## A novel two-axis MEMS scanning mirror with a PZT actuator for laser scanning projection |

Optics Express, Vol. 20, Issue 24, pp. 27003-27017 (2012)

http://dx.doi.org/10.1364/OE.20.027003

Acrobat PDF (1924 KB)

### 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

2. C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express **18**(4), 3805–3819 (2010). [CrossRef] [PubMed]

3. J. Tsai and M. C. Wu, “Gimbal-less MEMS two-axis optical scanner array with high fill-factor,” J. Microelectromech. Syst. **14**(6), 1323–1328 (2005). [CrossRef]

5. X. Y. Li, Q. Jin, D. Y. Qiao, B. P. Kang, B. Yan, and Y. B. Liu, “Design and fabrication of a resonant scanning micromirror suspended by V shaped beams with vertical electrostatic comb drives,” Microsyst. Technol. **18**(3), 295–302 (2012). [CrossRef]

6. Y. Xu, J. Singh, T. Selvaratnam, and N. Chen, “Two-axis gimbal-less electrothermal micromirror for large-angle circumferential scanning,” IEEE J. Sel. Top. Quantum Electron. **15**(5), 1432–1438 (2009). [CrossRef]

8. A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague, “Two-axis electromagnetic microscanner for high resolution displays,” J. Microelectromech. Syst. **15**(4), 786–794 (2006). [CrossRef]

9. K. H. Kim, B. H. Park, G. N. Maguluri, T. W. Lee, F. J. Rogomentich, M. G. Bancu, B. E. Bouma, J. F. de Boer, and J. J. Bernstein, “Two-axis magnetically-driven MEMS scanning catheter for endoscopic high-speed optical coherence tomography,” Opt. Express **15**(26), 18130–18140 (2007). [CrossRef] [PubMed]

14. A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague, “Two axis electromagnetic microscanner for high resolution displays,” J. Microelectromech. Syst. **15**(4), 786–794 (2006). [CrossRef]

15. X. Chu, L. Ma, S. Yuan, M. Li, and L. Li, “Two-dimensional optical scanning of a piezoelectric cantilever actuator,” J. Electroceram. **21**(1-4), 774–777 (2008). [CrossRef]

16. K. H. Koh, T. Kobayashi, and C. Lee, “A 2-D MEMS scanning mirror based on dynamic mixed mode excitation of a piezoelectric PZT thin film S-shaped actuator,” Opt. Express **19**(15), 13812–13824 (2011). [CrossRef] [PubMed]

17. K. H. Gilchrist, R. P. McNabb, J. A. Izatt, and S. Grego, “Piezoelectric scanning mirrors for endoscoptic optical coherence tomography,” J. Micromech. Microeng. **19**(9), 095012 (2009). [CrossRef]

18. S. Moon, S. W. Lee, M. Rubinstein, B. J. F. Wong, and Z. Chen, “Semi-resonant operation of a fiber-cantilever piezotube scanner for stable optical coherence tomography endoscope imaging,” Opt. Express **18**(20), 21183–21197 (2010). [CrossRef] [PubMed]

## 2. Two-axis mirror design and modeling

*ω*

_{n}_{,}

*of the fast scanning can be written as*

_{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}*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}19. H. Urey, C. Kan, and W. O. Davis, “Vibration mode frequency formulae for micromechanical scanners,” J. Micromech. Microeng. **15**(9), 1713–1721 (2005). [CrossRef]

### 2.1 Fast scanning: 4-DOF discrete vibration model

*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 where

*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 toThe equivalent spring constant

*k*

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

*I*

_{2}are given as

*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}19. H. Urey, C. Kan, and W. O. Davis, “Vibration mode frequency formulae for micromechanical scanners,” J. Micromech. Microeng. **15**(9), 1713–1721 (2005). [CrossRef]

*I*

_{4}and

*k*

_{4}can be calculated as

*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}*M*

_{0}produced by the piezoelectric actuator can be estimated as follows:where

*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*.

*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

*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.

*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.

*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

*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.

*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.

*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

*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

- 1. Set fast and slow frequencies. The dimension of the torsion bar can be estimated based on [19].
**15**(9), 1713–1721 (2005). [CrossRef] - 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

*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.

*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.

## 4. Scanning performance of the device

*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

*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}.

*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°.

*mW*.

