Abstract

Thermal expansion-induced curvature becomes a major effect in micromirrors as the mirror diameter exceeds 100 µm. Such mirrors are used for optical switching, scanning, and many other applications. By using multilayer coatings instead of a single metal reflector, one can use the mechanical properties of the multilayer to create mirrors with zero curvature across temperature. We demonstrate the fabrication of such thermally invariant mirrors using dielectric coatings. A semianalytic model based on free-plate elastic theory is developed that uses empirical parameters in place of the true thermal expansion coefficients of the coating materials. Micromirrors are demonstrated that maintain their design curvature to within λ/60 for λ = 633 nm across an operating range from 21 °C to 58 °C.

© 2002 Optical Society of America

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References

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  1. Y.-H. Min, Y.-K. Kim, “Modeling, design, fabrication, and measurement of a single layer polysilicon micromirror with initial curvature compensation,” Sens. Actuators A 78, 8–17 (1999).
    [CrossRef]
  2. J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
    [CrossRef]
  3. K. Cao, W. Liu, J. J. Talghader, “Curvature compensation in micromirrors with high-reflectivity optical coatings,” IEEE J. Microelectromech. Syst. 10, 409–417 (2001).
    [CrossRef]
  4. J. T. Nee, R. A. Conant, R. S. Muller, K. Y. Lau, “Lightweight, optically flat micromirrors for fast beam steering,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 9–10.
  5. H.-Y. Lin, M. C. Wu, M.-L. Tsai, “Towards a lightwave MEMS platform using MOSBE process,” in Proceedings of the 2001 IEEE/LEOS International Conference on Optical MEMS, (Institute of Electric and Electronics Engineers, Piscataway, N.J., 2001), pp. 27–28.
  6. A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.
  7. U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.
  8. R. A. Conant, J. T. Nee, K. Y. Lau, R. S. Muller, “A flat high-frequency scanning micromirror,” in Proceedings of the Solid-State Sensor and Actuator Workshop, (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 6–9.
  9. G.-D. J. Su, H. Toshiyoshi, M. C. Wu, “Surface-micromachined 2-D optical scanners with high-performance single-crystalline silicon micromirrors,” IEEE Photon. Technol. Lett. 13, 606–608 (2001).
    [CrossRef]
  10. R. N. Supino, J. J. Talghader, “Average optical power monitoring in micromirrors,” IEEE J. Sel. Top. Quantum Electron. 8, 12–18 (2002).
    [CrossRef]
  11. A. J. Chapman, Heat Transfer, 4th ed. (Macmillan, New York, 1984).
  12. The linear extrapolation is a slight overestimate that is due to plastic deformation in the metal that reduces the magnitude of the deflection by several nanometers.
  13. S. Timoshenko, “Analysis of bi-metal thermostats,” J. Opt. Soc. Am. 11, 233–255 (1925).
    [CrossRef]
  14. M. Vasudevan, W. Johnson, “On multimetal thermostats,” Appl. Sci. Res. Sect. B 9, 420–430 (1962).
    [CrossRef]
  15. It is also noted that a material with any CTE can be used as an invariance layer if its thickness is allowed to go to infinity. Since this is not practical, this case has been ignored.
  16. J. Thurn, R. F. Cook, “Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films,” J. Appl. Phys. 91, 1988–1992 (2002).
    [CrossRef]
  17. W. C. Oliver, G. M. Pharr, “An improved technique for determining hardness and electic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7, 1564–1583 (1992).
    [CrossRef]
  18. W. A. Brantley, “Calculated elastic constants for stress problems associated with semiconductor devices,” J. Appl. Phys. 44, 534–544 (1973).
    [CrossRef]
  19. D. R. Harding, L. T. Ogbuji, “Temperature dependence of the intrinsic stress and biaxial modulus of plasma deposited silicon nitride and silicon oxynitride films,” Mater. Res. Soc. Symp. Proc. 356, 221–226 (1995).
    [CrossRef]
  20. M. Ohring, Material Science of Thin Films (AcademicBoston, 1992).
  21. J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
    [CrossRef]
  22. Y. X. Li, P. J. French, R. F. Wolffenbuttel, “Plasma planarization for sensor applications,” IEEE J. Microelectromech. Syst. 4, 132–138 (1995).
    [CrossRef]
  23. J. H. Apfel, “Graphical method to design multilayer phase retarders,” Appl. Opt. 20, 1024–1029 (1981).
    [CrossRef] [PubMed]

