end;

end;

mesh(Effarea); % draw the effective area of CCR reflection.

I = abs((U*plane_step^2*c2*10^(-6)/lamda).^2);

figure; imshow(I, [], 'notruesize'); colormap(jet); colorbar % draw the far-field pattern.

117

APPENDIX

APPENDIX B – MATLAB SCRIPTS TO MODEL DSCS RELATED

WITH MISALIGNMENT ANGLE OF CCRS

% This program calculates the relationship between DSCS and the misalignment angle.

% misalign is the misalignment angle between two mirrors of CCRs.

% (theta, fai) is the direction of the incident light.

% (x0, y0), (x1, z1), (y2, z2) represent the size of three side mirror planes.

% count is the electrical field of the light reflected by the misaligned CCR along the

direction of the incident light.

% DSCS is the light intensity reflected by the misaligned CCR along the direction of the

incident light.

clear;

misalign = 0:0.0001:0.005; % define the misalignment angle between two mirrors.

lamda = 0.6328;

klamda = 2*pi/lamda;

% define the direction of incident light. In this case, it's the body diagonal direction.

theta = acos(1/sqrt(3));

fai = pi/4;

a = sin(theta)*cos(fai);

b = sin(theta)*sin(fai);

c = cos(theta);

% define the size of three side mirror planes with unit of um.

x0 = 640; y0 = 450; x1 = 750; z1 = 600; y2 = 750; z2 = 600;

size_max = max([x0,y0,x1,z1,y2,z2]);

plane_size = 2*size_max;

plane_step = 10;

118

APPENDIX

plane_num = plane_size/plane_step;

xmin = sqrt(1-b^2)*min([y0; z1*b/c; y2+z2*b/c]);

ymin = sqrt(1-a^2)*min([x0; x1+z1*a/c; z2*a/c]);

zmin = sqrt(1-c^2)*min([x0*b/a+y0; x1*b/a; y2]);

c1 = b/a*sqrt(1-b^2)/sqrt(1-a^2);

c2 = c/sqrt(1-b^2)/sqrt(1-a^2);

c3 = a*b/sqrt(1-b^2)/sqrt(1-a^2);

count = 0;

for j = -plane_num/2:plane_num/2

x = j*plane_step;

xfactor1 = c1*x;

xfactor2 = c3*x;

x_orth = c2*x;

for k = -plane_num/2:plane_num/2

y = k*plane_step;

z = y-xfactor1;

y_orth = y-xfactor2;

if abs(y) <= xmin

if abs(x) <= ymin

if abs(z) <= zmin

count = count+exp(-i*klamda*abs(y*c/sqrt(1-b^2))*2.*sin(misalign));

end;

end;

end;

end;

end;

dscs = abs(count*plane_step^2*c2*10^(-6)/lamda).^2;

figure;

plot(misalign,dscs);

title('DSCS vs. Misaligned Angle'); xlabel('Misaligned Angle (rad)'); ylabel('DSCS');

119

APPENDIX

APPENDIX C – SOI/SOI WAFER BONDING PROCESS FLOW

This appendix provides a detailed description of the SOI/SOI wafer bonding process

flow, the design rules, and a few processing features.

SCS

bonding layer

shallow trench

Buried Oxide

low_SCSdeep trench

high_SCS

SOI2

SOI50

SCS

bonding layer

shallow trench

Buried Oxide

low_SCSdeep trench

high_SCS

SOI2

SOI50

Fig. A.1: Cross section of a device after the backside patterning of bonded wafer.

C1. Layout Features / Design Rules

Put large-radius rounded corner to every mechanical connections whenever possible

in order to reduce the stress concentration.

Add floating structures to decrease the area of open oxide membrane.

Have substrate holes under structures where high voltage is applied to.

Design rule has to take care of the fact that the bonding alignment accuracy achieved

by Karl Suss aligner is within ± 15 µm.

120

APPENDIX

Thermal stress from oxide membrane causes cracks or even breaks off part of the

membrane during and after DRIE handle wafer etch. This sets the narrowest pushing

beam defined by shallow trench.

Alignment tolerance between deep trench and shallow trench: ± 6 µm.

