## Optical Fourier transform based in-plane vibration characterization for MEMS comb structure |

Optics Express, Vol. 21, Issue 4, pp. 5063-5070 (2013)

http://dx.doi.org/10.1364/OE.21.005063

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### Abstract

On-line and on-wafer characterizations of mechanical properties of Micro-Electro-Mechanical-System (MEMS) with efficiency are very important to the mass production of MEMS foundry in the near future. However, challenges still remain. In this paper, we present an in-plane vibration characterizing method for MEMS comb using optical Fourier transform (OFT). In the experiment, the intensity distribution at the focal plane was captured to characterize the displacement of the vibrator in the MEMS comb structure. A typical MEMS comb was tested to verify the principle. The shape and the movement of MEMS comb was imitated and tested to calibrate the measurement by using a spatial light modulator (SLM). The relative standard deviations (RSD) of the measured displacements were better than 5%, where the RSD is defined as the ratio of the standard deviation to the mean. It is convinced that the presented method is feasible for on-line and on-wafer characterizations for MEMS with great convenience, high efficiency and low cost.

© 2013 OSA

## 1. Introductions

1. R. Legtenberg, A. W. Groeneveld, and M. Elwenspoek, “Comb-drive actuators for large displacements,” J. Micromech. Microeng. **6**(3), 320–329 (1996). [CrossRef]

2. S. Kang, H. C. Kim, and K. Chun, “A low-loss, single-pole, four-throw RF MEMS switch driven by a double stop comb drive,” J. Micromech. Microeng. **19**(3), 035011 (2009). [CrossRef]

7. S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub) nanometer resolution,” J. Micromech. Microeng. **14**(9), S97–S101 (2004). [CrossRef]

8. D. A. Wang, F. W. Sheu, and Y. S. Chiu, “In-plane vibration characterization of microelectromechanical systems using acousto-optic modulated partially incoherent stroboscopic imaging,” Opt. Lasers Eng. **49**(7), 954–961 (2011). [CrossRef]

9. J. M. Dawson, L. Wang, P. Famouri, and L. A. Hornak, “Grating-enhanced through-wafer optical microprobe for microelectromechanical system high-resolution optical position feedback,” Opt. Lett. **28**(14), 1263–1265 (2003). [CrossRef] [PubMed]

10. G. Y. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. **15**(2), 388–395 (2006). [CrossRef]

11. A. Bosseboeuf, C. Bréluzeau, F. Parrain, P. Coste, J. Gilles, S. Megherbi, and X. Roux, “In-plane vibration measurement of micro devices by the knife-edge technique in reflection mode,” Proc. SPIE **6345**, 63451D, 63451D-8 (2006). [CrossRef]

12. Y. Zhong, G. X. Zhang, C. L. Leng, and T. Zhang, “A diﬀerential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement **40**(6), 623–627 (2007). [CrossRef]

## 2. Principle

*a*” is the width of the teeth, “

*b”*is the overlap of the teeth,

*“s”*is the offset of the two opposite parts and

*“T”*is the spatial period respectively. In driving and sensing situations, the vibrator usually moves asymmetrically. Assuming that the feature along the teeth can be ignored and the number of teeth is very large, it is valid to treat the comb as a periodic function, which is typically a plane periodic pattern. OFT has the great advantage of characterizing the periodic feature of MEMS comb structure. The transmittance “

*t”*of comb structure is described by:

_{0}14. G. J. Zhang and S. H. Ye, “Online measurement of the sizes of standard wire sieves using an optical Fourier transform,” Opt. Eng. **39**(4), 1098–1102 (2000). [CrossRef]

*t*(

_{0}*x,y*). Then, the field distribution

*U*across the back focal plane of the lens is given by [13]:

_{f}*λ*is the wavelength of the incident plane wave and

*f*is the focal length. Thus the intensity distribution

*I*is given by [13]:

_{f}*I*(

_{x,f}*f*) with the comb structure can be described as a discrete function, which means the intensity distribution is made of discrete points. Therefore, the interval of discrete points along the

_{x}*x*axis is given by:

*T*of the MEMS comb can also be measured by the interval of the spectral lines. To simplify,

*f*is set to zero, where

_{y}*I*(

_{y,f}*f*) reaches its maximum b

_{y}^{2}. Non-zero value of

*I*(

_{x,f}*f*) can only be considered when

_{x}*x*=

_{f}*n*Δ

*x*(n ∈N), which is called the

_{f}*n*

^{th}order of the spectrum pattern. Substituting

*n*= 1 and 2 into Eq. (4), we can get:

*a*, b,

*λ*,

*A, f*and

*T*are constant, while only

*s*is variable. That means the intensity

*I*of the first diffraction order and the intensity

_{1}*I*of the second diffraction order are modulated by the offset

_{2}*s*. Therefore, the offset

*s*can be obtained by measuring

*I*and

_{1}*I*.

