01638482.pdf

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 3, JUNE 2006

553

Microfabricated Torsional Actuators Using

Self-Aligned Plastic Deformation of Silicon

Jongbaeg Kim, Hyuck Choo, Liwei Lin

, Member, IEEE, Fellow, ASME

, and

Richard S. Muller

, Life Fellow, IEEE, Member, ASME

Abstract—

In this paper, we describe angular vertical-comb-

drive torsional microactuators made in a new process that induces

residual plastic deformation of single-crystal-silicon torsion bars.

Critical dimensions of the vertically interdigitated moving-and

fixed-comb actuators are self-aligned in the fabrication process

and processed devices operate stably over a range of actuation

voltages. We demonstrate MEMS scanning mirrors that resonate

at 2.95 kHz and achieve optical scan angles up to 19.2 degrees

with driving voltages of

40V

plus

13V

. After continuous

testing of five billion cycles at the maximum scanning angle, we do

not observe any signs of degradation in the plastically deformed

silicon torsion bars.

[1550]

Index Terms—

Electrostatic actuators, plastic deformation, self-

alignment, scanning micromirrors, torsional actuators, vertically

interdigitated combs.

I. I

NTRODUCTION

ESEARCHERS have used electrostatic comb-drive ac-

tuators for many diverse MEMS applications. Measured

performance of these actuators has proven their capabilities for

achieving extended ranges-of-movement stably and reliably

over a wide range of resonant frequencies, and they have been

especially useful for optical scanners and switches. For ex-

ample, lateral comb-drives with mechanical hinges or linkages

made of polycrystalline- or single-crystalline silicon have been

used to drive torsional actuators [1], [2]. Experiments with

these devices revealed reliability problems and limitations on

maximum operational frequencies. In one design for torsional

actuators Hah and co-workers interleaved vertically aligned

comb-finger sets with planarized polysilicon structures [3]

using a process employing chemical–mechanical polishing

(CMP) to achieve both higher frequencies and larger scan

angles than those obtained in earlier designs built with lateral

comb-drives. Other vertically aligned comb-drive designs have

been fabricated using polysilicon-on-SOI [4] or single-crystal

silicon coupled with a wafer-bonding technique [5]. Krisna-

murthy and Solgaard demonstrated a self-aligned vertical comb

[6] made using wafer-bonding, grinding, and polishing, in

addition to an anisotropic-etch step of single-crystal silicon.

Manuscript received March 18, 2005; revised November 10, 2005. This paper

was presented in part at the 12th International Conference on Solid-State Sen-

sors, Actuators and Microsystems (Transducers ’03, Boston, MA, June 9–12,

2003). Subject Editor H. Zappe.

J. Kim is with the School of Mechanical Engineering, Yonsei University,

Seoul, Korea (e-mail: jongbaeg@gmail.com).

H. Choo, L. Lin, and R. S. Muller are with Berkeley Sensor and Actu-

ator Center, University of California, Berkeley, CA 94720 USA (e-mail:

r.muller@ieee.org).

Digital Object Identifier 10.1109/JMEMS.2006.876789

Collectively, the vertical-comb-drive actuators described above

can be described as staggered vertical comb-drive (SVC) actu-

ators [5]. SVCs commonly face a severe fabrication challenge

posed by their need for precise alignment between the two

comb-finger layers.

Recent research has demonstrated that when the mate-

rial forming the two vertical combs is not co-planar, but rather

angled relative to one another, the achievable torsional displace-

ment is significantly increased. When the comb geometries are

similar, for example, these angular vertical comb-drive (AVC)

