Transcript
Page 1: A 2-DOF Circular-Resonator-Driven In-Plane Vibratory Grating … · a two-degree-of-freedom (2-DOF) comb-driven circular resonator for high-speed laser scanning applications. Diffraction

892 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

A 2-DOF Circular-Resonator-Driven In-PlaneVibratory Grating Laser Scanner

Yu Du, Guangya Zhou, Koon Lin Cheo, Qingxin Zhang, Hanhua Feng, and Fook Siong Chau

Abstract—In this paper, we present the design, modeling, fabri-cation, and measurement results of a microelectromechanical sys-tems (MEMS)-based in-plane vibratory grating scanner driven bya two-degree-of-freedom (2-DOF) comb-driven circular resonatorfor high-speed laser scanning applications. Diffraction gratingdriven by a 2-DOF circular resonator has the potential to scanat large amplitudes compared with those driven by a one-degree-of-freedom (1-DOF) comb-driven circular resonator or a 2-DOFelectrical comb-driven lateral-to-rotational resonator. We havedemonstrated that our prototype device, with a 1-mm-diameterdiffraction grating is capable of scanning at 20.289 kHz with anoptical scan angle of around 25◦. A refined theoretical model withfewer assumptions is proposed, which can make the prediction ofdynamic performance much more accurate. [2009-0017]

Index Terms—Diffraction grating, micro-opto-electro-mechanical systems, microresonators, microscanners.

I. INTRODUCTION

H IGH-SPEED laser scanning technology has numerousapplications, such as raster scanning for automotive head-

up displays, head-worn displays [1]–[4], and other wearabledisplays for personal electronic devices or mobile computing.Currently, microelectromechanical systems (MEMS)-based mi-crolaser scanners, particularly for micromirror scanners [5],[6], which utilize out-of-plane deflection to cause the laserbeam to scan, were mostly developed due to their outstandingadvantages compared with macrolaser scanners, such as havinga low mass, a high scanning frequency, low power consumption,and a potentially low unit cost. However, due to the nature of themicrofabrication process, the mirror plate is usually very thin.This brings about significant aberration to the optical systemduring high-speed scanning because of the dynamic nonrigidbody deformation of the mirror plate under out-of-plane accel-eration forces. Instead of using out-of-plane deflection, MEMS-based in-plane vibratory grating scanners [9]–[11] utilizein-plane rotation of a diffraction grating to cause the laser beamto scan. Since the nonrigid body deformation of a thin plateunder in-plane excitation is much smaller than that under out-

Manuscript received January 20, 2009; revised May 5, 2009. First publishedJune 23, 2009; current version published July 31, 2009. This work wassupported by the Ministry of Education Singapore AcRF Tier 1 funding underGrant R-265-000-211-112/133. Subject Editor S. Merlo.

Y. Du is with the National University of Singapore, Singapore 117576 andInstitute of Microelectronics, A*STAR (Agency for Science, Technology andResearch), Singapore 117685.

G. Zhou, K. L. Cheo, and F. S. Chau are with the National University ofSingapore, Singapore 117576 (e-mail: [email protected]).

Q. Zhang and H. Feng are with the Institute of Microelectronics, A*STAR(Agency for Science, Technology and Research), Singapore 117685.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2009.2023844

Fig. 1. Operation principle of a MEMS vibratory grating scanner.

of-plane excitation, MEMS in-plane vibratory grating scannerhas the potential to scan at high frequencies with little opticaldegradation.

Fig. 1 shows the operation principle of the vibratory gratingscanner. The diffraction grating lies in the XOY plane andthe grating lines orientated parallel to the X-axis. The diffrac-tion grating is illuminated by an incident laser beam, whichlies in the Y OZ plane, with an incident angle of θi. Whenthe diffraction grating rotates about the Z-axis in the XOYplane, the diffraction beam (except the zeroth-order beam) willscan accordingly. Bow-free scanning trajectory can be achievedwhen the incident angle, grating period, diffraction orders, andwavelength of incident laser beam obeys the bow-free scanningconditions [10]. High-diffraction efficiency of more than 75%can be achieved when a transverse magnetic (TM)-polarizedlaser beam is utilized [11].

Since diffraction grating is a dispersive optical element, agrating scanner with a single grating is only suitable for nar-rowband laser scanning applications, e.g., monochromatic laserscanning displays. However, by configuring multiple diffractiongrating elements on a common platform, a vibratory gratingscanner can also be used in multiwavelength collinear scanningapplications [10], such as color displays. In addition, the opticalefficiency of each wavelength can be optimized by optimizingthe corresponding grating profile, which can be realized byusing multistep lithography and an etching process.

In our previous work, high-speed high-optical-efficiencybow-free laser scanning without dynamic deformation has been

1057-7157/$26.00 © 2009 IEEE

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DU et al.: 2-DOF CIRCULAR-RESONATOR-DRIVEN IN-PLANE VIBRATORY GRATING LASER SCANNER 893

Fig. 2. Different driving schemes for grating platform’s in-plane rotation. (a) 1-DOF comb-driven circular resonator. (b) 2-DOF electrical comb-driven lateral-to-rotational resonator. (c) 2-DOF electrical comb-driven lateral-to-rotational resonator with extra support suspensions. (d) 2-DOF electrical comb-driven circularresonator.

successfully demonstrated with the prototype devices fabri-cated using silicon-on-insulator (SOI) micromachining tech-nology [11]. The optical scan angle of the previous prototypedevice is limited by the maximum allowable deformation of theflexural beams due to their excessive internal stress. To furtherenhance the optical scanning angle, a new structure design withlower maximum internal stress in the flexural beams is required.

