An all glass Fresnel lens (AGFL) was fabricated by glass molding with a vitreous carbon (VC) micro mold. In the glass molding process, a glass plate was heated up to its softening temperature and pressed against to the VC mold to replicate the Fresnel pattern. The VC molds having negative shape Fresnel profile were fabricated by carbonization of replicated Furan precursor using a diamond turning machined nickel master. During the carbonization process, the Furan precursor shrank due to the thermal decomposition, and this shrinkage must be compensated to obtain a precise AGFL. In this study, we examined the shrinkage ratio during the carbonization process using a preliminary experiment using the commercially available PMMA Fresnel lens as the master, and fabricated a nickel master with an enlarged Fresnel profile for shrinkage compensation. To verify the compensation method, the surface profiles of the fabricated VC mold and molded AGFL were measured and compared with the designed profile. The deviations between measured and designed profiles were less than 4 μm. In addition, the tip radii of the grooves and draft angle of the molded AGFL were within the acceptable tolerance for CPV applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In a concentrator photovoltaic (CPV) systems, the sunlight is concentrated into a highly efficient small area multi-junction solar cell via concentrating optics (lenses or mirrors) [1–4]. Recently, Fresnel lenses have been widely used as a primary optical lens due to their small volume and light weight [5–7]. Injection molded polymethyl-methacrylate (PMMA) Fresnel lenses have been commonly used for CPV systems due to their cost effectiveness [8,9]. However, PMMA may not be suitable for CPV systems because it has a lower transmittance in the infrared region  and lower durability in desert climates [11,12] than glass, while the multi-junction solar cells generate electricity from infrared light, and CPV systems are more advantageous than silicon photovoltaic in high direct normal insolation (DNI) regions, which include desert environments. To overcome these problems, lenses composed of glass substrate and imprinted thin silicone Fresnel lens layer (silicone on glass, SOG) have been proposed . However, this structure has delamination and large focal length change problems due to the high thermal expansion coefficient of silicone material . An all-glass Fresnel lens (AGFL) can be regarded as an ideal solution for primary lens of CPV systems, because it has high optical transmittance for infrared light, high durability and no delamination problem. However, a suitable method to fabricate AGFL for CPV system has not been reported. The AGFL can be fabricated by pattern transfer into the glass substrate with dry etching, which has been widely used for micro/nano patterning process of glass materials . However, the pattern transfer process is not suitable for fabrication of AGFL for CPV system, because it is too difficult to fabricate Fresnel lens shape etch barrier and a long etching time is required to obtain a AGFL with a heights of 50 ~300 µm due to the low etching rate of glass material. In this study, a glass molding process was used for the production of precise AGFLs. The glass molding process has been developed for fabricating glass aspherical lens for mobile phone camera . In the glass molding process, the mold and glass material are heated up to the softening temperature of glass and are pressed to fill the cavity. The molded glass is then cooled down, and released from the mold. Since the glass molding process requires very high processing temperatures, the mold material should have a high hot hardness and high temperature resistance. A precision ground tungsten carbide (WC) mold was commonly used for glass molded aspherical lens [17,18]. Suzuki et al., fabricated Φ4 mm AGFL by glass molding with a precision grinding machined WC mold . Since the sharp diamond wheel was easily damaged during the grinding process of WC, a repeated truing process was required to obtain sharp edge structures in Fresnel shape. Therefore, it is difficult to fabricate large area Fresnel lens WC molds at low-cost. In addition, it also has a size limitation problem due to the tip radius of diamond wheel.
