Compressional Deformation in Indentation Process for Microlens Array Mold

Yaqun Bai, Xibin Wang, Tianfeng Zhou, Zhiqiang Liang and Guang Li

(School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China)

Microlens array (MLA) has become an important element in various applications such as flat panel display[1], micro-scanning system[2], fiber-optic probe imaging[3], optical data storage and optical communication etc., for its multi-functional capability. Recently, many manufacturing method of MLA have been proposed and studied, like hot embossing[4], femtosecond and CO2lasers[5], reflow techniques, UV proximity printing[6], injection molding[7], and other molding processes[8]. Among these, injection forming process is regarded as the best method for replicating MLA mass-production[9], and the mold accuracy determines the forming accuracy. Conventional MLA mold are fabricated by micro-turning, micro-milling and other machining methods, but they are complicated and time-consuming[10]. Indentation process, which is widely used for measuring material properties such as hardness, elastic modulus etc.[11-12], has been studied recently as a novel method for MLA mold manufacturing. By pressing the mold surface with a shaped indenter, a single dimple is formed, which is corresponding to a microlens unit in injection forming.By repeating the indentation, MLA mold can be obtained.

In a single indentation, springback of the workpiece is the main factor affecting the dimple dimensional accuracy. Jiwang Yan et al. investigated the dimensional error caused by springback and observed that the depth of the dimple was remarkably smaller than the nominal indentation depth as elastic deformation played a significant role in the deformation[13]. Repetitive indentation was proposed by them to reduce the form error, but the form error is reduced by only 50%. In multi-indentation, smaller pitch may lead to compressional deformation on the former indented dimples. Yasunori Kobayashi proposed a method to avoid compressional deformation in the manufacture of MLA mold which combined ball-end milling process and sphere indentation[14]. In their method, U-shape grooves intersected at right angle were machined by a ball-end milling, and then indentation was utilized to generate lens at the intersection between U-shape grooves. With this method the deformation of neighboring lens forms caused by following indentation was effectively mitigated. Nevertheless, when the pitch is above a critical value, U-shape grooves won’t be necessary when no compressional deformation between two adjacent dimples.

In this paper, single indentation and multi-indentation were studied to produce a precise MLA mold. Indenter compensation method, by compensating the indenter shape in single indentation, was introduced to increase the single dimple form accuracy. Then, multi dimples at seven different pitches were indented with simulations and experiment to find the critical pitch for MLA manufacturing.

1 Experimental Setup and Simulation

Fig.1 shows the schematic of the indentation process to manufacture MLA mold, which was conducted on a forming process platform as shown in Fig.2, which is a self-developed equipment in Beijing Institute of Technology. An effective displacement of the indenter is controlled by the grating encoder with a resolution of 0.1 μm, and the servo motor is controlled by a force sensor feedback at a resolution of 0.1 N. The working platform is driven by anXY-stage to move the workpiece in the horizontal plane.

Fig.1 Schematic of indentation process manufacturing MLA mold

Fig.2 Forming process platform conducting indentation process

Metal block made of oxygen-free copper was prepared as a work piece for MLA mold manufacturing. The size of workpiece was 5 mm×5 mm×2 mm, and working surface was polished to Ra 0.08 μm. Johnson-Cook (J-C) constitutive model was utilized for indentation simulation shown as

(1)

(2)

whereσyis the equivalent plastic stress;εpis the equivalent plastic strain;A,B,C,nandmare material parameters, exponentndescribing strain hardening, and exponentmis strain rate hardening.

The mechanical property of the material and its parameters are listed in Tab.1.

As shown in Fig.3, a tungsten steel ball with a diameterDof 1.0 mm is glued on the end of Aluminium alloy rod as the indenter, which is used to generate spherical dimples at a specified depthhof 0.1 mm. Diameter of the indented dimpled,Dandhtake a geometrical relationship as described with

Tab.1 Characteristics of oxygen-free copper and J-C model parameters

(3)

Fig.3 Photograph of the indenter

2 Results and Discussion

2.1 Indenter compensation in single indentation

Single indentation on the oxygen-free copper was simulated using MSC.Marc code. Loading and unloading velocity was 0.1 mm/s, and holding time was 0.1 s. The cross-sectional profile of indented dimple was measured and shown in Fig.4. Due to the springback, a profile shift occurs comparing to the profile of the indenter.

