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Abstract
A novel laser direct writing lithography equipment system was proposed to realize rapid and μm-precision fabrication on curved surfaces with large curvatures and large sag heights. Through detailed design, analysis, simulation, and measurement, it showed that the system was able to continuously, linearly and rapidly change the focus position in z coordinate. For demonstration, a concentric-circular photoresist grating with a sag height of 5.2 mm and a designed line width/space of 12.5 μm/25 μm was fabricated within 40 s on a convex K9 glass substrate surface with a curvature radius of 32.77 mm. When combining with the movement of the x-y-z stage, the system could fabricate the micropatterns on curved surfaces with larger dimensions. Further, the system possessed the general principles of optics, mechanics, and automation for μm-precision 3D microfabrication.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The high-efficiency, high-precision and high-accuracy fabrication of high line/space resolution micropatterns on non-planar surfaces has been a research hotspot and difficulty for many years. It has huge application prospects in such areas as hybrid refractive-diffractive optical elements [1, 2], aspheric surface testing [3, 4], smart optical-fiber sensors [5, 6], and artificial compound eyes [7–9]. Recently, many efforts have been made to realize the micropatterns on curved surfaces, and several technologies including diamond milling [10, 11], soft lithography [12–15], holographic photolithography [16, 17] and laser direct writing lithography [18, 19] have been adopted.
Diamond milling is hard to fabricate relatively smooth and slowly varying relief micropatterns because of the limit of line/space resolution. Soft lithography requires a soft mask with designed patterns. Holographic photolithography utilizes a holographic mask to modulate the incident wavefront and to project three-dimensional (3D) light intensity distribution [17], but the fabrication accuracy is limited to several tens of micrometers. Laser direct writing lithography (LDWL) utilizes a focused laser beam to directly write micropatterns on a photoresist film. It is a non-contact, maskless and flexible patterning technology, and has great potential for the fabrication on non-planar surfaces. Thus, LDWL has attracted a lot of interest in recent years. Using this technology and the corresponding fabrication equipment systems, many concentric circular or linear gratings with different periods on different concave lens surfaces (with different diameters and curvature radii) have been fabricated [19–21]. Also, hydrogenated amorphous silicon (a-Si:H) thin-film transistors (TFTs) with a channel length of 10 μm on a spherical substrate have been fabricated [22].
However, the above LDWL technology and equipment systems only realized the micro-fabrication on the curved surfaces with the large curvature radii in the range of hundreds of millimeters, and the sag height usually did not exceed 4 mm. Although Radtke et al. had developed a modified LDWL equipment system to allow for the sag height of up to 30 mm [23], the system was very complicated and difficult for precision and quick manipulation. The reason was that these equipment systems kept laser focus on curved surfaces by slowly (i.e., ≤10 mm/s speed) and vertically moving the heavy optical head and by slowly rotating the heavy sample stage. For example, it would take more than 10 minutes to fabricate micro circular gratings with a line width/space of 12.5 μm/25 μm within a radius of 20 mm on curved surfaces by the laser system in Radtke’s work [23]. And it would take about 25 minutes to fabricate micropatterns with a sag height of 5 mm by diamond milling [10]. Obviously, they were time-consuming and extremely low-efficiency.
In this paper, a novel LDWL equipment system was introduced and demonstrated. This system could realize rapid micropattern fabrication on non-planar surfaces. It employed a dynamic focusing lens unit to always keep laser focus on curved surfaces during processing. The dynamic focusing lens was driven by a voice coil motor and had a movement range of 10 mm. Because of the ultra-light load of the lens, the motor could move tens or hundreds of times faster than that of mechanical translation stage. When combining with z stage, the system could allow for a sag height of more than 50 mm. Using this system, within 40 s, a concentric circular photoresist grating with a sag height of 5.2 mm and a designed line width/space of 12.5 μm/25 μm was fabricated on the convex K9 glass substrate surface with a curvature radius of 32.77 mm.
2. Materials and methods
2.1 Materials
Commercially available SUN-110P photoresist and SUN-238D developer purchased from Suntific Materials Co., Ltd. (Weifang, China) were adopted. While the SUN-110P was a diazonaphthoquinone (DNQ) ultraviolet (UV) positive photoresist, and the SUN-238D was a tetramethylammonium hydroxide (TMAH) aqueous solution. Substrate material K9 convex glass was purchased from Sintec Optronics Co., Ltd. (Wuhan, China). The refractive indices of the photoresist and glass were about 1.612 and 1.516, respectively. Poly(dimethylsiloxane) (PDMS) precursor (Sylgard 184, Dow Corning) was used to indirectly test the dimension details of the micropatterns.
