## Theoretical and experimental study of optothermal expansion and optothermal microactuator

Optics Express, Vol. 16, Issue 17, pp. 13476-13485 (2008)

http://dx.doi.org/10.1364/OE.16.013476

Acrobat PDF (496 KB)

### Abstract

A new type of microactuators based on optothermal (OT) expansion is introduced. The mechanism of the OT expansion is theoretically analyzed, and comprehensive models for OT expansion and bi-direction microactuator are presented in this paper. An expansion arm and a microswitch-like OT microactuator with 1200µm-length are fabricated by an excimer laser micromachining system using single layer material. A laser diode (650nm) is employed as the external power source to activate the arm and the microactuator. Experimental results indicate that the OT expansion increment is approximately linear with the laser power irradiating the expansion arm, coinciding with theoretical predictions quite well. As to the switch-like microactuator, an enlarged bi-direction deflection has been obviously observed. The OT expansion and deflection amplitude that can reach micron scale is generally large enough for most microsystems. The new technique of OT microactuators can be widely applied in those fields where simple structure, easy fabrication, large displacement, wireless and remote controlling are required.

© 2008 Optical Society of America

## 1. Introduction

2. J. L. Yeh, C. Y. Hui, and N. C. Tien, “Electrostatic model for an asymmetric comb drive,” Journal of Microelectromechanical Systems **9**, 126–130 (2000). [CrossRef]

3. D. L. Devoe and A. P. Pisano, “Modeling and optimal design of piezoelectric cantilever microactuators,” Journal of Microelectromechanical Systems **6**, 266–270(1997). [CrossRef]

4. X. Huang and H. Shen, “Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators,” International Journal of Mechanical Sciences **47**, 187–208 (2005). [CrossRef]

6. C. N. Saikrishna, K. V. Ramaiah, and S. K. Bhaumik, “Effects of thermo-mechanical cycling on the strain response of Ni-Ti-Cu shape memory alloy wire actuator,” Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing **428**, 217–224 (2006). [CrossRef]

7. T. Lalinský, M. Držík, J. Chlpík, M. Krnáč, Š Haščík, Ž. Mozolová, and I. Kostič, “Thermo-mechanical characterization of micromachined GaAs-based thermal converter using contactless optical methods,” Sensors and Actuators A **123–124**, 99–105 (2005). [CrossRef]

8. L. J. Li and D. Uttamchandani, “Modified asymmetric microelectrothermal actuator: analysis and experimentation,” J. Micromech. Microeng. **14**, 1734–1741 (2004). [CrossRef]

9. M. F. Pai and N. C. Tien, “Low voltage electrothermal vibromotor for silicon optical bench applications,” Sensors Actuators A **83**, 237–243 (2000). [CrossRef]

10. J. K. Luo, A. J. Flewitt, S. M. Spearing, N. A. Fleck, and W. I. Milne, “Comparison of microtweezers based on three lateral thermal actuator configurations,” J. Micromech. Microeng. **15**, 1294–1302 (2005). [CrossRef]

11. S. C. Chen, C. P. Grigoropoulos, H. K. Park, P. Kerstens, and A. C. Tam, “Photothermal displacement measurement of transient melting and surface deformation during pulsed laser heating,” Appl. Phy. Lett. **73**, 2093–2095 (1998). [CrossRef]

## 2. Theoretical model of optothermal expansion and deflection

12. Y. L. He, H. J. Zhang, and D. X. Zhang, “Theoretical and experimental study of photo-thermal expansion using an atomic force microscope,” J. Micromech. Microeng. **15**, 1637–1640 (2005). [CrossRef]

*L*due to its temperature increases and volume expands (Fig. 1(a)). In order to acquire an enlarged lateral deflection, an actuator with two slender arms is proposed as shown in Fig. 1(b). As the free ends of the arms are connected, when the laser irradiates one of the arms, thermal expansion will make the actuator laterally deflect for

*d*. When the other arm being irradiated, the direction of deflection will reverse.

*L*, width

*W*, thickness

*D*and the initial temperature

*T*

_{0}is connected with the base on the left end. A laser spot with radius

*R*is formed when a laser of power

*P*

_{0}irradiates the arm. Set the left end of the arm as the coordinate origin (

*x*=0), the center of the spot as

*x*=

*L*

_{1}, the free right end as

*x*=

*L*, and

*L*

_{2}=

*L*-

*L*

_{1}. The power-density distribution along the

*X*direction is named

*Q*(

*x*). The power distribution of the spot is usually Gaussian, however, as the diameter of the spot is much smaller than the length of the arm and the integral compensation, the power-density distribution can be assumed to be constant. Therefore,

*Q*(

*x*) can be expressed as:

*ρ*

_{A}is the ratio of absorption,

*q*

_{0}the incident laser power density, i.e.,

*P*

_{0}/(π

*R*

^{2}). We choose an arbitrary infinitesimal element with

*dx*length at the position

*x*on the right (Fig. 2 (b), so does on the left) of the spot center to analyze the OT transmission. The element gains heat from the laser irradiation and inner heat conduction, and losses heat through surface heat convection and conduction. The heat balance equation is:

*K*is the thermal conductivity of the material,

*T*(

*x*) the temperature distribution when the arm is irradiated, the temperature rise Δ

*T*(

*x*)=

*T*(

*x*)-

*T*

_{0},

*h*

_{D}is the coefficient of the convective heat transfer on the side surface,

*h*

_{W}is that on the up and down surfaces (their

*h*

_{W}is nearly the same as the arm thickness is on micrometer scale). Eq. (2) can also be written in the form of second-order differential equation:

*b*and

*f*(

*x*) are defined by

*x*

_{0}ranges from 0 to

*L*. As the heat environment at the left end (fixed) is different from the right end (free), the coefficients of the convective heat transfer are different, named

*h*

_{1},

*h*

_{2}respectively.

*h*

_{2}is the same with

*h*

_{D}. So the thermal boundary condition can be expressed as:

*sh()*and

*ch()*are hyperbolic sine and cosine functions, the constant

*C*

_{3}is

*L*along the

*X*direction can be expressed as:

*α*is the linear thermal expansion coefficient of the material. With Eq. (7) and (8), Δ

*L*can be derived:

*L*into lateral deflection

*d*. The deflection can be expressed and calculated by the following Eqs., where the geometrical parameters are indicated in Fig. 4. For clarity, the deflection and bending of the actuator are not to scale.

*L*of the unirradiated arm, BC is the length difference of the two arms due to OT expansion, CO’, i.e.

*S*, is the gap distance between the two arms. The deflection angle

*θ is*actually quite small, cos

*θ*≈1, so the deflection

*d*could be given:

*L*is dominantly determined by the laser power. Although the unirradiated arm might slightly reduce the longitudinal expansion Δ

*L*of the irradiated arm, as

*L*is much larger than

*S*, an enlarged lateral deflection could be acquired.

## 3. Experiments

^{×}objective lens, while the zoomed images (right columns) are snapshots from videos using a 40

^{×}objective lens, corresponding to the marked areas in the left images. We can precisely measure the data of expansion increment by using a self-designed sub-pixel video analysis software for microactuators.

^{×}objective lens is about 0.3 µm, therefore, the measurement accuracy (sub-pixel accuracy) is on the scale of less than 0.1 µm.

13. Jeffrey T. Butler, Victor M. Bright, and William D. Cowan, “Average power control and positioning of polysilicon thermal actuators,” Sensors and Actuators **72**, 88–97(1999). [CrossRef]

*et al.*) [14

14. Lijie Li and Deepak Uttamchandani, “Modified asymmetric micro-electrothermal actuator,” J. Micromech. Microeng. **14**, 1734–1741(2004). [CrossRef]

13. Jeffrey T. Butler, Victor M. Bright, and William D. Cowan, “Average power control and positioning of polysilicon thermal actuators,” Sensors and Actuators **72**, 88–97(1999). [CrossRef]

14. Lijie Li and Deepak Uttamchandani, “Modified asymmetric micro-electrothermal actuator,” J. Micromech. Microeng. **14**, 1734–1741(2004). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

1. | J. Kyokane, K. Tsujimoto, Y. Yanagisawa, T. Ueda, and M. Fukuma, “Actuator using electrostriction effect of fullerenol-doped polyurethane elastomer (PUE) films,” IEICE Transactions on Electronics E |

2. | J. L. Yeh, C. Y. Hui, and N. C. Tien, “Electrostatic model for an asymmetric comb drive,” Journal of Microelectromechanical Systems |

3. | D. L. Devoe and A. P. Pisano, “Modeling and optimal design of piezoelectric cantilever microactuators,” Journal of Microelectromechanical Systems |

4. | X. Huang and H. Shen, “Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators,” International Journal of Mechanical Sciences |

5. | Y. W. Park and D. Y. Kim, “Development of a magnetostrictive microactuator,” Journal of Magnetism and Magnetic Materials E |

6. | C. N. Saikrishna, K. V. Ramaiah, and S. K. Bhaumik, “Effects of thermo-mechanical cycling on the strain response of Ni-Ti-Cu shape memory alloy wire actuator,” Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing |

7. | T. Lalinský, M. Držík, J. Chlpík, M. Krnáč, Š Haščík, Ž. Mozolová, and I. Kostič, “Thermo-mechanical characterization of micromachined GaAs-based thermal converter using contactless optical methods,” Sensors and Actuators A |

8. | L. J. Li and D. Uttamchandani, “Modified asymmetric microelectrothermal actuator: analysis and experimentation,” J. Micromech. Microeng. |

9. | M. F. Pai and N. C. Tien, “Low voltage electrothermal vibromotor for silicon optical bench applications,” Sensors Actuators A |

10. | J. K. Luo, A. J. Flewitt, S. M. Spearing, N. A. Fleck, and W. I. Milne, “Comparison of microtweezers based on three lateral thermal actuator configurations,” J. Micromech. Microeng. |