2002 (2)

R. N. Supino, J. J. Talghader, “Average optical power monitoring in micromirrors,” IEEE J. Sel. Top. Quantum Electron. 8, 12–18 (2002).
[CrossRef]

J. Thurn, R. F. Cook, “Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films,” J. Appl. Phys. 91, 1988–1992 (2002).
[CrossRef]

2001 (2)

K. Cao, W. Liu, J. J. Talghader, “Curvature compensation in micromirrors with high-reflectivity optical coatings,” IEEE J. Microelectromech. Syst. 10, 409–417 (2001).
[CrossRef]

G.-D. J. Su, H. Toshiyoshi, M. C. Wu, “Surface-micromachined 2-D optical scanners with high-performance single-crystalline silicon micromirrors,” IEEE Photon. Technol. Lett. 13, 606–608 (2001).
[CrossRef]

1999 (2)

Y.-H. Min, Y.-K. Kim, “Modeling, design, fabrication, and measurement of a single layer polysilicon micromirror with initial curvature compensation,” Sens. Actuators A 78, 8–17 (1999).
[CrossRef]

J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
[CrossRef]

1998 (1)

J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
[CrossRef]

1995 (2)

Y. X. Li, P. J. French, R. F. Wolffenbuttel, “Plasma planarization for sensor applications,” IEEE J. Microelectromech. Syst. 4, 132–138 (1995).
[CrossRef]

D. R. Harding, L. T. Ogbuji, “Temperature dependence of the intrinsic stress and biaxial modulus of plasma deposited silicon nitride and silicon oxynitride films,” Mater. Res. Soc. Symp. Proc. 356, 221–226 (1995).
[CrossRef]

1992 (1)

W. C. Oliver, G. M. Pharr, “An improved technique for determining hardness and electic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7, 1564–1583 (1992).
[CrossRef]

1981 (1)

1973 (1)

W. A. Brantley, “Calculated elastic constants for stress problems associated with semiconductor devices,” J. Appl. Phys. 44, 534–544 (1973).
[CrossRef]

1962 (1)

M. Vasudevan, W. Johnson, “On multimetal thermostats,” Appl. Sci. Res. Sect. B 9, 420–430 (1962).
[CrossRef]

1925 (1)

Apfel, J. H.

Brantley, W. A.

W. A. Brantley, “Calculated elastic constants for stress problems associated with semiconductor devices,” J. Appl. Phys. 44, 534–544 (1973).
[CrossRef]

Butler, J.

J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
[CrossRef]

Cao, K.

K. Cao, W. Liu, J. J. Talghader, “Curvature compensation in micromirrors with high-reflectivity optical coatings,” IEEE J. Microelectromech. Syst. 10, 409–417 (2001).
[CrossRef]

Chapman, A. J.

A. J. Chapman, Heat Transfer, 4th ed. (Macmillan, New York, 1984).

Comtois, J.

J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
[CrossRef]

Conant, R. A.

J. T. Nee, R. A. Conant, R. S. Muller, K. Y. Lau, “Lightweight, optically flat micromirrors for fast beam steering,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 9–10.

R. A. Conant, J. T. Nee, K. Y. Lau, R. S. Muller, “A flat high-frequency scanning micromirror,” in Proceedings of the Solid-State Sensor and Actuator Workshop, (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 6–9.

Cook, R. F.

J. Thurn, R. F. Cook, “Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films,” J. Appl. Phys. 91, 1988–1992 (2002).
[CrossRef]

Cowan, W.

J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
[CrossRef]

Dewa, A. S.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

French, P. J.

Y. X. Li, P. J. French, R. F. Wolffenbuttel, “Plasma planarization for sensor applications,” IEEE J. Microelectromech. Syst. 4, 132–138 (1995).
[CrossRef]

Gill, J. J.-Y.

J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
[CrossRef]

Harding, D. R.