Fig.4 Cross-sectional profile generated by sphere indenter

By subtracting the ideal round profile from the dimple profile, form error was calculated in Fig.5. As it can be seen in the figure, the maximum form error is about 2.6%h(2.6 μm). By compensating the form error to indenter shape,the dimple with a cross-sectional profile approximating to the ideal spherical curve can be obtained, and the maximum form error was reduced to 0.007 5%h(7.5 nm)as shown in Fig.6.The following simulations of MLA indentation were all performed using this compensated indenter.

Fig.5 Cross-sectional form error

Fig.6 Cross-sectional profile generated by sphere indenter

2.2 Indentation interaction in multi-indentation

Multi-indentation was simulated to investigate indentation interaction in adjacent areas at different pitches.

Fig.7 Schematic of dimples array generated by multi-indentation and the pitch

Fig.8a and Fig.8b show the form of dimples array generated by multi-indentation and the distribution of residual Von Mises stress and strain in top view and cross section whenk=1.00. Former indented dimple was seriously distorted by the indentation of its two neighboring dimples, where is termed compressional deformation. Maximum residual stress concentrates on the center of the last formed dimple. But,within former indented dimple, area along new neighbor shows higher stress than anywhere else. Residual strain has the largest value around the interaction area between two neighboring dimples.

Fig.8 Multi-dimples forms and distribution of residual Von Mises stress and strain from top view andcross section when k=1.00

Compressional deformation of the former indented dimple alongX-axis andZ-axis are not the same. Here we definedcto quantify compressional deformation which is the value of the difference between the ideal diameter of the dimple and the diameter of the distorted dimple. Fig.9a and Fig.9b display the cross-sectional profiles inYZplane andXYplane of the first indented dimple before and after the neighboring dimple indented respectively, where compressional deformationcis marked. InYZplane, dimple profile is coincident with the shape of indenter, which means that there is no compressional deformation occurring alongZ-axis. On the contrary, cross-sectional profile inXYplane is seriously distorted. Effective maximum compressional deformationcreaches 0.14d(84.0 μm) distinctly, and only occurs on the right half. Far away from neighbor dimple, the other half is not affected.

Fig.9 Cross-sectional profiles when k=1.00

In the simulation, indentation load is also affected by the formation of its neighbor dimples. Load-displacement curves during the forming of three dimples whenk=1.00 are depicted in Fig.10. The curves are all near-linear, and the afterward formed dimple needs larger indentation load resulting in larger curve slope. The maximum indentation force to form the three dimples are approximately 210 N, 230 N and 240 N in sequece. Residual stress and strain and pile-ups around the dimple are the mere differences in the three indentations regardless of the variation of material inherent structure.

Fig.10 Load-displacement curves

Fig.11 Top-view of contours at different pitches in simulation

2.3 Indentation pitch

On account of the indentation interaction, a critical pitch should be calculated and utilized to ensure the dimension accuracy of the dimples array.

Fig.11 illustrates multi-dimple contours at seven different pitches in simulation, and whenkis larger than 2.00, no compressional deformation can be observed, while whenkis smaller than 1.41, profile of neighboring dimple is severly distorted. Fig.12 displays the cross-sectional profiles of the distorted dimples at seven different pitches compared with the dimples’ original cross-sectional profile. It can be obviously observed that compressional deformation decreases with the increase ofk.

The maximum compressional deformationcvarying withkis recorded in Fig.13. Whenkis smaller than 1.41, compressional deformation decreases rapidly askincreases, whilekis larger than 1.41, the decrease becomes slower. By curve fitting method, it can be calculated that whenkis larger than 1.47,cis smaller than 0.01d. Hence,kmore than 1.47 can be utilized in the manufacture of MLA mold whose precision is larger than 0.01. Under this condition, critical pitch should be 1.47d, then accurate MLA mold can be obtained. Therefore, critical pitch is a variable related to the processing precision. Whenkis larger than 2.36, there is no compressional deformation.

Fig.12 Cross-sectional profiles influenced by various pitches

Fig.13 Maximum compressional deformation c vs. k

3 Experiment Verification

Multi-indentation experiments were performed to validate the numerical results and reveal the deformation mechanism.

