Abstract

Continuous deformable membrane mirrors are becoming more attractive for use in adaptive optics because they cause no diffraction in the reflected beam and ensure smooth and continuous phase variations across the mirrors. However, when such mirrors are used to correct a high-power incident wave front, the absorption in the coatings causes the temperature of the membrane to increase, thereby creating in-plane thermal stress due to the rigidly clamped boundaries. We present a technique to measure thermal stress in such nondeforming membrane structures. The directional stress and temperature effects are simultaneously measured and decoupled in micromachined membrane mirrors by using a group of three ion-implanted silicon resistors with different orientations. In stress measurements made with incident power, the sensors measure changes in compressive thermal stress to within 8090kPa.

© 2006 Optical Society of America

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References

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  1. G. Vdovin and P. M. Sarro, 'Flexible mirror micromachined in silicon,' Appl. Opt. 34, 2968-2972 (1995).
    [CrossRef] [PubMed]
  2. S. Sinha, J. Mansell, and R. Byer, 'Deformable mirrors for high-power lasers,' in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 55-63 (2002).
    [CrossRef]
  3. E. Chason and B. W. Sheldon, 'Monitoring stress in thin films during processing,' Surf. Eng. 19, 387-391 (2003).
    [CrossRef]
  4. C. Kylner and L. Mattsson, 'An optical instrument for overall stress and local stress relaxation analysis in thin metal films,' Rev. Sci. Instrum. 68, 143-149 (1997).
    [CrossRef]
  5. A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
    [CrossRef]
  6. C. L. Tien, C. C. Lee, and C. C. Jaeng, 'The measurement of thin film stress using phase shifting interferometry,' J. Mod. Opt. 47, 839-849 (2000).
    [CrossRef]
  7. M. A. Maden and R. J. Farris, 'Stress analysis of thin polyimide films using holographic interferometry,' Exp. Mech. 31, 178-184 (1991).
    [CrossRef]
  8. B. L. French and J. C. Bilello, 'In-situ observation of real-time stress-evolution and delamination of thin Ta films on Si(100),' Thin Solid Films 446, 91-98 (2004).
    [CrossRef]
  9. T. Bourouina, C. Vague, and H. Mekki, 'Variational method for tensile stress evaluation and application to heavily doped square-shaped silicon diaphragms,' Sens. Actuators A 49, 21-27 (1995).
    [CrossRef]
  10. B. J. Lwo and S. Y. Wu, 'Calibrate piezoresistive stress sensors through the assembled structure,' J. Electron. Packag. 125, 289-293 (2003).
    [CrossRef]
  11. L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
    [CrossRef]
  12. A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
    [CrossRef]
  13. P. Matei and I. Pavelescu, 'Uniaxial silicon piezoresistive accelerometer,' in Proceedings of International Semiconductor Conference (Institute of Electrical and Electronics Engineers, 2000), pp. 479-482.
  14. L. Lin, H. C. Chu, and Y. W. Lu, 'A simulation program for the sensitivity and linearity piezoresistive pressure sensors,' J. Microelectromech. Syst. 8, 514-522 (1999).
    [CrossRef]
  15. Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
    [CrossRef]
  16. M. J. Madou, Fundamentals of Fabrication: the Science of Miniaturization (CRC, 2002).
  17. Y. Kanda, 'Piezoresistance effect of silicon,' Sens. Actuators A 28, 83-91 (1991).
    [CrossRef]
  18. S. A. Campbell, The Science and Engineering of Microelectronic Fabrication (Oxford U. Press, 2001).
  19. Z. Gniazdowski and P. Kowalski, 'Practical approach to extraction of piezoresistance coefficient,' Sens. Actuators A 68, 329-332 (1998).
    [CrossRef]
  20. M. Kasper, Mikrosystementwurf (Springer-Verlag, 2000).
    [CrossRef]
  21. S. Chowdhury, M. Ahmadi, and W. C. Miller, 'Nonlinear effects in MEMS capacitive microphone design,' in Proceedings of the International Conference on MEMS, NANO and Smart Systems (IEEE Computer Society, 2003), pp. 297-302.