actuators have been driven with maximum 50% more torsional

displacement than the nonangled SVC types [7], [8]. The

fabrication processes for AVCs start by defining stationary and

movable comb structures in the same silicon layer. Next, either

the stationary comb structure or the movable comb structure

is deflected into an offset position. The deflection process has,

in previous work, been induced either through residual stress

by adding a metal overlayer [7] or through the surface-tension

forces that result from reflowing a patterned-photoresist layer

[8]. For the metal overlayer method to be effective, the structure

to be deformed must be sufficiently flexible for the applied

force to induce a useful offset value. This requirement directly

affects the resonant frequencies of the deformed structures,

limiting them in practice to a few hundreds of Hz. In addition,

for the polymer hinges, precisely controlling the reflow of the

hinge material and consistently achieving good mechanical re-

liability have proven to be the challenging tasks. More recently,

AVCs were fabricated using intentionally induced stiction on

the designated plates giving quite limited offset angle between

stator and rotor combs [9], [10]. These methods are simple to

get AVC, but the achievable initial tilt angle is quite limited

since they are using limited thickness of buried oxide layer

(typically,

–

m) for the stiction plates to be displaced for

angular tilting of the mirror.

Our research demonstrates a new way to build AVC torsional

actuators that show higher resonant frequencies as well as

other performance advantages. We use single-crystal silicon

and achieve the angled orientation between comb fingers by

deforming one of the pair plastically in an anneal step [11].

MEMS researchers have, in recent years, demonstrated several

applications for plastic deformation in silicon including the

fabrication of domes [12] and deformed membranes [13] in

polycrystalline and single-crystal silicon under the pressure

of heated gases. Plastically deformed polysilicon structures

have also been used in a self-assembled MEMS process [14].

On a larger scale, silicon-chip-mounting using plastically

deformed single-crystal-silicon cantilever beams has been

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 3, JUNE 2006

Fig. 1. Batch-processed plastic deformation of microactuator torsion bars

(before and after plastic deformation of torsion bars).

Fig. 2.

Higher aspect ratio of vertical comb

ngers by new fabrication

approach; taller comb

ngers (and larger actuation angle) are achieved with

plastic deformation process than with conventional SVC fabrication.

demonstrated [15]. In our paper, self-aligned vertically inter-

digitated comb-sets are fabricated in a precisely controlled,

repeatable batch process.

We describe both the fabrication process and the dynamic

performance of the actuators, using them to drive scanning mi-

cromirrors. The scanners have resonant frequencies that are an

order-of-magnitude higher than those reported in earlier AVCs

based upon residual stress process. Measurements on scanning

mirrors made with these AVCs have con

rmed their repeatable

and stable operation.

II. D

ESIGN AND

ABRICATION

A torsional scanning-mirror actuator is composed of four

components to generate mirror motions out of the substrate

plane; the mirror plate, the torsion bars, the moving comb

set, and the

xed comb set. An ideal scanning-mirror actuator

should have smooth and

at mirror surface for optical quality

and precisely aligned moving- and

xed-comb sets for stable

operation. Our design for AVC scanning mirrors provides both

of these requirements. Fig. 1 shows schematically how, in

our process, the torsion bars are permanently deformed and

actuated. Initially, both the moving- and

xed-combs, formed

in the same device layer of an SOI wafer, are coplanar. In the

coplanar con

guration, voltages applied between the comb

ngers cannot cause vertical displacement, and therefore in

the following step, the combs attached to mirror structures are

depressed from their original orientations by pushing on them

with a separately prepared silicon substrate. This substrate is

processed separately so that it has a precisely spaced array of

pillar structures. The pillars are spaced such that each of them

Fig. 3.

The permanent plastic deformation and elastic recovery explained

in a stress-strain curve of silicon where



is maximum yield stress,



ow stress, the stress needed to continue plastic deformation, at an elevated

temperature. (From [11].)

Fig. 4. Stress distribution in the torsion bars; stress induced in the mirror is

negligibly small

—

the maximum stress on the mirror is less than 10 Mpa except

the boundary between the mirror and torsion bars (unit of the scale bar: Mpa).

deforms one pair of torsion bars by pushing the associated

mirror edge downward from its original position (parallel to

its comb partner). A subsequent high-temperature (900

annealing step converts the initially elastic deformations of the

torsion bars that connect the two comb

nger sets into perma-

nent plastic deformations [Fig. 1(b)]. With the comb pairs in

this angled con

guration, voltages applied between them will

induce torque in the torsion-bar supports that connect them.