### 4.2 Linearity test

*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

## 6. Conclusions

## Acknowledgments

## References and links

1. | M. Scholles, K. Frommhagen, C. Gerwig, H. Lakner, H. Schenk, and M. Schwarzenberg, “Ultracompact laser projection systems based on two-dimensional resonant microscanning mirrors,” J. Micro-Nanolith. MEM |

2. | C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express |

3. | J. Tsai and M. C. Wu, “Gimbal-less MEMS two-axis optical scanner array with high fill-factor,” J. Microelectromech. Syst. |

4. | J. Tsai, S. Chiou, T. Hsieh, C. Sun, D. Hah, and M. C. Wu, “Two-axis MEMS scanners with radial vertical combdrive actuators-design, theoretical analysis, and fabrication,” J. Opt. A: Pure Appl. Opt. |

5. | X. Y. Li, Q. Jin, D. Y. Qiao, B. P. Kang, B. Yan, and Y. B. Liu, “Design and fabrication of a resonant scanning micromirror suspended by V shaped beams with vertical electrostatic comb drives,” Microsyst. Technol. |

6. | Y. Xu, J. Singh, T. Selvaratnam, and N. Chen, “Two-axis gimbal-less electrothermal micromirror for large-angle circumferential scanning,” IEEE J. Sel. Top. Quantum Electron. |

7. | J. Singh, T. Gan, A. A. Mohanraj, and S. Liw, “3D free space thermally actuated micromirror device,” Sensor Actuat. A. |

8. | A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague, “Two-axis electromagnetic microscanner for high resolution displays,” J. Microelectromech. Syst. |

9. | K. H. Kim, B. H. Park, G. N. Maguluri, T. W. Lee, F. J. Rogomentich, M. G. Bancu, B. E. Bouma, J. F. de Boer, and J. J. Bernstein, “Two-axis magnetically-driven MEMS scanning catheter for endoscopic high-speed optical coherence tomography,” Opt. Express |

10. | J. H. Park, J. Akedo, and H. Sato, “High-speed metal-based optical microscanner using stainless-steel substrate and piezoelectric thick films prepared by aerosol deposition method,” Sensor Actuat. A. |

11. | Y. Yasuda, M. Akamatsu, M. Tani, T. Iijima, and H. Toshiyoshi, “Piezoelectric 2D-optical micro scanners with PZT thick films,” Integr. Ferroelectr. |

12. | M. Tani, M. Akamatsu, Y. Yasuda, and H. Toshiyoshi, “A Two-axis piezoelectric tilting micromirror with a newly developed PZT-meandering actuator,” IEEE MEMS Inter. Con. 2007 (Kobe, Japan) 21–25 (2007). |

13. | H. Urey, “Torsional MEMS scanner design for high-resolution display systems,” Proc. SPIE |

14. | A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague, “Two axis electromagnetic microscanner for high resolution displays,” J. Microelectromech. Syst. |

15. | X. Chu, L. Ma, S. Yuan, M. Li, and L. Li, “Two-dimensional optical scanning of a piezoelectric cantilever actuator,” J. Electroceram. |

16. | K. H. Koh, T. Kobayashi, and C. Lee, “A 2-D MEMS scanning mirror based on dynamic mixed mode excitation of a piezoelectric PZT thin film S-shaped actuator,” Opt. Express |

17. | K. H. Gilchrist, R. P. McNabb, J. A. Izatt, and S. Grego, “Piezoelectric scanning mirrors for endoscoptic optical coherence tomography,” J. Micromech. Microeng. |

18. | S. Moon, S. W. Lee, M. Rubinstein, B. J. F. Wong, and Z. Chen, “Semi-resonant operation of a fiber-cantilever piezotube scanner for stable optical coherence tomography endoscope imaging,” Opt. Express |

19. | H. Urey, C. Kan, and W. O. Davis, “Vibration mode frequency formulae for micromechanical scanners,” J. Micromech. Microeng. |

**OCIS Codes**

(120.5800) Instrumentation, measurement, and metrology : Scanners

(230.4000) Optical devices : Microstructure fabrication

(230.4040) Optical devices : Mirrors

(230.4685) Optical devices : Optical microelectromechanical devices

**ToC Category:**

Optical Devices

**History**

Original Manuscript: August 14, 2012

Revised Manuscript: October 27, 2012

Manuscript Accepted: October 28, 2012

Published: November 15, 2012

**Citation**

Chung-De Chen, Yu-Jen Wang, and Pin Chang, "A novel two-axis MEMS scanning mirror with a PZT actuator for laser scanning projection," Opt. Express **20**, 27003-27017 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27003

