Open Access
Add to BibSonomyAbstract
A new microlens fabrication method using an excimer laser is described in this paper. This method is based on the light vignetting effect. An excimer laser beam was propagated through two groups of fly’s-eye lens arrays and separated by the groups, after which divergent beams were formed. When the beams were sectioned by a mask and passed through a circular diaphragm, a vignetting effect was produced relative to an excimer laser mask projection image lens. Then the irradiating intensity at the processing plane varied from the beam center to its margin. This intensity difference in the transverse distribution would result in microlens curvature forming. This diaphragm method has the extinct advantage of short production time, few steps and easy setup construction.
©2009 Optical Society of America
1. Introduction
Different refractive microlens fabrication methods have been exploited to the present time; they include: micromolding, melting photoresist, step heat-forming photoresist, gray mask, and laser chemical vapor deposition [1-8]. As a direct method, excimer laser micromachining can be used for microlens production [9-10]. The principal microlens fabrication method by excimer laser can be combined with a two-step dynamic mask method [10]. In that method, shown in Fig. 1, a photomask with an arch-patterned hole intercepts a laser beam and is imaged by a projection reduction lens on the surface of the material being processed. The platform carrying the material to be processed is moved relative to the mask, with moving direction parallel to the axis of the central arch of the mask pattern. While, at the same time, excimer laser pulses are triggered to etch the material. This is the first step in the etching process. The points exposed corresponding to the longer sectional line within the arch enable a longer exposure time in the scanning time, and consequently result in a deeper etching depth. The etching profile shape will correspond well with the arch part of the mask because of the characteristic cold processing effect of the excimer laser. After the first scanning step, the mask is rotated by 90 degrees and the platform is then moved perpendicular to the first scanning direction, initiating a second step scan. Finally, the shapes produced by the two scan etchings form a three dimensional (3D) spherical structure. The 3D spherical structure is the basic pattern of the microlens. Figure 2 shows an example of a microlens array fabricated by this method. The processing laser was an excimer KrF (Krypton Fluoride) laser with a wavelength of 248 nm, the scanning speed was 4~8 mm/min, the laser pulse repetition rate was 30~40 Hz, and the etching rate was 2~4 µm/pulse which varied with the incident laser fluence which was between 5 J/cm2 and 23 J/cm2.
The two-step scanning method skillfully utilizes the distribution of light beams modulated by a combination of two factors: the shape of the aperture mask and moving dynamic exposure. This method easily controls the shape and the dimension of the processing area. It also has fewer processing steps. Unfortunately, the second scan can sometimes affect the result of the first scan; the third scan would be needed and would affect the first and the second scan in a processing application with more steps for other complex 3D microstructures. This situation leads to a non-rotationally symmetric polynomial aspheric surface on the microlens, which reduces the effective surface area. The disadvantages of the method are inevitable. Other methods for microlens processing can be applied, using an annular interval dynamic mask [11, 12]. This method slices 3D structure into a series of 2D masks through the contour lines, with every contour forms a mask pattern. These mask patterns, a series of light transmission rings with their inner circle diameter gradually reduced, were produced on a mask plate, arranged in a straight line direction. The mask plate is moved along the straight line direction, following the beat of excimer laser etching the microstructure. By synchronized moving these masks while excimer laser firing and keeping each mask exposure concentric, the outer exposed area will get more exposure times and result in deep etching, whereas the center is shallow. The laser pulse has a different firing frequency in different contour lines pitch. Laser etching will produce a solid surface structure when a laser scans a series of annular masks with a uniform motion. This method is already used in non-silicon 3D MEMS (Micro-Electro-Mechanical Systems) processing. However the manufacture of a series of mask patterns is tedious. Another method using gray-scale mask processing, introduced by C. J. Hayden [13], is not practical for the fabrication of microlenses, although it can fabricate 3D structures. That method of manufacturing a gray-scale mask, where the transmittance changes gradually from the center to the edge, is very difficult.
In this paper, an improved method for laser processing microlenses by using an excimer laser with diaphragm was introduced. The diaphragm method and our research are given below. This method holds the distinct advantage of short production time, simple steps, easy setup construction, which is prominent compared to other microlens fabrication methods.
