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space patterns on nonplanar substrates using a digital micromirror device-based point-array scanning technique
Optics and Lasers in Engineering 101 (2018) 106–112
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Printing line/space patterns on nonplanar substrates using a digital micromirror device-based point-array scanning technique Hung-Fei Kuo a,∗, Guan-Hsuan Kao a, Liang-Xiu Zhu a, Kuo-Shu Hung b, Yu-Hsin Lin b a b
Graduate Institute of Automation and Control at National Taiwan University of Science and Technology, #43, Sec.4, Keelung Road, Taipei 106, Taiwan, ROC Shuztung Machinery Industrial Co., Ltd, No.30, Houke S. Rd., Houli Dist., Taichung 421, Taiwan ROC
a r t i c l e
i n f o
Keywords: Nonplanar lithography Digital micromirror device (DMD) Point-array scanning Multiobjective particle swarm optimization (MOPSO)
a b s t r a c t This study used a digital micromirror device (DMD) to produce point-array patterns and employed a selfdeveloped optical system to define line-and-space patterns on nonplanar substrates. First, field tracing was employed to analyze the aerial images of the lithographic system, which comprised an optical system and the DMD. Multiobjective particle swarm optimization was then applied to determine the spot overlapping rate used. The objective functions were set to minimize linewidth and maximize image log slope, through which the dose of the exposure agent could be effectively controlled and the quality of the nonplanar lithography could be enhanced. Laser beams with 405-nm wavelength were employed as the light source. Silicon substrates coated with photoresist were placed on a nonplanar translation stage. The DMD was used to produce lithographic patterns, during which the parameters were analyzed and optimized. The optimal delay time-sequence combinations were used to scan images of the patterns. Finally, an exposure linewidth of less than 10 μm was successfully achieved using the nonplanar lithographic process. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction As electronic components have become increasingly advanced, improving the fabrication of nonplanar structures in newer-generation electronic components has attracted increasing attention. How to define layout patterns on nonplanar substrates has emerged as a key issue. Previously, antenna patterns have been defined on integrated circuits using a planar micromirror process; however, this process can only be used on relatively regular and flat substrates. Special polydimethylsiloxane (PDMS) soft mold patterns can be created to transfer and print high-gain antennas, array-type antennas, or radio-frequency identification patterns onto substrates with low curvature [1,2]. Other techniques to solve this problem include using PDMS soft-mold-based pattern transfer printing for the creation of metallic gratings on curved substrates [3,4]; combining nonlinear micromirror and plasma etching techniques to define structural patterns on nonplanar inorganic optical component substrates [5]; and using computer-generated holograms to define 3D patterns on nonplanar substrates [6,7]. Nevertheless, conventional lithography techniques that focus on planar materials still have stable mass-production processes and are widely employed in the manufacture of printed circuit boards (PCBs) for the creation of designed component patterns. Maskless lithography, a laser
∗
Corresponding author. E-mail address: [email protected] (H.-F. Kuo).
direct imaging (LDI) technique, is currently used to define circuit patterns with a width of 10–30 μm [8]. Two exposure modes are involved in this technique. The first projects laser beams onto focusing lenses using reflective polygon mirrors as beam splitters. The beams thus produced can be focused on substrates to form lithographic patterns. This technique has large depth of focus (DOF) and high throughput; however, the system is expensive [9]. In response to the market’s demand for small-quantity and high-variety patterns, another LDI technique has been developed that employs a digital micromirror device (DMD) as a digital mask. The technique uses a conventional projection-based optical system design that contains microlens arrays (MLAs), thereby enabling beam spot arrays to exhibit more satisfactory resolution regarding the line width. Additionally, this technology is silicon-based and can thus produce DMDs with higher reliability at lower costs than other techniques. As a result, the development of this technology has attracted considerable interest [10]. Multiobjective planning, first proposed by researchers Charnes and Cooper, can be used to solve quality control problems in optical processes [11,12]. Numerous approaches can be used to solve multiobjective problems, including the popular simulated annealing [13] and genetic algorithms [14,15] and also particle swarm optimization (PSO), which has been commonly employed in recent research. The advantage of the PSO algorithm is its global search capability. The concept for the algorithm derived from the foraging behavior of a flock of birds. Each bird in a flock occupies a distinct spatial area and must search for the ideal foraging area. When an optimal foraging spot has been determined
https://doi.org/10.1016/j.optlaseng.2017.10.009 Received 10 February 2017; Received in revised form 4 September 2017; Accepted 14 October 2017 0143-8166/© 2017 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 101 (2018) 106–112
Table 1 Distribution of beam intensity at different distances from the DMD.
Distance (mm)
0
114
142
171
Aerial image (AI)
locally, each bird flies toward the currently defined optimal spot. Over time, birds tend to flock together to the optimal foraging spot [16]. This study investigated how existing techniques for the definition of layout patterns on nonplanar substrates might be improved using a DMD-based maskless lithography system. The PSO multiobjective algorithm was also integrated to plan the point-array scanning parameters and stage moving velocity. The efficient and highly repetitive LDI technique could then be used to define lithographic patterns on nonplanar substrates. 2. Aerial image analysis In this study, field tracing (VirtualLab) was used to design the locations of the optical components in the DMD-based scanning lithography system. The locations of the focal lenses in the beam guiding system were first arranged according to the intensity distribution of DMD-deflected laser beams. The incident beam was assumed to consist of linearly polarized plane-waves with a wavelength of 405 nm, and the beam shone on a DMD of diameter 1.3 mm, with the surface area of each mirror in the DMD equal to 13.7 μm × 13.7 μm. Table 1 presents the intensity distribution at different distances from the DMD of light reflected by the device. When the distance was 0 mm, diffraction was observed because of the gaps between micromirrors. As the distance was between 114 and 142 mm, the diffraction side lobe gradually separated from the diffraction main lobe. The first focal lens was placed at a distance of 135 mm from the DMD mirror, and its intensity distribution is presented in Fig. 1(a). To determine the size of the diffraction main lobe, the beam intensity distribution in Fig. 1(a) was crisscrossed into a black line segment. Fig. 1(b) illustrates the beam intensity distribution of this cross section, wherein the beam diameter was approximately 0.3 mm. An aperture was positioned 80 mm behind the first focal lens to eliminate effects of the higher-order side lobes. The beam continued to propagate after passing through the aperture. The second focal lens was placed 155 mm behind the first. An analysis of the optical field intensity 30, 60, 90, and 120 mm behind the second focal lens was subsequently conducted, and the results are summarized in Table 2. Beams 30, 60, 90, and 120 mm behind the second focal lens that were formulated through focused imaging had a diameter of 480, 40, 240, and 600 μm, respectively. In terms of intensity distribution, the beam formulated 60 mm behind the second focal lens exhibited a more satisfactory beam quality than the beams formulated at other distances, and that beam was most similar to the TEM00 Gaussian beam mode. Therefore, the objective lens was positioned 60 mm behind the second focal lens. The optical beam intensity distribution obtained at various focal positions behind the objective lens was then analyzed, and the results are presented in Table 3. The beam formulated 28 mm behind the objective lens exhibited the smallest spot size, having a diameter of 18 μm. This beam spot characteristic was employed in this study to determine the effect of point-array scanning lithography. When a nonplanar substrate is exposed, the limited DOF can affect image quality when performing point-array scanning. To effectively con-
Fig. 1. (a) Distribution of beam intensity 135 mm from the DMD mirror plane; and (b) beam intensity on the crisscrossed black line segment in (a).