In this paper, we demonstrate the design, modeling, fabri-cation, and experimental results of an improved MEMS vibra-tory grating scanner driven by a novel two-degree-of-freedom(2-DOF) electrical comb-driven circular resonator, which has amuch better optical performance. The prototype device with a1-mm-diameter diffraction grating can achieve an optical scanangle of around 25◦ for a 632.8-nm-wavelength laser beam atits resonant frequency of 20.289 kHz.

II. 2-DOF ELECTRICAL COMB-DRIVEN

CIRCULAR RESONATOR

Microcomponents in a MEMS device can be actuated bymicroactuators either directly or indirectly [7], [8]. High-speedin-plane rotational vibration of a micromachined diffractiongrating can be realized by a one-degree-of-freedom (1-DOF)electrostatic comb-driven circular resonator, which is illustratedin Fig. 2(a). However, under this direct actuation scheme, thein-plane rotational range of the grating platform is determinedby the travel range of the comb-driven circular actuator, whichis limited due to the pull-in of comb fingers. This design willinevitably lead to a small scanning angle when the diameter ofthe grating platform is large. However, in many optical scanningapplications, a larger beam size is always preferred to achievehigher optical resolution.

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894 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

Fig. 3. FE simulation results of the maximum internal stress versus thenumber of main flexural beams when the grating platform’s rotational an-gle is 8◦.

To overcome this problem, an improved driving mecha-nism using an indirect actuation method that utilizes a 2-DOFelectrical comb-driven lateral-to-rotational resonator [shown inFig. 2(b) and (c)] was reported in our previous work [9]–[11].Under this indirect actuation scheme, the rotational motionof the grating platform is excited by the symmetric linearmotions of several electrostatic comb-driven microactuatorsthrough several flexural beams. The rotational range of thegrating platform is no longer determined by the travel rangeof microactuators but only by the mode shape design andmaximum allowable deformation of the flexural suspensionbeams, which is the deformation when the internal maximumstress reaches their rupture stress. Without changing the totalstiffness, hence, maintaining the same resonant frequency, theinternal maximum stress can be reduced by reducing the widthof each flexural beam and increasing the total number of sus-pension beams, which has been proved by finite element (FE)simulations [type of analysis: static stress analysis; elementtype: C3D8R; number of elements: 19 128; degrees of freedom(DOFs): 6] using the commercial software package ABAQUS.The simulation results are shown in Fig. 3. However, due tolimited space, the number of flexural suspensions is typicallylimited, even if extra supporting springs are added [shown inFig. 2(c)]. Consequently, the rotational range of the grating plat-form still cannot be very large. In addition, due to uncertaintiesand imperfections of the microfabrication process, the resonantfrequency of each microresonator is typically different, whichcan cause variation of the diffraction grating’s rotational centerand marked performance deviations from the original design.Although this problem can be solved by adding feedbackcontrol to each individual microresonator, the complexity of thesystem will increase significantly.

To further increase the rotational range of the grating plat-form, a novel driving mechanism that utilizes a 2-DOF elec-trical comb-driven circular resonator is proposed, as shown inFig. 2(d). Under this driving scheme, the rotational motion ofthe grating platform is excited by the outer comb-driven circularresonator’s rotation and is not determined by the maximum dis-

Fig. 4. Schematic of the micromachined 2-DOF electrical comb-drivencircular-resonator-driven in-plane vibratory grating scanner.

placement of the actuator but by the mode shape design and themaximum allowable deformation of the main flexural beams.Significantly, the internal maximum stress in each beam canbe much lower because increasing the number of main flexuralbeams for this driving method is feasible, resulting in furtherincreased rotational range of the grating platform. Furthermore,since only one microresonator rather than previously severalsymmetrically configured microresonators is adopted, it willnot encounter any resonant frequency mismatch problem due touncertainties and imperfections in the microfabrication process.

III. SCANNER DESIGN AND MODELING

The schematic of the micromachined 2-DOF electricalcomb-driven circular-resonator-driven in-plane vibratory grat-ing scanner is illustrated in Fig. 4, where we can see that theround platform with the diffraction grating is connected to theouter comb-driven circular resonator through 16 single-beamflexures, and each of them has two pairs of perpendicularlyconnected stress alleviation beams, which are used to reduceits axial stress during large deformation [11], [12]. Among the16 single-beam suspensions, eight of them are designed to belonger than the others to save space. The outer comb-drivencircular resonator is suspended by symmetrically configuredcircular folded beam suspensions and is driven by electrostaticcomb-driven circular actuators.

A. Modeling of the Main Flexural Beams

We take advantage of the stiffness matrix [13] of a singlebeam to obtain the model of the main flexural beams. Themodel of a main flexural beam and its corresponding localvariables are shown in Fig. 5. In this model, when an externaltorque τ0 is applied, the grating platform will rotate θ. Thespring constant of one main flexural beam can be expressed asthe ratio of τ0 to θ.