D. R. Harding, L. T. Ogbuji, “Temperature dependence of the intrinsic stress and biaxial modulus of plasma deposited silicon nitride and silicon oxynitride films,” Mater. Res. Soc. Symp. Proc. 356, 221–226 (1995).
[CrossRef]

Helmbrecht, M.

U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.

Howe, R. T.

U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.

Hudson, M.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

Johnson, W.

M. Vasudevan, W. Johnson, “On multimetal thermostats,” Appl. Sci. Res. Sect. B 9, 420–430 (1962).
[CrossRef]

Kim, C.-J.

J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
[CrossRef]

Kim, Y.-K.

Y.-H. Min, Y.-K. Kim, “Modeling, design, fabrication, and measurement of a single layer polysilicon micromirror with initial curvature compensation,” Sens. Actuators A 78, 8–17 (1999).
[CrossRef]

Krozier, D.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

Laor, H.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

Lau, K. Y.

R. A. Conant, J. T. Nee, K. Y. Lau, R. S. Muller, “A flat high-frequency scanning micromirror,” in Proceedings of the Solid-State Sensor and Actuator Workshop, (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 6–9.

J. T. Nee, R. A. Conant, R. S. Muller, K. Y. Lau, “Lightweight, optically flat micromirrors for fast beam steering,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 9–10.

Li, Y. X.

Y. X. Li, P. J. French, R. F. Wolffenbuttel, “Plasma planarization for sensor applications,” IEEE J. Microelectromech. Syst. 4, 132–138 (1995).
[CrossRef]

Lin, H.-Y.

H.-Y. Lin, M. C. Wu, M.-L. Tsai, “Towards a lightwave MEMS platform using MOSBE process,” in Proceedings of the 2001 IEEE/LEOS International Conference on Optical MEMS, (Institute of Electric and Electronics Engineers, Piscataway, N.J., 2001), pp. 27–28.

Liu, W.

K. Cao, W. Liu, J. J. Talghader, “Curvature compensation in micromirrors with high-reflectivity optical coatings,” IEEE J. Microelectromech. Syst. 10, 409–417 (2001).
[CrossRef]

Michalicek, A.

J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
[CrossRef]

Min, Y.-H.

Y.-H. Min, Y.-K. Kim, “Modeling, design, fabrication, and measurement of a single layer polysilicon micromirror with initial curvature compensation,” Sens. Actuators A 78, 8–17 (1999).
[CrossRef]

Muller, R. S.

J. T. Nee, R. A. Conant, R. S. Muller, K. Y. Lau, “Lightweight, optically flat micromirrors for fast beam steering,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 9–10.

R. A. Conant, J. T. Nee, K. Y. Lau, R. S. Muller, “A flat high-frequency scanning micromirror,” in Proceedings of the Solid-State Sensor and Actuator Workshop, (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 6–9.

U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.

Nee, J. T.

R. A. Conant, J. T. Nee, K. Y. Lau, R. S. Muller, “A flat high-frequency scanning micromirror,” in Proceedings of the Solid-State Sensor and Actuator Workshop, (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 6–9.

J. T. Nee, R. A. Conant, R. S. Muller, K. Y. Lau, “Lightweight, optically flat micromirrors for fast beam steering,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 9–10.

Nelson, P. R.

J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
[CrossRef]

Ngo, L. V.

J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
[CrossRef]

Ogbuji, L. T.

D. R. Harding, L. T. Ogbuji, “Temperature dependence of the intrinsic stress and biaxial modulus of plasma deposited silicon nitride and silicon oxynitride films,” Mater. Res. Soc. Symp. Proc. 356, 221–226 (1995).
[CrossRef]

Ohring, M.

M. Ohring, Material Science of Thin Films (AcademicBoston, 1992).

Oliver, W. C.

W. C. Oliver, G. M. Pharr, “An improved technique for determining hardness and electic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7, 1564–1583 (1992).
[CrossRef]

Orcutt, J. W.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

Pharr, G. M.

W. C. Oliver, G. M. Pharr, “An improved technique for determining hardness and electic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7, 1564–1583 (1992).
[CrossRef]

Rembe, C.