Alignment tolerance between deep trench and substrate pattern: ± 20 µm.

Alignment tolerance between deep trench and bonding layer: ± 15 µm.

Narrowest torsion beam defined by deep trench: 4 µm.

Narrowest pushing beam defined by shallow trench: 10 µm.

Minimum gap distance for comb drive actuator: 2 µm.

C2. Detailed Process Flow

The detailed process flow is listed here and the names in parenthesis indicate the

machine and recipe names used in U. C. Berkeley Microlab.

1. starting wafers: SOI50 and SOI2.

one SOI wafer with 50 µm device layer, 1~2 µm buried oxide layer and 350 ~ 400

µm substrate layer, named SOI50; one SOI wafer with 2 µm device layer, 1 µm

buried oxide layer and 350 ~ 400 µm substrate layer, named SOI2.

2. SOI50: standard clean (sink8/sink6) and MOS tube wet oxidation.

The thickness of oxidation layer depends on the thickness of buried oxide, 7500 Å

for wafers with 1 µm’s buried oxide layer, and 1500 Å for 2 µm’s.

3. SOI50: deep trench lithography (10:1 stepper, chrome mask).

10 mins’ hard bake at 120°C (hard bake oven), 5 mins’ HMDS (sink5), 1.6 µm I-

line photo resist spin-on (svgcoat), mask exposure (gcaws), post exposure bake for 60

121

APPENDIX

secs (svgdev), photo resist develop, discum (technics-c), hard bake for 45 mins ~ 2

hours (hard bake oven).

4. SOI50: deep trench pattern transfer on oxidation layer.

oxide etching (lam2), photo resist strip with PRS3000 (sink5).

5. SOI50: backside alignment mark patterning (contact, chrome mask).

spin coat a layer of 1.6 µm protection photo resist on the front side of the wafer

first, 1.6 µm I-line photo resist lithography on the back of the wafer, backside

alignment mask exposure (ksaligner with soft contact mode), hard bake, oxide

etching (lam2), photo resist strip with PRS3000 (sink5).

6. SOI50: shallow trench mask patterning (contact, emulsion mask).

1.6 µm I-line photo resist lithography on the front side of the wafer, shallow

trench mask exposure (ksaligner with vacuum contact mode).

7. SOI50: deep reactive ion etching.

sts etching by VEE1 program for 20 minutes until deep trench is around 30 µm

thick, PRS3000 strip off shallow trench photo resist, sts etching by VEE1 program for

10 minutes, continued with ANITA1B program (about 15 minutes) until all trenches

are clear and low_SCS layer is about 6 µm thick.

8. SOI50: strip off front side oxidation mask by HF.

standard clean (sink8/sink6), coat SOI50 backside with thick photo resist to

protect the alignment mark (svgcoat1), hard bake for three hours (hard bake oven),

10:1 HF etching for 45 minutes until all front side oxide is gone and the exposed

buried oxide is around 6000 Å (or more accurately, calculate the etching time by

using the etching speed of 230 Å/min, don’t disturb the dish mechanically during the

122

APPENDIX

etching, otherwise, photo resist is easy to peel off from the coated surface), PRS3000

photo resist strip.

9. SOI2: standard clean (sink8/sink6) and MOS tube wet oxidation.

the thickness of oxidation layer is 1000 Å ~ 3000 Å.

10. SOI2: bonding layer mask patterning (10:1 stepper, chrome mask).

1.6 µm I-line photo resist lithography on the front side of the wafer as in step 3,

oxide etching (lam2, no need to strip off photo resist at this stage).

11. SOI2: deep reactive ion etching.

sts etching by Anita1B program for 2 minutes, strip off photo resist with PRS3000.

12. SOI2: strip off front side oxidation mask by HF.

standard clean (sink8/sink6), 10:1 HF etching for 22 minutes until all front side

oxide is gone and the exposed buried oxide is around 5000 Å (or more accurately, to

calculate the etching time by using the etching speed of 230 Å/min).