2. The optical layout and calculations for the diaphragm method of microlens fabrication
The optical system arrangement and light path for the diaphragm method is shown in Fig. 3.
The excimer laser beams are passed through an alignment lens group, which included a concave cylindrical lens (flat-concave type, f=-78.7 mm, transverse segment size 20 mm) and a convex lens (flat-convex type, f=174.5 mm, transverse segment size 40 mm). Then, two groups of 9×9 fly’s-eye lenses, a concave group and a convex group, were used to divide the wavefront of the laser beam. Both groups of fly’s-eye lenses have an outer size of 36 mm×36 mm. The distance between two groups of fly’s-eye lens arrangements was adjustable to control the width of the beam and divergence angle. All of the divided light beams were converged using a bi-convex spherical lens (diameter of 60 mm, focal length of 600 mm) to form a multi-wavelet front beam having different propagation direction light. The multi-wavelets beam irradiated a mask with a circular hole. After passing the mask, the beams irradiated the aperture stop. The beams passing the aperture stop were reduced and imaged using a projection lens. Then the light beams irradiated the surface of the material being processed. The image plane and the material surface were coincidental. The projection lens was composed of three fused silica lenses. Its reduction ratio was 15×, and its clear aperture was 11.28 mm. The projection lens was mainly used to image the excimer laser through the mask pattern on the processing platform. The designed projection lens MTF (Modulation Transfer Function) was required to meet the class B requirement (Class B requirement is the requirement between the ideal optical system MTF in the defocused distance of one focal depth and the MTF in the defocused distance of half of focal depth under the same condition).
The optical system has an obvious vignetting effect. The aperture stop acts as a vignetting diaphragm. Its working principle is shown in Fig. 4. The divergent, parallel and convergent rays of beam 1 can pass the diaphragm. The divergent and parallel rays of beam 2 can pass the diaphragm while the convergent ray cannot pass. The divergent ray of beam 3 can pass the diaphragm while parallel and convergent rays cannot pass. The divergent, parallel and convergent rays of the beam 4 cannot pass. Therefore the different propagating rays in different areas result in a variable energy distribution. The energy is low in the central zone and high in the marginal zone. This is the anticipated distribution for the processing microlens. However, confirmation is needed to confirm whether the energy distribution can meet the requirement of the energy distribution for the excimer laser spot. The diameter of the vignetting diaphragm and position parameter need to be decided based on the processing requirements and conditions.
A minimum number of excimer laser pulses should be used to fabricate a microlens in order to reduce the processing time and improve the processing efficiency. It is necessary to ensure that the difference between the energy in the margin area surrounding a spot and the energy at the spot center is as large as possible. In optical design theory [14], the vignetting effect requires that Eq. (1) and Eq. (2) should be met:
where dd——diameter of diaphragm aperture, dm——diameter of the hole on the mask, l——distance between aperture diaphragm and mask, dP——diameter of reduction projection lens, L——distance between reduction projection lens and mask.
Equation (1) limits the diameter range of the vignetting diaphragm. Equation (2) limits the position range of the vignetting diaphragm. Equation (1) and Eq. (2) commonly ensure that the phenomenon that some beams were totally blocked in the optical path system (light path system) does not happen, so as to ensure that the fabricated microlens does not experience the flat-top phenomenon. The flat-top phenomenon means the central curvature of the microlens is infinite. According to the vignetting effect in optical design theory, when Eq. (1) and Eq. (2) are applied using the equal sign, the energy difference between the edge and the center of the laser spot, which is used to fabricate the microlens, will reach its maximal value. Also, when all spots from every point of the mask can cover the whole diaphragm, Eq. (1) and Eq. (2) can use the equal sign. At this time, the energy difference between the spot edge and the spot center reaches a maximum. In the existing excimer laser microprocessing system, one requirement of the mask design is that all spots from the mask can cover the whole reduction projection lens. This requirement can be expressed as:
where θ——beam half divergent angle of the central position of the design required mask in the excimer laser microprocessing system. According to this condition, the design requirement of the existing excimer laser microprocessing system, that is, that all spots from the mask can cover the whole reduction projection lens, can just meet the requirement that the energy difference between the edge and the center of the laser spot is maximal. This means that all spots from every point of the mask can cover the whole diaphragm. The derivation process is as follows:
(1) Equation (4) expresses the requirement that all spots from every point of the mask can cover the whole diaphragm, as:
where θ′—beam half divergent angle of the central position of the design required mask in the excimer laser diaphragm method for the microlens.