U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.

Richards, A.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

Srinivasan, U.

U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.

Su, G.-D. J.

G.-D. J. Su, H. Toshiyoshi, M. C. Wu, “Surface-micromachined 2-D optical scanners with high-performance single-crystalline silicon micromirrors,” IEEE Photon. Technol. Lett. 13, 606–608 (2001).
[CrossRef]

Supino, R. N.

R. N. Supino, J. J. Talghader, “Average optical power monitoring in micromirrors,” IEEE J. Sel. Top. Quantum Electron. 8, 12–18 (2002).
[CrossRef]

Talghader, J. J.

R. N. Supino, J. J. Talghader, “Average optical power monitoring in micromirrors,” IEEE J. Sel. Top. Quantum Electron. 8, 12–18 (2002).
[CrossRef]

K. Cao, W. Liu, J. J. Talghader, “Curvature compensation in micromirrors with high-reflectivity optical coatings,” IEEE J. Microelectromech. Syst. 10, 409–417 (2001).
[CrossRef]

Thurn, J.

J. Thurn, R. F. Cook, “Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films,” J. Appl. Phys. 91, 1988–1992 (2002).
[CrossRef]

Timoshenko, S.

Toshiyoshi, H.

G.-D. J. Su, H. Toshiyoshi, M. C. Wu, “Surface-micromachined 2-D optical scanners with high-performance single-crystalline silicon micromirrors,” IEEE Photon. Technol. Lett. 13, 606–608 (2001).
[CrossRef]

Tsai, M.-L.

H.-Y. Lin, M. C. Wu, M.-L. Tsai, “Towards a lightwave MEMS platform using MOSBE process,” in Proceedings of the 2001 IEEE/LEOS International Conference on Optical MEMS, (Institute of Electric and Electronics Engineers, Piscataway, N.J., 2001), pp. 27–28.

Vasudevan, M.

M. Vasudevan, W. Johnson, “On multimetal thermostats,” Appl. Sci. Res. Sect. B 9, 420–430 (1962).
[CrossRef]

Wolffenbuttel, R. F.

Y. X. Li, P. J. French, R. F. Wolffenbuttel, “Plasma planarization for sensor applications,” IEEE J. Microelectromech. Syst. 4, 132–138 (1995).
[CrossRef]

Wu, M. C.

G.-D. J. Su, H. Toshiyoshi, M. C. Wu, “Surface-micromachined 2-D optical scanners with high-performance single-crystalline silicon micromirrors,” IEEE Photon. Technol. Lett. 13, 606–608 (2001).
[CrossRef]

H.-Y. Lin, M. C. Wu, M.-L. Tsai, “Towards a lightwave MEMS platform using MOSBE process,” in Proceedings of the 2001 IEEE/LEOS International Conference on Optical MEMS, (Institute of Electric and Electronics Engineers, Piscataway, N.J., 2001), pp. 27–28.

Appl. Opt. (1)

Appl. Sci. Res. Sect. B (1)

M. Vasudevan, W. Johnson, “On multimetal thermostats,” Appl. Sci. Res. Sect. B 9, 420–430 (1962).
[CrossRef]

IEEE J. Microelectromech. Syst. (3)

K. Cao, W. Liu, J. J. Talghader, “Curvature compensation in micromirrors with high-reflectivity optical coatings,” IEEE J. Microelectromech. Syst. 10, 409–417 (2001).
[CrossRef]

J. J.-Y. Gill, L. V. Ngo, P. R. Nelson, C.-J. Kim, “Elimination of extra spring effect at the step-up anchor of surface-micromachined structure,” IEEE J. Microelectromech. Syst. 7, 114–121 (1998).
[CrossRef]

Y. X. Li, P. J. French, R. F. Wolffenbuttel, “Plasma planarization for sensor applications,” IEEE J. Microelectromech. Syst. 4, 132–138 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. N. Supino, J. J. Talghader, “Average optical power monitoring in micromirrors,” IEEE J. Sel. Top. Quantum Electron. 8, 12–18 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G.-D. J. Su, H. Toshiyoshi, M. C. Wu, “Surface-micromachined 2-D optical scanners with high-performance single-crystalline silicon micromirrors,” IEEE Photon. Technol. Lett. 13, 606–608 (2001).
[CrossRef]

