## Abstract

This study presents a novel design for a two-axis scanning device driven by lead-zirconate-titanate (PZT) ceramic. The proposed device consists of a scanning mirror and a Y-shaped piezoelectric actuator. The scanning mirror was fabricated using an MEMS process involving three masks. Experimental results show that the fast and slow frequencies at resonance are 25.0 kHz and 0.56 kHz, respectively. The optical scanning angles are 27.6° and 39.9°. The power consumption of the device is 13.4 *mW* at a driving voltage of 10 V. This study also develops a laser projection module integrated with the scanning device. The module can project a 2-D image at a resolution of 640 x 480.

© 2012 OSA

## 1. Introduction

A microelectromechanical system (MEMS) scanning laser projector has the advantages of a high projection resolution, compact optical engine, and the always-in-focus function [1,2]. A key component in a laser projector is the MEMS scanning device. There are various mechanisms to actuate the scanning device. Electrostatic actuation is the most mature scanning method [3–5], and it offers a fast switching speed of up to tens of kilohertz (kHz) and low power consumption. However, the cost of electrostatic devices is relatively high because of their complex MEMS process and high driving voltage, which is typically more than 100 V. Electrothermally actuated scanners provide low driving voltage and feature simple fabrication process, making them suitable for applications with low scanning speeds. However, this approach has difficulty achieving both a large scanning angle and a high scanning frequency of up to 1 kHz [6,7]. Electromagnetic actuation [8,9] possesses a low driving voltage and a high scanning frequency exceeding 15 kHz. However, this design relies on a complex microcoil fabrication process.

Lead-zirconate-titanate (PZT) ceramic is suitable for driving a scanning mirror because of its simple structure, quick response, anti-interference, and good stability. Recent research has reported a PZT ceramic actuated scanner with these advantages [10–14]. X. Chu [15] developed a 2D piezoelectric scanner with a 0.282° bending scanning angle at 1056 Hz and a 0.12° torsional scanning angle at 4612 Hz at a driving voltage of 5 V. K. H. Koh et al. [16] presented an s-shaped PZT actuator integrated with a silicon micromirror micromachined from a silicon-on-insulator (SOI) wafer. The device was driven by superimposed AC voltages, and the optical angles obtained at 3 Vpp are ± 38.9° and ± 2.1°, respectively, for bending and torsional modes at 27 Hz and 70 Hz, respectively. K. H. Gilchrist et al. [17] presented a dual-scanner system to allow 2D beam steering up to ± 7° mechanical angle at resonance frequencies of hundreds of Hz to 1-2 kHz. S. Moon et al. [18] developed a fiber-cantilever piezotube scanner using a semi-resonant scan strategy to achieve a low scanning frequency of 63 Hz for optical coherence tomography scanning.

These studies have all had some success in developing piezoelectric MEMS scanners. However, a scanner of laser scanning projector should possess these characteristics, including a larger scanning angle, faster scanning frequency (horizontal frequency up to 20 KHz), low power consumption, and compact size. This study proposes a novel design for a scanning device consisting of an MEMS mirror and a pair of bimorph piezoelectric cantilever actuators. This study also develops a multi-degree-of-freedom (DOF) vibration model as an auxiliary to design the scanning device. The proposed scanning device can perform 2D scanning. The fast and slow frequencies are 25.0 kHz and 0.56 kHz, respectively. The fast and slow driving signals can be added so that the actuator can receive the two signals simultaneously by using an adder with operational amplifier (OP). The fast and slow optical scanning angles are 27.6° and 39.9° at a driving voltage of 10 V.

The structure of this paper is as follows. Chapter 1 provides an introduction. Chapter 2 presents an analytical multi-DOF vibration model, developed to design the scanning device. Chapter 3 shows the performance of the scanning device, such as resonance frequency, scanning angle, and linearity. Chapter 4 presents the fabrication process, including the MEMS process of the scanning mirror and assembly process of the device. Chapter 5 presents a projection module based on an optical engine integrated with a PZT scanning device. Finally, Chapter 6 presents the conclusion.