(2) If Eq. (2) is divided by dd, and divided by 2, then we get:
(3) If Eq. (5) is divided by 2, and the direction of inequality sign is changed, combined with Eq. (4), then we get:
Equation (3) represents the requirement for the excimer laser micro processing system, which is that all spots from the mask can cover the whole reduction projection lens, and Eq. (4) represents the requirement for the microlens fabrication system, which is all spots from every point of the mask can cover the whole diaphragm. Comparing Eq. (4) with Eq. (6), it can be seen that the beam half divergent angle at the mask central point to meet Eq. (3), is more than the beam half divergent angle at the mask central point to meet Eq. (4). When the Eq. (3) is met, Eq. (4) is met naturally. Therefore, Eq. (6) indicates the design requirement was met.
Under the conditions of Eq. (7) and Eq. (8), if the intensity of the light spots from every point in the mask in all of the directions is equal, then the shielding function of the energy of the 2D excimer laser spot, represented by Eq. (9), can be deduced from the geometric relationship shown in Fig. 5.
where α——the sheltered angle of the light spot from a point in the mask sectioned by the diaphragm and x——relative position between a point in the mask and optical axis.
Using the Taylor expansion near the zero, we get:
Because the intensities of the light spots emitted from every point on the mask in every direction are equal, the sheltered angle of the light spot from a point in the mask sectioned by the diaphragm, angle α, directly characterizes the situation of the laser spot energy shelter. If the value of angle α is subtracted from the total angle of the spot from the corresponding point on the mask, the 2D energy distribution of the laser spot can be deduced. Consequently, the main part of the Taylor expansion of this energy distribution function is a quadratic function. The quadratic coefficient is not zero. These characteristics will guarantee the requirements for the continuity of the excimer laser energy distribution in the excimer laser diaphragm method for fabricating the microlens.
The actual conditions of the mask, diaphragm and reduction projection lens for the excimer laser diaphragm method can be stimulated using the optical design software, ZEMAX [15]. The simulation light trajectory scheme is shown in Fig. 6.
In Fig. 6, Label 1 represents the mask, Label 2 represents the diaphragm, Label 3 is the reduction projection lens, and Label 4 represents the processing platform. The diameter of the mask is 2 mm. The diameter of diaphragm is also 2 mm. The diameter of the reduction projection lens is 28.3 mm. The distance between the mask and the diaphragm is 87.6 mm. The distance between the mask and the reduction projection lens is 519.42 mm. The distance between the reduction projection lens and processing platform is 32.60 mm. The energy distribution of the laser spot on the platform is shown in Fig. 7, where it can be seen that the center of the excimer laser spot has fewer tiny spots and lower energy density, while the edge has a denser distribution of tiny spots and higher energy density. That means the density of the tiny spots changes gradually from the laser spot center to the edge.
The energy transmission of the excimer laser is shown in Fig. 8. It can be seen that the transmission ratio and the energy density are both lower in the excimer laser spot center, while the transmission ratio and the energy density are higher at the edge. The transmission ratio changes gradually from the excimer laser spot center to the edge. The simulated result also shows that adding a vignetting diaphragm into the excimer laser optical path system can get an energy distribution where the energy in the center is lower and higher at the edge. Near the axis, the energy transmission curve is nearly flat, but about half way to the edge, there is a little slope. In the near part, half way to the edge, the energy transmission increases noticeably. The increased line part has a gradually increasing slope. This energy distribution could satisfy the requirement of the excimer laser diaphragm method for fabricating a microlens. The gradual change of energy meets the requirement of the continuity of excimer laser energy distribution in this method.
3. Experimental procedure
The experiment uses polymethyl methacrylate (PMMA) as the processing material. PMMA has strong absorbability for the UV excimer laser, and so it meets the processing requirement. It is also one of the generally used optical plastics. The experimental setup is shown in Fig. 9.