For the mass production of AGFL for CPV system, a low-cost mold fabrication method is essential, because the multiple molds are required for progressive glass molding system with high productivity . As a mold material for glass molding, a vitreous carbon (VC) has been proposed. VC is a non-graphite carbon material, which provides high temperature resistance, high hot hardness, extreme resistance to chemical attack, and low adhesion to the glass, which are the key characteristics required for mold material of glass molding process. Various methods have been proposed for fabricating VC molds with micro or nanoscale structures, such as focused ion beam machining [21,22], laser machining , electrochemical machining , reactive ion etching process [25,26] and carbonization of a replicated polymer precursor [27,28]. Among the methods for fabricating VC mold, the carbonization of polymer precursor can be regarded as a most suitable method for mass production of glass molded product requiring multiple molds, because the multiple polymer precursors with high dimensional accuracy can be easily obtained by replication process and those can be turned to VC molds by single carbonization process. In addition, a precise polymer precursor with a complex Fresnel shape can be easily obtained by replication with conventional diamond turning machined nickel master.
In this study, we fabricated a 40 mm X 40 mm AGFL by glass molding with Φ80 mm VC mold prepared by carbonization of a Furan polymer precursor with Fresnel lens shape. During the carbonization process, a large shape change (shrinkage) was observed due to the thermal decomposition of the polymer. Since the shrinkage affects the shape of the Fresnel lens, focal length, and optical efficiency, it should be compensated for fabricating precise AGFL. To estimate the shrinkage ratio in the carbonization process, a VC mold with Fresnel lens shape was fabricated by the carbonization of replicated Furan precursor from a commercially available PMMA Fresnel lens. To fabricate the AGFL with designed surface profile, a nickel master with shrinkage compensated surface profile was fabricated. A polydimethylsiloxane (PDMS) intermediate mold was replicated from the nickel master and a Furan precursor was replicated form the PDMS mold. Finally the VC mold with designed surface profile was obtained by carbonization process. To determine the feasibility of the proposed method, an AGFL was fabricated by a glass molding process with the VC mold. To verify the proposed shrinkage compensation method, we compared the measured surface profiles of fabricated VC mold and molded AGFL to the designed profile. Cross-sectional images were also obtained to examine the tip radius and draft angle, which are also important for optical efficiency of Fresnel lens.
2. Fabrication method
Figure 1 shows a schematic of the proposed fabrication process for molded AGFL using a VC mold prepared by carbonization of a Furan precursor and the photographs of fabricated sample or equipment in each processing step. Although the proposed VC mold fabrication method does not require a durable master, a nickel master prepared using diamond turning machining (DTM) with a diameter of 100 nm was used for AGFL with high surface quality. A PDMS intermediate mold was fabricated from the nickel master in order to protect the nickel master from surface damage, which can occur in the direct replication process of the Furan precursor from the nickel master. The PDMS mold were obtained by curing of a mixture of PDMS elastomer (Sylgard 184 A, Dow Corning Co. Ltd., USA) and curing agent (Sylgard 184 B, Dow Corning Co. Ltd., USA) with a weight ratio 10:1. The mixture of PDMS was poured on the master and placed in a vacuum oven under 10−1 Torr for 2 hours for degassing, and it was then cured at room temperature for 24 hours to minimize the shrinkage. After curing, the PDMS mold was released from the nickel master.
To fabricate a Furan precursor, a mixture of 89.8 wt% Furan resin (C4H4O, Gangnam Chemical Inc., Republic of Korea), 0.2 wt% p-toluenesulfonic acid monohydrate (CH3C6H4SO3H H2O, PTSA, Kanto chemical Co. Inc., Japan), and 10 wt% ethanol (Ethyl alcohol 99%, Duksan Co. Ltd., Republic of Korea) was mixed by hand stirring process . To eliminate the bubbles generated in the mixing process, the Furan mixture was placed in a vacuum chamber under 10−1 Torr for 2 hours. The Furan mixture was then poured on the PDMS mold. The 1st curing process was conducted at room temperature for 5 days, and the 2nd curing process was carried out at a maximum temperature of 100 °C in a convection oven. In order to minimize the warpage and protect from cracking due to a rapid polymerization process, the heating rate of 2nd curing was set to be 0.1 °C/min and the temperature was maintained for 60 min at every 5 °C temperature increment until the maximum temperature was reached. After curing process, the replicated Furan precursor was released from the PDMS mold and the backside of Furan precursor was polished to obtain uniform thickness.