Fig. 2. Mathematical model of particle swarm algorithm.
trol nonplanar lithography quality, this study adopted multiobjective particle swarm optimization (MOPSO) to calculate the optimal lithography parameters. In this technique, particles are first randomly arranged in the solution space (Fig. 2). Each particle knows the position of the optimal solution it has identified so far (Pibest ) and the position of the optimal solution currently identified by other particles in the group (Pgbest ). When a particle needs to move, it integrates the moving velocities at 107
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Optics and Lasers in Engineering 101 (2018) 106–112
Table 2 Intensity distribution observed at various distances behind the second focal lens.
Distance (mm)
30
60
90
120
31
34
AI
Field intensity in the line
Table 3 Intensity distribution observed at various distances behind the objective lens.
Distance (mm)
24
28
AI
Field intensity in the line
three positions: its current position, Pibest , and Pgbest to produce the new moving direction, then moves to the new position in the solution space. Therefore, individual particles adjust their velocity with reference to those of particles at Pibest and Pgbest , as defined in Eq. (1). The location of each particle in the solution space can then be updated [Eq. (2)]. Individual particles arrive at the new position in the solution space at their newly integrated velocity and continue searching for a more satisfactory solution to ultimately obtain the optimal location. The current solutions generated by the individual and the group then serve as referencing directions for each particle as it updates, thereby increasing the possibility of finding the optimal solution. To use PSO to solve multiobjective optimization problems, the objective function(s) should first be established: {𝑓𝑚 (𝑥)}𝑘𝑚=1 , where k is the number of objective functions and k ≥ 2. x ∈ X, where the set X is the feasible set of decision vectors. When the optimal function {𝑓𝑚 (𝑥)}𝑘𝑚=1 is subject to the bounds of x, x ranges between 𝑥𝑢𝑝𝑝𝑒𝑟 and 𝑥𝑙𝑜𝑤𝑒𝑟 , and the inequality and equality constraints 𝑗 𝑗 are gi (x) and hl (x), respectively. A point x∗ ∈ Ω is Pareto-optimal if, for everyx ∈ Ω, eitherfm (x) ≥ fm (x∗ ) for every 𝑚 ∈ I = [1, 2...., 𝑘] or there is at least one m ∈ I such that fi (x) > fi (x∗ ). The point x∗ is defined as the optimal if no objective can be improved without worsening at least one other objective. Pareto’s optimum usually gives not one single solution,
but a set of solutions called nondominated solutions [17,18]. 𝑣𝑡𝑖+1 = 𝑣𝑡𝑖 + 𝑐1 × 𝑟𝑎𝑛𝑑𝑖𝑏𝑒𝑠𝑡 (𝑝𝑖𝑏𝑒𝑠𝑡 − 𝑥𝑡𝑖 ) + 𝑐2 × 𝑟𝑎𝑛𝑑𝑔𝑏𝑒𝑠𝑡 (𝑝𝑔𝑏𝑒𝑠𝑡 − 𝑥𝑡𝑖 )
(1)
x𝑡𝑖+1 = 𝑥𝑡𝑖 + 𝑣𝑡𝑖+1
(2)
where 𝑣𝑡𝑖 and 𝑣𝑡𝑖+1 are the moving velocity of particle i at times t and t + 1, respectively; 𝑥𝑡𝑖 and 𝑥𝑡𝑖+1 are the position of particle i at t and t + 1 in the solution space, respectively; c1 and c2 are learning factors; r1 and r2 are randomly generated particle numbers; Pibest is the optimal particle position identified by an individual; and Pgbest is the optimal particle position identified by the group. In this study, an MOPSO procedure was developed to control the quality of the photoresist imaging. Table 4 presents the relationship between the parameters of the designed MOPSO procedure and the corresponding point-array scanning parameters. The solution space in the MOPSO algorithm corresponds to the design of DMD delay time; the searching particle position 𝑥𝑡𝑖 corresponds to the solution of the DMD delay time Δtdelay searched by particle i at t; and the particle moving velocity corresponds to the direction of the DMD delay time Δtdelay in this search. Pibest is the optimal DMD delay time Δtdelay that can be searched by an individual particle, Pgbest is the optimal DMD delay time Δtdelay 108
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Table 4 Definitions of nonplanar lithographic parameters in MOPSO.
Table 5 Procedure of the MOPSO algorithm. 1: Initialize particles 2: threshold←0.4 target←4 3: FOR ipso = 1 to n_particles 4. Δtdelay ←Rand: 5: 𝑥𝑡𝑖 ← ProcessParameter(f) 6: OV(vstage, 𝑥𝑡𝑖 ) ←EvaluateOverlay(vstage, 𝑥𝑡𝑖 ) 7: Cost ← minimum LE and maximum ILS 8: ILS(I(x))←EvaluateImageLog-Slope 9: LE(𝐿Pr int )←EvaluateLinwidthError 10: end FOR 11: Create an empty External Archive (EA) 12: Copy the non-dominated solutions to the EA; 13: Select a particle leader from the EA 14: Pibest is the Best of 𝑥𝑡𝑖 ; Pgbest is the leader of EA 15: WHILE k = 1 to max_iter 16: FOR ipso = 1 to n_particles 17: Select a particle leader from the EA 18: Update particle Velocity & Position &Cost 19: end FOR 20: end WHILE
Parameter definition
𝑥𝑡𝑖 𝑣𝑡𝑖 Pibest Pgbest c1 and c2 rand
The solution of the DMD delay time Δtdelay searched by particle i at t The searching direction of the DMD delay time The optimal DMD delay time Δtdelay searched by the individual particle The optimal DMD delay time Δtdelay searched by the group of particles Acceleration constants Uniformly distributed random numbers
Z DOF
θ X Fig. 3. Schematic diagram of exposure on the inclined plane.
