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Improving the imaging quality of MOEs in DMD-based maskless lithography
Microelectronic Engineering 87 (2010) 1100–1103
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Improving the imaging quality of MOEs in DMD-based maskless lithography XiaoWei Guo *, Yongzhi Liu School of Optoelectronic Information, University of Electronic Science and Technology, Chengdu 610054, PR China
a r t i c l e
i n f o
Article history: Received 28 September 2009 Received in revised form 11 November 2009 Accepted 11 November 2009 Available online 17 November 2009 Keywords: Optical lithography Digital-micromirror device Corrugation Simulated annealing algorithm
a b s t r a c t Digital-micromirror device (DMD)-based maskless lithography technique has been applied to fabricate microoptical elements (MOEs). Due to the binary pulse-width modulation in DMD, however, some ruled corrugations will appear on the aerial image of MOEs when a laser light is used as exposure source. In this paper, the forming mechanism of the corrugations is explored and simulated annealing algorithm is adopted to remove the corrugations. The experimental results demonstrate that DMD-based maskless lithography technique is an effective tool for the fabrication of MOEs. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction To explore the lithography technique with mass production and low cost of fabricating MOEs is still a hot topic. In 2004, DMD as an electronic mask was used by Lars Erdmann et al. [1] to fabricate arbitrary MOEs because of its ability to realize grayscale display on projection screen. It provides a new way to get MOEs with high optical efficiency and low cost efficiency. In 2005 we also reported to obtain some good MOEs using the lithography technique with a white light as exposure source [2,3]. In 2006, we built a theoretical model [4] for precisely describing its imaging process according to the special timedependent properties of DMD, namely binary pulse-width modulation, with which a gray-tone pattern is transformed into some binary figures in a given rule and each binary figure obtains different exposure time. We found that, however, some ruled corrugations would appear on the aerial image when the approach is used for fabricating MOEs with continuous surface relief with a laser light as exposure source. In this paper, we firstly explored the physical mechanism of forming the corrugations, and then adopted simulated annealing algorithm as an optimization method to remove surface corrugations. 2. The ruled corrugations and its forming mechanism Fig. 1 illustrates schematically the maskless lithography system. The pattern is shown on the DMD screen. Light modulated by DMD * Corresponding author. Tel.: +86 28 83202342. E-mail address: [email protected] (X. Guo). 0167-9317/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2009.11.055
is directed into the Fourier lens, and then the diffractive light is filtered on the pupil plane and irradiate into a reduction-objectivelens group, and finally a demagnified aerial image is formed on the wafer. Fig. 2 gives out the corrugations on the aerial image of MOEs in a resist. Fig. 2a and b denotes the simulated and experimental imaging results of a microaxicon lens, respectively, and Fig. 2c and d shows a microlens case. For both cases, the height of the lens is 2 lm and the radius is 64 lm. We clearly observe that there are some ruled corrugations on the lens surface no matter in the simulated or experimental results, which greatly worsens the optical performance of MOEs. Also, the simulated and experimental results agree well with each other. To reduce the effect of the ruled corrugations, it is necessary to understand its forming mechanism. Fig. 3 shows the binary figures of the above microlens transformed by DMD. The number of the binary figures is dependent on the grayscale DMD offers and given by n ¼ log2 N where N is the grayscale. For a DMD with 256 grayscale, the number of the binary figures is eight. The exposure time P consumed by i-th binary figure is t i ¼ 2i1 t total = ni 2i1 and ttotal means total exposure time. It is easily found that most of the binary figures are circular gratings with different periods except for the two latter binary figures. The cross section of the simulated aerial image of the microlens is shown in Fig. 4a. As a comparison, the aerial image of the lattermost binary figure is also presented in Fig. 4b. The incidence wavelength is 0.442 lm. The partial coherence factor of the illumination source and the numerical aperture are 0.5. Under the same exposure conditions, the aerial image of the lattermost binary figure has no ruled corrugations, which indicates the corrugations are produced by the method of pulse-width modulation or the binary circular gratings. Due to the different periods of the circular grat-
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X. Guo, Y. Liu / Microelectronic Engineering 87 (2010) 1100–1103
3. Removal of the corrugations 3.1. The removal method Simulation annealing algorithm [5] is an efficient algorithm for global minimization technique, which is mostly used to solve various optimization problems. Here we adopt it to find a mask distribution on DMD for obtaining the right aerial image. If the mask distribution designed is E0 ðx; yÞ and the normalized field distribution of its aerial image E1 ðx; yÞ; we have
DEðx; yÞ ¼ E1 ðx; yÞ E0 ðx; yÞ
ð1Þ
Then the mask distribution to be solved can be expressed to be a function of E0 ðx; yÞ and DEðx; yÞ; defined by
Eðx; yÞ ¼ E0 ðx; yÞ þ c1 DEðx; yÞ þ c2 DE2 ðx; yÞ þ c0
ð2Þ
where c0 ; c1 and c2 compose of a constant group. And an evaluation function Q is set to control the computation time as follows: Fig. 1. Scheme of DMD-based maskless lithography system.