The VC mold with a diameter of ~80 mm was obtained by carbonization of the replicated Furan precursor. A tube furnace with a chamber size of Φ 310 mm x 1,050 mm (modified MIR- TB1001-2, Mirfurnace Co. Ltd., Republic of Korea) was used for the carbonization step. The tube furnace had a maximum temperature of 1,200 °C and allowed for control of the temperature history. The carbonization process was conducted in a vacuum environment to protect the Furan precursor against oxidation. To minimize the warpage of the VC mold and generate decomposed gas slowly from the precursor in the carbonization process, the heating rate was set to be 0.5 °C/min up to a temperature of 600 °C, and was changed to 1 °C/min to a maximum temperature of 1000 °C under 2 X10−2 Torr, because most of thermal decomposition of Furan precursor was occurred below 600 °C. After 10 hours holding time at maximum temperature, the carbonized VC mold was cooled in natural cooling condition for 24 hours. The total fabrication time for VC mold from the master pattern was ~10 days (1 day for PDMS mold, 5 days for 1st furan curing, 1.5 days for 2nd curing and 2.5 days for carbonization). The slow curing and carbonization conditions were selected to minimize the warpage, the internal crack and the void which deteriorate the durability of VC mold . Although we did not conduct a durability test for VC mold, we did not found any defects on the VC mold after 10 glass molding processes at the optimum molding condition.
Finally the AGFL was obtained by a glass molding process. A low-iron soda-lime glass (White Clear Glass, JMCglass Inc. Republic of Korea) with a glass transition temperature of 564 °C, a thickness of 3.1 mm and a size of 40 mm X 40 mm was used as a material for molded AGFL. A glass molding system with a maximum molding temperature of 1050 °C, a maximum heating rate of 10 °C/min, a maximum applied force of 8,000 kgf, and an available sample size of 100 mm X 100 mm was used in this study. The fabricated VC mold was first placed on a graphite jig in a chamber and the initial glass material was placed on it. After the evacuation process, the chamber was purged by nitrogen gas with a flow rate of 150 cc/min for inert environment. The temperature of chamber in which the VC mold and glass plate were placed, was increased with a heating rate of 6 °C/min up to 720°C by resistance heater, and maintained for 15 min. After the holding time (15 min), the upper graphite jig, which can apply compression pressure by hydraulic unit, moved down to contact glass plate and pressed the VC mold and glass plate stack with a pressure of 140 kPa for 30 min. After the pressing time, the upper jig released from the glass and the chamber was cooled in natural cooling condition. When the temperature of chamber cooled down to the room temperature, the chamber was opened and molded AGFL was released from the VC mold. The total cycle time for the glass molding in this study was ~5 hr (~2.5 hr for heating, 0.5 hr for pressing and 2 hr for cooling).
3. Design of shrinkage compensated master profile
3.1 Expectation of shrinkage ratio
Before the main experiment for fabricating AGFL, a preliminary experiment to determine the shrinkage rate in the VC mold fabrication process was carried out. The VC mold was fabricated using a commercially available PMMA Fresnel lens master having a focal length of 300 mm and a maximum sag height of 150 μm instead of the nickel master in Fig. 1, because the DTM nickel master was too expensive for the preliminary experiment. The Furan precursor was replicated from the replicated PDMS from the PMMA Fresnel lens, and was carbonized to form a VC mold. To examine the shrinkage rate, the diameters of the center, 5th, 10th, and 15th pitch circles of the PMMA Fresnel lens master, PDMS mold, Furan precursor and VC mold were measured using an optical microscope (STM-6, Olympus Co. Ltd., Japan). Three sets of PDMS mold, Furan Precursor and VC mold were fabricated from the single PMMA Fresnel lens master, and the mean values were used for bar graph in Fig. 2. The measured diameters of the PMMA Fresnel lens and the replicated Furan precursor were similar, but significant decrease in diameters was observed in VC mold due to the carbonization process. The shrinkage rate for each pitch circle of VC mold comparing the PMMA master was also noted in Fig. 2 and the shrinkage ratio for each pitch circle was similar and ~22.5% ± 0.4%.