_{2}*I*and

_{1max}*I*are required when

_{2max}*s*from

*I*or

_{1}*I*needs to be calculated independently. However, the situations of

_{2}*I*and

_{1max}*I*may be impossible to reach directly because the available displacement may be limited. So it is essential to find the values of

_{2max}*I*and

_{1max}*I*by some indirect means.

_{2max}*I*has a semi-linear relationship with

_{2}*I*, which gives a great help of finding the values of

_{1}*I*and

_{1max}*I*. In Fig. 3(c), it shows the curve of the semi-linear relationship between

_{2max}*I*and the square root of

_{1}*I*. Therefore, the values of

_{2}*I*and

_{1max}*I*can be acquired by the linear extrapolation.

_{2max}## 3. Experimental configurations

15. L. P. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang, and A. K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Appl. Opt. **45**(1), 90–94 (2006). [CrossRef] [PubMed]

*T*was set to 20 pixels and

*a*was set to 2 pixels. The offset

*s*varied from 3 pixels to 10 pixels. As it has the same magnitude as common MEMS combs in size, therefore it was valid for the SLM to imitate a MEMS comb structure.

## 4. Results and discussion

*I*and

_{1}*I*were obtained by summing the digitalized intensity of the pixels throughout the corresponding areas together instead of finding the maximum of intensity. The experimental results of the relationship between

_{2}*I*and square root of

_{1}*I*are illustrated by Fig. 7 . As a result of digitalization,

_{2}*I*and

_{1}*I*have no units in Fig. 7. It is indicated that

_{2}*I*and square root of

_{1}*I*fit the theoretical semi-linear relationship.

_{2}*I*was calculated by linear fitting from Fig. 7. Substituting

_{1max}*I*into Eq. (6), the displacement of vibrator, or the offset

_{1max}*s*, was calculated and plotted in Fig. 8 . Most data points fitted the theoretical curve well except the points of 9-pixels real displacement. It is speculated that the point of 9 pixels was close to the symmetric point and that the intensity

*I*was close to zero. Thus the intensities of many pixels in the first order could be less than the minimum CCD resolution, which caused the measured

_{1}*I*was lower than it should be and the corresponding displacement was shift to the symmetric point (

_{1}*s*=

*T/*2). From Fig. 8, it is obvious that the measured results of displacement matched the theoretical results. The average measured displacements and the RSDs were listed in Table 1 . The RSD is defined as the ratio of the standard deviation to the mean here. The observed RSDs were below 5%, which meant that the compensation could be very effective to eliminate the nonlinearity of the average measured displacement.

*s”*varies asymmetrically [3–5], in other words, it always above or below

*T*/2, therefore, the proposed method can be quantitative.

*I*and

_{1max}*I*are required before measuring displacement. As a result, the calibration procedure is essential as a pre-measuring step.

_{2max}## 5. Conclusion

12. Y. Zhong, G. X. Zhang, C. L. Leng, and T. Zhang, “A diﬀerential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement **40**(6), 623–627 (2007). [CrossRef]

## Acknowledgment

## References and links

1. | R. Legtenberg, A. W. Groeneveld, and M. Elwenspoek, “Comb-drive actuators for large displacements,” J. Micromech. Microeng. |

2. | S. Kang, H. C. Kim, and K. Chun, “A low-loss, single-pole, four-throw RF MEMS switch driven by a double stop comb drive,” J. Micromech. Microeng. |

3. | M. J. Thompson and D. A. Horsley, “Resonant MEMS magnetometer with capacitive read-out,” in IEEE Sensors 2009 Conference. (Christchurch, New Zealand, Oct. 25–28, 2009), 992–995. |

4. | H. Chen, M. Chen, W. J. Zhao, and L. M. Xu, “Equivalent electrical modeling and simulation of MEMS comb accelerometer,” in 2010 International Conference on Measuring Technology and Mechatronics Automation. (Changsha City, China, 13–14 March 2010), 116–119. |

5. | Y. Zhu, M. R. Yuce, and S. O. R. Moheimani, “A low-loss MEMS tunable capacitor with movable dielectric,” in IEEE Sensors 2009 Conference. (Christchurch, New Zealand, Oct. 25–28, 2009), 651–654. |

6. | C. Rembe, L. Muller, R. S. Muller, and R. T. Howe, “Full three-dimensional motion characterization of a gimballed electrostatic microactuator,” in Proc. IEEE Int. Rel. Symp. (Orlando, FL, Apr. 30,2001),91–98. |

7. | S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub) nanometer resolution,” J. Micromech. Microeng. |

8. | D. A. Wang, F. W. Sheu, and Y. S. Chiu, “In-plane vibration characterization of microelectromechanical systems using acousto-optic modulated partially incoherent stroboscopic imaging,” Opt. Lasers Eng. |

9. | J. M. Dawson, L. Wang, P. Famouri, and L. A. Hornak, “Grating-enhanced through-wafer optical microprobe for microelectromechanical system high-resolution optical position feedback,” Opt. Lett. |