13. SOI50 and SOI2: standard clean (sink8/sink6), HF 25:1 dip for 25 seconds and RCA

clean with DI water in between.

modified RCA1 (NH4OH : H2O2 : H2O = 0.01-0.25 : 1 : 5) cleaning for 10 ~ 20

minutes, RCA2 (HCl : H2O2 : H2O = 1 : 1 : 6 to 1 : 2 : 8) cleaning for 20 ~ 40

minutes.

14. SOI50 and SOI2: bond with alignment.

pre-fusion bonding (ksba6), with prevac time = 30 seconds, fullvac time = 30

seconds, purge time = 10 seconds.

15. Bonded SOI50/SOI2: anneal in non-MOS tube for 10 hours at 1050°.

123

APPENDIX

check the bonding quality with IR scope and check the alignment accuracy with

Quintel.

16. Bonded SOI50/SOI2: deep reactive ion etching to have partial of front side handle

wafer released.

sts etching by BORIS02/VEE6 program for about 140 minutes or until the

thickness of the front side handle layer is decreased to 100 µm (no need to have an

extra handle wafer attached to the bonded wafer).

17. Bonded SOI50/SOI2: substrate lithography (contact, chrome mask).

8 µm thick photo resist lithography on the backside of the wafer, substrate pattern

exposure (ksaligner with soft contact mode).

18. Bonded SOI50/SOI2: handle wafer attachment for sts etching.

coat the handle wafer with 8 µm thick photo resist without soft bake, attach it to

the frontside of the bonded wafer manually, primeoven to expose to the vacuum, hard

bake for 3 hours.

19. Bonded SOI50/SOI2: deep reactive ion etching to etch backside substrate wafer.

sts etching by VEE6 program for about 140 minutes or until the pattern on the

backside wafer is cleared.

20. Bonded SOI50/SOI2: dicing.

8 µm thick photo resist protection on the backside of the wafer, dice to single dies

(disco, mode A with z step = 0.5 mm), PRS3000 overnight to release the bonded

chips from the sts handle wafer, piranha cleaning.

21. Die: front side handle wafer full release.

124

APPENDIX

coat a handle wafer with 8 µm thick photo resist glue layer, attach it to the

backside of the diced chip, primeoven to expose it to the vacuum, hard bake for three

hours, sts VEE6 etching until all front side gone.

22. Die: debond with handle wafer and HF release.

PRS3000 to debond the chip with the handle wafer, piranha cleaning, 5:1 BHF for

twelve minutes.

23. Die: package with westbond.

wirebond (westbond), set second clamping option, i.e. drop before clamp, to 0, the

power and time for bond 1 on Au to be 300 mW and 30 ms, bond 2 on Si to be 370

mW and 30 ms, bonding force to be 31 grams (note that the maximum power to apply

on Si is 470 mW).

125

APPENDIX

APPENDIX D – ANSYS SCRIPTS TO MODEL MECHANICS OF

SCANNING MICROMIRRORS

! ANSYS script to simulate the rotation angle under the lateral actuation force.

/batch, list

/prep7, Use T-bar as torsional beam

et, 1, 92 ! solid92 element for meshing structures

mat, 1

mpread, si_blk_ln, si_mpl, , lib

! dimensions (microns) / parameters

bl = 300 ! Beam web length (Bonding layer)

btw = 3 ! Beam web height (Bonding layer)

bb = 70 ! Beam web width (Bonding layer)

btf = 3 ! Beam flange width (High_SCS layer)

bh = 50 ! Beam flange height (High_SCS layer)

pl = 300 ! Push beam (Low_SCS layer)

ph = 6 ! Push height (Low_SCS layer)

pw = 10 ! Push width (Low_SCS layer)

fymag = 3 ! Magnitude of lateral actuation force

! Create model

block, -bl-50, -50, -bb/2, bb/2, 0, btw ! Create torsional beam web 1

block, 50, bl+50, -bb/2, bb/2, 0, btw ! Create torsional beam web 2

block, -bl-50, -50, -btf/2, btf/2, -bh, 0 ! Create torsional beam flange 1

block, 50, bl+50, -btf/2, btf/2, -bh, 0 ! Create torsional beam flange 2

block, -30, 30, 0, 200, -bh, btw ! Create a dummy to show the rotation of the beam

block, -pw/2, pw/2, -pl, 0, -50, -50+ph ! Create pushing arm

block, -50, -30, -bb/2, 200, -bh, btw ! Create linkage between pushing and torsion beam