Our new AVC, shown in Fig. 1, has several advantages over

previous SVC actuators. Fig. 2(a) and (b) shows typical fab-

rication processes for SVCs and AVCs, respectively, to pro-

duce self-aligned comb

ngers. In these structures, a high aspect

ratio for the comb

ngers is desired to produce a large actua-

tion range, and the achievable aspect ratio is essentially limited

to that which can be obtained using deep-reactive-ion-etching

(DRIE). In our fabrication process, we can displace one comb

KIM

et al.

: MICROFABRICATED TORSIONAL ACTUATORS

555

Fig. 5.

Two base designs of scanning mirror actuators.

TABLE I

YPICAL

ESIGN

XAMPLES OF

YPES OF

AVCs B

UILT AND

TUDIED IN

HIS

ESEARCH

nger set through its entire thickness and thereby achieve the

comb

nger aspect ratio twice as large as those in SVCs. There-

fore, the range of actuation can be also larger under the similar

conditions such as torsion bar dimension, location of comb

gers and operation voltage.

Fig. 3 shows a typical stress-strain curve measured in single-

crystal silicon at high temperature [13]. At room temperature,

silicon is a brittle material with a yield stress of GPa order.

At elevated temperatures, its mechanical properties change; for

example, its maximum yield stress

decreases due to the

increased mobility of dislocations in the crystal. At tempera-

ture exceeding roughly 600

C, silicon structures begin to de-

form plastically and the

ow stress

(the stress needed to

continue plastic deformation) decreases with rising tempera-

ture. For our AVC-process, we have designed the pillar struc-

tures such that the torsion bars are stressed above

at the

annealing temperature, causing them to yield plastically. Fig. 4

shows the room-temperature stress distribution in the torsion bar

supporting a mirror when the mirror comb-

nger is angled at 4

to its mate. The distribution is calculated using

nite-element

analysis on the torsion bars that measure 16

600

m and support a mirror of 800

1400

m. Fixed boundary

condition was set at the ends of torsion bars that are connected

to anchors and a point load is applied at the edge of the mirror

to simulate the real case loading where a mirror is pushed down

by a pillar. The deformation process also induces stresses in the

mirror plate; however, their magnitudes are much smaller than

and negligible compared to the stresses in the torsion

bars. The maximum stress in the mirror plate was calculated to

be smaller than 10 Mpa even at the positions close to the tor-

sion bars, while the stresses in the torsion bars are well above

150

–

200 MPa. During the high-temperature anneal, the stresses

in the torsion bars are relieved by plastic deformation, but the

mirror plates are unaffected.

Two scanning-mirror designs that we fabricated and studied

are shown in Fig. 5 where they are designated as type I and II.

For type I AVCs, a torsion bar connects the mirror to comb

gers at the middle of the mirrors while in type II, the torsion bars

are off-centered from the mirror and all the comb

ngers are on

the other side of the torsion bar to balance the mass moment of

inertia with respect to the axis of rotation. The bigger size and

symmetry with respect to the rotation axis of the mirror in type I

design allows slight misalignment of incident light on the mirror

while the resonant frequency is lower due to the larger mass mo-

ment of inertia. In type II, more comb

ngers were involved for

larger actuation forces and faster scanning is expected compared

to type I. Table I provides design data for the type I and II de-

vices.

Fig. 6 shows all steps in our AVC fabrication process. We

start the fabrication process by de

ning the moving- and

xed-comb

ngers in the same device layer of an SOI substrate

[Fig. 6(a)

–

(c)]. During the DRIE step, not only the comb-drive

actuators, but also the key-slots, shown in Fig. 6(b) are formed.