10. | G. Y. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst. |

11. | A. Bosseboeuf, C. Bréluzeau, F. Parrain, P. Coste, J. Gilles, S. Megherbi, and X. Roux, “In-plane vibration measurement of micro devices by the knife-edge technique in reflection mode,” Proc. SPIE |

12. | Y. Zhong, G. X. Zhang, C. L. Leng, and T. Zhang, “A diﬀerential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement |

13. | J. W. Goodman, |

14. | G. J. Zhang and S. H. Ye, “Online measurement of the sizes of standard wire sieves using an optical Fourier transform,” Opt. Eng. |

15. | L. P. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang, and A. K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Appl. Opt. |

16. | A. Vyas, M. B. Roopashree, and B. R. Prasad, “Digital long focal length lenslet array using spatial light modulator,” in Proceedings of the international conference on optics and photonics. (Chandigarh, India, 30 Oct. −1 Nov. 2009) |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: December 27, 2012

Revised Manuscript: February 8, 2013

Manuscript Accepted: February 8, 2013

Published: February 21, 2013

**Citation**

Yongfeng Gao, Liangcai Cao, Zheng You, Jiahao Zhao, Zichen Zhang, and Jianzhong Yang, "Optical Fourier transform based in-plane vibration characterization for MEMS comb structure," Opt. Express **21**, 5063-5070 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-5063

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### References

- R. Legtenberg, A. W. Groeneveld, and M. Elwenspoek, “Comb-drive actuators for large displacements,” J. Micromech. Microeng.6(3), 320–329 (1996). [CrossRef]
- S. Kang, H. C. Kim, and K. Chun, “A low-loss, single-pole, four-throw RF MEMS switch driven by a double stop comb drive,” J. Micromech. Microeng.19(3), 035011 (2009). [CrossRef]
- M. J. Thompson and D. A. Horsley, “Resonant MEMS magnetometer with capacitive read-out,” in IEEE Sensors 2009 Conference. (Christchurch, New Zealand, Oct. 25–28, 2009), 992–995.
- H. Chen, M. Chen, W. J. Zhao, and L. M. Xu, “Equivalent electrical modeling and simulation of MEMS comb accelerometer,” in 2010 International Conference on Measuring Technology and Mechatronics Automation. (Changsha City, China, 13–14 March 2010), 116–119.
- Y. Zhu, M. R. Yuce, and S. O. R. Moheimani, “A low-loss MEMS tunable capacitor with movable dielectric,” in IEEE Sensors 2009 Conference. (Christchurch, New Zealand, Oct. 25–28, 2009), 651–654.
- C. Rembe, L. Muller, R. S. Muller, and R. T. Howe, “Full three-dimensional motion characterization of a gimballed electrostatic microactuator,” in Proc. IEEE Int. Rel. Symp. (Orlando, FL, Apr. 30,2001),91–98.
- S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub) nanometer resolution,” J. Micromech. Microeng.14(9), S97–S101 (2004). [CrossRef]
- D. A. Wang, F. W. Sheu, and Y. S. Chiu, “In-plane vibration characterization of microelectromechanical systems using acousto-optic modulated partially incoherent stroboscopic imaging,” Opt. Lasers Eng.49(7), 954–961 (2011). [CrossRef]
- J. M. Dawson, L. Wang, P. Famouri, and L. A. Hornak, “Grating-enhanced through-wafer optical microprobe for microelectromechanical system high-resolution optical position feedback,” Opt. Lett.28(14), 1263–1265 (2003). [CrossRef] [PubMed]
- G. Y. Zhou and F. S. Chau, “Grating-assisted optical microprobing of in-plane and out-of-plane displacements of microelectromechanical devices,” J. Microelectromech. Syst.15(2), 388–395 (2006). [CrossRef]
- A. Bosseboeuf, C. Bréluzeau, F. Parrain, P. Coste, J. Gilles, S. Megherbi, and X. Roux, “In-plane vibration measurement of micro devices by the knife-edge technique in reflection mode,” Proc. SPIE6345, 63451D, 63451D-8 (2006). [CrossRef]
- Y. Zhong, G. X. Zhang, C. L. Leng, and T. Zhang, “A diﬀerential laser Doppler system for one-dimensional in-plane motion measurement of MEMS,” Measurement40(6), 623–627 (2007). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics(third edition) (Robert & Company Publishers, 2005), Chap. 5.
- G. J. Zhang and S. H. Ye, “Online measurement of the sizes of standard wire sieves using an optical Fourier transform,” Opt. Eng.39(4), 1098–1102 (2000). [CrossRef]
- L. P. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang, and A. K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Appl. Opt.45(1), 90–94 (2006). [CrossRef] [PubMed]
- A. Vyas, M. B. Roopashree, and B. R. Prasad, “Digital long focal length lenslet array using spatial light modulator,” in Proceedings of the international conference on optics and photonics. (Chandigarh, India, 30 Oct. −1 Nov. 2009)

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