The beam is assumed to have small deformations so that theaxial deformation is ignored and the stress alleviation springsare not considered at the moment. The relationship between the

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Fig. 5. Model of the main flexural beam and its corresponding local variables.

local variables of force (F1, τ1, F2, and τ2) and displacement(ν1, α1, ν2, and α2) for a single beam can be expressed as⎡

⎢⎣F1

τ1

F2

τ2

⎤⎥⎦ =

EI

L3

⎡⎢⎣

12 6L −12 6L6L 4L2 −6L 2L2

−12 −6L 12 −6L6L 2L2 −6L 4L2

⎤⎥⎦

⎡⎢⎣

v1

α1

v2

α2

⎤⎥⎦ (1)

where L is the beam length, I is the area moment of inertia ofthe beam, and E is the Young’s modulus of the material.

By applying the boundary condition shown in Fig. 5 into (1),we can obtain⎡

⎢⎣F1

τ1

F2

τ2

⎤⎥⎦ =

EI

L3

⎡⎢⎣

12 6L −12 6L6L 4L2 −6L 2L2

−12 −6L 12 −6L6L 2L2 −6L 4L2

⎤⎥⎦

⎡⎢⎣

00

−R0θθ

⎤⎥⎦ (2)

where R0 is the radius of the grating platform.Because the grating platform is in rotational equilibrium

(shown in Fig. 5), the external torque τ0 can be expressed as

τ0 = τ2 − F2R0. (3)

From (2) and (3), we can obtain

τ0 =EI

L3

(12R2

0 + 12R0L + 4L2)θ. (4)

The spring constant for one main flexural beam is

kc =EI

L3

(12R2

0 + 12R0L + 4L2). (5)

Since two types of the main flexural beams are adopted, thespring constant for each type, which is expressed as kci, isshown in the following:

kci =EIi

L3i

(12R2

0 + 12R0Li + 4L2i

), i = 1, 2. (6)

Therefore, the total spring constant of the main flexuralbeams, which is expressed as Kc, is given as follows:

Kc = n1kc1 + n2kc2 (7)

where n1 and n2 are the numbers of each type of the mainflexural beams.

Fig. 6. Schematics of the lateral folded beam suspension and the circularfolded beam suspension.

Fig. 7. Model of one set of circular folded beam suspension.

B. Modeling of the Suspensions for a Circular Resonator

In this design, we use the circular folded beams as thesuspensions of the outer circular resonator. Fig. 6 shows theschematics of the lateral folded beam suspension and the circu-lar folded beam suspension. In Fig. 6, we can see that similar tothe lateral folded beam suspension, one set of circular foldedbeam suspension is composed of four identical single-beamflexures with one end connected to each other through a rigidtruss structure. Two of them are connected to the movablestructure, and the other two are connected to the fixed boundary.However, the axial lines of the four beams are no longer parallelto each other but are coincident with the rotation center, and therigid truss structure is also changed from a rectangular shape toa sector-annular shape.

Fig. 7 shows the model of one set of circular folded beamsuspension. In Fig. 7, we can see that beams 1, 2, 3, and 4are connected in series, respectively, and the two sets of theserially connected beams are then connected in parallel. Sincethe dimensions of the four beams are same, the rotationalspring constant of one set of circular folded beam suspension

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896 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

Fig. 8. Schematics of the simplified 2-DOF undamped vibration systems.

is equivalent to that of one single beam. According to (5), wecan obtain

kf =EIf

L3f

(12R2

1 + 12R1Lf + 4L2f

)(8)

where Lf and If are the length and area moment of inertia ofthe beam in circular folded beam suspension, respectively.

If the number of the circular folded beam suspension isnf , the total spring constant of the suspensions of the circularresonator, which is expressed as Kf , is given as follows:

Kf = nf · kf . (9)

C. Simplified Model of the Scanner

As shown in Fig. 8, the scanner can be simplified to a 2-DOFspring-mass vibration system. All the connection suspensionsare considered as ideal springs whose weights are ignored.

The total kinetic and potential energy of the system duringvibration, which are expressed as Ek and Ep, respectively, areshown in the following:

Ek =12J0θ

20 +

12J1θ

21 (10)

Ep =12Kfθ2

1 +12Kc(θ0 − θ1)2 (11)

where J0 and J1 are the moment of inertias of the gratingplatform and outer circular resonator, respectively, and R1 isthe radius of the connection part where the circular folded beamsuspension connected to.

Then, the linear model of the system is obtained by applyingthe Euler–Lagrange formulation [13][

J0 00 J1

] [θ0

θ1

]+

[Kc −Kc

−Kc Kf + Kc

] [θ0

θ1

]= 0. (12)

Through (12), we can obtain the natural frequencies andmode shapes, which can be defined as the ratio of the rotationalangle of the grating platform and the outer driving circularresonator, for both the first and second vibratory modes. Thesecan be used to get a preliminary estimation of the vibrationcharacteristics of the system.

