Microsystem Technologies

, Volume 18, Issue 3, pp 295–302

Design and fabrication of a resonant scanning micromirror suspended by V shaped beams with vertical electrostatic comb drives

Authors

    • Micro and Nano Electromechanical System LaboratoryNorthwestern Polytechnical University
  • Qian Jin
    • Micro and Nano Electromechanical System LaboratoryNorthwestern Polytechnical University
  • Da-Yong Qiao
    • Micro and Nano Electromechanical System LaboratoryNorthwestern Polytechnical University
  • Bao-Peng Kang
    • Micro and Nano Electromechanical System LaboratoryNorthwestern Polytechnical University
  • Bin Yan
    • Micro and Nano Electromechanical System LaboratoryNorthwestern Polytechnical University
  • Yao-Bo Liu
    • Micro and Nano Electromechanical System LaboratoryNorthwestern Polytechnical University
Technical Paper

DOI: 10.1007/s00542-011-1384-x

Cite this article as:
Li, X., Jin, Q., Qiao, D. et al. Microsyst Technol (2012) 18: 295. doi:10.1007/s00542-011-1384-x

Abstract

A scanning micromirror suspended by a pair of V-shaped beams with vertical electrostatic comb drives was designed, modeled, fabricated and characterized. The dynamic analyses were carried out by both theory calculation and FEM simulation to obtain frequency response, stiffness characteristics, oscillation modes and their resonance frequencies. The device was fabricated using the silicon-on-insulator process by only two photolithography masks. Some problems during the process such as the micromirror distortion and the side sticking of the comb fingers were effectively solved by thermal annealing and alcohol-replacement methods, respectively. Based on the fabricated device, the typical scanning patterns for 1-D and 2-D operation were obtained. The experimental results reveal that the micromirror can work in resonant mode with the resonant frequency of 2.38 kHz. The maximum deflection angles can reach ±4.8°, corresponding to a total optical scanning range of 19.2° at a driving voltage of 21 V.

1 Introduction

Scanning micromirrors have been widely used in diverse applications such as barcode scanning (Arslan et al. 2010), head-up and head-worn displays (Ilgar and Ipek 2010), telecommunication systems (Toshiyoshi and Fujita 1996), display systems (Davis et al. 2008), adaptive optics (Huang et al. 2004), and etc. Their prominent advantages of small size, low power consumption, high-resolution and high-scanning speed make them attractive to increase the performance of existing devices and to expand the application fields of scanners (Schenk et al. 2001).

Vertical electrostatic comb drives is the most desirable actuation for scanning micromirrors because of its design flexibility, low driving voltages, large displacement, high resonant frequency and absence of pull-in phenomenon (Tsou et al. 2005). Theoretically, an oscillation would start only with an initial deflection of the mirror plate. So the previous configuration with an additional starting electrode on top of the driving electrode separated by an oxide layer was adopted to generate asymmetric force (Schenk et al. 1999). The initial deflection could be achieved when the mirror plate was excited by a DC voltage. The other method to start an oscillation by dual comb drives was presented by Lin et al. (2005). It used the polysilicon layer separated from device layer by insulated layer as a starting electrode which could provide an effective initial deflection before oscillation. The scanning micromirrors with these asymmetric configurations could work in both static mode and resonant mode. However, the fabrication processes of both methods were relatively complex.

The challenge of designing a scanning micromirror is to realize the relatively simple and feasible structure which can meet with the excellent performances such as large scanning angle, low driving voltages, mechanical stability, and etc. Furthermore, the limitations of the fabrication process should be taken into consideration. In order to increase finished product rate, the fabrication process should be as simple as possible. In this paper, a scanning micromirror realized by simple process was proposed and its structural design, SOI fabrication and performance test were implemented.