Q¼
m;n X i;j
ings, the diffraction of a binary figure differs from another when they go through part coherence imaging system. The grating with small period will obtain wide spatial spreading. On the other hand, different gratings are assigned with different exposure times, which results in different exposure depths for the binary figures. The two reasons explain the forming mechanism of the ruled corrugations.
, jEðxi ; yi Þ E0 ðxi ; yi Þj
m;n X
E0 ðxi ; yi Þ
ð3Þ
i;j
where m and n are the number of DMD pixels along two dimensions, respectively, and (i, j) determines one of the pixels. The algorithm will randomly perturb the images and will calculate the change in the evaluation function DQ . If DQ < 0 then it will accept the perturbation. If DQ > 0 then it will accept the perturbation with the probability expðDQ =TÞ, where T is the temperature parameter. The algorithm will start with a large value of T and gradually lower it as the iteration process progresses. In every iter-
Fig. 2. (a) and (b) denote the simulated and experimental imaging results of a microaxicon lens, respectively. (c) and (d) show the microlens case.
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X. Guo, Y. Liu / Microelectronic Engineering 87 (2010) 1100–1103
Fig. 3. The gray-tone pattern of a microlens is transformed into eight sheets of binary figures.
Fig. 4. The cross sections of the aerial images of the microlens (a) and the lattermost binary figure (b).
ation process, a new constant group with respect to ðc0 ; c1 ; c2 Þ is generated. When T is large, the algorithm is unlikely to become trapped in local minima of Q ; since the perturbations which increase Q can be accepted. Once the right constant group is obtained, the mask distribution we need is also deduced from the Eq. (2). 3.2. The removal results The mask distribution for the microlens after the optimization is shown in Fig. 5a. In the optimization process, the evaluation
Fig. 5. (a) The mask distribution for the microlens after the optimization. (b) The experimental imaging result of the microlens after the optimization. (c) The fabricated microlens array after the optimization.
X. Guo, Y. Liu / Microelectronic Engineering 87 (2010) 1100–1103
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function is 5%. Fig. 5b gives out the corresponding experimental imaging result in which the ruled corrugations are almost removed. With the optimization technique, we fabricate a microlens array shown in Fig. 5c. Maybe due to insufficient chemical transfer, the lens height is lower than the designed, which needs further study.
Acknowledgments
4. Conclusion
[1] Lars Erdmann, Arnaud Deparnay, Falk Wirth, et al., Proc. SPIE 5347 (2004) 79– 84. [2] Xiaowei Guo, Jinglei Du, Mingyong Chen, et al., Proc. SPIE 5874 (2005) 1–9. [3] Xiaowei Guo, Mingyong Chen, Jianhua Zhu, et al., Proc. SPIE 6032 (2006) 60320K-1. [4] Xiaowei Guo, Jinglei Du, Yongkang Guo, et al., Microelectron. Eng. 83 (2006) 1012–1016. [5] Yu Zhaoxian, Mo Dang, Thin Solid Films 425 (1–2) (2003) 108–112.
In conclusion, we discuss the forming mechanism of the ruled corrugations and its removal method. The programmable flexibility of DMD ensures the possibility of fabricating MOEs with the DMD-based lithography technique. For further work, we focus on the optimal chemical process parameters for the fabrication of good MOEs. It is expected that the fabricated components are able to compete in quality and price with those fabricated with existing techniques.