To ensure enough beam size of the scanned light, weattempted a design to have a 1-mm-diameter grating plat-form. The suspension flexural beams were designed to achieve

TABLE IMATERIAL PROPERTIES USED IN THE CALCULATION

TABLE IISUMMARY OF THEORETICAL AND SIMULATION RESULTS

enough scanning frequency and appropriate mode shapes. Six-teen main flexural beams were adopted, where eight beamsare 15 μm wide and 1050 μm long and the rest are 18 μmwide and 1400 μm long. Two pairs of beams with a width of7 μm and a length of 410 μm were perpendicularly connectedto each main flexural beam. The outer circular resonator issuspended by 40 sets of circular folded beam suspensionswith beams of width 18 μm and length 405 μm. There are264 movable circular fingers for one side driving with fingerwidth 7 μm, finger gap 4 μm, and initial finger overlap angle 1◦.The thickness of all the structures is 80 μm. The materialproperties of the single crystal silicon used in this model areshown in Table I. The calculated natural frequencies and modeshapes for the proposed prototype grating scanner using thesimplified dynamic model are compiled in Table II.

D. Weight Influence of the Suspension Beams

A simplified model has been obtained in Section III-B, withan assumption that the mass of all the suspension springsis ignored. However, a more rigorous model considering theeffects of the mass of the suspension springs, stress alleviationbeams, and fabrication imperfections is necessary to obtain amore accurate estimation. The mass of the main flexural beamsand beams of the circular folded beam suspensions will beincluded into the dynamic model in this section.

Fig. 9 shows the model of a deformed single-beam suspen-sion. This model essentially considers the deformation profileof the beam suspension due to the rotation of both the grating

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DU et al.: 2-DOF CIRCULAR-RESONATOR-DRIVEN IN-PLANE VIBRATORY GRATING LASER SCANNER 897

Fig. 9. Model of a deformed single beam suspension.

platform and the outer circular resonator. The deflection profileof a main flexural beam is approximated by a third-orderpolynomial expression that satisfies the boundary conditionsgiven in the following, where all the angles are assumed to bevery small⎧⎪⎨

⎪⎩f(0) = R0 sin θ0 ≈ R0θ0

f(L) = (R0 + L) sin θ1 ≈ (R0 + L)θ1

f ′(0) = tan θ0 ≈ θ0

f ′(L) = tan θ1 ≈ θ1.

(13)

The function of θ0 and θ1 of the resulting deformed profile is

f(u) =(

2R0 + L

L3u3 − 3R0 + 2L

L2u2 + u + R0

)θ0

+(

3R0 + 2L

L2u2 − 2R0 + L

L3u3

)θ1. (14)

The additional kinetic energy for the main flexural beamΔEkc can be computed by

ΔEkc =

L∫0

12f2(u)dm =

12ρSiWT

L∫0

f2(u)du. (15)

The resulting additional kinetic energy for two types of mainflexural beams, which is expressed as ΔEkci, is shown in thefollowing:

ΔEkci =12ρSiWiTLi

×[ (

1335

R20 +

11105

R0Li +1

105L2

i

)θ20

+(

1335

R20 +

67105

R0Li +29105

L2i

)θ21

+(

970

R20 +

970

R0Li +142

L2i

)θ0θ1

],

i = 1, 2 (16)

where ρSi is the density of silicon.Using (16), we can directly obtain the additional kinetic

energy for the beams in the circular folded beam suspen-sion, which is expressed as ΔEkf , by applying correspondingboundary conditions

ΔEkf =12ρSiWfTLf

(8770

R21 +

4142

R1Lf +67210

L2f

)θ21.

(17)

Fig. 10. FE simulation results without stress alleviation beams showing (a) thefirst resonating vibration mode and (b) the second resonating vibration mode.

Therefore, the modified kinetic energy of the whole system,which is expressed as ΔEk, is then

ΔEk = Ek + n1ΔEkc1 + n2ΔEkc2 + nfΔEkf . (18)

By applying the Lagrange formulation again, where only thekinetic component changed, we can obtain the linear model ofthe system to be[

J0 + ΔJ0 ΔJc

ΔJc J1 + ΔJ1

] [θ0

θ1

]

+[

Kc −Kc

−Kc Kf + Kc

] [θ0

θ1

]= 0 (19)

where

ΔJ0 = ρSiT

2∑i=1

niWiLi

(1335

R20 +

11105

R0Li +1

105L2

i

)

ΔJc = ρSiT

2∑i=1

niWiLi

(970

R20 +

970

R0Li +142

L2i

)

ΔJ1 = ρSiT

2∑i=1

niWiLi

(1335

R20 +

67105

R0Li +29105

L2i

)

+ ρSinfWfLfT

(8770

R21 +

4142

R1Lf +67210

L2f

).

If we ignore the mass of the main flexural beams, the gratingplatform’s moment of inertia estimation error can be calculatedby ε = ΔJ0/(J0 + ΔJ0) × 100%, and the calculation resultsshow that when the number of the main flexural beams increase

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898 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

Fig. 11. (a) Effect of the stress alleviation beams. (b), (c) FE simulated torque–angle curves for the two types of main flexural beams.

from 4 to 40, the moment of inertia estimation error increasesfrom 18.4% to 51.1%, which will introduce a significant errorto the natural frequency and mode shape analysis.

FE simulations (type of analysis: natural frequency extrac-tion; element type: C3D8R; number of elements: 109 296;DOFs: 6) investigating the natural frequencies and mode shapesof the system were conducted to verify whether the approxi-mations were reasonable using ABAQUS. Fig. 10 shows theFE simulation results. The results obtained from the simplifiedmodel [see (12)], modified model considering the mass of thesuspensions [see (19)], and FE simulation were compared inTable II.