A backside-etching step carried out underneath the mirrors and

combs removes suf

cient silicon to provide clearance for the

mirror motion. Alignment for this backside-etch step is not

critical; misalignments are tolerable as long as the backside

etch area is designed to provide enough clearance for the mirror

motion. In the next processing step, we make use of a second

chip processed by single step of DRIE that has been con

gured

with pillars to displace the comb structures to the desired tilt

angles. On this chip are protrusions (keys) that align to key-slots

in the comb-actuator chip when the two are brought together,

sandwich style, and placed into a furnace. The temperature

of the furnace is linearly increased by 15

C/min rate up to

900

C, and this temperature is maintained for 30 min inducing

plastic deformation of the torque-loaded torsion bars. The

furnace is then cooled down to room temperature in 1 h. The

whole annealing process is performed at nitrogen environment

to prevent unnecessary oxidation of the silicon surface. After

separation from the processing substrate, the comb pairs are

angled one to another as shown in Fig. 6(f). No critical align-

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 3, JUNE 2006

Fig. 6. Process

ow for plastically deformed vertical actuators. (a) Pattern

thermal-oxide layers on top and bottom surfaces of SOI wafer. (b) Etch device

and handle layers of SOI wafer using DRIE. (c) Remover thermal-oxide layers

and exposed buried oxide layer. (d) Create pillar structures on the lid wafer using

DRIE. (e) Place lid wafer on the device wafer and heat the stacked wafers to

900

in furnace. (f) Cool down and remove the lid wafer.

Fig. 7. SEM picture of AVC with scanning mirrors made using new process.

ment steps are necessary to carry out the process that we have

described. The comb-

nger pairs are self-aligned because they

are de

ned in a single masking step, and the device and lid

chips are precisely assembled by the lithographically de

ned

keys and key-slots. No damage in the pillars or processing

chips is observed indicating that these processing chips could

be used repeatedly.

Fig. 7 is an SEM microphotograph of batch-fabricated

micromirrors produced by our plastic-deformation process.

A close-up view of tilted comb

ngers is presented in Fig. 8,

showing the precisely aligned vertical-comb sets. Fig. 9 is a

close-up view of a plastically deformed torsion bar showing

Fig. 8.

Plastically tilted mirror and precisely aligned vertical combs. The

upper-left photo shows the top view of comb

ngers and the upper-right photo

is the close-up oblique view of the angular vertical combs.

Fig. 9.

Close-up view of plastically deformed torsion bar.

that the deformation appears to be uniform along the torsion

bar. We did not observe cracking in any of the torsion bars.

Fig. 10 shows pillars formed on the processing chip used to

deform the microactuators in Fig. 7.

The maximum initial tilt angle that can be formed by the

method of plastic deformation that we have described above

is limited by the fracture strength of the single-crystal silicon

at room temperature. For example, the torsion bar dimensions

presented in Table I easily allows 20

–

of elastic deformation

without fracture, and more than 90% of the angles can be turned

into plastically deformed initial tilt angle. These elastically de-

formed angles are determined both by the height of the pillars

on the processing chip and by the locations at which the pillars

push on the mirror (Fig. 11). Clearly, a given tilt angle can be

induced either by using a taller pillar and applying the force at

point P or by using a shorter pillar and applying the force at

point Q. Although the tilt angles are the same in these two cases

(as, therefore, are the torque values in the torsion bar), the forces

(and, hence, the stresses) in the torsion bars are not equal.

For the two cases described earlier, the corresponding forces

and

vary inversely with their moment arm distances

. These vertical forces are balanced by equal

forces in the torsion bar causing it to de

ect downward (as a

doubly supported beam loaded at its midpoint) which leads to

KIM

et al.

: MICROFABRICATED TORSIONAL ACTUATORS

557

Fig. 10. Micropillar structures fabricated on the lid wafer; the right side inset shows the close-up of a pillar.

Fig. 11.

Different forces applied on the mirror surface depending on the position and height of the pillar structure.

unwanted bending of the torsion bar or distortion in mirror sur-

faces. To reduce this undesirable effect, the pillars should load

the mirrors at the longest moment arm or, therefore, at the mirror

tips. In our type II design with 5.22

initial-angle de

ection, the

measured vertical de

ections of torsion bars after plastic defor-

mation using 50

m pillars were smaller than 0.3

Fig. 12(a) presents the three-dimensional (3-D) image gen-

erated by white light interferometric measurement (WYKO

NT3300). The measured radii-of-curvature of the mirrors using

WYKO were in the order of meters, which indicate there can

be only very little deformation or warpage induced in the

mirror plate after high temperature plastic deformation process.