## 2. Two-axis mirror design and modeling

Figure 1 shows a sketch of the scanning device, which comprises a Y-shaped actuator and a dual-axis scanning mirror. The Y-shaped actuator has two arms, each of which is a bimorph PZT structure composed of lead zirconate titanate ceramics. The middle layer of the actuator is a sheet of brass. The clamped end of the actuator has only one brass layer. The arm tips are connected to the scanning mirror, and the end of the root is fixed on an anchored structure.

The proposed scanning mirror comprises a frame, two pairs of torsion bars, a mass block, and a reflective mirror. The reflective mirror is connected by the fast torsion bars so that it can oscillate along the fast torsion bars. The natural frequency *ω _{n}*

_{,}

*of the fast scanning can be written as ${\omega}_{n,s}=\sqrt{{k}_{f}/{I}_{f}}$,where*

_{f}*k*is the torsional stiffness of the fast torsion bars, and

_{f}*I*is the mass moment of inertia of the reflective mirror.

_{f}The slow torsion bars connect the frame and the mass block, and the mass block and the reflective mirror can oscillate along the slow torsion bars. The natural frequency is ${\omega}_{n,s}=\sqrt{{k}_{s}/{I}_{s}}$, where *ω _{n}*

_{,}

*is the natural frequency of the slow scanning,*

_{s}*k*is the torsional stiffness of the slow torsion bars, and

_{s}*I*is the mass moment of inertia of the mass block and the reflective mirror. These two equations neglect the mass of the torsion bars. This is a relatively reasonable assumption because the masses of the torsion bars are several orders less than that of the reflective mirror and mass block. A more accurate approach that considers the mass of the torsion bars is available in [19].

_{s}#### 2.1 Fast scanning: 4-DOF discrete vibration model

Figure 2(a) shows a 4-DOF discrete vibration model for the fast scanning. If the four mass elements are modeled as decoupled structures, each mass element is equivalent to a corresponding sub-structure of the scanning device (Figs. 2(b)-2(e)). To simplify the model, only bending moment or the twisting moment of one mass element can be transferred to the adjacent element. This model neglects the transfer of the shear force.

The sub-structures in Figs. 2(d) and 2(e) are easily modeled as 1D vibration, and the corresponding mass moments of inertia and torsional spring constants can be determined. The material of the scanning mirror is silicon. The sub-structure shown in Fig. 2(c) can be considered a cantilever beam carrying a mass at its end. Assume that the frame deforms according to the fundamental mode. The lateral displacement is assumed as

where*w*

_{2}is the mode shape of the frame,

*w*

_{20}=

*W*sin(

*ωt*),

*x*is the coordinate that is measured from the base of the frame,

*W*is a constant, and

*ω*is the frequency. The lateral displacement

*w*

_{2}is aligned with the Z-direction as shown in Fig. 1. The elastic potential energy

*V*

_{2}and kinetic energy

*T*

_{2}are then

*ρ*is the density of silicon,

*m*

_{20}is the end mass of the frame, and

*A*

_{2},

*EI*, and

*L*

_{2}are the cross-sectional area, bending rigidity, and length of the beam of the frame, respectively. Substituting Eq. (1) into Eq. (2) leads toBecause the displacement behaves harmonically, substituting Eq. (1) into Eq. (3) leads to

*k*

_{2}and mass moment of inertia of the frame

*I*

_{2}are given as

Similar to Fig. 2(c), the sub-structure in Fig. 2(b) can be considered a cantilever beam carrying a mass at its end. The equivalent moment of inertia and spring constant can be obtained following the same procedure. However, the formulation in this case is more complex than Eqs. (1)-(7), and the results are too lengthy to present here.