that can be searched by a group of particles, and c1 and c2 are equal to 2. Fig. 3 presents a schematic diagram of printing photoresist patterns on a nonplanar substrate. The pink area indicates the film stacked on the silicon substrate that serves as the photoresist coating. The silicon substrate is placed on a nonplanar translation stage, the spatial profile of which can be defined by height z and angle 𝜃. When the film stack enters the exposure area, scanning on the photoresist begins using the point array technique. The exposure area is defined as the area within the DOF and the area of the point array that falls on the inclined plane. The moving velocity of the translation stage is defined as vstage = z/Δt × tan 𝜃, where Δtis the time required for the translation stage to move a distance z/sin 𝜃. The spot overlapping rate is defined as 𝑂𝑉 = 1 − 𝑣𝑠𝑡𝑎𝑔𝑒 × Δ𝑡𝑑𝑒𝑙𝑎𝑦 ∕𝐷, where D is the beam diameter. In the developed MOPSO procedure, the objective functions include designs of linewidth error [LE; expressed as Eq. (3)] and image log slope [ILS; expressed as Eq. (4)] [19,20]. When the maximal intensity of the AI exceeds the threshold of the photoresist reaction, Eq. (4) is used to calculate the ILS. | | |𝐿Pr int − 𝐿Target | | × 100% LE = | (3) 𝐿Target
Fig. 4. Pareto solutions based on the proposed MOPSO procedure.
ations (i.e., k > 1) are compared with the saved solution. If the solution generated in iteration k + 1 is dominated by that generated in iteration k and saved in the EA, the newly generated solution is discarded. If the solution generated in iteration k + 1 is not dominated by those previously saved in the EA, then the newly generated solution is added to the EA. Thus, nondominated solutions are stored in the EA and every searching particle i can move to the optimal position currently available according to the current 𝑣𝑡𝑖 and 𝑥𝑡𝑖 . The velocity of searching particle i is updated to 𝑣𝑡𝑖+1 using Eq. (1), and its position to 𝑥𝑡𝑖+1 using Eq. (2). To determine the optimal group position (Pgbest ) in iteration k, the roulette-wheel selection mechanism is employed to randomly select a Pgbest from the nondominated solutions stored in the EA, and the Pareto solutions obtained in each iteration can be calculated and compared. To predict the scanning trajectory, the AI intensity of the beam and the beam diameter D can be calculated using field tracing in Table 3. The optimal DMD delay time (Δtdelay ) and spot overlapping rate (OV) can be calculated using the procedure presented in Table 5. Fig. 4 presents the Pareto solutions calculated using the developed MOPSO algorithm. Of the 500 iterations performed in this study, the red and black circles indicate nondominated and dominated solutions, respectively. The calculated OV were used for the prediction of point-array scanning trajectory. Given the target linewidth was 6 μm, LE = ± 10%, ILS ≥ tan70°, and vstage = 71 μm/s, predictions of the scanning trajectory were made and are illustrated in Fig. 6. After the MOPSO algorithm calculations, the optimal DMD delay time was calculated to be Δ𝑡𝑑𝑒𝑙𝑎𝑦 = 12ms and the spot overlapping rate OV was 68%. Fig. 5(a) illustrates the scan-
where Lprint represents the linewidth defined on the inclined plane in Figs. 2, and Ltarget represents the target linewidth. ILS =
𝑑 ln 𝐼 (𝑥) 𝑑𝑥
(4)
where I(x) is the intensity obtained at 90% of the maximal AI intensity. Table 5 summarizes the procedure of the MOPSO algorithm developed in this study. Steps 1–7 involve initializing all particle group parameters (i.e., 𝑣𝑡𝑖 , 𝑥𝑡𝑖 , Δtdelay , and vstage ) and setting the spot overlapping rate (OV) as a function of vstage and𝑥𝑡𝑖 . In Steps 8 and 9, cost functions are defined as LE and ILS according to Eqs. (3) and (4). Steps 11–18 involve searching for 𝑥𝑡𝑖 in the solution space, and this process proceeded as follows. In the first iteration, initial conditions of the individual parameters are used to start the MOPSO procedure. The optimal DMD delay time Δtdelay produced by individual particle i is saved as Pibest . The Pibest of all individual particles in the group are collected and the optimal Pibest is identified, which is subsequently saved as Pgbest . Pgbest is defined as a nondominated solution, serving as a reference point for sequencing particle positions when particles update in the kth iteration. The nondominated solution obtained when k = 1 is first saved in an external archive (EA). The nondominated solutions obtained in subsequent iter109
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Fig. 6. Optical setup for point-array-based scanning lithography.
Fig. 5. (a) AI scanning trajectory using a single point source; (b) 3D distribution of AI intensity; and (c) Intensity profile of AI on a cross section at X = 0. Fig. 7. (a) Using different output powers and focuses to determine DOF as 300 μm approximately when exposing film stack samples on a planar translation stage; (b) space width on the photoresist film was 4.8 μm.
ning trajectory produced when using 1 × 1 micromirrors in the DMD to perform array scanning on a wafer plane. Fig. 5(b) presents the 3D distribution of the scanning trajectory, which indicates that the linewidth uniformity can be satisfactorily controlled after the lithography parameters are calculated using the developed MOPSO procedure. Fig. 5(c) displays the beam intensity distribution on the AI of an arbitrary cross section.