2 Device design and operations principle

A schematic diagram of the scanning micromirror is given in Fig. 1. The device consists of three layers: device layer, buried oxide (BOX) layer and handle layer. The deflectable mirror plate is suspended by a pair of V-shaped beams. The movable comb-fingers are placed on the symmetrical sides of the mirror plate and the fixed comb-fingers are anchored to the frame which is fixed by the BOX layer. The bulk silicon of handle layer which is underneath the device structures is removed so that the deflection is not limited by the substrate.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig1_HTML.gif
Fig. 1

Schematic view of the scanning micromirror

In practice, the fabrication factors such as residual stress, alignment deviation and process variance could generate asymmetries which were sufficient to start the oscillation. For this reason all the additional starting electrodes have been abandoned since this actuation method was much easier to implement. Only exciting the driving electrode the micromirror plate could oscillate in a resonant scanning mode.

3 Modeling and analysis

3.1 Geometric modeling

A schematic diagram of the configuration of the micromirror is shown in Fig. 2. Dimensions of the scanning micromirror are listed in Table 1, including micromirror plate width (Wm), micromirror plate length (Lm), comb finger length (Lf), comb finger width (Wf), comb finger gap (g), overlapped length (Lo), thickness of device layer (t), beam length (Ls), beam width (Ws), beam gap (b), and separate angle (Ψ) with a value of 6.8°.
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Fig. 2

Configuration of the micromirror

Table 1

Geometric dimensions of the micromirror

Items

Lm

Wm

Lf

Wf

Lo

g

t

Ls

Ws

b

Values (μm)

1,000

1,000

100

4

90

4

30

400

5

20

3.2 Modal analysis

Modal analysis is used to determine the vibration characteristics of the device by finite element methods. For a 1-D scanning micromirror, the first five oscillation modes including torsional motion around spring axis, vertical motion perpendicular to mirror plane, horizontal motion in mirror plane, rocking around the axis perpendicular to spring beams and rolling motion in mirror plane are obtained, as shown in Fig. 3. Among these modes the 1st torsional mode is the main operation one, so the theoretically calculated frequency of the torsional mode for the device was carried out.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig3_HTML.gif
Fig. 3

Five different oscillation modes for a 1-D scanning micromirror

The mode eigenfrequency can be described as
$$ f = \frac{1}{2\pi }\sqrt {\frac{{K_{\varphi } }}{{I_{\varphi } }}} $$
(1)
where Kφ is the torsional stiffness of spring beams and Iφ is the moment of inertia.
The 1st torsional mode stiffness Kφ had been extracted with FEM method and linearly fitted in Matlab. For rectangular mirror plate, the moment of inertia for torsional mode can be calculated by
$$ I_{\varphi } = \frac{\rho t}{12}\left[ {\left( {W_{m} - N_{f} W_{f} } \right)L_{m}^{3} + N_{f} W_{f} \left( {L_{f} + L_{m} } \right)^{3} } \right] $$
(2)
where ρ is the material density, Nf is the number of movable fingers on single side, and the other signs such as t, Wm, Lm, Wf, Lf have already been illustrated in previous paragraphs. Furthermore, the simulated resonance frequencies for the first five oscillation modes were performed with ANSYS, as listed in Table 2. The FEM simulation result agrees well with the theoretically calculated one for the torsional mode. To ensure that the micromirror can work on stable state and not readily tend to be ruined, the first mode frequency should be low enough to separate sufficiently with frequencies of other modes.
Table 2

FEM simulated frequencies of the first five modes and theoretically calculated frequency of the first mode for the 1-D scanning micromirror

Mode order

Vibration

fFEM (Hz)

ftheoretically (Hz)

Deviation (%)

1

Torsional

2,829

2,821

0.28

2

Vertical

17,139

  

3

Horizontal

30,331

  

4

Rocking

43,377

  

5

Rolling

72,033

  
In this section, we compared different separate angle (Ψ) values of the V-shaped torsional beam to research the possibility of increasing the mode frequencies and torsional stiffness ratio. When Ls, Ws and b were kept constants, only the separate angle Ψ was varied from zero to some specific value, the frequency ratio of the 2nd order mode to the 1st order mode was obtained and shown in Fig. 4. It is proved that in the vicinity of 0.10 rad, frequency ratio peak is obtained. In our design, an actual separate angle Ψ of 0.12 rad (6.8°) was chosen as mentioned in Sect. 3.1.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig4_HTML.gif
Fig. 4

Frequency ratio of the 2nd order mode to the 1st order mode

3.3 Capacitance analysis

In ANSYS environment, with the element type solid122, capacitance for different tilt angle of one pair of comb fingers was extracted using the ‘CMATRIX’ command. Then at different tilt angle, the total capacitance value was multiplied by 2Nf. In our design, Nf was set to be 63.