2.2 Experiment equipment system and fabrication process
Experiment equipment is a novel LDWL system including a laser dynamic focusing lens unit. It is mainly composed of a Q-switched low power laser (TEM00 mode, Gaussian beam), an optical path unit, a controlling and monitoring unit and an x-y-z 3D translation stage, as shown in Fig. 1. The laser is with a wavelength of 355 nm and a maximum output power of 0.5 W. In the optical path unit, an acousto-optic modulator (AOM) is used as an external laser switch, and it eliminates the effect of the leaky laser. A beam expander is used to expand and collimate the laser beam. The dynamic focusing lens unit is used to control the focal spot in vertical direction. The moveable lens is driven by a voice coil motor ( ± 1 μm movement precision) and it has a movement range of 10 mm. A high-speed galvanometer scanner is used to rapidly manipulate the laser beam. An F-theta lens with a focal length of 103 mm and a numerical aperture (NA) of about 0.33 is employed to focus the laser beam, and its depth of focus (DOF) is about 100 μm. A CCD camera is used as the monitoring unit to monitor and locate the substrate surface. A laser distance meter is employed to measure the relative distances between the substrate and objective lens. The x and y translation stages both have a movement range of 200 mm and a movement precision of ± 1 μm, and the z stage has a movement precision of ± 3 μm and can carry the scanner and F-theta lens moving vertically in a range of 50 mm. The whole equipment system was placed in a clean room with constant temperature (25 ± 1 °C) and humidity ((80 ± 5) %). These provide the system with the ability for μm-precision microfabrication on curved surfaces in large range.
Referring to the document [24], it was probable for spin-coating technique to acquire nearly homogeneous-thickness photoresist films when the substrates had the ratios below 0.816 of its radii (r) to its curvature radii (R). Therefore, in our experiment, the photoresist was spin-coated on the K9 glass convex substrate surface because the substrate had a diameter of 50 mm (i.e., r = 25 mm) and a curvature radius of 32.77 mm (i.e., R = 32.77 mm), and thus, the ratio r/R = 0.763 (<0.816). After that, the coated substrate was baked in a 100°C hotplate for 1 min to dry and improve the adhesion strength between the substrate and photoresist. Next, the coated substrate was mounted on the X-Y stage, and the direct writing process (i.e., exposure) was implemented (the micropattern data were programmed by a self-developed software and it contained the corresponding space coordinates (x, y, z)). Subsequently, the exposed substrate was developed in the developer solution, and rinsed in deionized water, respectively. Thus, the photoresist micropatterns on the K9 glass substrate surface were obtained.
2.3 Measurements and characterization
The fabricated photoresist micropatterns were observed with an optical microscope (Motic China Group Co., Ltd., China). Due to the inconvenient and inaccurate measurement on curve surfaces, the dimension details of the micropatterns were transferred onto a plane through a PDMS film. Specifically, the PDMS precursor was first spin-coated on the whole surface of the micropatterns, as shown in Fig. 2(a). After the PDMS precursor was cured and solidified, a small piece of the PDMS containing the corresponding dimension details was detached, and then placed unaffectedly onto a plane substrate, as shown in Fig. 2(b). Compared with the whole area of the PDMS film, the detached area was very small (usually about 0.5 mm × 0.5 mm), so it could be regarded as a plane. Additionally, because of the unaffected placement, the deformation of the detached PDFS was also negligible. Finally, the dimension details were measured by a KTA TencorP-16 + surface probe profiler.
Fig. 2 Indirect dimension measurement for micropattern on curved surface. (a) Coating with PDMS, and (b) peeling off PDMS and spreading onto a planar substrate.
3. Results and discussion
3.1 Optical path analysis of LDWL equipment system including dynamic focusing lens unit
Basing on design, analysis and simplification, the optical path unit of the LDWL equipment system could be shown in Fig. 3(a). After the UV laser beam was expanded through an expander, it was with a diameter of D0 = 8 mm. Then, it propagated through the dynamic focusing lens unit. The dynamic focusing lens unit was composed of two lens groups, i.e., one contains a concave lens with a designed focal length of f1 = −200 mm, and the other contains two convex lenses with the corresponding focal lengths of f2 = 300 mm and f3 = 800 mm. Finally, the laser beam was focused by a lens 4 (i.e., F-theta lens) with a focal length of f4 = 103 mm. Here, the focal spot diameter was designated as DF.