2004 (1)

B. L. French and J. C. Bilello, 'In-situ observation of real-time stress-evolution and delamination of thin Ta films on Si(100),' Thin Solid Films 446, 91-98 (2004).
[CrossRef]

2003 (3)

E. Chason and B. W. Sheldon, 'Monitoring stress in thin films during processing,' Surf. Eng. 19, 387-391 (2003).
[CrossRef]

A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
[CrossRef]

B. J. Lwo and S. Y. Wu, 'Calibrate piezoresistive stress sensors through the assembled structure,' J. Electron. Packag. 125, 289-293 (2003).
[CrossRef]

2002 (1)

S. Sinha, J. Mansell, and R. Byer, 'Deformable mirrors for high-power lasers,' in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 55-63 (2002).
[CrossRef]

2000 (3)

L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
[CrossRef]

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

C. L. Tien, C. C. Lee, and C. C. Jaeng, 'The measurement of thin film stress using phase shifting interferometry,' J. Mod. Opt. 47, 839-849 (2000).
[CrossRef]

1999 (1)

L. Lin, H. C. Chu, and Y. W. Lu, 'A simulation program for the sensitivity and linearity piezoresistive pressure sensors,' J. Microelectromech. Syst. 8, 514-522 (1999).
[CrossRef]

1998 (1)

Z. Gniazdowski and P. Kowalski, 'Practical approach to extraction of piezoresistance coefficient,' Sens. Actuators A 68, 329-332 (1998).
[CrossRef]

1997 (1)

C. Kylner and L. Mattsson, 'An optical instrument for overall stress and local stress relaxation analysis in thin metal films,' Rev. Sci. Instrum. 68, 143-149 (1997).
[CrossRef]

1995 (3)

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

G. Vdovin and P. M. Sarro, 'Flexible mirror micromachined in silicon,' Appl. Opt. 34, 2968-2972 (1995).
[CrossRef] [PubMed]

T. Bourouina, C. Vague, and H. Mekki, 'Variational method for tensile stress evaluation and application to heavily doped square-shaped silicon diaphragms,' Sens. Actuators A 49, 21-27 (1995).
[CrossRef]

1991 (2)

Y. Kanda, 'Piezoresistance effect of silicon,' Sens. Actuators A 28, 83-91 (1991).
[CrossRef]

M. A. Maden and R. J. Farris, 'Stress analysis of thin polyimide films using holographic interferometry,' Exp. Mech. 31, 178-184 (1991).
[CrossRef]

Ahmadi, M.

S. Chowdhury, M. Ahmadi, and W. C. Miller, 'Nonlinear effects in MEMS capacitive microphone design,' in Proceedings of the International Conference on MEMS, NANO and Smart Systems (IEEE Computer Society, 2003), pp. 297-302.

Bilello, J. C.

B. L. French and J. C. Bilello, 'In-situ observation of real-time stress-evolution and delamination of thin Ta films on Si(100),' Thin Solid Films 446, 91-98 (2004).
[CrossRef]

Bing, A.

A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
[CrossRef]

Bourouina, T.

T. Bourouina, C. Vague, and H. Mekki, 'Variational method for tensile stress evaluation and application to heavily doped square-shaped silicon diaphragms,' Sens. Actuators A 49, 21-27 (1995).
[CrossRef]

Byer, R.

S. Sinha, J. Mansell, and R. Byer, 'Deformable mirrors for high-power lasers,' in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 55-63 (2002).
[CrossRef]

Campbell, S. A.

S. A. Campbell, The Science and Engineering of Microelectronic Fabrication (Oxford U. Press, 2001).

Cao, L.

L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
[CrossRef]

Chason, E.

E. Chason and B. W. Sheldon, 'Monitoring stress in thin films during processing,' Surf. Eng. 19, 387-391 (2003).
[CrossRef]

Chow, E. M.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Chowdhury, S.

S. Chowdhury, M. Ahmadi, and W. C. Miller, 'Nonlinear effects in MEMS capacitive microphone design,' in Proceedings of the International Conference on MEMS, NANO and Smart Systems (IEEE Computer Society, 2003), pp. 297-302.

Chu, H. C.

L. Lin, H. C. Chu, and Y. W. Lu, 'A simulation program for the sensitivity and linearity piezoresistive pressure sensors,' J. Microelectromech. Syst. 8, 514-522 (1999).
[CrossRef]

Chui, B. W.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Cui, K.

A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
[CrossRef]

Farris, R. J.

M. A. Maden and R. J. Farris, 'Stress analysis of thin polyimide films using holographic interferometry,' Exp. Mech. 31, 178-184 (1991).
[CrossRef]

Fitzgerald, A. M.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

French, B. L.

B. L. French and J. C. Bilello, 'In-situ observation of real-time stress-evolution and delamination of thin Ta films on Si(100),' Thin Solid Films 446, 91-98 (2004).
[CrossRef]

Gniazdowski, Z.