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### References

- M. Scholles, K. Frommhagen, C. Gerwig, H. Lakner, H. Schenk, and M. Schwarzenberg, “Ultracompact laser projection systems based on two-dimensional resonant microscanning mirrors,” J. Micro-Nanolith. MEM7(2), 021001 (2008).
- C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express18(4), 3805–3819 (2010). [CrossRef] [PubMed]
- J. Tsai and M. C. Wu, “Gimbal-less MEMS two-axis optical scanner array with high fill-factor,” J. Microelectromech. Syst.14(6), 1323–1328 (2005). [CrossRef]
- J. Tsai, S. Chiou, T. Hsieh, C. Sun, D. Hah, and M. C. Wu, “Two-axis MEMS scanners with radial vertical combdrive actuators-design, theoretical analysis, and fabrication,” J. Opt. A: Pure Appl. Opt.10(4), 044006 (2008). [CrossRef]
- X. Y. Li, Q. Jin, D. Y. Qiao, B. P. Kang, B. Yan, and Y. B. Liu, “Design and fabrication of a resonant scanning micromirror suspended by V shaped beams with vertical electrostatic comb drives,” Microsyst. Technol.18(3), 295–302 (2012). [CrossRef]
- Y. Xu, J. Singh, T. Selvaratnam, and N. Chen, “Two-axis gimbal-less electrothermal micromirror for large-angle circumferential scanning,” IEEE J. Sel. Top. Quantum Electron.15(5), 1432–1438 (2009). [CrossRef]
- J. Singh, T. Gan, A. A. Mohanraj, and S. Liw, “3D free space thermally actuated micromirror device,” Sensor Actuat. A.123–124(23), 468–475 (2005).
- A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague, “Two-axis electromagnetic microscanner for high resolution displays,” J. Microelectromech. Syst.15(4), 786–794 (2006). [CrossRef]
- K. H. Kim, B. H. Park, G. N. Maguluri, T. W. Lee, F. J. Rogomentich, M. G. Bancu, B. E. Bouma, J. F. de Boer, and J. J. Bernstein, “Two-axis magnetically-driven MEMS scanning catheter for endoscopic high-speed optical coherence tomography,” Opt. Express15(26), 18130–18140 (2007). [CrossRef] [PubMed]
- J. H. Park, J. Akedo, and H. Sato, “High-speed metal-based optical microscanner using stainless-steel substrate and piezoelectric thick films prepared by aerosol deposition method,” Sensor Actuat. A.135(1), 86–91 (2007).
- Y. Yasuda, M. Akamatsu, M. Tani, T. Iijima, and H. Toshiyoshi, “Piezoelectric 2D-optical micro scanners with PZT thick films,” Integr. Ferroelectr.76(1), 81–91 (2005). [CrossRef]
- M. Tani, M. Akamatsu, Y. Yasuda, and H. Toshiyoshi, “A Two-axis piezoelectric tilting micromirror with a newly developed PZT-meandering actuator,” IEEE MEMS Inter. Con. 2007 (Kobe, Japan) 21–25 (2007).
- H. Urey, “Torsional MEMS scanner design for high-resolution display systems,” Proc. SPIE4773, 27–37 (2002). [CrossRef]
- A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague, “Two axis electromagnetic microscanner for high resolution displays,” J. Microelectromech. Syst.15(4), 786–794 (2006). [CrossRef]
- X. Chu, L. Ma, S. Yuan, M. Li, and L. Li, “Two-dimensional optical scanning of a piezoelectric cantilever actuator,” J. Electroceram.21(1-4), 774–777 (2008). [CrossRef]
- K. H. Koh, T. Kobayashi, and C. Lee, “A 2-D MEMS scanning mirror based on dynamic mixed mode excitation of a piezoelectric PZT thin film S-shaped actuator,” Opt. Express19(15), 13812–13824 (2011). [CrossRef] [PubMed]
- K. H. Gilchrist, R. P. McNabb, J. A. Izatt, and S. Grego, “Piezoelectric scanning mirrors for endoscoptic optical coherence tomography,” J. Micromech. Microeng.19(9), 095012 (2009). [CrossRef]
- S. Moon, S. W. Lee, M. Rubinstein, B. J. F. Wong, and Z. Chen, “Semi-resonant operation of a fiber-cantilever piezotube scanner for stable optical coherence tomography endoscope imaging,” Opt. Express18(20), 21183–21197 (2010). [CrossRef] [PubMed]
- H. Urey, C. Kan, and W. O. Davis, “Vibration mode frequency formulae for micromechanical scanners,” J. Micromech. Microeng.15(9), 1713–1721 (2005). [CrossRef]

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