Another concern is the probable scratches on the mirror sur-

faces when the pillar structures push down the mirrors. It was

impossible to point out the points-of-contact on the mirror

exactly since there were no observable scratches or damages

found under WYKO or SEM inspection. The surface roughness

of the mirror was also measured on the presumptive contact

positions of the pillar using an atomic force microscope (AFM)

as shown in Fig. 12(b). The average roughness was less than

4 nm for the measured positions, which is a typical value for

polished SOI wafer surface.

III. D

EVICE

HARACTERIZATION AND

ISCUSSION

As depicted in Fig. 3, silicon has a

nite modulus of elasticity

even at an elevated temperature at which the yield strength is

reduced. This means that plastic deformation does not com-

pletely relax the strain in the torsion bar and, therefore, there is

some elastic recovery upon removal of the load after cooldown.

This

“

springback

”

results in the mirror initial angular de

ec-

tions being smaller than the values set by the pillars on the

processing chips. We investigated springback by fabricating a

series of identically sized mirrors having different torsion-bar

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 3, JUNE 2006

Fig. 12.

Structure and surface inspection using white light interferometer and AFM. (a) 3-D image generated from WYKO measurement. (b) The surface ro

ughness

measurements of mirror surface on the presumptive contact positions of the pillar using AFM. The scanned area is 5



and the average surface roughness

is 2.7 nm.

dimensions on the 50-

m-thick single-crystal-silicon (100)

SOI device layer. An SEM photograph of this chip is shown

in Fig. 13. The dimensions of all the test mirrors were 50

600

1200

m, and each mirror was supported

by two identical torsion bars attached symmetrically on the

longer sides. The dimensions of torsion bars were picked from

stress calculation such that the test structure arrays include

different torsion bar groups with the elastically induced stresses

slightly smaller than

, slightly larger than

and well above

. After loading with the processing chips, the sandwiched

chips were heated above room temperature using the same

annealing schedule used for device chips and described earlier.

The test results in Fig. 14 show that elastic recovery depends

both on the torsion bar dimension and the amount of initial

elastic deformation. Each plotted data point is an averaged value

of eight measurements of identical test structures from four dif-

ferent batches of plastic deformation processes. The applied

elastic deformation is calculated from the pillar height and lo-

cation, and the plastically deformed angle was measured using

white light interferometer. In the

rst plot (a), the location of

m-height pillar to give elastic strain is varied from 100

to 350

m from the edge of the mirrors for the same dimen-

sion of 16

1000

m torsion bars. As depicted

in Fig. 11, the farther position of pillar from the edge gives

larger elastic deformation on the torsion bars. The scale on the

Fig. 13.

Test structures used to characterize springback; the

rst and second

of three arrays contain varied width and length of beams with identical angle

deformed elastically. For the third array, varied elastically deformed angle is

applied on each mirror to induce different stresses in torsion bars.

left-hand side of the

axis shows the rotation angles of the mir-

rors while that on the right hand side shows the percentages of

the amount of springback with respect to the applied elastic tilt

angles. For an elastic tilt angle smaller than 10

, larger strain

KIM

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: MICROFABRICATED TORSIONAL ACTUATORS

559

Fig. 14.

Applied initial deformation angle set by the pillar and measured plastically deformed angle depending on the torsion bar dimension. The set a

ngle is

calculated from the pillar height and the location of the pillar, and the plastically deformed angle is measured using white light interferometer. (a

) Location of pillar

to give elastic strain is varied from 100 to 350



m from the edge of the mirrors. (b) Width of torsion bars is varied from 6 to 26



m for the same length of 1000



and elastically deformed tilt angle applied. (c) Lengths of the torsion bars are varied from 500 to 1000



m for the same width of 16



m and elastically deformed

tilt angle applied. (d) Springback percentage values with respect to the initial deformation angle set by the pillar versus the shear stress induced i

n torsion bars is

plotted based on the measurements in (a), (b), and (c). The stress values are calculated from the set angle and torsion bar dimensions.

gives smaller springback/strain ratio. However, for the test struc-

tures with larger than 10

of elastic torsion, we have found that

elastic recovery saturates or even increases slightly. This means

the

ow stress

in Fig. 3 in fact increases for a larger shear

strain from torsion, and other researchers observed similar test

results for a tensile test [11] and a bending test [16] of single

crystalline silicon. Similarly, Fig. 14(b) is plotted with respect

to the width change of torsion bars from 6

mto26

m for

the same length of 1000

m and elastically deformed tilt angle

applied. The elastic recovery for 6

m bar is larger than 95%

of applied elastic torsion since the largest stress induced on this

thin bar is just as large as the yield stress at high temperature.

