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

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References

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  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]
  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.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. SPIE6345, 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,” Measurement40(6), 623–627 (2007).
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics(third edition) (Robert & Company Publishers, 2005), Chap. 5.
  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]
  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]
  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)

2011 (1)

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]

2009 (1)

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]

2007 (1)

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]

2006 (3)

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]

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]

2004 (1)

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]

2003 (1)

2000 (1)

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]

1996 (1)

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

Asundi, A. K.

Bai, N.

Bosseboeuf, A.

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]

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]

Bréluzeau, C.

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]

Chau, F. S.

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]

Chiu, Y. S.

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]

Chun, K.

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]

Coste, P.

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]

Dawson, J. M.

Elwenspoek, M.

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

Famouri, P.

Fang, Z. P.

Gilles, J.

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]

Groeneveld, A. W.

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

Hornak, L. A.

Kang, S.

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]

Kim, H. C.

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]

Legtenberg, R.

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

Leng, C. L.

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]

Li, X.

Megherbi, S.

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]

Ong, L. S.

Parrain, F.

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]

Petitgrand, S.

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]

Roux, X.

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]

Sheu, F. W.

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]

Wang, D. A.

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]

Wang, L.

Ye, S. H.

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]

Zhang, G. J.

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]

Zhang, G. X.

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]

Zhang, T.

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]

Zhao, L. P.

Zhong, Y.

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]

Zhou, G. Y.

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]

Appl. Opt. (1)

J. Microelectromech. Syst. (1)

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]

J. Micromech. Microeng. (3)

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]

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]

Measurement (1)

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]

Opt. Eng. (1)

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]

Opt. Lasers Eng. (1)

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]

Opt. Lett. (1)

Proc. SPIE (1)

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]

Other (6)

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.

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)

J. W. Goodman, Introduction to Fourier Optics(third edition) (Robert & Company Publishers, 2005), Chap. 5.

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Figures (8)

Fig. 1
Fig. 1

Simplified comb structure (a): structure model, (b): cross-section view. (a: width of the teeth; b: overlap of the teeth; s: offset of the two opposite parts; T: the spatial period).

Fig. 2
Fig. 2

Performing the Fourier transform operation with a positive lens.

Fig. 3
Fig. 3

Theoretical intensity distribution of the spectral plane when s = 0.25T (a) and s = 0.5T (b) (c) the semi-linear relationship between I1 and square root of I2.

Fig. 4
Fig. 4

Schematic diagram of the experiment. (1: He-Ne laser (632.8nm); 2, 3: lens; 4: Stop; 5: DUT or SLM; 6: Fourier Lens; 7: CCD sensor or Photodiode array; 8: Computer).

Fig. 5
Fig. 5

Photograph of the spectrum pattern.

Fig. 6
Fig. 6

CCD image and intensity distribution of the spectrum of the MEMS DUT (a) and the SLM calibration (b).

Fig. 7
Fig. 7

Experimental results of semi-linear relationship between I1 and square root of I2.

Fig. 8
Fig. 8

Measured results compared with the theoretical plot.

Tables (1)

Tables Icon

Table 1 Average Values and RSDs of the Measured Displacements

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

t 0 (x,y)=[ ( Rec( x T )Rec( x a )+Rec( xs a ) )comb( x T ) ]Rec( y b )
U f ( x,y )= Aexp[ j k 2f ( x f 2 + y f 2 ) ] jλf t 0 (x,y)exp[ j 2π λf (x x f +y y f ) ] dxdy
I f ( x,y )= A 2 λ 2 f 2 | t 0 (x,y)exp[ -j 2π λf (x x f +y y f ) ] dxdy | 2
{ I f ( f x , f y )= A 2 λ 2 f 2 I x,f ( f x ) I y,f ( f y ), I x,f ( f x )= | [ Tsinc(πT f x )asinc(πa f x )( 1+exp(j2πs f x ) ) ]comb( f x T ) | 2 , I y,f ( f y )= | bsinc( πb f y ) | 2
Δ f x =1/T , i.e., Δ x f = λf /T
I 1 = I f | n=1 = 4 A 2 b 2 T 2 λ 2 f 2 sin c 2 ( π a T ) cos 2 ( π s T )= I 1max cos 2 ( πf s T )
I 2 = I f | n=2 = 4 A 2 b 2 T 2 λ 2 f 2 sin c 2 ( 2π a T ) cos 2 ( 2π s T )= I 2max cos 2 ( 2π s T )
I 2 = I 2max ( 2 I 1 I 1max -1 ) 2 I 2 = I 2max | 2 I 1 I 1max -1 |

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