The altitude of torque produced by the comb drive actuators is given by the following expression:
$$ M(\theta ) = 2N_{f} \frac{1}{2}C^{\prime}(\theta )\,V(t)^{2} $$
(3)
where M(θ) is the torque, θ is the tilt angle, C′(θ) is the derivative of capacitance with respect to θ for one pair of comb fingers, and V(t) is the periodic excitation voltage signal. The relationship between the capacitance of one pair comb fingers and the tilt angle was obtained by ANSYS and fitted with a 20th order polynomial expression for numerical simulations with Matlab to compute C′(θ). Then a 3rd order cubic fit to C′(θ) for the small angle region (|θ| ≤ 0.01 rad) which would be employed in the analytical formulations was obtained. The 3rd order cubic fitted resultant function can be expressed as:
$$ \frac{\partial C}{\partial \theta } = {\text{c}}_{3} \theta^{3} + {\text{c}}_{ 2} \theta^{2} + {\text{c}}_{1} \theta + {\text{c}}_{0} $$
(4)
where ci are the coefficients listed in Table 3. Figure 5 shows C(θ) and C′(θ) and their polynomial fits. The curves show that the capacitance reaches the maximal value in mirror rest position and changes little when the rotational angle reaches about ±0.08 rad.
Table 3

Coefficients of the 3rd order cubic fit to C′(θ)

c3

c2

c1

c0

1.9712e-006

−4.8955e-012

−1.2338e-009

2.4971e-016

https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig5_HTML.gif
Fig. 5

C(θ) and C′(θ) and their polynomial fits

Analytically, the equation of motion for the torsional micromirror is given as:
$$ I_{\varphi } \frac{{d^{2} \theta }}{{dt^{2} }} + d\frac{d\theta }{dt} + K_{\varphi } \theta = M(\theta ) $$
(5)
where d is the air damping. According to Eqs. 3, 4 and 5, the numerical simulations using Matlab ODE45 solvers could be obtained. Frequency response is given in Fig. 6 showing that the micromirror illustrates a hysteresis phenomenon during descending and ascending input frequency sweepings.
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Fig. 6

Frequency response of a scanning micromirror with hysteresis

3.4 Stress analysis

Torsional stress impacts the durability of a micromirror and the tilt angle tremendously. Stress analysis was carried out to forecast the maximum stress at variable tilt angles critically, aiming to avoid fracture happening during the oscillation. The stress distribution contour under different tilt angles was easily obtained by ANSYS. When tilt angle reaches 0.05 rad, the stress distribution contour is shown in Fig. 7a. Obviously the maximum stress concentrates at the fixed ends of the torsional beams. Figure 7b gives the deflection displacements of the mirror plate and the close-up of the distortion torsional beams, which indicates that the distortion consists of bending and twisting deflection effect.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig7_HTML.gif
Fig. 7

a FEM simulated torsional stress distributed contour plot and b the deflection displacement color map of the mirror

Figure 8 shows that the stress is linearly proportional to the tilt angle θ. The slope of the curve, i.e. the stress per angle is computed to be 71 Mpa/rad approximately, greater than 58 MPa/rad got by Wolter et al. (2000).
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig8_HTML.gif
Fig. 8

Stress versus torsional angle curve

4 Fabrication

4.1 Fabrication technology

The scanning micromirror was manufactured by greatly simplifying the SOI-MEMS fabrication technology. The base material was highly doped silicon-on-insulator (SOI) wafer with a device layer thickness of 30 μm and BOX layer of 5 μm. The process consisted of two photolithography masks: one for frontside etching the structures (mask #1), and the other one for backside etching to release the designed structures (mask #2). The most important steps of the process are depicted in Fig. 9.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig9_HTML.gif
Fig. 9