(Fig. 6). A laser light source with a wavelength of 405 nm served as the UV light source, and its maximum power was 120 mW. For the DMD, a TI DLP7000 module with 0.7-inch micromirror array composed of 1024 × 768 pixels was used. Each single micromirror in the DMD was 13.68 × 13.68 μm and they were spaced 0.8 μm apart. The point arrays of the light reflected by the DMD were propagated to the objective lens (NA = 0.1) through the projection lens module to form an exposure plane. The distances between the laser source and the convex lens, between the beam expander and the planar reflection mirror, between the DMD and the first imaging lens, between the second reflection mirror and the objective lens, and between the objective lens and the
3. Implementation of point-array-based scanning lithography on nonplanar substrates The optical setup for point-array-based scanning lithography that was used in this study comprised four parts: the UV optical source, a DMD, a projection lens module, and a controllable translation stage 110
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translation stage were 85, 460, 135, 60, and 28 mm, respectively. The movements of the translation stage in the X, Y, and Z directions were controlled by a computer. To test the experimental DOF of the optical module illustrated in Fig. 7, AZ-1518 photoresist (manufactured by AZ Electronic Materials) was spin-coated on a 15 mm × 15 mm silicon substrate at a rotation speed of 3000 rpm to form a 6-μm photoresist film. The silicon film stack samples that served as the photoresist were then baked on a hot plate at 100 °C for 1 min. The samples were then placed on a planar translation stage. Line-and-space (L/S) patterns were then defined under various exposure conditions to analyze the DOF. The point-array scanning of the DMD 3 × 1 reflection mirror was employed to project the laser beam onto the sample on the stage. Point-array scanning was performed at a stage velocity of 125 μm/s. Scanned images were then developed, from which the L/S patterns were discerned. The linewidth of the photoresist was measured. The individual source points used in the point arrays had a diameter of 13 μm. Fig. 7(a) illustrates the relationship between photoresist linewidth and DOF. L/S patterns were printed at different z positions using 40-, 60-, 80-, and 100-mW laser sources. The process window was defined as the area enclosed by black dotted lines. For all laser powers used, the DOF was approximately 300 μm. Under the set exposure conditions, the photoresist space width (i.e., 4–5 μm) could be adequately defined as Ltarget (1 ± 10%) (Fig. 7[b]). After the DOF was determined, an inclined plane (Fig. 3) was placed on top of the planar translation stage. The inclined plane was 20-mm high, 40-mm long, and had an incline of 25°. The point-array scanning of the DMD 3 × 1 reflection mirror was employed to project the laser beam onto the silicon film stack sample (photoresist) on the inclined plane. Point-array scanning was performed, after which the scanned images were developed and the L/S patterns were discerned. The linewidth of the photoresist was measured. The exposure conditions were set as
the optimal DMD delay time (Δtdelay )12 ms and the spot overlapping rate 68%. Fig. 8(a) presents the developed 3 × 1 array L/S photoresist pattern of the sample on the inclined plane, for which the laser power used was 40 mW, and the distance between spaces was approximately 46 μm. Fig. 8(b) displays a magnification of the 3 × 1 array L/S photoresist pattern, showing that the single space width in this pattern was approximately 5 μm. The shadows formed on the edges of the spaces corresponded to photoresist side walls and line edge roughness. The linewidth thus measured was smaller than that obtained from the scanning simulation. This error may be the result of this study overlooked lithographic process factors such as photoresist type, baking temperature, and photoresist thickness. These parameters should be incorporated in future research on the MOPSO procedure to strengthen the optimization and to improve side walls and line edge roughness in the photoresist pattern. 4. Conclusion This study successfully defined L/S patterns on a photoresist on an inclined plane using point-array scanning technique. The developed methodology can be used in the PCB industry that currently use DMD based lithography systems. This study employed a self-developed smart MOPSO procedure to calculate the DMD-control time sequence and optimize the spot overlapping rate. Point-array-based scanning exposure was also integrated. Compared with other existing methods for defining patterns on inclined planes, the proposed technique is more readily applicable for the PCB industry. Integrating the point-array-based scanning exposure mode with a smart algorithm optimizes the lithographic parameters and enhances the quality of the lithography patterns. Future research should combine visual inspection systems with this pointarray-based scanning technique to detect exposed lithography linewidth in real time and return the results as feedback to the MOPSO algorithm. Timely correction of exposure parameters can thus be made, and a smart lithography process can be created. Acknowledgment This study was supported by the Ministry of Economic Affairs of Taiwan under Project No. 104-EC-17-A-05-I4-0006. References [1] Pfeiffer C, Xu X, Forrest SR, Grbic A. Direct transfer patterning of electrically small antennas onto three‐dimensionally contoured substrates. Adv Mater 2012;24:1166–70. [2] Noh J-H, Kim I, Park SH, Jo J, Kim DS, Lee T-M. A study on the enhancement of printing location accuracy in a roll-to-roll gravure offset printing system. Int J Adv Manuf Technol 2013;68:1147–53. [3] Patel JN, Kaminska B, Gray BL, Gates BD. A sacrificial SU-8 mask for direct metallization on PDMS. J Micromech Microeng 2009;19:115014. [4] Park J, Fujita H, Kim B. Fabrication of metallic microstructure on curved substrate by optical soft lithography and copper electroplating. Sens Actuators, A 2011;168:105–11. [5] Mizoshiri M, Nishiyama H, Nishii J, Hirata Y. Silica-based microstructures on nonplanar substrates by femtosecond laser-induced nonlinear lithography. Journal of physics: conference series; 2009. [6] Maiden A, McWilliam R, Purvis A, Johnson S, Williams G, Seed N, et al. Nonplanar photolithography with computer-generated holograms. Opt Lett 2005;30:1300–2. [7] Williams GL, McWilliam RP, Toriz-Garcia J, Curry R, Maiden A, Seed NL, et al. A photolithographic process for grossly non-planar substrates. SPIE Advanced Lithography; 2008. 69212E-69212E-9. [8] Wang X, Li Z, Chen T, Lok B, Low D. DPSS UV laser cutting of FR4 and BT/epoxy-based PCB substrates. Opt Lasers Eng 2008;46:404–9. [9] Uematsu T. High sensitivity dry film photoresist for laser direct imaging system. In: Environmentally conscious design and inverse manufacturing, 2001. Proceedings EcoDesign 2001: second international symposium on; 2001. p. 1036–9. [10] Kuo H-F, Huang Y-J. Resolution enhancement using pulse width modulation in digital micromirror device-based point-array scanning pattern exposure. Opt Lasers Eng 2016;79:55–60. [11] Alam HS, Soetraprawata D. Multi-objective optimization of the structural design of double end beam load cell. In: 2015 international conference on automation, cognitive science, optics, micro electro-mechanical system, and information technology (ICACOMIT); 2015. p. 52–7. [12] Shroff YA, Chen Y, Oldham WG. Optical analysis of mirror-based pattern generation. Microlithography 2003 2003:550–9.
Fig. 8. Using point-array scanning to define the L/S pattern on the inclined plane with the slanted angle 25°: (a) 3 × 1 array L/S photoresist pattern; (b) A single space width was 5 μm approximately.