Fig.17 Top-viewed shape of dimplesat different pitches in experiment

Fig.14 shows the microscopic photograph of dimples whenk=1.00. Pile-ups can be observed around the dimples. The far right dimple was indented at last and has a better shape. A cross-sectional profile of the indented dimples is shown in Fig.15. It can be seen that the profile of the last formed dimple agrees very well with an ideal one and the compressional deformation is 0.13d(80.0 μm).

The indentation force during the three indentations is recorded in Fig.16 and a linear relation between indentation load and displacement with a maximum load of 250 N can be observed.

Fig.14 Microscopic photograph of dimples when k=1.00

Fig.15 Experimental cross-sectional profile of dimples when k=1.00

Fig.16 Load-displacement curves of three sequent indentations

Micro-grinding process was performed after indentation to remove pile-ups. The effective contours of dimple arrays at seven different pitches are shown in Fig.17. Whenkwas smaller than 1.41, the former indented dimples were severly distorted, which agrees well with the simulation result.

4 Conclusions

Indenter compensation in single indentation and compressional deformation in a multi-indentation process to manufacture MLA mold were studied in this paper. The following conclusions can be drawn.

① Indenter compensation by compensating form deviation to the shape of an indenter is an effective way to eliminate form error in single indentation.

② In multi-indentation process, a small pitch affects the shape accuracy significantly with compression deformation between adjacent dimples. When the pitch is larger than 1.47d, compressional deformation is less than 0.01d. While the pitch is larger than 2.36d, there will be no compressional deformation.

③ Simulation results agree well with the experiment results, which can be utilized for further study on manufacturing MLA molds by an indentation process.

[1] Chao C L, Chen C C, Chou W C. Ultra precision diamond shaping of an elliptical micro-lens array[J]. Key Engineering Materials, 2009, 806(407):380-383.

[2] Pang K, Song L, Fang F Z, et al. An imaging system with a large depth of field based on an overlappen micro-lens array[C]∥66th General Assembly of the International Academy for Production Engineering (CIRP),Guimaraes, Portugal, 2016.

[3] Shinoj V K, Murukeshan V, Tor S B, et al. Design fabrication and characterization of thermoplastic microlenses for fiber-optic probe imaging[J]. Applied Optics, 2014, 53(6):1083-1088.

[4] Xi Qiufan. Realization of mass production of microlens array by hot embossing on silicon substrate[J]. Advanced Materials Research, 2010, 1037(139):1562-1565.

[5] Choi H K, Ryu J, Kim C, et al. Formation of micro-lens array using femtosecond and CO2lasers[J]. Journal of Laser Micro Nanoengineering, 2016, 11(3):341-345.

[6] Shen Y K. A novel fabrication method for mold insert of injection molded microlens array[J]. Materials Science Forum, 2006, 532-533: 665-668.

[7] Kim J S, Ko Y B, Hwang C J, et al. A study on the fabrication method of middle size LGP using continuous microlens array made by LIGA reflow[J]. Korea-Australia Rheology Journal, 2007, 19(3):171-176.

[8] Moore S, Gomez J, Lek D, et al. Experimental study of polymer micro-lens fabrication using partial-filling hot embossing technique[J]. Microelectronic Engineering, 2016, 162(16):57-62.

[9] Chang C Y, Yang S Y, Chu M H. Rapid fabrication of ultraviolet-cured polymer micro-lens arrays by soft roller stamping process[J]. Microelectroinc Engineering, 2007,84(2): 355-361.

[10] Davies M A, Evans C J,Patterson S R, et al. Application of precision diamond machining to the manufacture of micro-photonics components [J]. Proc SPIE 5183, Lithographic and Micromachining Techniques for Optical Component Fabrication II, 2003, 12(4): 94-108.

[11] Moussa C, Hernot X, Bartier O, et al. Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain[J]. Journal of Material Science, 2014, 49(2): 592-603.

[12] Oliver W C, Pharr G M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refineness to methodology[J]. Journal of Materials Research, 2004, 19(1): 3-20.

[13] Yan J W, Akihiro H, Tsunemoto K, et al. Manufacturing structured surface by combining microindentation and ultraprecision cutting[J]. CIRP Journal of Manufacturing Science and Technology, 2012, 5(1): 478-487.

[14] Yasunori K, Ryo I, Haruhisa S. Proposal of finishing method of MLA mold applied sphere indentation[J]. Advanced Materials Research,2013, 2631(797): 475-480.