As the width increases, the amount of elastic recovery decreases

and approaches to about 8% of given elastic deformation since

the maximum shear stress in the torsion bar also increases. We

also plotted applied elastic deformation, plastic deformation,

and percentages of springback against different lengths of the

bars in Fig. 14(c). Here the lengths of the torsion bars (width

of 16

m) vary from 500 to 1000

m, and as we expected, the

amount of springback is larger for longer bars on which smaller

stresses are induced.

To extend the usage of the measurement data to general cases,

springback percentages are plotted in Fig. 14(d) in terms of

maximum shear stresses induced in the torsion bars from the

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 3, JUNE 2006

Fig. 15.

Standard deviation of plastically formed tilting angles for the tested

mirrors in Fig. 14. The angles are measured using white light interferometer

with the vertical resolution of sub nanometer.

applied elastic deformation. The exact form of the torsion bar

stiffness and stress with uniform rectangular cross section are

represented as a summation of in

nite series of terms. How-

ever, good approximation of the torsional stiffness and max-

imum shear stress of a torsion bar can be written as [17]

(1)

(2)

where

Fig. 14(d) is generated from the data plotted in (a)

–

(1) and (2). Again, it is obvious that the springback effect is

signi

cant at lower stress level and converges to a

nite value.

These

gures provide design guidelines for the plastically

deformed AVC actuators, especially for achieving speci

plastically deformed tilt angles.

Standard deviations of the plastically deformed tilt angles

with respect to the average values are plotted in Fig. 15. The

angles were measured on the structures used for the plots

in Fig. 13. The typical standard deviation is in the range of

0.08

–

0.19

. There seems to be no correlation between the

tilt angle and the uniformity. Possible sources of deviation

are: particles entrapped between the device substrate and lid

substrate, or the tolerance for self-alignment between the

depressions on the device substrate and the protrusions on the

lid substrate. The maximum tolerance used in our process is

m, and the uniformity can be improved by mating the

lid and device substrates with more tight tolerances and in a

cleaner environment.

Fig. 16.

Frequency response of the type II microactuator.

IV. E

XPERIMENTAL

ESULTS AND

ELIABILITY

The measured frequency response of the type II actuator with

the initial tilt angle of 5.22

is presented in Fig. 16. The mirror,

whose dimensions were 1000

1000

m, was driven with

and

. The maximum scanning angle of 19.2

achieved at the resonant frequency of 2953 Hz. The quality

factor measured in air is 120. For the type I actuator with the

initial tilt angle of 3.75

, 24.8

of optical scanning angle was

measured at the resonant frequency of 2499 Hz and with the 45

and 20

driving voltage. For both designs, the moving

and

xed combs were 50

m thick.

The plastically deformed angular vertical comb actuator has

proven to operate very reliably and stably. Its design is simple,

and its fabrication is straightforward. To test long-term relia-

bility, we resonated type II scanner at full amplitude for 5.1 bil-

lion cycles, using the same driving voltages used to measure

the frequency response in Fig. 16. For this test, the mirror ac-

tuator was set to be operated at its resonance frequency with a

1-mW helium-neon laser beam directing at the mirror surface

and re

ected on a distal screen 135 cm away from the actu-

ator to measure the scanning angle constancy over the long pe-

riod of time. In Fig. 17 the changes in resonant frequency and

scanning angle were measured at every 255 million cycles that

corresponds to 24 h of operation. The maximum variations of

resonant frequency and scanning angle were 0.064% and 3.6%,

respectively. The error bars on the frequency curve are shown

because the change of the amplitude of the re

ected laser pat-

tern on the screen was undetectable to 0.2 Hz variation of the

operational frequency.