11. | S. C. Chen, C. P. Grigoropoulos, H. K. Park, P. Kerstens, and A. C. Tam, “Photothermal displacement measurement of transient melting and surface deformation during pulsed laser heating,” Appl. Phy. Lett. |

12. | Y. L. He, H. J. Zhang, and D. X. Zhang, “Theoretical and experimental study of photo-thermal expansion using an atomic force microscope,” J. Micromech. Microeng. |

13. | Jeffrey T. Butler, Victor M. Bright, and William D. Cowan, “Average power control and positioning of polysilicon thermal actuators,” Sensors and Actuators |

14. | Lijie Li and Deepak Uttamchandani, “Modified asymmetric micro-electrothermal actuator,” J. Micromech. Microeng. |

**OCIS Codes**

(120.6780) Instrumentation, measurement, and metrology : Temperature

(120.6810) Instrumentation, measurement, and metrology : Thermal effects

(120.7000) Instrumentation, measurement, and metrology : Transmission

(230.4000) Optical devices : Microstructure fabrication

(350.5340) Other areas of optics : Photothermal effects

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: July 3, 2008

Revised Manuscript: August 4, 2008

Manuscript Accepted: August 5, 2008

Published: August 15, 2008

**Citation**

Dongxian Zhang, Haijun Zhang, Chao Liu, and Jianzhong Jiang, "Theoretical and experimental study of optothermal expansion and optothermal microactuator," Opt. Express **16**, 13476-13485 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13476

Sort: Year | Journal | Reset

### References

- J. Kyokane, K. Tsujimoto, Y. Yanagisawa, T. Ueda, and M. Fukuma, "Actuator using electrostriction effect of fullerenol-doped polyurethane elastomer (PUE) films," IEICE Transactions on Electronics E 87C, 136-141 (2004).
- J. L. Yeh, C. Y. Hui, and N. C. Tien, "Electrostatic model for an asymmetric comb drive," Journal of Microelectromechanical Systems 9,126-130 (2000). [CrossRef]
- D. L. Devoe and A. P. Pisano, "Modeling and optimal design of piezoelectric cantilever microactuators," Journal of Microelectromechanical Systems 6,266-270(1997). [CrossRef]
- X. Huang and H. Shen, "Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators," International Journal of Mechanical Sciences 47,187-208 (2005). [CrossRef]
- Y. W. Park and D. Y. Kim, "Development of a magnetostrictive microactuator," Journal of Magnetism and Magnetic Materials E 1765-1766,272-276 (2004).
- C. N. Saikrishna, K. V. Ramaiah, and S. K. Bhaumik, "Effects of thermo-mechanical cycling on the strain response of Ni-Ti-Cu shape memory alloy wire actuator," Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing 428,217-224 (2006). [CrossRef]
- T. Lalinský, M. Držík, J. Chlpík, M. Krná�?, Š. Haš�?ík, Ž. Mozolová, and I. Kosti�?, "Thermo-mechanical characterization of micromachined GaAs-based thermal converter using contactless optical methods," Sensors and Actuators A 123-124,99-105 (2005). [CrossRef]
- L. J. Li and D. Uttamchandani, "Modified asymmetric microelectrothermal actuator: analysis and experimentation," J. Micromech. Microeng. 14, 1734-1741 (2004). [CrossRef]
- M. F. Pai, and N. C. Tien, "Low voltage electrothermal vibromotor for silicon optical bench applications," Sensors Actuators A 83, 237-243 (2000). [CrossRef]
- J. K. Luo, A. J. Flewitt, S. M. Spearing, N. A. Fleck, and W. I. Milne, "Comparison of microtweezers based on three lateral thermal actuator configurations," J. Micromech. Microeng. 15,1294-1302 (2005). [CrossRef]
- S. C. Chen, C. P. Grigoropoulos, H. K. Park, P. Kerstens, and A. C. Tam, "Photothermal displacement measurement of transient melting and surface deformation during pulsed laser heating," Appl. Phy. Lett. 73,2093-2095 (1998). [CrossRef]
- Y. L. He, H. J. Zhang, and D. X. Zhang, "Theoretical and experimental study of photo-thermal expansion using an atomic force microscope," J. Micromech. Microeng. 15,1637-1640 (2005). [CrossRef]
- J. T. Butler, V. M. Bright, and W. D. Cowan, "Average power control and positioning of polysilicon thermal actuators," Sensors and Actuators 72, 88-97 (1999). [CrossRef]
- L. Li and D. Uttamchandani, "Modified asymmetric micro-electrothermal actuator," J. Micromech. Microeng. 14, 1734-1741(2004). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Supplementary Material

» Media 1: MOV (1699 KB)

» Media 2: MOV (2413 KB)

» Media 3: MOV (1740 KB)

» Media 4: MOV (1950 KB)

« Previous Article | Next Article »

OSA is a member of CrossRef.