This work was supported by National Natural Science Foundation of China (Nos. 60906052, 60736038). References
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Improving the imaging quality of MOEs in DMD-based maskless lithography XiaoWei Guo *, Yongzhi Liu School of Optoelectronic Information, University of Electronic Science and Technology, Chengdu 610054, PR China
a r t i c l e
i n f o
Article history: Received 28 September 2009 Received in revised form 11 November 2009 Accepted 11 November 2009 Available online 17 November 2009 Keywords: Optical lithography Digital-micromirror device Corrugation Simulated annealing algorithm
a b s t r a c t Digital-micromirror device (DMD)-based maskless lithography technique has been applied to fabricate microoptical elements (MOEs). Due to the binary pulse-width modulation in DMD, however, some ruled corrugations will appear on the aerial image of MOEs when a laser light is used as exposure source. In this paper, the forming mechanism of the corrugations is explored and simulated annealing algorithm is adopted to remove the corrugations. The experimental results demonstrate that DMD-based maskless lithography technique is an effective tool for the fabrication of MOEs. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction To explore the lithography technique with mass production and low cost of fabricating MOEs is still a hot topic. In 2004, DMD as an electronic mask was used by Lars Erdmann et al. [1] to fabricate arbitrary MOEs because of its ability to realize grayscale display on projection screen. It provides a new way to get MOEs with high optical efficiency and low cost efficiency. In 2005 we also reported to obtain some good MOEs using the lithography technique with a white light as exposure source [2,3]. In 2006, we built a theoretical model [4] for precisely describing its imaging process according to the special timedependent properties of DMD, namely binary pulse-width modulation, with which a gray-tone pattern is transformed into some binary figures in a given rule and each binary figure obtains different exposure time. We found that, however, some ruled corrugations would appear on the aerial image when the approach is used for fabricating MOEs with continuous surface relief with a laser light as exposure source. In this paper, we firstly explored the physical mechanism of forming the corrugations, and then adopted simulated annealing algorithm as an optimization method to remove surface corrugations. 2. The ruled corrugations and its forming mechanism Fig. 1 illustrates schematically the maskless lithography system. The pattern is shown on the DMD screen. Light modulated by DMD * Corresponding author. Tel.: +86 28 83202342. E-mail address: [email protected] (X. Guo). 0167-9317/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2009.11.055
is directed into the Fourier lens, and then the diffractive light is filtered on the pupil plane and irradiate into a reduction-objectivelens group, and finally a demagnified aerial image is formed on the wafer. Fig. 2 gives out the corrugations on the aerial image of MOEs in a resist. Fig. 2a and b denotes the simulated and experimental imaging results of a microaxicon lens, respectively, and Fig. 2c and d shows a microlens case. For both cases, the height of the lens is 2 lm and the radius is 64 lm. We clearly observe that there are some ruled corrugations on the lens surface no matter in the simulated or experimental results, which greatly worsens the optical performance of MOEs. Also, the simulated and experimental results agree well with each other. To reduce the effect of the ruled corrugations, it is necessary to understand its forming mechanism. Fig. 3 shows the binary figures of the above microlens transformed by DMD. The number of the binary figures is dependent on the grayscale DMD offers and given by n ¼ log2 N where N is the grayscale. For a DMD with 256 grayscale, the number of the binary figures is eight. The exposure time P consumed by i-th binary figure is t i ¼ 2i1 t total = ni 2i1 and ttotal means total exposure time. It is easily found that most of the binary figures are circular gratings with different periods except for the two latter binary figures. The cross section of the simulated aerial image of the microlens is shown in Fig. 4a. As a comparison, the aerial image of the lattermost binary figure is also presented in Fig. 4b. The incidence wavelength is 0.442 lm. The partial coherence factor of the illumination source and the numerical aperture are 0.5. Under the same exposure conditions, the aerial image of the lattermost binary figure has no ruled corrugations, which indicates the corrugations are produced by the method of pulse-width modulation or the binary circular gratings. Due to the different periods of the circular grat-
1101
X. Guo, Y. Liu / Microelectronic Engineering 87 (2010) 1100–1103
3. Removal of the corrugations 3.1. The removal method Simulation annealing algorithm [5] is an efficient algorithm for global minimization technique, which is mostly used to solve various optimization problems. Here we adopt it to find a mask distribution on DMD for obtaining the right aerial image. If the mask distribution designed is E0 ðx; yÞ and the normalized field distribution of its aerial image E1 ðx; yÞ; we have
DEðx; yÞ ¼ E1 ðx; yÞ E0 ðx; yÞ
ð1Þ
Then the mask distribution to be solved can be expressed to be a function of E0 ðx; yÞ and DEðx; yÞ; defined by
Eðx; yÞ ¼ E0 ðx; yÞ þ c1 DEðx; yÞ þ c2 DE2 ðx; yÞ þ c0
ð2Þ
where c0 ; c1 and c2 compose of a constant group. And an evaluation function Q is set to control the computation time as follows: Fig. 1. Scheme of DMD-based maskless lithography system.