Flow chart of the SOI processes for the scanning micromirror

The process started with a SOI wafer has been mentioned in Sect. 2. In fact there was another oxide layer below the handle layer which must be removed in the first step. But during this step remarkable stress would be introduced, which would lead to the micromirror plate distortion after the released step. To release the stress, the thermal annealing at 1,050° for 2 h was followed. After that, a 200 nm Al film was deposited by sputter deposition and patterned (mask #2) on the handle layer to form the etching window of the backside. Then a DRIE etching was employed to etch the silicon substrate using ICP where etching stop would occur at the BOX layer. The removal of the Al film at the backside of the handle layer was followed to prevent the chemical attacking of Al in the HF etchant which would be used in the released step. After that, the device structures were defined through lithography with mask #1 and formed by the deep silicon etching. Finally, the structures were released with HF etching to remove the BOX layer below the micromirror plate and the comb fingers. To prevent the side sticking of the comb fingers produced in HF released step, an alcohol-replacement method was used.

4.2 Fabrication results

SEM-photographs of the fabricated scanning micromirror with vertical comb drives are shown in Fig. 10. The mirror plate is 1 × 1 mm2 and the chip size is 3.28 × 4.6 mm2 as shown in Fig. 10a. Figure 10b shows a scanning micromirror with two comb-driven actuators which have 63 movable fingers in each bank and a pair of V-shaped beams. Figure 10c gives the close-up SEM micrograph of the fabricated comb fingers. Obviously that the movable fingers and the fixed fingers have the static deflection caused by the fabrication processes which plays a part in starting the oscillation.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig10_HTML.gif
Fig. 10

a Photo of the micromirror chip beside a matchstick. b SEM micrograph of fabricated scanning micromirror with comb drives. c SEM micrograph of the fabricated comb fingers with the static deflection

5 Experiments and results

All measurements were carried out at atmospheric pressure. The experimental setups to generate 1-D and 2-D scanning patterns are illustrated in Figs. 11 and 12, respectively. In Fig. 11, a laser beam which is reflected by the micromirror surface projects directly onto an accepted screen. The close-up of the accepted screen reveals the typical scanning pattern for 1-D operation. Figure 12 shows 2-D scanning pattern generated by two scanning micromirrors. A laser beam is focused on the #1 micromirror plate and the reflected beam is centered on the #2 micromirror plate. When the two micromirrors actuated synchronously, the 2-D scanning patterns changed by the two excitation frequencies can be generated.
https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig11_HTML.gif
Fig. 11

Experimental setup for the scanning micromirror measurement and typical scanning pattern for 1-D operation

https://static-content.springer.com/image/art%3A10.1007%2Fs00542-011-1384-x/MediaObjects/542_2011_1384_Fig12_HTML.gif
Fig. 12

Experimental setup for 2-D scanning pattern with different frequencies

The experimental setup for 1-D operation was also used to measure the characteristics of the scanning micromirror. The scanning micromirror only works in the resonant scanning mode at a resonant frequency of 2.38 kHz. The maximum deflection angles can reach ±4.8°, corresponding to an optical scan range of 19.2° when actuated at twice its natural frequency at a rectangular pulsed voltage of 21 V.

6 Conclusion

A resonant scanning micromirror driven by vertically electrostatic comb drives, suspended by a pair of V-shaped beams was designed, modeled, fabricated and characterized. The dynamic analyses including modal analysis, resonant frequency analysis, capacitance analysis and stress analysis were carried out to obtain the device characteristics. The device which has comb fingers placed around the perimeter of the scanning micromirror was fabricated on a SOI wafer with a CMOS compatible process. Difficulties during the process such as the micromirror distortion caused by the stress, the side sticking of the comb fingers caused by the HF released step were effectively eliminated by thermal annealing and alcohol-replacement method, respectively. The typical scanning patterns for 1-D operation and 2-D operation were obtained by experimental setups. The maximum optical scan range can reach 19.2° when actuated at twice its natural frequency at a rectangular pulsed of 21 V, which proves that the scanning micromirror has good modulation performances.

Acknowledgments

This work was sponsored by the Program for the New Century Excellent Talents in University, Ministry of Education of China (Grant No. NCET-10-0075) and the National Natural Science Foundation of China (Grant No. 50805123)

Copyright information

© Springer-Verlag 2011