The distance between lenses 1 and 2 was designated as d1, and it could vary between 90 mm and 100 mm. d2 was the distance between lenses 2 and 3, it was designed as 0 to shorten the unit structure. d3 was the distance between lenses 3 and 4, and its initial value was designed as 600 mm. The concave lens was driven by a linear motor, and when it moved forward a distance of ∆d along the optical axis, the image distance lF (i.e., the distance between the focus and F-theta lens) would enlarge ∆lF, as shown in Fig. 3(b). Thus, when the micropatterns on non-planar substrates were directly written, the laser spot could be focused on the curved surfaces by accurately controlling the position of concave lens in real-time.
Under the paraxial approximation, the optical path propagation characteristics could be analyzed through the method of ray transfer matrix analysis (or ABCD matrix analysis) [25] and the mathematic expression of the above optical path could be simplified and expressed as Eq. (1).
From Eq. (1), the relationship between the dynamic lens movement (∆d) and the focus movement (∆lF) was simulated by software MATLAB, as shown in Fig. 4. The measured values were also listed. It could be seen that the measured values were nearly linear, and after linear fitting, they had a linear correlation coefficient of up to 99.9%. Furthermore, the fitting straight line was well coincident with the theoretical line from the software simulation values. It showed that the dynamic focusing lens unit could be well and automatically controlled to continuously and linearly change the focus position in z coordinate. Besides, from Eq. (1) and Fig. 4, it was found that the focal spot diameter (DF) had a slight decrease when dynamic focusing lens moved forward. When the dynamic focusing lens moved to maximum distance (i.e., ∆d = 10 mm), the sag height of focus position reached up to 7.38 mm, and the focal spot diameter decreased by 9.8% from 10.2 μm to 9.2 μm. The deviation of the diameter was below 10%, and this error was much lower and acceptable.
Fig. 4 Laser focal spot diameter, and the relationship between dynamic lens position and focal spot position from experimental measurement and MATLAB software simulation.
3.2 Variation of focal spot diameter on convex surface
When a laser beam focused on a convex surface, the focal spot was usually enlarged. The tilted angle of the surface to the focal plane was a main influencing factor of beam deformation, and the larger the angle, the bigger the deformation. If DFR was designated as the focal spot diameter on a convex surface with a curvature radius of R and the tilted angle to the focal plane was defined as θ [Fig. 5(a)], then the relationship between θ, R, ∆lF, DF and DFR could be expressed as Eq. (2).
Fig. 5 Schematic diagram of focal spot diameter on convex surface (a), and the relationship curves between focal spot diameter, dynamic focusing lens movement, focus movement and curvature radius (b).
Combining Eq. (1) with Eq. (2), the changes of the focal spot diameters with the dynamic focusing lens movement were shown in Fig. 5(b). When R = 41 mm, the focal spot diameter (DFR) was 11.2 μm at maximum dynamic focusing lens movement (∆d = 10 mm), and the corresponding focus movement was up to the maximum value (i.e. 7.38 mm). At this point, the focal spot diameter had a 9.8% deviation from the initial value of 10.2 μm. Thus, when the curvature radius of convex surface was larger than 41 mm, the focal spot diameter deviation was below 10%. In other words, the dynamic focusing lens unit was able to realize uniform fabrication with the sag heights up to 7.38 mm on the convex surface of curvature radius larger than 41 mm. On the other hand, when the curvature radii were below 40 mm, e.g., 30 mm and 20 mm, the uniform fabrication could be implemented in the sag height ranges of 4.36 mm and 2.38 mm, respectively.
3.3 Fabrication of micropattern on convex surface
During the fabrication, in order to balance the processing efficiency and line/space resolution, laser power was set as 20 mW and scan speed was set as 1000 mm/s. In the condition of these laser parameters, the minimum linewidth of the direct-writing lithography was about 10 μm. If increasing the laser power, the minimum linewidth would become wider. This was because that the photoresist was positive (i.e., the exposure region was more soluble than the unexposure region in the developer solution). On the other hand, the laser was a Gaussian beam, and the laser intensity distribution would be broadened because of PSF (point-spread-function) when laser power was further increased. For example, if the laser power was increased to 200 mW, the maximum direct-writing lithography linewidth could reach about 60 μm.