J. Appl. Phys. (2)

J. Thurn, R. F. Cook, “Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films,” J. Appl. Phys. 91, 1988–1992 (2002).
[CrossRef]

W. A. Brantley, “Calculated elastic constants for stress problems associated with semiconductor devices,” J. Appl. Phys. 44, 534–544 (1973).
[CrossRef]

J. Mater. Res. (1)

W. C. Oliver, G. M. Pharr, “An improved technique for determining hardness and electic modulus using load and displacement sensing indentation experiments,” J. Mater. Res. 7, 1564–1583 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Mater. Res. Soc. Symp. Proc. (1)

D. R. Harding, L. T. Ogbuji, “Temperature dependence of the intrinsic stress and biaxial modulus of plasma deposited silicon nitride and silicon oxynitride films,” Mater. Res. Soc. Symp. Proc. 356, 221–226 (1995).
[CrossRef]

Sens. Actuators A (2)

Y.-H. Min, Y.-K. Kim, “Modeling, design, fabrication, and measurement of a single layer polysilicon micromirror with initial curvature compensation,” Sens. Actuators A 78, 8–17 (1999).
[CrossRef]

J. Comtois, A. Michalicek, W. Cowan, J. Butler, “Surface micromachined polysilicon MOEMS for adaptive optics,” Sens. Actuators A 78, 54–62 (1999).
[CrossRef]

Other (9)

A. J. Chapman, Heat Transfer, 4th ed. (Macmillan, New York, 1984).

The linear extrapolation is a slight overestimate that is due to plastic deformation in the metal that reduces the magnitude of the deflection by several nanometers.

J. T. Nee, R. A. Conant, R. S. Muller, K. Y. Lau, “Lightweight, optically flat micromirrors for fast beam steering,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), pp. 9–10.

H.-Y. Lin, M. C. Wu, M.-L. Tsai, “Towards a lightwave MEMS platform using MOSBE process,” in Proceedings of the 2001 IEEE/LEOS International Conference on Optical MEMS, (Institute of Electric and Electronics Engineers, Piscataway, N.J., 2001), pp. 27–28.

A. S. Dewa, J. W. Orcutt, M. Hudson, D. Krozier, A. Richards, H. Laor, “Development of a silicon two-axis micromirror for an optical cross-connect,” in Proceedings of the Solid-State Sensor and Actuator Workshop (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 93–96.

U. Srinivasan, M. Helmbrecht, C. Rembe, R. S. Muller, R. T. Howe, “Fluidic self-assembly of micromirrors on surface micromachined actuators,” in Proceedings of the 2000 IEEE/LEOS International Conference on Optical MEMS, (Institutes of Electrical and Electronics Engineers, Piscataway, N.J., (2000), pp. 59–60.

R. A. Conant, J. T. Nee, K. Y. Lau, R. S. Muller, “A flat high-frequency scanning micromirror,” in Proceedings of the Solid-State Sensor and Actuator Workshop, (Transducers Research Foundation, Cleveland, Ohio, 2000), pp. 6–9.

M. Ohring, Material Science of Thin Films (AcademicBoston, 1992).

It is also noted that a material with any CTE can be used as an invariance layer if its thickness is allowed to go to infinity. Since this is not practical, this case has been ignored.

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Figures (10)

Fig. 1
Fig. 1

Conceptual diagram of the piston micromirrors used in this study. Electrostatic forces were used to actuate the mirror. The mirror structure is polysilicon and is coated by a dielectric multilayer stack.

Fig. 2
Fig. 2

Definitions of the thickness, forces, and moments in a multilayer structure: P, the force on a layer; M, the moment; E, the elastic modulus; α, the CTE; t, the thickness of a layer.

Fig. 3
Fig. 3

Theoretical change in deflection versus invariance layer thickness for a free plate with a coating and invariance layer. Note that zero thermal deformation is sensitive to the CTE of the invariance layer. Since one has only limited ability to choose this value, tight thickness control (± 10 nm) is generally required to reach zero deformation. The simulated layer structure is (from bottom to top): 1.0-µm polysilicon, 0.1-µm SiO2, and the hypothetical invariance layer. The temperature range is 100 K and the mirror diameter is 250 µm. The mechanical parameters for the layers were taken from Ref. 16-19.