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Printing line/space patterns on nonplanar substrates using a digital micromirror device-based point-array scanning technique Hung-Fei Kuo a,∗, Guan-Hsuan Kao a, Liang-Xiu Zhu a, Kuo-Shu Hung b, Yu-Hsin Lin b a b
Graduate Institute of Automation and Control at National Taiwan University of Science and Technology, #43, Sec.4, Keelung Road, Taipei 106, Taiwan, ROC Shuztung Machinery Industrial Co., Ltd, No.30, Houke S. Rd., Houli Dist., Taichung 421, Taiwan ROC
a r t i c l e
i n f o
Keywords: Nonplanar lithography Digital micromirror device (DMD) Point-array scanning Multiobjective particle swarm optimization (MOPSO)
a b s t r a c t This study used a digital micromirror device (DMD) to produce point-array patterns and employed a selfdeveloped optical system to define line-and-space patterns on nonplanar substrates. First, field tracing was employed to analyze the aerial images of the lithographic system, which comprised an optical system and the DMD. Multiobjective particle swarm optimization was then applied to determine the spot overlapping rate used. The objective functions were set to minimize linewidth and maximize image log slope, through which the dose of the exposure agent could be effectively controlled and the quality of the nonplanar lithography could be enhanced. Laser beams with 405-nm wavelength were employed as the light source. Silicon substrates coated with photoresist were placed on a nonplanar translation stage. The DMD was used to produce lithographic patterns, during which the parameters were analyzed and optimized. The optimal delay time-sequence combinations were used to scan images of the patterns. Finally, an exposure linewidth of less than 10 μm was successfully achieved using the nonplanar lithographic process. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction As electronic components have become increasingly advanced, improving the fabrication of nonplanar structures in newer-generation electronic components has attracted increasing attention. How to define layout patterns on nonplanar substrates has emerged as a key issue. Previously, antenna patterns have been defined on integrated circuits using a planar micromirror process; however, this process can only be used on relatively regular and flat substrates. Special polydimethylsiloxane (PDMS) soft mold patterns can be created to transfer and print high-gain antennas, array-type antennas, or radio-frequency identification patterns onto substrates with low curvature [1,2]. Other techniques to solve this problem include using PDMS soft-mold-based pattern transfer printing for the creation of metallic gratings on curved substrates [3,4]; combining nonlinear micromirror and plasma etching techniques to define structural patterns on nonplanar inorganic optical component substrates [5]; and using computer-generated holograms to define 3D patterns on nonplanar substrates [6,7]. Nevertheless, conventional lithography techniques that focus on planar materials still have stable mass-production processes and are widely employed in the manufacture of printed circuit boards (PCBs) for the creation of designed component patterns. Maskless lithography, a laser
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Corresponding author. E-mail address: [email protected] (H.-F. Kuo).
direct imaging (LDI) technique, is currently used to define circuit patterns with a width of 10–30 μm [8]. Two exposure modes are involved in this technique. The first projects laser beams onto focusing lenses using reflective polygon mirrors as beam splitters. The beams thus produced can be focused on substrates to form lithographic patterns. This technique has large depth of focus (DOF) and high throughput; however, the system is expensive [9]. In response to the market’s demand for small-quantity and high-variety patterns, another LDI technique has been developed that employs a digital micromirror device (DMD) as a digital mask. The technique uses a conventional projection-based optical system design that contains microlens arrays (MLAs), thereby enabling beam spot arrays to exhibit more satisfactory resolution regarding the line width. Additionally, this technology is silicon-based and can thus produce DMDs with higher reliability at lower costs than other techniques. As a result, the development of this technology has attracted considerable interest [10]. Multiobjective planning, first proposed by researchers Charnes and Cooper, can be used to solve quality control problems in optical processes [11,12]. Numerous approaches can be used to solve multiobjective problems, including the popular simulated annealing [13] and genetic algorithms [14,15] and also particle swarm optimization (PSO), which has been commonly employed in recent research. The advantage of the PSO algorithm is its global search capability. The concept for the algorithm derived from the foraging behavior of a flock of birds. Each bird in a flock occupies a distinct spatial area and must search for the ideal foraging area. When an optimal foraging spot has been determined
https://doi.org/10.1016/j.optlaseng.2017.10.009 Received 10 February 2017; Received in revised form 4 September 2017; Accepted 14 October 2017 0143-8166/© 2017 Elsevier Ltd. All rights reserved.
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Table 1 Distribution of beam intensity at different distances from the DMD.
Distance (mm)
0
114
142
171
Aerial image (AI)
locally, each bird flies toward the currently defined optimal spot. Over time, birds tend to flock together to the optimal foraging spot [16]. This study investigated how existing techniques for the definition of layout patterns on nonplanar substrates might be improved using a DMD-based maskless lithography system. The PSO multiobjective algorithm was also integrated to plan the point-array scanning parameters and stage moving velocity. The efficient and highly repetitive LDI technique could then be used to define lithographic patterns on nonplanar substrates. 2. Aerial image analysis In this study, field tracing (VirtualLab) was used to design the locations of the optical components in the DMD-based scanning lithography system. The locations of the focal lenses in the beam guiding system were first arranged according to the intensity distribution of DMD-deflected laser beams. The incident beam was assumed to consist of linearly polarized plane-waves with a wavelength of 405 nm, and the beam shone on a DMD of diameter 1.3 mm, with the surface area of each mirror in the DMD equal to 13.7 μm × 13.7 μm. Table 1 presents the intensity distribution at different distances from the DMD of light reflected by the device. When the distance was 0 mm, diffraction was observed because of the gaps between micromirrors. As the distance was between 114 and 142 mm, the diffraction side lobe gradually separated from the diffraction main lobe. The first focal lens was placed at a distance of 135 mm from the DMD mirror, and its intensity distribution is presented in Fig. 1(a). To determine the size of the diffraction main lobe, the beam intensity distribution in Fig. 1(a) was crisscrossed into a black line segment. Fig. 1(b) illustrates the beam intensity distribution of this cross section, wherein the beam diameter was approximately 0.3 mm. An aperture was positioned 80 mm behind the first focal lens to eliminate effects of the higher-order side lobes. The beam continued to propagate after passing through the aperture. The second focal lens was placed 155 mm behind the first. An analysis of the optical field intensity 30, 60, 90, and 120 mm behind the second focal lens was subsequently conducted, and the results are summarized in Table 2. Beams 30, 60, 90, and 120 mm behind the second focal lens that were formulated through focused imaging had a diameter of 480, 40, 240, and 600 μm, respectively. In terms of intensity distribution, the beam formulated 60 mm behind the second focal lens exhibited a more satisfactory beam quality than the beams formulated at other distances, and that beam was most similar to the TEM00 Gaussian beam mode. Therefore, the objective lens was positioned 60 mm behind the second focal lens. The optical beam intensity distribution obtained at various focal positions behind the objective lens was then analyzed, and the results are presented in Table 3. The beam formulated 28 mm behind the objective lens exhibited the smallest spot size, having a diameter of 18 μm. This beam spot characteristic was employed in this study to determine the effect of point-array scanning lithography. When a nonplanar substrate is exposed, the limited DOF can affect image quality when performing point-array scanning. To effectively con-
Fig. 1. (a) Distribution of beam intensity 135 mm from the DMD mirror plane; and (b) beam intensity on the crisscrossed black line segment in (a).