Q¼
m;n X i;j
ings, the diffraction of a binary figure differs from another when they go through part coherence imaging system. The grating with small period will obtain wide spatial spreading. On the other hand, different gratings are assigned with different exposure times, which results in different exposure depths for the binary figures. The two reasons explain the forming mechanism of the ruled corrugations.
, jEðxi ; yi Þ E0 ðxi ; yi Þj
m;n X
E0 ðxi ; yi Þ
ð3Þ
i;j
where m and n are the number of DMD pixels along two dimensions, respectively, and (i, j) determines one of the pixels. The algorithm will randomly perturb the images and will calculate the change in the evaluation function DQ . If DQ < 0 then it will accept the perturbation. If DQ > 0 then it will accept the perturbation with the probability expðDQ =TÞ, where T is the temperature parameter. The algorithm will start with a large value of T and gradually lower it as the iteration process progresses. In every iter-
Fig. 2. (a) and (b) denote the simulated and experimental imaging results of a microaxicon lens, respectively. (c) and (d) show the microlens case.
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X. Guo, Y. Liu / Microelectronic Engineering 87 (2010) 1100–1103
Fig. 3. The gray-tone pattern of a microlens is transformed into eight sheets of binary figures.
Fig. 4. The cross sections of the aerial images of the microlens (a) and the lattermost binary figure (b).
ation process, a new constant group with respect to ðc0 ; c1 ; c2 Þ is generated. When T is large, the algorithm is unlikely to become trapped in local minima of Q ; since the perturbations which increase Q can be accepted. Once the right constant group is obtained, the mask distribution we need is also deduced from the Eq. (2). 3.2. The removal results The mask distribution for the microlens after the optimization is shown in Fig. 5a. In the optimization process, the evaluation
Fig. 5. (a) The mask distribution for the microlens after the optimization. (b) The experimental imaging result of the microlens after the optimization. (c) The fabricated microlens array after the optimization.
X. Guo, Y. Liu / Microelectronic Engineering 87 (2010) 1100–1103
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function is 5%. Fig. 5b gives out the corresponding experimental imaging result in which the ruled corrugations are almost removed. With the optimization technique, we fabricate a microlens array shown in Fig. 5c. Maybe due to insufficient chemical transfer, the lens height is lower than the designed, which needs further study.
Acknowledgments
4. Conclusion
[1] Lars Erdmann, Arnaud Deparnay, Falk Wirth, et al., Proc. SPIE 5347 (2004) 79– 84. [2] Xiaowei Guo, Jinglei Du, Mingyong Chen, et al., Proc. SPIE 5874 (2005) 1–9. [3] Xiaowei Guo, Mingyong Chen, Jianhua Zhu, et al., Proc. SPIE 6032 (2006) 60320K-1. [4] Xiaowei Guo, Jinglei Du, Yongkang Guo, et al., Microelectron. Eng. 83 (2006) 1012–1016. [5] Yu Zhaoxian, Mo Dang, Thin Solid Films 425 (1–2) (2003) 108–112.
In conclusion, we discuss the forming mechanism of the ruled corrugations and its removal method. The programmable flexibility of DMD ensures the possibility of fabricating MOEs with the DMD-based lithography technique. For further work, we focus on the optimal chemical process parameters for the fabrication of good MOEs. It is expected that the fabricated components are able to compete in quality and price with those fabricated with existing techniques.
This work was supported by National Natural Science Foundation of China (Nos. 60906052, 60736038). References