Z. Gniazdowski and P. Kowalski, 'Practical approach to extraction of piezoresistance coefficient,' Sens. Actuators A 68, 329-332 (1998).
[CrossRef]

Jaeng, C. C.

C. L. Tien, C. C. Lee, and C. C. Jaeng, 'The measurement of thin film stress using phase shifting interferometry,' J. Mod. Opt. 47, 839-849 (2000).
[CrossRef]

Kanda, Y.

Y. Kanda, 'Piezoresistance effect of silicon,' Sens. Actuators A 28, 83-91 (1991).
[CrossRef]

Kasper, M.

M. Kasper, Mikrosystementwurf (Springer-Verlag, 2000).
[CrossRef]

Kenny, T. W.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Kim, T. S.

L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
[CrossRef]

Kowalski, P.

Z. Gniazdowski and P. Kowalski, 'Practical approach to extraction of piezoresistance coefficient,' Sens. Actuators A 68, 329-332 (1998).
[CrossRef]

Kylner, C.

C. Kylner and L. Mattsson, 'An optical instrument for overall stress and local stress relaxation analysis in thin metal films,' Rev. Sci. Instrum. 68, 143-149 (1997).
[CrossRef]

Lee, C. C.

C. L. Tien, C. C. Lee, and C. C. Jaeng, 'The measurement of thin film stress using phase shifting interferometry,' J. Mod. Opt. 47, 839-849 (2000).
[CrossRef]

Li, Z.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Lin, L.

L. Lin, H. C. Chu, and Y. W. Lu, 'A simulation program for the sensitivity and linearity piezoresistive pressure sensors,' J. Microelectromech. Syst. 8, 514-522 (1999).
[CrossRef]

Lu, Y. W.

L. Lin, H. C. Chu, and Y. W. Lu, 'A simulation program for the sensitivity and linearity piezoresistive pressure sensors,' J. Microelectromech. Syst. 8, 514-522 (1999).
[CrossRef]

Lwo, B. J.

B. J. Lwo and S. Y. Wu, 'Calibrate piezoresistive stress sensors through the assembled structure,' J. Electron. Packag. 125, 289-293 (2003).
[CrossRef]

Maden, M. A.

M. A. Maden and R. J. Farris, 'Stress analysis of thin polyimide films using holographic interferometry,' Exp. Mech. 31, 178-184 (1991).
[CrossRef]

Madou, M. J.

M. J. Madou, Fundamentals of Fabrication: the Science of Miniaturization (CRC, 2002).

Maluf, N. I.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Mansell, J.

S. Sinha, J. Mansell, and R. Byer, 'Deformable mirrors for high-power lasers,' in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 55-63 (2002).
[CrossRef]

Mantell, S. C.

L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
[CrossRef]

Matei, P.

P. Matei and I. Pavelescu, 'Uniaxial silicon piezoresistive accelerometer,' in Proceedings of International Semiconductor Conference (Institute of Electrical and Electronics Engineers, 2000), pp. 479-482.

Matsuoka, Y.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Matsuzaka, H.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Mattsson, L.

C. Kylner and L. Mattsson, 'An optical instrument for overall stress and local stress relaxation analysis in thin metal films,' Rev. Sci. Instrum. 68, 143-149 (1997).
[CrossRef]

Mekki, H.

T. Bourouina, C. Vague, and H. Mekki, 'Variational method for tensile stress evaluation and application to heavily doped square-shaped silicon diaphragms,' Sens. Actuators A 49, 21-27 (1995).
[CrossRef]

Miller, W. C.

S. Chowdhury, M. Ahmadi, and W. C. Miller, 'Nonlinear effects in MEMS capacitive microphone design,' in Proceedings of the International Conference on MEMS, NANO and Smart Systems (IEEE Computer Society, 2003), pp. 297-302.

Partridge, A.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Pavelescu, I.

P. Matei and I. Pavelescu, 'Uniaxial silicon piezoresistive accelerometer,' in Proceedings of International Semiconductor Conference (Institute of Electrical and Electronics Engineers, 2000), pp. 479-482.

Polla, D.

L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
[CrossRef]

Reynolds, J. K.

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

Sarro, P. M.

Sheldon, B. W.

E. Chason and B. W. Sheldon, 'Monitoring stress in thin films during processing,' Surf. Eng. 19, 387-391 (2003).
[CrossRef]

Shimada, S.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Sinha, S.

S. Sinha, J. Mansell, and R. Byer, 'Deformable mirrors for high-power lasers,' in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 55-63 (2002).
[CrossRef]

Tanabe, M.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Tien, C. L.