3.2 Machining profile for master pattern
In this study, a commercial ray tracing software, Lighttools (Synopsys Co. Ltd., U.S.A.) was used for design and tolerance analysis of AGFL. A variable pitch method was used for designing AGFL with a focal length of 300 mm. The maximum sag height of 150 μm and the maximum pitch of 2 mm were set as design constraints. The designed AGFL was composed of the facets with fixed pitch and variable heights until 6th pitch, and the facets with fixed height and variable pitch after 7th pitch. The maximum aspect ratio of 0.252 was observed at the last pitch. The simulated optical efficiency of designed Fresnel lens was 91.26%. The optical efficiency of Fresnel lens was easily deteriorated by the fabrication errors such as groove tip radius and draft angle. To examine the tolerance in fabrication process, the effects of (a) groove tip radius and (b) draft angle on the optical efficiency of AGFL were examined as shown in Fig. 3. The designed AGFL showed more than 90% optical efficiency when the groove tip radius and draft angle were less than 5 μm and 5 °, respectively. To compensate the shrinkage occurred during the carbonization process, we machined an enlarged negative nickel master. Since the shrinkage rate of sag height was similar to that of the pitch circle diameters, we assumed that isotropic shrinkage occurred during the carbonization process. Figure 4(a) and 4(b) shows the comparison of Fresnel lens design profile (inverted) and the nickel master machining profile (enlarged for shrinkage compensation). The machining profiles of the master was expanded by 29.03% in both height and pitch direction to compensate the isotropic shrinkage.
4. Evaluation of fabricated samples
Surface profiles of the VC mold fabricated from the nickel master were measured to examine the feasibility of the proposed shrinkage compensation method. Figure 5 shows the surface profiles of the fabricated VC mold and molded AGFL using a confocal microscope (OLS4100, Olympus Co. Ltd., Japan). The full length (~80 mm) line surface profiles of samples were obtained from line stitched images using a 20X objective lens. Figure 5(a) and 5(b) show the comparisons of the surface profiles of the fabricated VC mold and the designed negative Fresnel lens at the (a) center and (b) edge pitch circle regions. The deviation was less than 3 μm except in the vertical area as shown Fig. 6(a) and 6(b). Since a sag height error of 5 μm is an acceptable tolerance in non-imaging Fresnel lens, we confirmed that a precise VC mold for Fresnel lens was fabricated using the proposed shrinkage compensation method. Figure 5(c) and 5(d) show the comparisons of the surface profiles of the molded AGFL and the design. The deviation between the measured profiles and the design profiles was less than 4 μm except in the vertical region as shown Fig. 6(c) and 6(d). It clearly shows the deviation of surface profile between VC mold and AGFL is negligible. In this research, the thermal expansion coefficient of VC material was 2.6 x 10−6 /K and that of soda-lime glass was 9.5 x 10−6 /K, and the glass molding temperature was 720 °C. Although there was a slight thermal coefficient difference, the maximum height of Fresnel lens was just 150 μm. If a perfect replication is occurred at the molding temperature, the height deviation between mold and molded part after cooling process to 20 °C is 0.7245 μm. We thought this was the reason for negligible deviation of surface profiles between VC mold and AGFL. Since the amount of form error of AGFL was also acceptable for non-imaging optical systems, we confirmed that a precise AGFLs as primary optical lens of CPV system can be fabricated using the proposed glass molding process with the shrinkage compensated VC mold.