Fig. 4
Fig. 4

Stress versus temperature for Y2O3 film deposited on a 4-in. (10-cm-diameter) wafer. The sample undergoes three thermal cycles. In each cycle, the temperature increased from 30 °C to 100 °C (heatup stage), then decreased from 100 °C back to 30 °C (cooldown stage). The stress, as measured by the wafer curvature, undergoes dramatic hysteresis during the first two cycles, indicating plastic deformation, probably caused by slippage along the Y2O3–Si interface. After three cycles, the stress-versus-temperature curve becomes linear, indicating elastic thermal expansion.

Fig. 5
Fig. 5

Interferometric image of a 100 µm × 100 µm micromirror with a thermally invariant dielectric coating. This mirror corresponds to structure I listed in Table 1. Curvature from intrinsic stress has been specifically designed into the structure for eventual use in an optical cavity.

Fig. 6
Fig. 6

Generic layer structure of the mirrors we tested. The number of λ/4 pairs in the stack varied from three to five depending on which mirror structure from Table 1 was fabricated.

Fig. 7
Fig. 7

Change in thermal deflection and change in curvature versus invariance layer thickness. This graph shows the degree of bending caused by thermal expansion across a 37 °C temperature range for structure I in Table 1. Theoretical curve I was calculated with parameters for bulk materials,16-19 and theoretical curve II was fit by use of empirical parameters for the CTE of SiO2 and SiN. The specific empirical values were (αSiO2 - αpoly) = -21.9 × 10-6/K and (αSiN - αpoly) = 18.3 × 10-6/K. These values were subsequently used to obtain the theoretical curve in Fig. 8.

Fig. 8
Fig. 8

Change in thermal deflection and change in curvature versus invariance layer thickness for two samples of structure II from Table 1. This graph is identical to that of Fig. 7 except that the mirrors tested have a different coating design (three pairs plus top invariance layer). We used the same empirical values for the CTE of SiO2 and SiN as measured from structure I for the theoretical curve in this graph.

Fig. 9
Fig. 9

Surface profile of the dielectric micromirror of structure III from Table 1. In the two graphs, data are shown for the profiles at 21 °C and 58 °C. (a) The surface profile of the dielectric mirror without the invariance layer. (b) The surface profile of the dielectric micromirror after the invariance layer has been added. Note that the curvatures of the mirrors differ because of the intrinsic stress of the top layer. (The curvature has been designed so that the mirror can be used for a confocal cavity.)

Fig. 10
Fig. 10

Simulated reflectivity spectrum for a ten λ/4 pairs structure and structure III in Table 1. (a) The reflectivity spectrum for a ten λ/4 pairs structure before and after the invariance layer. The introduced spectral shift is negligible between 600 and 700 nm. (b) The reflectivity spectrum for structure III in Table 1 before and after the invariance layer. The introduced spectral shift is nonnegligible. The overall minimum reflectivity between 600 and 700 nm dropped by 4.7%. The structure in (b) is used primarily for thermal invariance and curvature control testing and was not specifically designed to achieve high reflectivity, in contrast with the structure in (a).

Tables (1)

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Table 1 Coating Structure for Three Micromirror Designs

Equations (7)

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q=kA ΔTΔx,
q=hAΔT,
i=1n Pi=0,
i=1n Mi=i=1n Pij=1i-1 tj+ti2,
αiΔT+PitiEi+ti2ρ=αi+1ΔT-Pi+1ti+1Ei+1-ti+12ρ,
1ρ=2 111110s2-s1000α2-α1s1s20s3-s200α3-α2s2s3000sn-sn-1αn-αn-1sn-1snl1l2l3ln-100111110s2-s1000-t1+t2s1s20s3-s200-t2+t3s2s3000sn-sn-1-tn-1+tnsn-1snl1l2l3ln-102 i=1n EiIiΔT+1ρ0,
1ρnet=1ρ0+1ρthermal.

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