In the MEMS scanner, the damping mainly originates from the air damping and material damping. The damping constants of the four sub-substructures can be estimated as

where*i*= 1 to 4 and

*ζ*is the damping ratio. The damping ratios of silicon and the actuator are assumed to be typical values of 0.0005 and 0.01, respectively.

_{j}The fast scanning frequency for the proposed device is designed as $25\pm 1$ kHz. For a silicon scanning mirror, a reflective mirror measuring 1 mm x 1 mm x 0.06 mm and a torsion bar measuring 0.45 mm x 0.045 mm x 0.06 mm meet the design of the fast scanning frequency. Following the formula proposed by [19], *I*_{4} and *k*_{4} can be calculated as

The natural frequency of the reflective mirror is then 25.5 kHz. For a scanning device measuring approximately 10 mm x 5 mm x 2 mm, a preliminary calculation of other lumped elements gives the orders of values of *I _{j}*,

*k*and

_{j}*c*. Table 1 shows a summary of the results. The values for the reflective mirror are calculated using an accurate size design. Other values are given in ranges rather than exact numbers according to the estimated size of the scanning device.

_{j}The moment *M*_{0} produced by the piezoelectric actuator can be estimated as follows:

*E*is the elastic modulus of the piezoelectric,

_{p}*d*

_{31}is the piezoelectric constant,

*V*is the applied voltage,

*b*is the width of the piezoelectric,

*h*is the thickness of one PZT layer, and

_{p}*h*is the thickness of the brass layer. A rough calculation shows that the order of the moment

_{m}*M*

_{0}is 10

^{−4}

*N*-

*m*.

The equation of motion of the 4-DOF vibration system can be written as

where the inertia matrix**m**, damping matrix

**c**, stiffness matrix

**k**, rotational displacement vector

**u**, and torque vector

**T**have the forms

*u*

_{1},

*u*

_{2},

*u*

_{3}, and

*u*

_{4}in Eq. (11) are the rotational displacements of the four lumped elements. The term

*u*

_{4}also refers to the mechanical scanning angle of the reflective mirror. The fast optical angle for projection

*θ*isThe factor 4 is due to the principle of optical lever, which indicates that the steering angle of the light beam is 4 times the angular position of the mirror. The natural frequency

_{f}*ω*,

_{i}*i*= 1, 2, 3, 4 can be related to the eigenvalues

*λ*of the dynamic matrix

_{i}**D**=

**k**

^{−1}

**m**, such thatAssume the forced term is harmonic in nature,where

*ω*is the frequency of the force vector and

*j*is the imaginary unit. The frequency response of the vibration system iswhere

**Z**(

*ω*) is the impedance matrix having the form

Figure 3
shows the numerical results, and Fig. 4
presents a numerical investigation of natural frequencies at various *k*_{1}. The parameters used as shown in Fig. 3 are *I*_{1} = 1x10^{−10} *kg*-*m*^{2}, *I*_{2} = 0.9x10^{−11} *kg*-*m*^{2}, *I*_{3} = 1.5x10^{−12} *kg*-*m*^{2}, *I*_{4} = 1.17x10^{−14} *kg*-*m*^{2}, *k*_{2} = 0.3 *N*-*m*, *k*_{3} = 0.02 *N*-*m*, *k*_{4} = 3.01x10^{−4} *N*-*m*, and *M*_{0} = 0.5x10^{−4} *N*-*m*. This study computes four natural frequencies of Eq. (10), *f*_{1}, *f*_{2}, *f*_{3}, and *f*_{4} (*f*_{1} < *f*_{2} < *f*_{3} < *f*_{4}) for a given *k*_{1}. The curves of *f*_{1} to *f*_{4} do not cross each other because of the coupled oscillation. The four frequency curves in Fig. 3 do not cross each other because of their coupled behavior. However, at a first glance at the four curves, three horizontal lines and an oblique line from the left-bottom to right-upper corner may be apparent; thus, the uncoupled case was examined to explain this tendency. The results are shown in Fig. 4. The uncoupled frequency can be computed as $(1/2\pi )\sqrt{{k}_{i}/{I}_{i}}$, where *i* = 1, 2, 3, and 4. Figure 4 shows the variations of the uncoupled frequencies. The frequency tendencies are the same between Figs. 3 and 4.