The surface roughness of randomly selected facets on VC mold and AGFL were also measured from the surface profile obtained by confocal microscope measurement. The measured surface roughness (Ra) was 7 ± 2 nm for VC mold and 16 ± 2 nm for AGFL. Although the surface roughness of AGFL was larger than the VC mold, the value was acceptable for non-imaging optical component.
In addition to the accurate surface profile, the small draft angle and tip radius of groove are also important factors for Fresnel lens with high optical efficiency. To examine the draft angle and tip radius of fabricated samples, the PDMS replicas of nickel master, VC mold and AGFL were prepared to prevent destruction of fabricated samples for cross-sectional imaging. The replicated PDMS was cut with the line passing the center and the cross-sectional image of PDMS was measured using optical microscope. Figure 7 shows cross-sectional microscope images of the third groove of the PDMS replicas from (a) nickel master, (b) VC mold and 7(c) AGFL. The radii of the top and bottom grooves were 0.258 μm and 2.584 μm for nickel master, 0.903 μm and 3.926 μm for VC mold, and 1.088 μm and 4.979 μm for AGFL, respectively. The draft angle was 1.530° for nickel master, 3.21° for VC mold, and 4.656°for AGFL, respectively. The positions of the top and bottom grooves were inverted in AGFL because the AGFL was replicated from a fabricated VC mold. Although the tip radii and draft angle of VC mold and AGFL were little larger than the nickel master, these values fell within the required tolerance, that is, the radii of the grooves were less than 5μm and the draft angle was less than 5°.
To measure the optical efficiency of the fabricated AGFL, a transmittance measurement setup was constructed. A 658 nm wavelength Laser was used as a light source and the expended and collimated beam with a diameter of ~15 mm was illuminated on the sample at normal direction. To determine the light power of the collimated beam, a transmitted power of Plano convex spherical lens with a diameter of 50 mm was measured and the initial power was calculated by dividing the measured power by 0.92. The transmitted light power of fabricated AGFL was measured at 5 different location of sample and the average value was used for calculating optical efficiency. The measured optical efficiency of fabricated AGFL were 86.7%. The deviation between measured efficiency and design target (90%) might be due to the form error (< 4μm) and small warpage occurring in carbonization process of VC mold.
In summary, a Φ80 mm VC mold and a 40 mm X 40 mm AGFL were fabricated from a nickel master having a shrinkage compensated surface profile. We assumed that isotropic shrinkage of 22.5% occurred in the carbonization process, and the machining profile of the nickel master was enlarged by 29.03% relative to the design profile. The form error observed in the fabricated VC mold was less than 3 μm, and that of the AGFL was less than 4 μm except in the vertical regions. Since the error was acceptable in a non-imaging optical lens, we confirmed the feasibilities of the proposed shrinkage compensation method and the glass molding process with VC mold. Although the tip radii and draft angle of molded AGFL were larger than those of the nickel master, the measured tip radii and draft angle were also acceptable considering the tolerance of AGFL. Although a slow curing and carbonization process (total ~10 days) was used for fabrication of defect-free VC mold in this research, the fabrication time might be reduced by process optimization, and the long fabrication time for VC mold is not a critical issue because many VC mold could be fabricated at a time and a VC mold can be used for multiple glass molding process. The long cycle time of glass molding (~5 hr) was mainly due to our stand-alone type glass molding system, and it could be overcome by using a progressive molding system . The proposed VC mold fabrication method using carbonization of the replicated precursor is more attractive for the progressive molding system than the conventional micro-machined mold in term of cost because the progressive molding system requires multiple molds for increasing productivity. The optimization of curing and carbonization process for VC mold to reduce the fabrication time, and the application of fabricated AGFL to real CPV system are the subject of on-going research.
National Research Foundation (NRF) of Korea grant funded by the Korean Government (MSIP) (No. 2015R1A5A1037668 and 2017R1A2B4011149), Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government - Ministry of Trade Industry and Energy(MOTIE) (No. N0001075).
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