Fig. 2. Mathematical model of particle swarm algorithm.
trol nonplanar lithography quality, this study adopted multiobjective particle swarm optimization (MOPSO) to calculate the optimal lithography parameters. In this technique, particles are first randomly arranged in the solution space (Fig. 2). Each particle knows the position of the optimal solution it has identified so far (Pibest ) and the position of the optimal solution currently identified by other particles in the group (Pgbest ). When a particle needs to move, it integrates the moving velocities at 107
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Table 2 Intensity distribution observed at various distances behind the second focal lens.
Distance (mm)
30
60
90
120
31
34
AI
Field intensity in the line
Table 3 Intensity distribution observed at various distances behind the objective lens.
Distance (mm)
24
28
AI
Field intensity in the line
three positions: its current position, Pibest , and Pgbest to produce the new moving direction, then moves to the new position in the solution space. Therefore, individual particles adjust their velocity with reference to those of particles at Pibest and Pgbest , as defined in Eq. (1). The location of each particle in the solution space can then be updated [Eq. (2)]. Individual particles arrive at the new position in the solution space at their newly integrated velocity and continue searching for a more satisfactory solution to ultimately obtain the optimal location. The current solutions generated by the individual and the group then serve as referencing directions for each particle as it updates, thereby increasing the possibility of finding the optimal solution. To use PSO to solve multiobjective optimization problems, the objective function(s) should first be established: {𝑓𝑚 (𝑥)}𝑘𝑚=1 , where k is the number of objective functions and k ≥ 2. x ∈ X, where the set X is the feasible set of decision vectors. When the optimal function {𝑓𝑚 (𝑥)}𝑘𝑚=1 is subject to the bounds of x, x ranges between 𝑥𝑢𝑝𝑝𝑒𝑟 and 𝑥𝑙𝑜𝑤𝑒𝑟 , and the inequality and equality constraints 𝑗 𝑗 are gi (x) and hl (x), respectively. A point x∗ ∈ Ω is Pareto-optimal if, for everyx ∈ Ω, eitherfm (x) ≥ fm (x∗ ) for every 𝑚 ∈ I = [1, 2...., 𝑘] or there is at least one m ∈ I such that fi (x) > fi (x∗ ). The point x∗ is defined as the optimal if no objective can be improved without worsening at least one other objective. Pareto’s optimum usually gives not one single solution,
but a set of solutions called nondominated solutions [17,18]. 𝑣𝑡𝑖+1 = 𝑣𝑡𝑖 + 𝑐1 × 𝑟𝑎𝑛𝑑𝑖𝑏𝑒𝑠𝑡 (𝑝𝑖𝑏𝑒𝑠𝑡 − 𝑥𝑡𝑖 ) + 𝑐2 × 𝑟𝑎𝑛𝑑𝑔𝑏𝑒𝑠𝑡 (𝑝𝑔𝑏𝑒𝑠𝑡 − 𝑥𝑡𝑖 )
(1)
x𝑡𝑖+1 = 𝑥𝑡𝑖 + 𝑣𝑡𝑖+1
(2)
where 𝑣𝑡𝑖 and 𝑣𝑡𝑖+1 are the moving velocity of particle i at times t and t + 1, respectively; 𝑥𝑡𝑖 and 𝑥𝑡𝑖+1 are the position of particle i at t and t + 1 in the solution space, respectively; c1 and c2 are learning factors; r1 and r2 are randomly generated particle numbers; Pibest is the optimal particle position identified by an individual; and Pgbest is the optimal particle position identified by the group. In this study, an MOPSO procedure was developed to control the quality of the photoresist imaging. Table 4 presents the relationship between the parameters of the designed MOPSO procedure and the corresponding point-array scanning parameters. The solution space in the MOPSO algorithm corresponds to the design of DMD delay time; the searching particle position 𝑥𝑡𝑖 corresponds to the solution of the DMD delay time Δtdelay searched by particle i at t; and the particle moving velocity corresponds to the direction of the DMD delay time Δtdelay in this search. Pibest is the optimal DMD delay time Δtdelay that can be searched by an individual particle, Pgbest is the optimal DMD delay time Δtdelay 108
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Table 4 Definitions of nonplanar lithographic parameters in MOPSO.
Table 5 Procedure of the MOPSO algorithm. 1: Initialize particles 2: threshold←0.4 target←4 3: FOR ipso = 1 to n_particles 4. Δtdelay ←Rand: 5: 𝑥𝑡𝑖 ← ProcessParameter(f) 6: OV(vstage, 𝑥𝑡𝑖 ) ←EvaluateOverlay(vstage, 𝑥𝑡𝑖 ) 7: Cost ← minimum LE and maximum ILS 8: ILS(I(x))←EvaluateImageLog-Slope 9: LE(𝐿Pr int )←EvaluateLinwidthError 10: end FOR 11: Create an empty External Archive (EA) 12: Copy the non-dominated solutions to the EA; 13: Select a particle leader from the EA 14: Pibest is the Best of 𝑥𝑡𝑖 ; Pgbest is the leader of EA 15: WHILE k = 1 to max_iter 16: FOR ipso = 1 to n_particles 17: Select a particle leader from the EA 18: Update particle Velocity & Position &Cost 19: end FOR 20: end WHILE
Parameter definition
𝑥𝑡𝑖 𝑣𝑡𝑖 Pibest Pgbest c1 and c2 rand
The solution of the DMD delay time Δtdelay searched by particle i at t The searching direction of the DMD delay time The optimal DMD delay time Δtdelay searched by the individual particle The optimal DMD delay time Δtdelay searched by the group of particles Acceleration constants Uniformly distributed random numbers
Z DOF
θ X Fig. 3. Schematic diagram of exposure on the inclined plane.