This experiment was performed with a mirror actuator un-

packaged and in the lab. It is not obvious if this variation is

from the degradation of the device or from other possible ef-

fects such as temperature variation, particle-contaminations or

variation in humidity. However, considering that the amount of

angle and frequency variation is very small and the actuator was

not packaged, the scanning mirror actuators made by plastic de-

formation method are robust and reliable.

KIM

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: MICROFABRICATED TORSIONAL ACTUATORS

561

Fig. 17.

Measured scanning angle and resonant frequency of the microactuator

over 5 billion cycles; the gap between each data point is 255 million cycles (1 d).

V. C

ONCLUSION

We have presented a straightforward batch process to fabri-

cate angular vertical comb-drive actuators in single-crystal sil-

icon using SOI chips. A separately processed chip is used to

apply torque to the torsion bars which are plastically deformed

at an anneal temperature of 900

C. We have studied actua-

tors formed by this method using scanning mirrors. The fabri-

cation and characterization of angular vertical combs for scan-

ning-mirror applications have been accomplished and the mea-

sured dynamic performance of the actuator was comparable to

or superior to that reported in earlier vertical-comb actuators.

Elastic recovery of the torsion bars that follows plastic defor-

mation process was quantitatively characterized for a variety of

torsion bar dimensions. We believe this can be guidelines for

the design of plastically deformed AVC actuators, especially for

achieving speci

c plastically deformed tilt angles.

A reliability test on an unpackaged mirror actuated through

more than

ve billion cycles of operation showed less than

0.064% decrease in the resonant frequency. The actuators have

many other potential applications where vertically driven linear

or torsional motions are required as well as the MEMS scanning

mirrors presented in this paper.

EFERENCES

[1] R. A. Conant, P. M. Hagelin, U. Krishnamoorthy, M. Hart, O. Solgaard,

K. Y. Lau, and R. S. Muller,

“

A raster-scanning full-motion video display

using polysilicon micromachined mirrors,

”

Sens. Actuators

, vol. A83,

no. 1

–

3, pp. 291

–

296.

[2] V. Milanovic, M. Last, and K. S. J. Pister, Torsional Micromirrors with

Lateral Actuators, Munich, Germany, pp. 1290

–

1301. Transducers 01.

[3] D. Hah, S. Huang, H. Nguyen, H. Chang, J.-C. Tsai, M. C. Wu, and

H. Toshiyoshi,

“

Low voltage MEMS analog micromirror arrays with

hidden vertical comb-drive actuators,

”

2002 Solid-State Sens., Actu-

ator and Microsystems Workshop

, pp. 11

–

14.

[4] J. A. Yeh, H. Jiang, and N. C. Tien,

“

Integrated polysilicon and DRIE

bulk silicon micromachining for an electrostatic torsional actuator,

”

Microelectromech. Syst.

, vol. 8, no. 4, pp. 456

–

465, Dec. 1999.

[5] R. A. Conant, J. T. Nee, K. Lau, and R. S. Mueller,

“

Flat high-frequency

scanning micromirror,

”

2000 Solid-State Sensor and Actuator Work-

shop

, Hilton Head, SC, pp. 6

–

[6] U. Krisnamoorthy and O. Solgaard,

“

Self-aligned vertical comdrive

actuators for optical scanning micromirrors,

”

2001 Int. Conf. Opt.

MEMS

, p. 41.

[7] H. Xie, Y. Pan, and G. K. Fedder,

“

A CMOS-MEMS micromirror with

large out-of-plane actuation,

”

2001 ASME Int. Mech. Eng. Congr.

Expo.

, vol. 3, pp. 89

–

92.

[8] P. R. Patterson, D. Hah, H. Nguyen, H. Toshiyoshi, R.-M. Chao, and M.

C. Wu,

“

A scanning micromirror with angular comb drive actuation,

”

Tech. Dig. MEMS 2002 IEEE Int. Conf.

, pp. 544

–

547, 2002.