The frequencies *f*_{2} and *f*_{3} are coupled at *k*_{1} = 3.4 *N*-*m*. Figure 3 shows the fast optical angles driven at *f*_{2} and *f*_{3}. For *k*_{1} values ranging from 2.5 to 4 *N*-*m*, the computed fast optical angles are higher than other *k*_{1}. The fast optical angle increases when *k*_{1} < 1 *N*-*m*, for which *f*_{3} couples *f*_{4}. The optimum optical angle does not occur when *k*_{1} = 3.4 *N*-*m*, which makes the smallest frequency difference between the actuator and the reflective mirror. This phenomenon is caused by the damping ratio of the actuator *ζ*_{1} (Fig. 5
). The fast optical angle reaches its optimum when *k*_{1} = 3.4 *N*-*m* only when *ζ*_{1} is small.

The actuator can be designed to optimize the fast optical angle following the guidance of Fig. 3. In this particular case, the best *k*_{1} value is 3.7 or 3.1 *N*-*m*, and the optimum fast optical angle is 41°. To realize the optimum design of a 2D scanner, we propose a further approach to optimize both fast and slow optical angle in Section 2.2. Consider the case in which *k*_{1} = 4 N-m and *k*_{2} = 0.3 *N*-*m*, which is not the optimum in Fig. 3. Figure 6
shows the variations of the natural frequencies at various *k*_{2} when *k*_{1} = 4 *N*-*m*. The frame can also be a tuning parameter to optimize the optical angle. Similar to Fig. 3, Fig. 6 shows two local optima.

#### 2.2 Slow scanning: 2-DOF discrete vibration model

The scanning device can be partitioned into two parts for slow scanning (Fig. 7
). The first partition consists of an actuator and frame, whereas the second partition is the slow-axis mirror. The slow scanning of the device can be modeled using a 2-DOF discrete vibration system. The mass moments of inertia *I*_{5} and *I*_{6} can be calculated directly. The spring constants *k*_{5} and *k*_{6} can be obtained by a torsion rod with a rectangular cross section.

Table 2
lists a design table similar to the 4-DOF model for fast scanning. Figure 8
shows the numerical results of the slow scanning model. The parameters used in this case are *I*_{5} = 4x10^{−10} *kg*-*m*^{2}, *I*_{6} = 1.8x10^{−11} *kg*-*m*^{2}, *k*_{6} = 2.24x10^{−4} *N*-*m*, and *T*_{0} = 1.5x10^{−6} *N*-*m*. Figure 8 shows that the slow optical angle can be optimized by tuning the stiffness of the actuator.

In the fast scanning model, the frame can significantly affect the fast optical angle (Fig. 6). In the slow scanning model, the frame does not deform when the device is driven by a low frequency. Theoretically, the mass of the frame can affect the optical angle. However, the contribution of the frame mass to *I*_{5} is small. This suggests that, unlike the fast scanning model, the role of the frame is relatively unimportant in the slow scanning mode.

#### 2.3 Overall considerations for designing a scanning device

According to analytical process, the solution of Eq. (19) can be written as

where*x*is the rotational displacement of the mirror,

*r*is the ratio of driving frequency and nature frequency, and

*ζ*is damping ratio. We drive the device at resonance (

*r*= 1) to maximize the scanning angle. However, this is insufficient for guaranteeing that the scanning angle is large enough. The factor has to be enlarged further to produce a larger scanning angle. In the previous section, we apply the fast and slow scan models to show that the coupled modes can increase the scanning angles. The coupled modes can result in a larger $\overline{x}$.