that can be searched by a group of particles, and c1 and c2 are equal to 2. Fig. 3 presents a schematic diagram of printing photoresist patterns on a nonplanar substrate. The pink area indicates the film stacked on the silicon substrate that serves as the photoresist coating. The silicon substrate is placed on a nonplanar translation stage, the spatial profile of which can be defined by height z and angle 𝜃. When the film stack enters the exposure area, scanning on the photoresist begins using the point array technique. The exposure area is defined as the area within the DOF and the area of the point array that falls on the inclined plane. The moving velocity of the translation stage is defined as vstage = z/Δt × tan 𝜃, where Δtis the time required for the translation stage to move a distance z/sin 𝜃. The spot overlapping rate is defined as 𝑂𝑉 = 1 − 𝑣𝑠𝑡𝑎𝑔𝑒 × Δ𝑡𝑑𝑒𝑙𝑎𝑦 ∕𝐷, where D is the beam diameter. In the developed MOPSO procedure, the objective functions include designs of linewidth error [LE; expressed as Eq. (3)] and image log slope [ILS; expressed as Eq. (4)] [19,20]. When the maximal intensity of the AI exceeds the threshold of the photoresist reaction, Eq. (4) is used to calculate the ILS. | | |𝐿Pr int − 𝐿Target | | × 100% LE = | (3) 𝐿Target
Fig. 4. Pareto solutions based on the proposed MOPSO procedure.
ations (i.e., k > 1) are compared with the saved solution. If the solution generated in iteration k + 1 is dominated by that generated in iteration k and saved in the EA, the newly generated solution is discarded. If the solution generated in iteration k + 1 is not dominated by those previously saved in the EA, then the newly generated solution is added to the EA. Thus, nondominated solutions are stored in the EA and every searching particle i can move to the optimal position currently available according to the current 𝑣𝑡𝑖 and 𝑥𝑡𝑖 . The velocity of searching particle i is updated to 𝑣𝑡𝑖+1 using Eq. (1), and its position to 𝑥𝑡𝑖+1 using Eq. (2). To determine the optimal group position (Pgbest ) in iteration k, the roulette-wheel selection mechanism is employed to randomly select a Pgbest from the nondominated solutions stored in the EA, and the Pareto solutions obtained in each iteration can be calculated and compared. To predict the scanning trajectory, the AI intensity of the beam and the beam diameter D can be calculated using field tracing in Table 3. The optimal DMD delay time (Δtdelay ) and spot overlapping rate (OV) can be calculated using the procedure presented in Table 5. Fig. 4 presents the Pareto solutions calculated using the developed MOPSO algorithm. Of the 500 iterations performed in this study, the red and black circles indicate nondominated and dominated solutions, respectively. The calculated OV were used for the prediction of point-array scanning trajectory. Given the target linewidth was 6 μm, LE = ± 10%, ILS ≥ tan70°, and vstage = 71 μm/s, predictions of the scanning trajectory were made and are illustrated in Fig. 6. After the MOPSO algorithm calculations, the optimal DMD delay time was calculated to be Δ𝑡𝑑𝑒𝑙𝑎𝑦 = 12ms and the spot overlapping rate OV was 68%. Fig. 5(a) illustrates the scan-
where Lprint represents the linewidth defined on the inclined plane in Figs. 2, and Ltarget represents the target linewidth. ILS =
𝑑 ln 𝐼 (𝑥) 𝑑𝑥
(4)
where I(x) is the intensity obtained at 90% of the maximal AI intensity. Table 5 summarizes the procedure of the MOPSO algorithm developed in this study. Steps 1–7 involve initializing all particle group parameters (i.e., 𝑣𝑡𝑖 , 𝑥𝑡𝑖 , Δtdelay , and vstage ) and setting the spot overlapping rate (OV) as a function of vstage and𝑥𝑡𝑖 . In Steps 8 and 9, cost functions are defined as LE and ILS according to Eqs. (3) and (4). Steps 11–18 involve searching for 𝑥𝑡𝑖 in the solution space, and this process proceeded as follows. In the first iteration, initial conditions of the individual parameters are used to start the MOPSO procedure. The optimal DMD delay time Δtdelay produced by individual particle i is saved as Pibest . The Pibest of all individual particles in the group are collected and the optimal Pibest is identified, which is subsequently saved as Pgbest . Pgbest is defined as a nondominated solution, serving as a reference point for sequencing particle positions when particles update in the kth iteration. The nondominated solution obtained when k = 1 is first saved in an external archive (EA). The nondominated solutions obtained in subsequent iter109
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Fig. 6. Optical setup for point-array-based scanning lithography.
Fig. 5. (a) AI scanning trajectory using a single point source; (b) 3D distribution of AI intensity; and (c) Intensity profile of AI on a cross section at X = 0. Fig. 7. (a) Using different output powers and focuses to determine DOF as 300 μm approximately when exposing film stack samples on a planar translation stage; (b) space width on the photoresist film was 4.8 μm.
ning trajectory produced when using 1 × 1 micromirrors in the DMD to perform array scanning on a wafer plane. Fig. 5(b) presents the 3D distribution of the scanning trajectory, which indicates that the linewidth uniformity can be satisfactorily controlled after the lithography parameters are calculated using the developed MOPSO procedure. Fig. 5(c) displays the beam intensity distribution on the AI of an arbitrary cross section.