As shown in Table II, the model considering the mass of thebeams shows much better approximation of natural frequenciesand mode shapes. Generally, the mass of the main flexuralbeams and beams in circular folded beam suspensions willreduce the effective frequencies in the device as expected. In

addition to a significant increase in the mode shape for thefirst resonating mode and a decrease in the second mode, thereis a significant frequency drop for the first resonating modecompared to the second mode. The reason is that the momentof inertia of the grating platform is much smaller than the outercircular resonator, ignoring the mass of the suspension beamshas a greater influence on the frequency of the grating platform.

E. Influence of the Stress Alleviation Beams

The stress alleviation beams were transversely connected tothe main flexural beam at the junction point to help reducethe nonlinearity of the device during operation. Ideally, onlytranslational motion of the junction point along the axial direc-tion of the main flexural beam is allowed to release its axialstress, and the rotation of the junction point is not allowedso that the bottom boundary condition of the main flexural

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Fig. 12. FE simulation results with stress alleviation beams showing (a) thefirst resonating vibration mode and (b) the second resonating vibration mode.

beam will not change. Therefore, adding a set of ideal stressalleviation beams has little influence on the linear harmonicanalysis. However, the actual stress release springs cannot fullyavoid the rotational motion of the junction point, hence, therotational spring constant was reduced due to the small tiltingangle at the anchor location, as shown in Fig. 11(a).

FE simulations (type of analysis: static stress analysis; el-ement type: C3D8R; number of elements: 19 128; DOFs: 6)considering the geometric nonlinearity using ABAQUS weredone to show that the linearity of the torque–angle relationshipis greatly improved when the stress alleviation beams wereadded [see Fig. 12(b) and (c)]. More importantly, the linearanalysis of the torque–angle relationships with and without thestress alleviation beams shows the reduction of the rotationalspring constant that we have to account for.

Define δ1 and δ2 as the reduction ratio of the rotational springconstant of two types of the main flexural beams, respectively,which can be directly obtained from the FE simulation results.We can then obtain the refined model considering the springconstant reduction as[

J0 + ΔJ0 ΔJc

ΔJc J1 + ΔJ1

] [θ0

θ1

]

+[

Kc −Kc

−Kc Kf + Kc

] [θ0

θ1

]= 0 (20)

where Kc = n1kc1δ1 + n2kc2δ2.FE simulations (type of analysis: natural frequency extrac-

tion; element type: C3D8R; number of elements: 182 844;DOFs: 6) investigating the natural frequencies and mode shapesof the system were again done to verify the overall effectson the system using ABAQUS. Fig. 12 shows the simulationresults. The predicted natural frequencies and mode shapes

TABLE IIISUMMARY OF THEORETICAL AND SIMULATION RESULTS

WITH STRESS ALLEVIATION BEAMS

obtained from the model considering the mass of the beams[see (19)], the model considering the mass of the beams as wellas the influence of stress alleviation beams [see (20)], and FEsimulation were compared in Table III.

In Table III, we can see the similar effect of the stress alle-viation beams and the mass of the beams in all the suspensionsin Section III-D: both change the mode shapes and reduce thenatural frequencies. However, the effective spring constant ofthe vibration structures was reduced instead of increasing itsmoment of inertia in Section III-D. The effects for the modeshapes are equally significant for both the first and secondresonating modes. In Table III, we can see that the theoreticalmodel considering both the mass of the beams and the effect ofthe stress alleviation beams shows closer agreement to the FEsimulation results.

F. Influence of Fabrication Imperfections

Fabrication imperfection is another very important issue thatwe need to address in the rigorous model. The imperfections[15] in the plasma etching process (such as etching slope,undercut, and notching effect) will change the dimensions andarea moment of the beams. This can induce a significant changein the stiffness of the suspension beams and finally bring asignificant error to the predictions of the natural frequencyand mode shape. Fig. 13 shows a cross-sectional profile modelof the beam after a deep reactive ion etching (DRIE) processand its corresponding SEM image obtained from the previousprocess.

The etching undercut ΔW1 and the sidewall etching slop αhave been included in this cross-sectional model. In addition,

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900 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

Fig. 13. Cross-sectional profile model of the beam after a DRIE process and its corresponding SEM image.

TABLE IVSUMMARY OF THEORETICAL RESULTS USING DIFFERENT MODELS

this cross-sectional model attempts to account for the notchingeffect, which is expressed by the thickness Tn and sidewallslope αn of the notching area. Since the trenches of everysuspension beams are the same, the parameters in the modelcan be directly obtained or calculated by using the measuredwidth of the trench at different positions. As shown in the SEMimage in Fig. 13, we measure the width of the trench at its top,bottom, and upper boundaries as well as the thickness of thenotching area. Therefore, we can obtain

Wi = W − 2ΔWi, i = 1, 2, 3 (21)

where Wi is the beam width at different positions shown inFig. 13.

The etching slope and sidewall slope of the notching area canbe calculated as ⎧⎨

⎩α = arctg

(T−Tn

ΔW2−ΔW1

)αn = arctg

(Tn

ΔW3−ΔW2

).

(22)

Then, the actual beam width W (u) can be expressed as afunction of beam thickness, i.e.,{

W (u) = W3 + 2u · ctgαn, 0 ≤ u < Tn

W (u) = W2 + 2u · ctgα, Tn ≤ u < T .(23)

Therefore, the new area moment of inertia based on the abovemodel, which is expressed as I , is then

I =196

tgαn

(W 4

2 − W 43

)+

196

tgα(W 4

1 − W 42

). (24)

The calculated natural frequencies and mode shapes using allthe models that we had explored so far are given in Table IV.We can see the decline of the natural frequencies when moredetailed compensation is added into models.