This analytical model shows that two major components, the actuator and the frame, can influence the optical angles of the scanning device. The stiffness of the actuator affects both the fast and slow optical angles. It is a difficult task to design an actuator that can simultaneously optimize the fast and slow optical angles. Section 2.2 shows that the frame is relatively unimportant to the slow scanning mode. Moreover, the frame can significantly affect the fast optical angle. Therefore, this study proposes the following design flow:

- 1. Set fast and slow frequencies. The dimension of the torsion bar can be estimated based on [19].
- 2. Design the frame to optimize the fast optical angle. Figure 6 shows an example.
- 3. Design the actuator to optimize the slow optical angle. Figure 8 shows an example.
- 4. After these three steps, perform a feasibility study and produce a preliminary design of the scanning device. The finite element method can be used to achieve a more accurate analysis and design.

## 3. Fabrication process

The PZT used in the scanning device was sintered from ceramic powder to form a bulk structure. It was provided by a PZT provider Eleceram Technology Company Limited with internal. The used PZT is soft ceramic with a piezoelectric constant of *d*_{33} = 500 x 10^{−12} *m*/*V*, elastic constants of *Y*_{33} = 5.4 x 10^{10} *N*/*m*^{2}, *Y*_{11} = 7.4 x 10^{10} *N*/*m*^{2}, and a density of 7800 kg/m^{3}. The actuator was assembled by gluing the PZT and the brass using 3M epoxy-1895.

Figure 9
shows the simple MEMS process used to produce the scanning mirror in this study. The starting material was an SOI wafer with a Si device layer thickness of 60 *μm*, buried oxide layer thickness of 1 *μm*, and Si handle layer of 400 *μm*. The process began with sputter deposition to form a Ti layer of 200 Å and an Al layer of 600 Å. The Ti layer is a good adhesion between the Si and Al layer. For the red (638 nm) green (512 nm) and blue (450 nm) lasers, the Al thin film provides a reflectivity of more than 75% at the mirror surface to ensure a better brightness of the projection image. The Ti/Al layer is protected by a 0.6-*μm*-thick SiO_{2} layer, which prevents the air from oxidizing it. The suspension structures, the torsion bars, were formed by inductively coupled plasma (ICP) etching of the device layer. Back-side ICP etching was then performed to complete the mirror structure. The scanning mirror was released by vapor Hydrogen Fluoride (HF) etching of silicon dioxide in Step (M). Figure 10
shows an SEM photo of the resulting scanning mirror.

After the fabrication process, the scanning mirror was glued to the actuator using 3M epoxy 1895. Figure 11 shows the completed assembly of the scanning device. The length, width, and thickness of the device are 11 mm, 5.9 mm, and 1 mm, respectively.

## 4. Scanning performance of the device

Figure 12 shows the experimental setup for measuring the scanning performance of the device. A blue laser was situated at the center of the screen with the laser beam emitting perpendicularly to the mirror and the reflective beam returning to the screen. The optical scanning angle can be calculated from the size of the projected area and the distance between the laser and the scanning device.

The electrical potential brass layer is grounded. The top and bottom surfaces of each arm of the actuator are electrically connected and subjected to electrical signals. The potential difference between the top (or bottom) surface of the PZT and the brass layer induces electrical fields. This experiment involved using three electrical signals generated by a function generator AFG3022. Three signals are considered: *A*, *B1,* and *B2*. These signals are square waveforms with 50% duty and 10 V peak to peak. The frequency of signals *B1* and *B2* are the same and denoted as *f*_{B}. The frequency of signal *A* is *f*_{A}. The only differences between signals *B1* and *B2* are their phase shifts. Signal *B2* has a 180° phase lag compared to signal *B1*.

#### 4.1 Frequency and optical scanning angle test

To find the fast frequency of the device, Signal *A* was applied to the two arms simultaneously. This excites only the fast scanning, and the projected pattern is a horizontal line. The fast optical scanning angle can be calculated from the length of the line and the distance between the device and the laser. The fast frequency for the largest optical scanning angle can be found by tuning the frequency *f*_{A}.

