Abstract

An aperiodic mask design method for fabricating a microlens array with an aspherical profile is proposed. The nonlinear relationship between exposure doses and lens profile is considered, and the select criteria of quantization interval and fabrication range of the method are given. The mask function of a quadrangle microlens array with a hyperboloid profile used in the infrared was constructed by using this method. The microlens array can be effectively fabricated during a one time exposure process using the mask. Reactive ion etching was carried out to transfer the structure into the substrate of germanium. The measurement results indicate that the roughness is less than 10  nm (pv), and the profile error is less than 40 nm (rms).

© 2007 Optical Society of America

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References

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2006 (1)

X. C. Dong, C. L. Du, C. T. Wang, Q. L. Deng, Y. D. Zhang, and X. G. Luo, "Mask-shift filtering for forming microstructures with irregular profile," Appl. Phys. Lett. 89, 261105 (2006).

2005 (1)

2004 (2)

C. L. Du, X. C. Dong, C. K. Qiu, Q. L. Deng, and C. X. Zhou, "Profile control technology for high performance microlens array," Opt. Eng. 43, 2595-2602 (2004).

M. P. Rao, M. F. Aimi, and N. C. MacDonald, "Single-mask, three-dimensional microfabrication of high-aspect-ratio structures in bulk silicon using reactive ion etching lag and sacrificial oxidation," Appl. Phys. Lett. 85, 6281-6283 (2004).

2000 (1)

1998 (1)

1997 (2)

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, "Micro-optic fabrication using one-level gray-tone lithography," Proc. SPIE 3008, 279-288 (1997).

M. E. Motamedi, M. C. Wu, and K. S. J. Pister, "Micro-opto-electro-mechanical devices and on-chip optical processing," Opt. Eng. 36, 1282-1297 (1997).

1996 (4)

R. Volkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, "Microlens array image system for photolithography," Opt. Eng. 35, 3323-3330 (1996).

B. Chen, L. R. Guo, J. Y. Tang, and W. J. Tian, "Refractive microlens arrays with parabolic section profile and no dead area," Proc. SPIE 2866, 420-423 (1996).

B. Chen, L. R. Guo, J. Y. Tang, and P. Xu, "Novel method for making parabolic grating," Proc. SPIE 2687, 142-149 (1996).

W. Daeschner, P. Long, R. Stein, C. Wu, and S. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) grey-level masks," Proc. SPIE 2689, 153-155 (1996).

1995 (1)

1992 (1)

G. Artzner, "Microlens arrays for Shack-Hartmann wavefront sensors," Opt. Eng. 31, 1311-1322 (1992).

1991 (2)

D. D. Amato and R. Centamore, "Two applications for microlens array: detector fill factor improvement and laser diode collimation," Proc. SPIE 1544, 166-177 (1991).

D. Kwo, G. Damas, and W. Zmek, "A Hartmann-Shack wavefront sensor using a binary optical lenslet array," Proc. SPIE 1544, 66-74 (1991).

1988 (1)

J. R. Leger, M. L. Scott, P. Bundman, and M. P. Griswold, "Astigmatic wavefront correction of a gain-guided laser diode array using diffractive microlenses," Proc. SPIE 884, 82-89 (1988).

Appl. Phys. Lett. (2)

M. P. Rao, M. F. Aimi, and N. C. MacDonald, "Single-mask, three-dimensional microfabrication of high-aspect-ratio structures in bulk silicon using reactive ion etching lag and sacrificial oxidation," Appl. Phys. Lett. 85, 6281-6283 (2004).

X. C. Dong, C. L. Du, C. T. Wang, Q. L. Deng, Y. D. Zhang, and X. G. Luo, "Mask-shift filtering for forming microstructures with irregular profile," Appl. Phys. Lett. 89, 261105 (2006).

Opt. Eng. (4)

C. L. Du, X. C. Dong, C. K. Qiu, Q. L. Deng, and C. X. Zhou, "Profile control technology for high performance microlens array," Opt. Eng. 43, 2595-2602 (2004).

G. Artzner, "Microlens arrays for Shack-Hartmann wavefront sensors," Opt. Eng. 31, 1311-1322 (1992).

M. E. Motamedi, M. C. Wu, and K. S. J. Pister, "Micro-opto-electro-mechanical devices and on-chip optical processing," Opt. Eng. 36, 1282-1297 (1997).

R. Volkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, "Microlens array image system for photolithography," Opt. Eng. 35, 3323-3330 (1996).

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (7)

K. Reimer, H. J. Quenzer, M. Jürss, and B. Wagner, "Micro-optic fabrication using one-level gray-tone lithography," Proc. SPIE 3008, 279-288 (1997).

D. D. Amato and R. Centamore, "Two applications for microlens array: detector fill factor improvement and laser diode collimation," Proc. SPIE 1544, 166-177 (1991).

D. Kwo, G. Damas, and W. Zmek, "A Hartmann-Shack wavefront sensor using a binary optical lenslet array," Proc. SPIE 1544, 66-74 (1991).

J. R. Leger, M. L. Scott, P. Bundman, and M. P. Griswold, "Astigmatic wavefront correction of a gain-guided laser diode array using diffractive microlenses," Proc. SPIE 884, 82-89 (1988).

W. Daeschner, P. Long, R. Stein, C. Wu, and S. Lee, "One-step lithography for mass production of multilevel diffractive optical elements using high energy beam sensitive (HEBS) grey-level masks," Proc. SPIE 2689, 153-155 (1996).

B. Chen, L. R. Guo, J. Y. Tang, and W. J. Tian, "Refractive microlens arrays with parabolic section profile and no dead area," Proc. SPIE 2866, 420-423 (1996).

B. Chen, L. R. Guo, J. Y. Tang, and P. Xu, "Novel method for making parabolic grating," Proc. SPIE 2687, 142-149 (1996).

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Figures (6)

Fig. 1
Fig. 1

(Color online) Schematic of the microlens formation procedure: (a) a 3D microlens to be fabricated; (b) the microlens is quantized to a number of slices, and their 2D average projection is obtained; (c) one of the submasks, which is obtained from the 2D average projection of the corresponding slice; (d) the whole mask, which is constructed by all submasks; (e) the mask is put on top of a photoresist in a lithographic system and driven to move with the distance D.

Fig. 2
Fig. 2

Nonlinear relationship curve between exposure dose and sag height.

Fig. 3
Fig. 3

One of the submasks and the gray scale in it.

Fig. 4
Fig. 4

(Color online) Part of the microlens array.

Fig. 5
Fig. 5

Part of the designed mask pattern, where the inset is the zoom in area of the dashed line.

Fig. 6
Fig. 6

(Color online) Experimental results of the microlens array: (a) the measured profile of the microlens array in germanium by Dektak 8; (b) curves of the fabricated profile and the ideal profile, where the solid curve shows the target profile and cross section of the fabricated profile; (c) the deviation between the fabricated profile and the ideal profile.

Tables (1)

Tables Icon

Table 1 Data Size for Different Intervals D

Equations (5)

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Q i ( x , y ) = I 0 v · h i ( x , y ) rect ( y D / 2 D ) .
Q ( x , y , z , t ) z = A C × ( e C × Q ( x , y , z , t ) 1 ) B × Q ( x , y , z , t ) ,
M ( x , y , z , t ) = e C × Q ( x , y , z , t ) .
D = L + L 2 + a d ,
z ( x , y ) = c ν × ( x 2 + y 2 ) 1 + ( 1 ( 1 + c c ) × c ν 2 × ( x 2 + y 2 ) ,

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