Compared to the initial simplified model, consideration ofthe mass of the suspension beams, stiffness reduction of thestress alleviation beams, and fabrication imperfections all re-duce the theoretical predictions of natural frequencies. Signif-icant changes also occur while predicting the mode shapes.Since the width difference between the main flexural beams andbeams in circular folded beam suspensions is not significant, theeffects of the stiffness reduction of the suspensions due to fabri-cation imperfections to the natural frequencies and mode shapesof two resonating modes are almost equal. Comparing all themodels, the overall effect of the mass of the suspension beamsis the most significant. This is because the multiple beam sus-pensions were adopted, which is used to reduce the maximumstress, hence, the total rotational moment of inertia of the beamsis too large to be ignored. Ignoring the weight influence of thebeams will introduce a large estimation error to the grating

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DU et al.: 2-DOF CIRCULAR-RESONATOR-DRIVEN IN-PLANE VIBRATORY GRATING LASER SCANNER 901

Fig. 14. Fabrication process flow of the prototype in-plane vibratory gratingscanner.

platform’s moment of inertia and will, therefore, significantlyinfluence the prediction results of the natural frequencies andmode shapes of both the first and second resonating modes.

IV. FABRICATION PROCESS

SOI micromachining technology was used to fabricate theprototype device, and four photo masks were used. The fabri-cation process flow is illustrated in Fig. 14. The SOI wafer usedhas an 80-μm-thick heavily doped silicon device layer, 2-μm-thick buried oxide (BOX) layer, and a 650 ± 25-μm-thick sili-con substrate. The overall die size is 6.5 mm × 6.5 mm.

As shown in Fig. 14, the diffraction grating with a 400-nmgrating period and a 50% duty cycle was patterned using deep-ultraviolet lithography and etched using timed plasma etching.The etching time is strictly controlled so that the depth ofthe grating groove is around 150 nm. Then, 1 μm undopedsilicon glass was deposited and patterned by using a reactiveion etching (RIE) process. Next, the SOI wafer was patternedon the backside followed by a DRIE process, which is used toremoved silicon and expose the region of all the structures. Theetching process stopped at the BOX layer. Subsequently, the80-μm-thick silicon device layer was etched by another DRIEprocess, which is also stopped at the BOX layer, to form thegrating platform, comb-driven circular actuator, and suspensionbeams. After that, the structures formed in the SOI devicelayer were release from backside by using a buffered oxideetchant solution, with six parts of 40% NH4F and one part of49% hydrofluoric acid. Then, the metal pads for wire bondingwere formed by evaporating 1000 Å/5000 Å thick Ti/Au layerthrough a shadow mask. Finally, a 100 Å/800 Å Ti/Au layerwas evaporated on the wafer surface to enhance the reflectivityof the diffraction grating.

The whole view and the center part of the fabricated deviceare shown by a microscope image and an SEM image inFigs. 15 and 16, respectively.

V. EXPERIMENTAL RESULTS

We use a linearly TM-polarized He–Ne laser beam with awavelength of 632.8 nm to test the optical performance of the

Fig. 15. Microscope image showing the whole image of the fabricated device.

Fig. 16. SEM image showing the center part of the fabricated device.

Fig. 17. Schematic of the experimental setup for the prototype scanner.

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902 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

Fig. 18. Measured frequency response of the MEMS grating scanner inatmosphere at frequency regions near the resonant frequencies of (a) the firstvibration mode and (b) the second vibration mode.

MEMS grating scanner, and the schematic of the experimentalsetup is illustrated in Fig. 17. Since the grating period of thediffracting grating that we adopted is 400 nm, the incidentangle was determined to be 71.8◦ so that bow-free scanningconditions [10] are fulfilled.

The dynamic performance of the MEMS vibratory gratingscanner was tested in atmosphere and vacuum. As expected,two resonating modes exist. The optical scan angle was mea-sured through measuring the length of the laser scanningtrajectory on the projection screen, which was aligned perpen-dicularly to the first-order diffracted beam when the gratingis motionless. The outer comb-driven circular resonator wasdriven by a push–pull mechanism [14] both in atmosphere andvacuum. While tested in atmosphere (760 torrs), the drivingvoltage was fixed at 80-V dc bias and 160-V ac peak-to-peak, and further increasing the driving power may cause theinstability of the electrostatic comb-driven circular actuator.Fig. 18(a) and (b) shows the measured frequency responses inatmosphere, and the resonant frequencies of the first and secondresonating modes were experimentally determined as 20.182and 21.910 kHz with an optical scan angle of 20.8◦ and 18.1◦,respectively.

Fig. 19. Measured frequency response of the MEMS grating scanner invacuum at frequency regions near the resonant frequencies of (a) the firstvibration mode and (b) the second vibration mode.

Fig. 20. Photograph of the experimental setup for the prototype scanner.