The optical elements were precisely adjusted to be concentric in order to insure the centre of laser spot, the He-Ne collimating laser beam, the beam expanding and alignment system, the homogenizer system, the mask, the diaphragm and reduction projection lens were kept on the same axis. The optical path of the excimer laser diaphragm method was improved to reduce or even to avoid the difference in curvature radius between the direction of the horizontal axis (X) and the vertical axis (Y). The simplest and most efficient improvement method was changing the circular diaphragm to an elliptic one (Fig. 10). This can reduce the difference in curvature radius between the horizontal direction (X) and the vertical direction (Y) of the microlens. After production, the difference in curvature radius was from a magnitude of 10-1mm to 10-2 mm. Three excimer laser pulses were used to process the microlens under the required conditions: both the sizes of the concave and convex fly’s-eye lens group were 36 mm×36 mm, the diameter of the mask at 2 mm, the diameter of the reduction production lens was 28.3 mm, the distance between the mask and the diaphragm was 87.6 mm, the distance between the mask and the reduction projection lens was 519.42 mm, the distance between the reduction projection lens and processing platform was 32.60 mm, the frequency of the excimer laser pulse was 5 Hz and the working voltage of the excimer laser device was 23 kV. After finishing the microlens structure formation processing, 30 excimer laser pulses were used to polish the surface of the microlens after moving the diaphragm away and get the fabricated microlens shown in Fig. 11. As shown in Fig. 12, an optical metric instrument (WYKO NT1100, Veeco Instruments Ins., US) was used to measure and calculate the contour with the following results: the diameter was ϕ100 µm, the curvature radius was -0.17 mm, focal length was 0.35 mm, F-number was 3.5 and the surface roughness was class 11 (indicating the Ra value is between in the 0.05 µm and 0.1µm).
4. Discussion
4.1 Interaction mechanism between excimer laser and material plate
Concerning the general idea about excimer laser interaction with polymer material, two main mechanisms play important roles: the photochemical decomposition and the photothermal induced disconnection. If the photon energy is larger than the material chemical bonding energy, the chemical bond will break up during laser interaction, and the correspondent mechanism is prone to the photochemical decomposition mechanism. This coincides with the situation of the F2 laser and ArF laser. For XeCl and XeF lasers, whose photon energy is relatively low, the photothermal induced disconnection is the main mechanism; the photons of excimer laser interact with PMMA molecules, making the molecular rotational and vibrational energy level vary, and inducing rapidly increasing temperatures which disconnect the polymer principal chain macromolecules. For common situations, the shorter the laser wavelength, the more distinct is the so called “cold processing” effect. For the KrF excimer laser, whose photon energy is 5.0 eV, even though both of the two mechanisms exist in the interaction period, the photodecomposition mechanism is more evident. In a photodecomposition period, the electron in the bonding absorbs part of photon energy directly, suppressing the temperature increase and reducing thermal disconnection procedure. This process of PMMA ablation by excimer laser is accompanied by carbon atom release processing. The C=O bonding in PMMA is broken up by absorption for photon, meanwhile the C-C bonding and C-O bonding are broken up through absorption energy transfer. Some details have been described in a previously published paper [16]. These mechanisms form the physical and material foundation for microlens fabrication by excimer laser. The etched depth per laser pulse (etching rate) is proportional to the laser fluence. The etching rate curve is indicated in Fig. 13. The etching rate fluence threshold is 0.65 J/cm2. Over the threshold, in the range of values before the saturation appearing point, when the laser fluence increases the etching rate value will increases near linearly, and reach the maximal etching rate 3.3 µm/pulse (correspondent fluence is 1.5 J/cm2) and saturation effects appear. Continual increase in fluence may cause the etching rate to fall, which can be attributed to the energy absorption by the laser induced plume and plasma. Therefore, in the linear zone of fluence from 0.65 J/cm2 to 1.5 J/cm2, at high intensity point in the laser beam, the corresponding etched depth is large. For cold processing, no melted material flow will take place to reduce the required fluctuant microstructure. To some extent, no material deformation induced by thermal plastics would be found.