In the conditions of laser power of 20 mW and scan speed of 1000 mm/s, a concentric-circle photoresist grating on the convex K9 glass substrate surface with a diameter of 50 mm and curvature radius of 32.77 mm was fabricated within 40 s by the above LDWL equipment system including the dynamic focusing lens unit. The grating was with a sag height of 5.2 mm [Fig. 6(a)]. Figure 6(b) was the photograph of the fabricated grating, and Figs. 6(c) and 6(d) were the local magnification details of the grating on the top and bottom, respectively.
Fig. 6 (a) Schematic diagram of a grating on convex surface, (b) Photograph of concentric circle gratings from photoresist film on convex glass surface, and (c) and (d) local magnification of the top and bottom of the grating, respectively (the scar bar was 20 μm).
It could be seen that the line width and line space of the circular grating were considerably uniform from the top to bottom. However, the circular lines seemed to be polygonal and not very smooth, especially in Fig. 6(c). This was because they were formed by line segment interpolation, i.e., many small line segments connected end-to-end to approach a circle. The more the line segment interpolation, the less the circle distortion, but the processing efficiency would become lower. In order to balance the efficiency and precision, usually, the circles within a radius of 5 mm were interpolated by the line segments with equal radian (𝜃), and the circles with a radius greater than 5 mm were interpolated by the line segments with equal length (l), as shown in Fig. 7.
The designed concentric-circle grating had a line width of 12.5 μm, and a line space of 25 μm. The line width and line space of the fabricated photoresist grating were determined by full width at half maximum (FWHM). Figure 8 was the measurement result of a piece of stochastically selective PDMS region. It showed that the maximum line width and line space were about 13.6 μm and 27.3 μm, and the minimum line width and line space were about 12.3 μm and 24.7 μm, respectively. The average line width and line space was about 13.0 μm and 25.8 μm, while the deviation was about 0.53 μm and 1.01 μm. Compared with the designed line width and line space, the errors were about 4% and 3.2%. From the analysis of the variation of focal spot diameter on convex surface, the focal spot diameter had a variation within 10% on surface with a curvature radius of 32.77 mm, thus the above errors were in a micrometer range (i.e., μm precision). In addition, the depth of the grooves was also measured, the maximum depth of the fabricated grooves was about 1.69 μm, and the minimum depth was about 1.62 μm. The average depth was about 1.65 μm and the deviation was about 0.03 μm. It could be seen that the thickness of the photoresist film was very uniform.
Because of the stochastic selection of the measured PDMS region, the above measurement results were credible and reliable. Further measurements of other stochastically selective PDMS regions testified this.
In our experiment, the exposure light source was a nanosecond laser with a wavelength of 355 nm. Although it was one-photon absorption process in fabrication, it still had the ability for 3D fabrication, like the work of Do. et al. [26]. It could be inferred that, if the output power of the above laser was increased further, 3D micropatterns on curved substrate surfaces would be fabricated through laser direct ablation; And if the laser source was changed to a femtosecond laser, 3D microfabrication would also be realized through multi-photon absorption and polymerization. Therefore, the novel laser direct writing lithography equipment system possessed the general principles of optics, mechanics and automation for μm-precision 3D microfabrication.
4. Conclusion
A novel LDWL equipment system containing a dynamic focusing lens unit and a high-speed galvanometer scanner was introduced and demonstrated for the rapid and precision fabrication on curved surfaces with large curvatures and large sag heights. It possessed the general principles of optics, mechanics and automation for μm-precision 3D microfabrication. Basing on design, analysis, simulation and measurement, it was found that the dynamic focusing lens unit could be well and automatically controlled by a voice coil motor to continuously, linearly, and rapidly change the focus position in z coordinate. Thus, the equipment system could realize the uniform microfabrication with the maximal sag height up to 7.38 mm (without z stage movement) on the curved surfaces of different curvature radii, and the deviation of the uniformity was below 10%. Finally, a concentric-circle photoresist grating with 13.00 μm line width and 25.80 μm line space was fabricated on a convex K9 glass substrate with a curvature radius of 32.77 mm and a diameter of 50 mm. During the process, laser power was only 20 mW and scan speed was up to 1000 mm/s. The sag height was about 5.2 mm and the total processing time was within 40 s. It could be inferred that the sample dimension could be much larger when combining with the movement of x-y-z stage.
Funding
National Natural Science Foundation of China (NSFC) (51775209).
Acknowledgments
The authors were grateful to the assistance from Engineer Haili Zhang in the Center of Micro-Fabrication and Characterization (CMFC) of WNLO for profile measurements.
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