Abstract

We demonstrate here the fabrication of a smooth mirror surface by bending a thin silicon plate. A spherical surface is achieved by the bending moment generated in the circumference of the micromirror. Both convex and concave spherical micromirrors are realized through the anodic bonding of silicon and Pyrex glass. Since the mirror surface is originated from the polished silicon surface and no additional etching is introduced for manufacturing, the surface roughness is thus limited to the polishing error. This novel approach opens possibilities for fabricating a smooth surface for micromirror and microlens applications.

© 2011 Optical Society of America

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References

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  1. H. P. Herzig, Micro-optics (Taylor & Francis, 1997).
  2. S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
    [CrossRef]
  3. G. Wang, S. Wang, and C. Chin, “Fabrication and molding of gray-scale mask based aspheric refraction microlens array,” JSME Int. J., Ser. C 46, 1598–1603(2003).
    [CrossRef]
  4. K. Totsu and M. Esashi, “Gray-scale photolithography using maskless exposure system,” J. Vac. Sci. Technol. B 23, 1487–1490 (2005).
    [CrossRef]
  5. C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
    [CrossRef]
  6. P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
    [CrossRef]
  7. S. Timoshenko, Strength of Materials II (Van Nostrand Reinhold, 1953).
  8. H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
    [CrossRef]
  9. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  10. V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

2006 (1)

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

2005 (1)

K. Totsu and M. Esashi, “Gray-scale photolithography using maskless exposure system,” J. Vac. Sci. Technol. B 23, 1487–1490 (2005).
[CrossRef]

2003 (2)

C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
[CrossRef]

G. Wang, S. Wang, and C. Chin, “Fabrication and molding of gray-scale mask based aspheric refraction microlens array,” JSME Int. J., Ser. C 46, 1598–1603(2003).
[CrossRef]

1976 (1)

Audran, S.

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Bernt, H.

P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
[CrossRef]

Chien, Y.-E.

C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
[CrossRef]

Chin, C.

G. Wang, S. Wang, and C. Chin, “Fabrication and molding of gray-scale mask based aspheric refraction microlens array,” JSME Int. J., Ser. C 46, 1598–1603(2003).
[CrossRef]

Chiu, Y.

C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
[CrossRef]

Conrad, H.

H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
[CrossRef]

Dragoi, V.

V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

Esashi, M.

K. Totsu and M. Esashi, “Gray-scale photolithography using maskless exposure system,” J. Vac. Sci. Technol. B 23, 1487–1490 (2005).
[CrossRef]

Farrens, S.

V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

Faure, B.

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Glinsner, T.

V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

Hadziioannou, G.

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Herzig, H. P.

H. P. Herzig, Micro-optics (Taylor & Francis, 1997).

Klose, T.

H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
[CrossRef]

Lakner, H.

H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
[CrossRef]

Lindner, P.

V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

Merz, P.

P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
[CrossRef]

Mortini, B.

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Noll, R. J.

Quenzer, H. J.

P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
[CrossRef]

Regolini, J.

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Sander, T.

H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
[CrossRef]

Schenk, H.

H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
[CrossRef]

Schlatter, G.

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Shieh, H.-P. D.

C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
[CrossRef]

Tien, C.-H.

C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
[CrossRef]

Timoshenko, S.

S. Timoshenko, Strength of Materials II (Van Nostrand Reinhold, 1953).

Totsu, K.

K. Totsu and M. Esashi, “Gray-scale photolithography using maskless exposure system,” J. Vac. Sci. Technol. B 23, 1487–1490 (2005).
[CrossRef]

Wagner, B.

P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
[CrossRef]

Wang, G.

G. Wang, S. Wang, and C. Chin, “Fabrication and molding of gray-scale mask based aspheric refraction microlens array,” JSME Int. J., Ser. C 46, 1598–1603(2003).
[CrossRef]

Wang, S.

G. Wang, S. Wang, and C. Chin, “Fabrication and molding of gray-scale mask based aspheric refraction microlens array,” JSME Int. J., Ser. C 46, 1598–1603(2003).
[CrossRef]

Wimplinger, M.

V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

Zoberbier, M.