4.2 Processing result affected by the number of laser pulses
It was of interest to fabricate a microlens with a diameter of ϕ100 µm using the diaphragm method. The processing experiment was carried out using a laser pulse frequency of 1Hz and a laser working voltage of 23kV. When the number of processing pulses and the number of polishing pulses were both changed, there was confirmation of the effect of the number of laser pulses on the result. The experimental results and data are presented in Fig. 14. From this figure, it can be seen that the curvature radius decreased with more production pulses and increased with more polishing pulses. The production pulses fulfill the microlens structure forming by the transverse intensity distribution, and the intensity difference causes the ablated depth difference between the centre and the margin of the microlens. Keeping the intensity difference will keep the ablated depth difference, which will result in the production pulse number increasing the microlens curvature. The polishing pulse was used to illuminate the microlens after the diaphragm was moved away, with the aiming of smoothing the ablated microstructure surface and modifying blemishes on the surface of the microstructure. These polishing pulses with even beam intensity at the processing plane had the tendency to reduce the curvature of the lens when the number increased. The curvature reduction may result from the material PMMA plastic deformation with latent thermal accumulation by the excimer laser photothermal effect during the polishing procedure. The diameter range of the fabricated microlenses was 63.12 µm-0.22 mm. According to calculations, the focal length was determined to be 128.29 µm-0.45 mm and the F-number were 1.28-4.5.
4.3 Processing result affected by the laser pulse repetition rate of the excimer laser
The effect of repetition rate was examined by taking a ϕ100 µm microlens as an example, using a working voltage of 23 kV, 5 production laser pulses and 30 polishing laser pulses. In Fig. 15, it can be seen that a change of the repetition rate has little influence on the curvature radius of a microlens. In the Fig. 15, it can be seen that a change of the repetition rate has little influence on the curvature radius of the microlens. Because the focal length and F-number are decided by the curvature radius while other parameters do not change, the change of laser pulse repetition rate had little influence on the focal length and F-number of the microlens.
4.4 Processing result affected by the energy of excimer laser pulses
The effect of varying the energy of the laser was examined by taking a ϕ100 µm microlens as an example, using a 1Hz laser pulse, 5 production laser pulses and 30 polishing laser pulses. The results are shown in Fig. 16. The energy of the excimer laser pulses directly related to the working voltage of the laser device; the laser at higher working voltage radiates higher pulse energy. The working voltage range of the excimer laser device was 15-23 kV, and its corresponding energy range was 300-1200 mJ. When the working voltage is 15-16 kV, it is not suitable for the fabrication of a microlens using the diaphragm method because of the low amount of energy, about 2.77 mJ at the processing platform and very unstable. However, when the working voltage is raised to 21kV, the curvature radius reaches a maximum. This maybe related with the excimer laser working condition. The laser pulse duration was 30ns, laser energy fluence was 38 J/cm2, and the material etching rate was 4.2 µm/pulse. Because the focal length and F-number are decided by the curvature radius while the other parameters do not change, the focal length and F-number both reach a maximum. Consequently, the change of energy in the laser pulse with this method has a great influence on the curvature radius of a microlens, as well as affecting the focal length and F-number.
4.5 The parameters of the microlens produced by the excimer laser diaphragm method compared with other methods.
Different methods use different technologies. The parameters are shown in Table 1.
Table 1. Comparison of parameters by different methods
Table 1 illustrates that the F-number range that can be produced by the excimer laser diaphragm method covers 53% of the ranges available from other methods, and the diameter range by the excimer laser diaphragm method covers 5% of the ranges from other methods. This feature shows the flexibility of the excimer laser diaphragm method in fabricating various curvature radii. The parameter control of the microlens by the diaphragm method is dexterous. To meet diameter control, it is necessary only to change the mask and diaphragm diameter. Curvature radius control is achieved through the production and polishing laser pulse parameters and beam optics layout and parameters including fly’s-eye, converging lens, mask, and diaphragm. Apart from this, the diaphragm method has the advantage of quick fabrication, usually allowing completion of one microlens in several seconds.
From Table 2, it can be seen that the surface roughness level of the microlens produced using the excimer laser diaphragm method is lower than that of microlenses produced using the mold method and the ink-jet method.
Table 2. Comparison of the roughness with different fabrication methods
However, the measuring area for the excimer laser diaphragm method result is much larger than the measuring area for the mold method result. The roughness level of the diaphragm method will rise if the measuring area is reduced for the diaphragm method.