[9] K. Isamoto, T. Makino, K. Kato, A. Morosawa, C. Chong, H. Fujita, and

H. Toshiyoshi,

“

A two-mask process for self-assembled vertical comb

drive mirrors,

”

IEEE/LEOS Int. Conf. Opt. MEMS and Their Applicat.

2004, pp. 172

–

173.

[10] J. Kim, D. Christensen, and L. Lin,

“

Selective stiction based vertical

comb actuators,

”

Tech. Dig. MEMS 2005 IEEE Int. Conf. Micro

Electro Mech. Syst.

, 2005, pp. 403

–

406.

[11] J. R. Patel and A. R. Chaudhuri,

“

Macroscopic plastic properties of

dislocation-free germanium and other semiconductor crystals,

”

J. Appl.

Phys.

, vol. 34, no. 9, pp. 2788

–

2799, 1963.

[12] M. M. Farooqui and A. G. R. Evans,

“

Polysilicon microstructures,

”

Proc. IEEE Micro Electro Mech. Syst.

, 1991, pp. 187

–

191.

[13] M. A. Huff, A. D. Nikolich, and M. A. Schmidt,

“

A threshold pressure

switch utilizing plastic deformation of silicon,

”

Transducers’91 Int.

Conf. Solid-State Sens. Actuators

, 1991, pp. 177

–

180.

[14] Y. Fukuta, D. Collard, T. Akiyama, E. H. Yang, and H. Fujita,

“

Microac-

tuated self-assembling of 3D polysilicon structures with reshaping tech-

nology,

”

Proc. IEEE. 10th Ann. Int. Workshop on Micro Electro Mech.

Syst.

, 1997, pp. 477

–

481.

[15] E. Gartner, J. Fruhauf, B. Hannemann, and E. Jansch,

“

Mounting of

Si-chips with plastically bent cantilevers,

”

Transducers’01 Eurosen-

sors XV. 11th Int. Conf. Solid-State Sens. Actuators

, vol. 1, 2001, pp.

206

–

209.

[16] J. Fruhauf, E. Gartner, and E. Jansch,

“

New aspects of the plastic

deformation of silicon

—

prerequisites for the reshaping of silicon

microelements,

”

Appl. Phys. A (Mater. Sci. Process.)

, vol. A68, no. 6,

pp. 673

–

679, 1999.

[17] W. C. Young and R. G. Budinas,

Roark’s Formulas for Stress and

Strain

New York: McGraw-Hill, 2002.

Jongbaeg Kim

received the B.S. degree in me-

chanical engineering from Yonsei University, Seoul,

Korea, in 1997, the M.S. degree in mechanical

engineering from the University of Texas, Austin,

TX, in 1999, and the Ph.D. degree in mechanical

engineering from the University of California,

Berkeley, in 2004.

He was with DiCon Fiberoptics, Inc., Richmond,

CA, from 2004 to 2005, where he designed and devel-

oped high-performance microactuators for telecom-

munication applications. He then joined the Yonsei

University, where he is currently an Assistant Professor with the School of Me-

chanical Engineering. His research interests are mechatronic system dynamics,

modeling, design and fabrication of MEMS, and nanotechnology.

Hyuck Choo

received the B.S. and M. Eng. degrees

in 1996 and 1997, respectively, in electrical engi-

neering from Cornell University, Ithaca, NY.

He is currently pursuing the Ph.D. degree in elec-

trical engineering and computer sciences at the Uni-

versity of California, Berkeley (UC Berkeley), under

Prof. R. S. Muller

’

s supervision. Before joining UC

Berkeley, he was with Kionix, Inc., Ithaca, NY, as a

MEMS test engineer. His current research interests

are microlens and microscanner systems and their ap-

plications to ocular refractive surgeries, biomedical

imaging systems, high-de

nition displays, and next-generation wavefront sen-

sors. He has two nonprovisional U.S. and international patents (in application)

on his microlens and microscanner systems. He

Mr. Choo won the UC Berkeley EECS Lim Prize in 2001 (Best Performance

on the Pre-Doctoral Exam) and is the two-time winner of the Berkeley Sensor

and Actuator Center presentation award.