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DU et al.: 2-DOF CIRCULAR-RESONATOR-DRIVEN IN-PLANE VIBRATORY GRATING LASER SCANNER 903

TABLE VSUMMARY OF THEORETICAL ANALYSES AND EXPERIMENTAL RESULTS

While tested in vacuum (0.12 mtorrs), the driving voltagewas fixed at 15 V dc bias and 30 V ac peak-to-peak, and furtherincreasing the driving power may cause the brittle fracture ofthe main flexural suspension beams. Fig. 19(a) and (b) showsthe measured frequency responses in vacuum and the resonantfrequencies of the first and second resonating modes wereexperimentally determined as 20.289 and 21.918 kHz with anoptical scan angle of 24.8◦ and 18.2◦, respectively.

According to the dynamic testing results, operating in vac-uum and scanning at the frequency near the resonant frequencyof the first resonating mode are preferred due to lower drivingvoltage, higher scanning amplitude, and less risk of brittlefracture of the main flexural suspension beams. High-speedlaser scanning was experimentally demonstrated, and Fig. 20shows a photograph of the projected laser scanning trajectoryon a projection screen, which is located at a distance of 100 mmfrom the grating scanner.

The scanner demonstrated some level of large-deflectionnonlinearity during the vibration, e.g., the scanner’s opticalscanning angle is different during the forward and backwardfrequency sweeping. Additionally, there are slight differencesbetween measured resonant frequencies in atmosphere andvacuum. The linearity of the vibration can be further improvedby reducing the stiffness of the stress alleviation beams alongthe axial direction.

In addition, the resonant frequencies and mode shapes of theprototype device were also measured on probe station under amicroscope in atmosphere. The driving power was selected tobe 50 V dc bias and 100 V ac peak-to-peak voltages to avoidlarge-deflection nonlinearity during the vibration. The mea-sured resonant frequencies and mode shapes of the prototypedevice are compiled in Table V, which shows the comparisonsbetween theoretical analyses and experimental results.

As shown in Table V, we can see that the modified rigorousmodel considering the mass of the suspension beams, stressalleviation beams, and fabrication imperfections can give amore accurate prediction of both resonant frequencies andmode shapes. The deviations between the theoretical and ex-perimental results are mainly due to the uncertainty in the fab-rication process, material properties, and imperfect boundaryconditions of all the suspension, which is acceptable. Addi-tionally, the measured resonant frequencies vary with differentdriving conditions, which is mainly due to the large-deflectionnonlinearity during the vibration and different viscous dampingin atmosphere.

VI. CONCLUSION

A prototype high-speed laser scanner using a vibratory grat-ing driven by a 2-DOF electrical comb-driven circular resonatorhas been successfully demonstrated. When illuminated by apolarized He–Ne laser beam (632.8 nm) with an incident angleof 71.8◦, the current prototype grating scanner is capable ofscanning at a frequency of 20.289 kHz with an optical scan an-gle of around 25◦. Some level of vibration nonlinearity appearsduring the operation due to the large deflection of the mainflexural beams, which can be improved by reducing the stiffnessof the stress alleviation beams along the axial direction.

We have also demonstrated the validity of a rigorous dynamicmodel that considers the effects of the mass of the suspensionbeams, stress alleviation beams, and fabrication imperfections.All affects the system significantly. However, for the currentsystem configuration, since the multiple beam suspensions isadopted, the influence of the mass of the suspension beams wasshown to have the largest effect on the system’s characteristics.Nevertheless, all of the issues were shown to affect to certaindegrees, and for the future designs, we would have to takeall of them into account. This paper provides a more accurateplatform on which future designs can be based.

REFERENCES

[1] H. Urey, D. Wine, and T. Osborn, “Optical performance requirements forMEMS-scanner based micro displays,” in Proc. SPIE, MOEMS Miniatur-ized Syst., 2000, vol. 4178, pp. 176–185.

[2] H. Urey, D. Wine, and J. R. Lewis, “Scanner design and resolutiontradeoffs for miniature scanning displays,” in Proc. SPIE Flat PanelDisplay Technol. Display Metrology, San Jose, CA, Jan. 1998, vol. 3636,pp. 60–68.

[3] D. Wine, M. P. Helsel, L. Jenkins, H. Urey, and T. D. Osborn, “Perfor-mance of a biaxial MEMS-based scanner for microdisplay applications,”in Proc. SPIE Conf. MOEMS Miniaturized Syst., Santa Clara, CA, 2000,vol. 4178, pp. 186–196.

[4] R. B. Sprague, T. Montague, and D. Brown, “Bi-axial magnetic drive forscanned beam display mirrors,” in Proc. SPIE, MOEMS Display ImagingSyst. III, 2005, vol. 5721, pp. 1–13.

[5] P. M. Hagelin and O. Solgaard, “Optical raster-scanning displays based onsurface-micromachined polysilicon mirrors,” IEEE J. Sel. Topics Quan-tum Electron., vol. 5, no. 1, pp. 67–74, Jan./Feb. 1999.

[6] R. S. Muller, K. Y. Lau, R. S. Muller, and K. Y. Lau, “Surface-micromachined micro optical elements and systems,” Proc. IEEE, vol. 86,no. 8, pp. 1705–1720, Aug. 1998.

[7] M. Yoda, K. Isamoto, C. Chong, H. Ito, A. Murata, and H. Toshiyoshi,“Design and fabrication of a MEMS 1D optical scanner using self assem-bled vertical combs and scan-angle magnifying mechanism,” in Proc. Int.Conf. Optical MEMS Appl., 2005, pp. 19–20.