C. L. Tien, C. C. Lee, and C. C. Jaeng, 'The measurement of thin film stress using phase shifting interferometry,' J. Mod. Opt. 47, 839-849 (2000).
[CrossRef]

Vague, C.

T. Bourouina, C. Vague, and H. Mekki, 'Variational method for tensile stress evaluation and application to heavily doped square-shaped silicon diaphragms,' Sens. Actuators A 49, 21-27 (1995).
[CrossRef]

Vdovin, G.

Wu, S. Y.

B. J. Lwo and S. Y. Wu, 'Calibrate piezoresistive stress sensors through the assembled structure,' J. Electron. Packag. 125, 289-293 (2003).
[CrossRef]

Yamada, K.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Yamamoto, Y.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Yasukawa, A.

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

Yuan, C.

A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
[CrossRef]

Zhang, T. J.

A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
[CrossRef]

Appl. Opt. (1)

Chin. Phys. Lett. (1)

A. Bing, T. J. Zhang, C. Yuan, and K. Cui, 'Apparatus for real-time measurement of stress in thin films at elevated temperatures,' Chin. Phys. Lett. 20, 1387-1389 (2003).
[CrossRef]

Exp. Mech. (1)

M. A. Maden and R. J. Farris, 'Stress analysis of thin polyimide films using holographic interferometry,' Exp. Mech. 31, 178-184 (1991).
[CrossRef]

J. Electron. Packag. (1)

B. J. Lwo and S. Y. Wu, 'Calibrate piezoresistive stress sensors through the assembled structure,' J. Electron. Packag. 125, 289-293 (2003).
[CrossRef]

J. Microelectromech. Syst. (2)

A. Partridge, J. K. Reynolds, B. W. Chui, E. M. Chow, A. M. Fitzgerald, Z. Li, N. I. Maluf, and T. W. Kenny, 'A high-performance planar piezoresistive accelerometer,' J. Microelectromech. Syst. 9, 58-66 (2000).
[CrossRef]

L. Lin, H. C. Chu, and Y. W. Lu, 'A simulation program for the sensitivity and linearity piezoresistive pressure sensors,' J. Microelectromech. Syst. 8, 514-522 (1999).
[CrossRef]

J. Micromech. Microeng. (1)

Y. Matsuoka, Y. Yamamoto, K. Yamada, S. Shimada, M. Tanabe, A. Yasukawa, and H. Matsuzaka, 'Characteristic analysis of a pressure sensor using the silicon piezoresistance effect for high-pressure measurements,' J. Micromech. Microeng. 5, 25-31 (1995).
[CrossRef]

J. Mod. Opt. (1)

C. L. Tien, C. C. Lee, and C. C. Jaeng, 'The measurement of thin film stress using phase shifting interferometry,' J. Mod. Opt. 47, 839-849 (2000).
[CrossRef]

Proc. SPIE (1)

S. Sinha, J. Mansell, and R. Byer, 'Deformable mirrors for high-power lasers,' in High-Resolution Wavefront Control: Methods, Devices, and Applications III, J. D. Gonglewski, M. A. Vorontsov, and M. T. Gruneisen, eds., Proc. SPIE 4493, 55-63 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

C. Kylner and L. Mattsson, 'An optical instrument for overall stress and local stress relaxation analysis in thin metal films,' Rev. Sci. Instrum. 68, 143-149 (1997).
[CrossRef]

Sens. Actuators (1)

L. Cao, T. S. Kim, S. C. Mantell, and D. Polla, 'Simulation and fabrication of piezoresistive membrane type MEMS strain sensors,' Sens. Actuators 80, 273-279 (2000).
[CrossRef]

Sens. Actuators A (3)

Y. Kanda, 'Piezoresistance effect of silicon,' Sens. Actuators A 28, 83-91 (1991).
[CrossRef]

T. Bourouina, C. Vague, and H. Mekki, 'Variational method for tensile stress evaluation and application to heavily doped square-shaped silicon diaphragms,' Sens. Actuators A 49, 21-27 (1995).
[CrossRef]

Z. Gniazdowski and P. Kowalski, 'Practical approach to extraction of piezoresistance coefficient,' Sens. Actuators A 68, 329-332 (1998).
[CrossRef]

Surf. Eng. (1)

E. Chason and B. W. Sheldon, 'Monitoring stress in thin films during processing,' Surf. Eng. 19, 387-391 (2003).
[CrossRef]

Thin Solid Films (1)

B. L. French and J. C. Bilello, 'In-situ observation of real-time stress-evolution and delamination of thin Ta films on Si(100),' Thin Solid Films 446, 91-98 (2004).
[CrossRef]

Other (5)

S. A. Campbell, The Science and Engineering of Microelectronic Fabrication (Oxford U. Press, 2001).

M. J. Madou, Fundamentals of Fabrication: the Science of Miniaturization (CRC, 2002).

P. Matei and I. Pavelescu, 'Uniaxial silicon piezoresistive accelerometer,' in Proceedings of International Semiconductor Conference (Institute of Electrical and Electronics Engineers, 2000), pp. 479-482.