(Fig. 6). A laser light source with a wavelength of 405 nm served as the UV light source, and its maximum power was 120 mW. For the DMD, a TI DLP7000 module with 0.7-inch micromirror array composed of 1024 × 768 pixels was used. Each single micromirror in the DMD was 13.68 × 13.68 μm and they were spaced 0.8 μm apart. The point arrays of the light reflected by the DMD were propagated to the objective lens (NA = 0.1) through the projection lens module to form an exposure plane. The distances between the laser source and the convex lens, between the beam expander and the planar reflection mirror, between the DMD and the first imaging lens, between the second reflection mirror and the objective lens, and between the objective lens and the
3. Implementation of point-array-based scanning lithography on nonplanar substrates The optical setup for point-array-based scanning lithography that was used in this study comprised four parts: the UV optical source, a DMD, a projection lens module, and a controllable translation stage 110
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translation stage were 85, 460, 135, 60, and 28 mm, respectively. The movements of the translation stage in the X, Y, and Z directions were controlled by a computer. To test the experimental DOF of the optical module illustrated in Fig. 7, AZ-1518 photoresist (manufactured by AZ Electronic Materials) was spin-coated on a 15 mm × 15 mm silicon substrate at a rotation speed of 3000 rpm to form a 6-μm photoresist film. The silicon film stack samples that served as the photoresist were then baked on a hot plate at 100 °C for 1 min. The samples were then placed on a planar translation stage. Line-and-space (L/S) patterns were then defined under various exposure conditions to analyze the DOF. The point-array scanning of the DMD 3 × 1 reflection mirror was employed to project the laser beam onto the sample on the stage. Point-array scanning was performed at a stage velocity of 125 μm/s. Scanned images were then developed, from which the L/S patterns were discerned. The linewidth of the photoresist was measured. The individual source points used in the point arrays had a diameter of 13 μm. Fig. 7(a) illustrates the relationship between photoresist linewidth and DOF. L/S patterns were printed at different z positions using 40-, 60-, 80-, and 100-mW laser sources. The process window was defined as the area enclosed by black dotted lines. For all laser powers used, the DOF was approximately 300 μm. Under the set exposure conditions, the photoresist space width (i.e., 4–5 μm) could be adequately defined as Ltarget (1 ± 10%) (Fig. 7[b]). After the DOF was determined, an inclined plane (Fig. 3) was placed on top of the planar translation stage. The inclined plane was 20-mm high, 40-mm long, and had an incline of 25°. The point-array scanning of the DMD 3 × 1 reflection mirror was employed to project the laser beam onto the silicon film stack sample (photoresist) on the inclined plane. Point-array scanning was performed, after which the scanned images were developed and the L/S patterns were discerned. The linewidth of the photoresist was measured. The exposure conditions were set as
the optimal DMD delay time (Δtdelay )12 ms and the spot overlapping rate 68%. Fig. 8(a) presents the developed 3 × 1 array L/S photoresist pattern of the sample on the inclined plane, for which the laser power used was 40 mW, and the distance between spaces was approximately 46 μm. Fig. 8(b) displays a magnification of the 3 × 1 array L/S photoresist pattern, showing that the single space width in this pattern was approximately 5 μm. The shadows formed on the edges of the spaces corresponded to photoresist side walls and line edge roughness. The linewidth thus measured was smaller than that obtained from the scanning simulation. This error may be the result of this study overlooked lithographic process factors such as photoresist type, baking temperature, and photoresist thickness. These parameters should be incorporated in future research on the MOPSO procedure to strengthen the optimization and to improve side walls and line edge roughness in the photoresist pattern. 4. Conclusion This study successfully defined L/S patterns on a photoresist on an inclined plane using point-array scanning technique. The developed methodology can be used in the PCB industry that currently use DMD based lithography systems. This study employed a self-developed smart MOPSO procedure to calculate the DMD-control time sequence and optimize the spot overlapping rate. Point-array-based scanning exposure was also integrated. Compared with other existing methods for defining patterns on inclined planes, the proposed technique is more readily applicable for the PCB industry. Integrating the point-array-based scanning exposure mode with a smart algorithm optimizes the lithographic parameters and enhances the quality of the lithography patterns. Future research should combine visual inspection systems with this pointarray-based scanning technique to detect exposed lithography linewidth in real time and return the results as feedback to the MOPSO algorithm. Timely correction of exposure parameters can thus be made, and a smart lithography process can be created. Acknowledgment This study was supported by the Ministry of Economic Affairs of Taiwan under Project No. 104-EC-17-A-05-I4-0006. References [1] Pfeiffer C, Xu X, Forrest SR, Grbic A. Direct transfer patterning of electrically small antennas onto three‐dimensionally contoured substrates. Adv Mater 2012;24:1166–70. [2] Noh J-H, Kim I, Park SH, Jo J, Kim DS, Lee T-M. A study on the enhancement of printing location accuracy in a roll-to-roll gravure offset printing system. Int J Adv Manuf Technol 2013;68:1147–53. [3] Patel JN, Kaminska B, Gray BL, Gates BD. A sacrificial SU-8 mask for direct metallization on PDMS. J Micromech Microeng 2009;19:115014. [4] Park J, Fujita H, Kim B. Fabrication of metallic microstructure on curved substrate by optical soft lithography and copper electroplating. Sens Actuators, A 2011;168:105–11. [5] Mizoshiri M, Nishiyama H, Nishii J, Hirata Y. Silica-based microstructures on nonplanar substrates by femtosecond laser-induced nonlinear lithography. Journal of physics: conference series; 2009. [6] Maiden A, McWilliam R, Purvis A, Johnson S, Williams G, Seed N, et al. Nonplanar photolithography with computer-generated holograms. Opt Lett 2005;30:1300–2. [7] Williams GL, McWilliam RP, Toriz-Garcia J, Curry R, Maiden A, Seed NL, et al. A photolithographic process for grossly non-planar substrates. SPIE Advanced Lithography; 2008. 69212E-69212E-9. [8] Wang X, Li Z, Chen T, Lok B, Low D. DPSS UV laser cutting of FR4 and BT/epoxy-based PCB substrates. Opt Lasers Eng 2008;46:404–9. [9] Uematsu T. High sensitivity dry film photoresist for laser direct imaging system. In: Environmentally conscious design and inverse manufacturing, 2001. Proceedings EcoDesign 2001: second international symposium on; 2001. p. 1036–9. [10] Kuo H-F, Huang Y-J. Resolution enhancement using pulse width modulation in digital micromirror device-based point-array scanning pattern exposure. Opt Lasers Eng 2016;79:55–60. [11] Alam HS, Soetraprawata D. Multi-objective optimization of the structural design of double end beam load cell. In: 2015 international conference on automation, cognitive science, optics, micro electro-mechanical system, and information technology (ICACOMIT); 2015. p. 52–7. [12] Shroff YA, Chen Y, Oldham WG. Optical analysis of mirror-based pattern generation. Microlithography 2003 2003:550–9.
Fig. 8. Using point-array scanning to define the L/S pattern on the inclined plane with the slanted angle 25°: (a) 3 × 1 array L/S photoresist pattern; (b) A single space width was 5 μm approximately.
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