P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
[CrossRef]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (1)

K. Totsu and M. Esashi, “Gray-scale photolithography using maskless exposure system,” J. Vac. Sci. Technol. B 23, 1487–1490 (2005).
[CrossRef]

Jpn. J. Appl. Phys. (1)

C.-H. TienY.-E. Chien, Y. Chiu, and H.-P. D. Shieh, “Microlens array fabricated by excimer laser micromachining with gray-tone photolithography,” Jpn. J. Appl. Phys. 42, 1280–1283(2003).
[CrossRef]

JSME Int. J., Ser. C (1)

G. Wang, S. Wang, and C. Chin, “Fabrication and molding of gray-scale mask based aspheric refraction microlens array,” JSME Int. J., Ser. C 46, 1598–1603(2003).
[CrossRef]

Microelectron. Eng. (1)

S. Audran, B. Faure, B. Mortini, J. Regolini, G. Schlatter, and G. Hadziioannou, “Study of mechanisms involved in photoresist microlens formation,” Microelectron. Eng. 83, 1087–1090 (2006).
[CrossRef]

Other (5)

H. P. Herzig, Micro-optics (Taylor & Francis, 1997).

V. Dragoi, P. Lindner, T. Glinsner, M. Wimplinger, and S. Farrens, “Advanced anodic bonding processes for MEMS applications,” in Proceedings of Materials Research Society Symposium (Materials Research Society, 2004), Vol.  782, pp. A5.80.1–A5.80.6.

P. Merz, H. J. Quenzer, H. Bernt, B. Wagner, and M. Zoberbier, “A novel micromachining technology for structuring borosilicate glass substrates,” in Proceedings of IEEE Conference on Solid State Sensors, Actuators and Microsystems (IEEE, 2003), pp. 258–261.
[CrossRef]

S. Timoshenko, Strength of Materials II (Van Nostrand Reinhold, 1953).

H. Conrad, T. Klose, T. Sander, H. Schenk, and H. Lakner, “Actuating methods of quasistatic micromirrors for active focus variation,” in Proceedings of International Students and Young Scientists Workshop, Photonics and Microsystems (IEEE, 2008), pp. 7–11.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of (a) convex spherical micromirror and its fabrication, (b) concave spherical micromirror.

Fig. 2
Fig. 2

(a) High-order spherical aberration mode surface, (b) cross-sectional schematic of the high-order spherical aberration mode mirror.

Fig. 3
Fig. 3

(a) Fabrication process of the silicon thin-plate mirror; (b) fabrication process of the glass chip for (I) convex micromirror, (II) concave micromirror, and (III) high-order spherical aberration surface; (c) schematic illustration of anodic bonding.

Fig. 4
Fig. 4

(a) Surface profile of the fabricated silicon plate with initial deflection, (b) surface profile of the fabricated silicon plate across the center.

Fig. 5
Fig. 5

(a) Surface profile of the fabricated convex micromirror expressed by a contour map, (b) height profile of the convex micromirror surface, (c) measured surface profile and fitted parabola, (d) residual errors deviating from the fitted parabola.

Fig. 6
Fig. 6

Focal length of the fabricated convex micromirror as a function of the diameter.

Fig. 7
Fig. 7

(a) Surface profile of the fabricated concave micromirror expressed by a contour map, (b) height profile of the concave micromirror surface, (c) measured surface profile and fitted parabola, (d) residual errors deviating from the fitted parabola.

Fig. 8
Fig. 8

(a) Optical micrograph of the glass chip, (b) height profile of the glass chip surface, (c) surface profile of the fabricated high-order polynomial surface expressed by a contour map, (d) height profile of the fabricated high-order polynomial surface, (e) measured surface profile and the fitted sixth-order polynomial curve, (f) residual errors deviating from the fitted sixth-order polynomial curve.

Equations (10)

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

{ d d r { 1 r d d r ( r ϑ ) } = 0 , ϑ = d z d r ,
r ϑ = 1 2 C 1 r 2 C 2 ,
z = 1 4 C 1 r 2 C 2 ln r + C 3 ,
z = C 1 4 ( r 2 a 2 ) ,
d z d r | r = a = C 1 a 2 = tan θ ,
tan θ = 3 h 2 d .
C 1 = 3 h d a .
z = 3 h 4 d a ( r 2 a 2 ) ,
f = d 3 h a .
Z 22 = 7 ( 20 r 6 30 r 4 + 12 r 2 1 ) ,

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