126

APPENDIX

block, 30, 50, -bb/2, 200, -bh, btw ! Create linkage between pushing and torsion beam

vglue, all

! Apply displacement boundary condition

da, 17, ALL, 0 ! Left side of the left torsional beams should be restricted

da, 54, ALL, 0

da, 24, ALL, 0 ! Right side of the right torsional beams should be restricted

da, 57, ALL, 0

da, 33, ux, 0 ! The lower end of pushing arm move only laterally in y direction

da, 33, uz, 0

fk, 42, fy, fymag/4 ! Acutating force is symmetrically acted on the pushing arm

fk, 44, fy, fymag/4

fk, 45, fy, fymag/4

fk, 46, fy, fymag/4

vsel, all ! Select all volumes

vatt, 1, , 1

smrtsiz, 2

vmesh, all ! Mesh all the structures

finish

! Commands for nonlinear analysis

/solu

antype, 0

nlgeom, on

autots, on

nsubst, 2, 100, 1

autots, 1

outres, NSOL, 1

solve ! Solve the problem

finish

127

APPENDIX

APPENDIX E – MATLAB SCRIPTS TO CALCULATE THE

CURVATURE OF A MULTILEVEL WAFER

% This program searches the optimal thickness of the oxide added on the backside of an

SOI wafer, so that the bow of the wafer induced by thermal stress is at its

minimum.

% Layer 1, 2, 3, 4 are the device layer, buried oxide layer, handle wafer, and the oxide

layer added on the backside of the SOI wafer.

t4 = 1e-8:1e-8:2e-6; % t4 is the thickness of the added oxide layer.

r = stress2(t4); % calculate the curvature of the multilayer wafer.

bow = 8100/8./r; % calculate the bow of the multilayer wafer

figure;

plot(t4*1e6, bow);

title('Bow of wafer vs. thickness of oxide under the handle wafer');

xlabel('Thickness of oxide under the handle wafer (\it\mum)');

ylabel('Bow of wafer (\it\mum)');

function r = stress2(t4)

t1 = 50e-6; % t1, t2, t3, t4 are the thickness of the individual layers.

t2 = 2e-6;

t3 = 350e-6;

mui1 = 0.12; % Poisson's ratio of Si;

mui2 = 0.2; % Poisson's ratio of SiO2;

mui3 = mui1;

mui4 = mui2;

alpha1 = 2.6e-6; % Coefficient of thermal expansion of Si;

alpha2 = 0.5e-6; % Coefficient of thermal expansion of SiO2;

alpha3 = alpha1;

alpha4 = alpha2;

128

APPENDIX

delta_T = 1000;

E1 = 160e9; % Young's modulus of Si;

E2 = 160e9; % Young's modulus of SiO2;

E3 = E1;

E4 = E2;

E1_bi = E1/(1-mui1);

E2_bi = E2/(1-mui2);

E3_bi = E3/(1-mui3);

E4_bi = E4/(1-mui4);

B = [0; 0; alpha2*delta_T-alpha1*delta_T; alpha3*delta_T-alpha2*delta_T;

alpha4*delta_T-alpha3*delta_T];

[m, n] = size(t4);

r = zeros(m, n);

for ii = 1:m

for jj = 1:n

A = [1 1 1 1 0; t1/2 t1+t2/2 t1+t2+t3/2 t1+t2+t3+t4(ii, jj)/2

E1_bi*t1^3/12+E2_bi*t2^3/12+E3_bi*t3^3/12+E4_bi*t4(ii, jj)^3/12;

1/E1_bi/t1 -1/E2_bi/t2 0 0 t1/2+t2/2; 0 1/E2_bi/t2 -1/E3_bi/t3 0 t2/2+t3/2;

0 0 1/E3_bi/t3 -1/E4_bi/t4(ii, jj) t3/2+t4(ii, jj)/2];

x = A\B; % Linear equation solves the curvature of SOI wafer.

r(ii, jj) = 1/x(5);

end;

end;

129

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