M. Kasper, Mikrosystementwurf (Springer-Verlag, 2000).
[CrossRef]

S. Chowdhury, M. Ahmadi, and W. C. Miller, 'Nonlinear effects in MEMS capacitive microphone design,' in Proceedings of the International Conference on MEMS, NANO and Smart Systems (IEEE Computer Society, 2003), pp. 297-302.

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Figures (10)

Fig. 1
Fig. 1

Conceptual cross section of a micromachined flexible adaptive mirror that uses electrostatic actuators (adapted from Ref. [1]).

Fig. 2
Fig. 2

Schematic of a diffused resistor (adapted from Ref. [19]), where σ l and σ t are the longitudinal and transverse stresses, respectively, and J is the current direction.

Fig. 3
Fig. 3

Piezoresistive coefficient for (100) silicon in a (001) plane for low-concentration p-type doping (adapted from Ref. [16]). The radial dimension represents the coefficient in units of 10 - 11 Pa - 1 .

Fig. 4
Fig. 4

Piezoresistance factor P ( N , T ) as a function of concentration impurity and temperature for p - Si . The piezoresistance coefficient is temperature invariant at high doping levels, but it is reduced by a low piezoresistance factor.

Fig. 5
Fig. 5

(Color online) Conceptual diagram of the stress-monitoring test structure with two of the sidewalls removed for illustration of the membrane. The close-up view is of a small localized region in which three resistive sensors are made by boron implantation. The origin of the coordinates is defined at the center of the membrane.

Fig. 6
Fig. 6

(Color online) Experimental and simulation results for nanoindentation calibration of (a) load versus deflection and (b) load versus Δ R / R to find the curve-fitting parameter for stress sensors and to verify the stress-free temperature sensors. In (b) the matched data for the stress sensor indicate a piezoresistive coefficient of 0.325. As expected from theory, the orientation of the temperature sensor gives it a negligible variation with stress in the load range of interest.

Fig. 7
Fig. 7

TCR measurement of the temperature sensors.

Fig. 8
Fig. 8

Experimental setup for the real-time stress measurement.

Fig. 9
Fig. 9

(a) Temperature at center and edge of membrane versus incident power; (b, c) Δ R / R for the sensors at the edge versus incident power; (d) ( Δ R / R strain sensor Δ R / R temp sensor ) versus incident power, which is an expanded view of (b) and (c). Temp, temperature; SS, stress sensor; TS, temperature sensor.

Fig. 10
Fig. 10

(Color online) Deduced stress-versus-temperature curve for an area near the edge of the sample under study.

Equations (15)

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σ = E αΔ T ,
Δ R / R = π t σ t + π l σ l ,
Δ R / R = 71.8 × 10 - 11 σ l 66.3 × 10 - 11 σ t .
π eff ( N , T ) = P ( N , T ) π ( 300 °K ) ,
Δ R = ( αΔ T ) R 0 ,
Δ R = ( αΔ T + π l σ l + π t σ t ) R 0 .
Δ R 1 / R 1 = π l σ x + π t σ y + αΔ T ,
Δ R 2 / R 2 = π l σ y + π t σ x + αΔ T ,
Δ R 3 / R 3 = αΔ T .
Δ R / R = P ( N ) [ ( 71.8 × 10 - 11 σ l ) ( 66.3 × 10 - 11 σ t ) ] ,
Δ R 1 / R 1 = ( A σ x B σ y ) + αΔ T = m 1 P incident ,
Δ R 2 / R 2 = ( A σ y B σ x ) + αΔ T = m 2 P incident ,
Δ R 3 / R 3 = αΔ T = m 3 P incident ,
σ x = ( B B A ) ( α m 3 ) ( m 1 m 2 A + B m 1 m 3 B ) Δ T ,
σ y = [ ( A B A ) ( α m 3 ) ( m 1 m 2 A + B m 1 m 3 B ) ( m 1 m 3 B ) ( α m 3 ) ] Δ T .

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