5. Conclusion
A PMMA-based refractive type microlens was fabricated using an existing excimer laser micro-machining system and the vignetting diaphragm method. The diameter of the produced lenses was ϕ80 µm-ϕ120 µm, curvature radius was 50 µm-0.25 mm, focal length was 100 µm-0.5 mm, F-number was 0.8-6.3 and the surface roughness reached level 10-11. The experiments verified the feasibility of fabricating microlenses with the excimer laser diaphragm method. Further research and discussion is needed to investigate factors influencing this process, such as slight vibration of the platform and mechanical supporting system, in order to improve the reproducibility of the excimer laser diaphragm method.
References and links
1. S. Moon, S. Kang, and J. U. Bu, “Fabrication of polymeric microlens hemispherical shape using micromolding,” Opt. Eng. 41, 2267–2270 (2002). [CrossRef]
2. B. K. Lee, D .S. Kim, and T. H. Kwon, “Replication of microlens arrays by injection molding,” Microsyst. Technol. 10, 531–535 (2004). [CrossRef]
3. Q. Xu, J. Ye, G. Y. Zhou, X. Y. Hou, G. G. Yang, Z. K. Bao, and Z. R. Yu, “Fabrication of refractive microlens array by melting photoresist,” Acta Opt. Sin. 16, 1326–1331 (1996). (in Chinese)
4. Q. Xu, L. M. Yang, X. W. Hu, and G. G. Yang, “Step heat-forming photoresist method for expanding the N.A. range of refractive microlens,” Acta Opt. Sin. 18, 1128–1133 (1998). (in Chinese)
5. X. Y. Zhang, X. J. Yi, X. G. Zhao, Z. H. Mai, M. He, and L. Q. Liu, “Fabrication of linear fused quartz microlens array using photolithography and Ar ion beam etching,” Chin. J. Quantum. Electron. 15, 66–73 (1998). (in Chinese)
6. J. Yao, J. Q. Su, F. H. Gao, F. Gao, Y. K. Guo, C. L. Du, H. J. Zeng, and C. K. Qiu, “Refraction microlens array made of bichromate gelatine by enzyme solution with coding gray tone mask,” Chin. J. Lasers A 28, 633–636 (2001). (in Chinese)
7. S. Biehl, R. Danzebrink, P. Oliveira, and M. A. Aegerter, “Replication microlens fabrication by ink-jet process,” J. Sol-Gel Sci. Technol. 13, 177–182 (1998). [CrossRef]
8. G. R. Song, H. Z. Yao, and Z. G. Lan, “Design and practice of film microlenses fabricated by laser chemical vapor deposition,” Optoelectron. Technol. 16, 201–208 (1996). (in Chinese)
9. F. Quentela, J. Fieretb, A. S. Holmesc, and S. Paineaua, “Multilevel diffractive optical element manufacture by excimer laser ablation and halftone masks,” Proc. SPIE 4274, 420–31 (2001). [CrossRef]
10. N. H. Rizvi, “Production of novel 3D microstructures using excimer laser mask projection techniques,” Proc. SPIE 3680, 546–52 (1999). [CrossRef]
11. A. S. Holmes, J. E. Pedder, and K. L. Boehlen, “Advanced Laser Micromachining Processes for MEMS and Optical Applications,” Proc. SPIE 6261, 62611E-1~9 (2006).
12. L. Herbst and R. Paetzel, “High-power excimer laser micromachining,” Proc. SPIE 6106, 610606-1~7 (2006).
13. C. J. Hayden, “Three-dimensional excimer laser micromachining using greyscale masks,” J. Micromech. Microeng. 13, 599–603 (2003). [CrossRef]
14. Z. J. Wang, X. P. Chen, H. M. Lu, and P. S. Gu, Optics Technical Manual (China Machine Press, Beijing, China,1987), Chap.2. (in Chinese)
15. ZEMAX EE, Optical Design Program User’s Guide, January 6, 2003.
16. X. L. Zhu, S. B. Liu, T. Chen, Y. J. Jiang, and T. C. Zuo, “Analysis of X-ray photoelectron spectroscopy of polymethyl methacrylate etched by a KrF excimer laser,” Chin. Phys. Lett. 22, 1526–9 (2005). [CrossRef]