In the next step, the two arms of the Y-shaped actuator are driven in slow scanning mode only by Signals *B1* and *B2* respectively to find the low frequency. The wave form, frequency, and the peak-to-peak voltage of the two signals are exactly the same. The only difference is a phase shift *π* between *B1* and *B2*. Figures 13(a)
and 13(b) show comparisons of the variation of the optical angle and driving frequency. The fast and the slow frequencies at resonance are 25001 Hz and 557.65 Hz, respectively. The measured optical angles at these two frequencies are 31.6° and 39.9°.

The analytical results for the test sample are also shown in Figs. 13(a) and 13(b) based on the lumped model proposed in Section 2. The fast and slow nature frequencies for the analytical model are 25765 Hz and 555.34 Hz, respectively. The variation in nature frequency between the analytical and experimental results is less than 3%. The damping ratio of the structure is a factor that affects the computed scanning angle. The numerical results for various damping ratios are shown in Figs. 13(a) and 13(b). A comparison of the experimental results indicates that the damping ratio of the structure is approximately 0.0002 to 0.0003, which is slightly smaller than 0.0005.

By using an adder with operational amplifier (OP), these two applied voltage conditions can be added to drive the device so that it can project a two-dimensional pattern. The driving frequencies are 25001 Hz and 557.65 Hz, and the optical scanning angles are 27.6° and 39.9°. It is unavoidable that the energy loss always exists when an adder is used. A comparison with Fig. 13(b) shows that the slow optical angle remains the same. The fast optical angle is 4° lower than the case in which the fast signal alone is applied to the device. This slight angle decease suggests that the energy loss is acceptable.

A current probe (Tektronix TCPA300) was used to measure the current when the device operates at resonance. The voltage and current was monitored by an oscilloscope (Agilent MSO6034A). The oscilloscope can also calculate the power consumption of the piezoelectric by integrating the voltage and current over time. The measured power consumption was 13.4 *mW*.

#### 4.2 Linearity test

Figure 14
shows the linearity test result of the scanning device. This experiment simultaneously applied fast and slow signals using an adder. The maximum optical angle is approximately 40°, and the resulting maximum mechanical rotation angle of the torsion bar is then 10°. For an angle *θ* = 10° = 0.1745 rad, its tangent function is tan*θ* = 0.1763, which is close to *θ*. This suggests that the nonlinearity caused by the large optical scanning angle can be neglected. The nonlinearity in Fig. 14 can be ascribed to the saturation of the PZT when it is subjected to a high voltage.

## 5. Laser projection module

The scanning device driven by PZT is integrated into a laser projection module. The module consists of red (635nm), green (512nm) and blue (445nm) semi-conductor lasers, a laser driver, scanner driving circuits, a video decoder and a field-programmable gate array (FPGA). Figure 15 shows the module projecting a 2-D image at a resolution of 640 x 480.

## 6. Conclusions

This paper presents a novel two-axis MEMS scanning mirror driven by PZT ceramics. This study also develops a multi-DOF vibration model as an auxiliary to design the scanning device. The model shows that the coupled modes can increase the scanning angles. Experiments show that the scanning device is capable of 2D scanning with 25.0 kHz and 0.56 kHz. Compared with other actuation mechanisms, such as electrostatics and electromagnetics, the proposed scanning device can scan at a larger optical angle with a voltage of 10 V and a power consumption of 13.4 mW. This study also develops a laser projection module integrated with the scanning device. The module can project a 2-D image at a resolution of 640 x 480.

## Acknowledgments

This study is supported by the Ministry of Economic Affairs, R.O.C., through grant number B327HK2410 and National Formosa University. The authors are also grateful to Mr. Chien-Shien Yeh for his help with the assembly of the scanning device, Mr. Yao-Hui Lee for the development of the FPGA of the testing system, and Mr. Han-Wei Su for his help with the assembly of the lasers and scanners.

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