[8] A. D. Yalçínkaya, H. Urey, D. Brown, T. Montague, and R. Sprague,“Two-axis electromagnetic microscanner for high resolution displays,”J. Microelectromech. Syst., vol. 15, no. 4, pp. 786–794, Aug. 2006.

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904 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 4, AUGUST 2009

[9] G. Zhou, V. J. Logeeswaran, F. S. Chau, and F. E. H Tay, “Microma-chined in-plane vibrating diffraction grating laser scanner,” IEEE Photon.Technol. Lett., vol. 16, no. 10, pp. 2293–2295, Oct. 2004.

[10] G. Zhou and F. S. Chau, “Micromachined vibratory diffraction gratingscanner for multiwavelength collinear laser scanning,” J. Microelectro-mech. Syst., vol. 15, no. 6, pp. 1777–1788, Dec. 2006.

[11] G. Zhou, Y. Du, Q. Zhang, H. Feng, and F. S. Chau, “High-speed, high-optical-efficiency laser scanning using a MEMS-based in-plane vibratorysub-wavelength diffraction grating,” J. Micromech. Microeng., vol. 18,no. 8, p. 085 013, Aug. 2008.

[12] R. W. Johnstone and M. Parameswaran, An Introduction to Surface-Micromachining. Norwell, MA: Kluwer, 2004.

[13] D. J. Inman, Engineering Vibration, 2nd ed. Upper Saddle River, NJ:Prentice-Hall, 2001.

[14] W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic-comb drive of lateral polysilicon resonators,” Sens. Actuators A, Phys.,vol. 21, no. 1–3, pp. 328–331, Feb. 1990.

[15] J. Li, Q. X. Zhang, A. Q. Liu, W. L. Goh, and J. Ahn, “Technique forpreventing stiction and notching effect on silicon-on-insulator microstruc-ture,” J. Vac. Sci. Technol. B, Microelectron. Process. Phenom., vol. 21,no. 6, pp. 2530–2539, 2003.

Yu Du received the B.S. degree in mechanical en-gineering from Xi’an Jiaotong University, Shaanxi,China, in 2005. He is currently working toward thePh.D. degree in the Micro- and Nano-system Initia-tive (MNSI) at the National University of Singapore,Singapore.

He is also an attached full-time research stu-dent working in the Semiconductor Process Tech-nology Laboratory, Institute of Microelectronics,Singapore. His research interests include opticalMEMS, and his current work focuses on the design

and fabrication of optical microdevices.

Guangya Zhou received the B.Eng. and Ph.D.degrees in optical engineering from Zhejiang Uni-versity, Hangzhou, China, in 1992 and 1997,respectively.

He is currently an Assistant Professor in the De-partment of Mechanical Engineering, National Uni-versity of Singapore, Singapore. His main researchinterests include bioimaging, microoptics, diffractiveoptics, MEMS devices for optical applications, andnanophotonics.

Koon Lin Cheo received the B.S. and M.S. degreesin mechanical engineering in 2003 and 2005, respec-tively, from the National University of Singapore,Singapore, where he is currently working towardthe Ph.D. degree in the Micro- and Nano-systemInitiative (MNSI).

His research interests include optical MEMS, andhis current work focuses on system-level applica-tions of optical microdevices.

Qingxin Zhang received the B.S. and M.S. de-grees in semiconductor devices and physics fromHarbin Institute of Technology, Harbin, China, in1986 and 1989, respectively, and the Ph.D. degree inmicroelectronics from Tsinghua University, Beijing,China, in 1997.

After working as a Research Fellow at NanyangTechnology University, Singapore, for two years, hejoined the Institute of Microelectronics’ Agency forScience, Technology and Research, Singapore, in1999, where he is currently a Member of Technical

Staff working in the Semiconductor Process Technologies Laboratory. Hismajor research interests include MEMS design and processes and systems-on-package and platform technologies for integrated MEMS, CMOS IC, andphotonics.

Hanhua Feng received the B.Eng. degree in semi-conductor physics and devices and the M.Eng. andPh.D. degrees from Huazhong University of Scienceand Technology (HUST), Wuhan, China, in 1985,1988, and 1991, respectively.

She was a Lecturer and Associate Professor inelectronic materials and devices for two years atHUST. She was a Postdoctoral and Research Fel-low at the Northern Ireland Bio-Engineering Center,University of Ulster, Newtownabbey, U.K., and theSchool of Electrical and Electronics Engineering,

Nanyang Technological University, Singapore. In January 1998, she joined theInstitute of Microelectronics, Singapore, where she is currently MEMS Pro-gram Manager. She is familiar with aspects of wafer fabrication, with expertiseparticularly in CMOS/MEMS integration, PECVD, and plasma etching, fromher many years of working experience in the microelectronics and MEMSareas.

Fook Siong Chau received the B.Sc. (Eng.) andPh.D. degrees from the University of Nottingham,Nottingham, U.K., in 1974 and 1978, respectively.

He is currently an Associate Professor in theDepartment of Mechanical Engineering, NationalUniversity of Singapore, Singapore, where he headsthe Applied Mechanics Academic Group. His mainresearch interests include development and applica-tions of optical techniques for nondestructive evalu-ation of components and modeling, simulation, andcharacterization of microsystems, particularly bio-

MEMS and MOEMS.

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