Carbide-bonded graphene-based Joule heating for embossing fine microstructures on optical glass

Journal Pre-proofs Full Length Article Carbide-bonded graphene-based Joule heating for embossing fine microstructures on optical glass Lihua Li, Gao Yang, Wing Bun Lee, Man Cheung Ng, Kin Leung Chan PII: DOI: Reference:

S0169-4332(19)32820-X https://doi.org/10.1016/j.apsusc.2019.144004 APSUSC 144004

To appear in:

Applied Surface Science

Received Date: Revised Date: Accepted Date:

15 February 2019 3 June 2019 12 September 2019

Please cite this article as: L. Li, G. Yang, W. Bun Lee, M. Cheung Ng, K. Leung Chan, Carbide-bonded graphenebased Joule heating for embossing fine microstructures on optical glass, Applied Surface Science (2019), doi: https:// doi.org/10.1016/j.apsusc.2019.144004

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Carbide-bonded graphene-based Joule heating for embossing fine microstructures on optical glass

Lihua Li, Gao Yang*, Wing Bun Lee, Man Cheung Ng and Kin Leung Chan The State Key Laboratory of Ultraprecision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Abstract This paper reports the fabrication of high-quality microstructures on optical glass via hot embossing using carbide-bonded graphene (CBG) based Joule heating for the first time. In this study, a tailor-made micro hot embossing tool equipped with a modified CBG-based Joule heating system was designed and developed for transferring microstructures (e.g., microlens arrays, MLAs for short) from the CBG-coated silicon mold insert into the optical glass (PSK57). Initially, the surface topographies of a typical 3×3 MLA from a bare silicon mold to an embossed glass replica were compared for evaluating form errors brought in during different preparation stages. The feasibility of the CBG-based Joule heating technique for the nonequilibrium thermal forming of optical glass was evaluated by the surface integrity and replication fidelity of the embossed MLA features. Thermally induced residual stress and imaging performance of the embossed glass lens were assessed as well. Experimental results indicate that the proposed CBG-assisted hot embossing technique, in combination with single point diamond turning technology, has the capability of producing high-quality glass MLAs.

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*Corresponding author. Tel: 852 5396-6448. E-mail: [email protected] (Gao Yang)

Moreover, this technique allows notably fine replication of surface shapes at the microscale, as well as roughness information at the nanoscale. Consequently, the embossed MLA replica shows satisfactory imaging performance.

Keywords: carbide-bonded graphene, Joule heating, optical glass, hot embossing, microlens array

1. Introduction Micro optics, such as MLAs, Fresnel lenses and diffraction gratings, are in great demand in the optics field due to their wide range of applications (e.g., customizing the amplitude and phase of the laser modes [1], breaking the focused spot size limit of light beams [2], and eliminating achromatic and apochromatic aberrations [3]). The commercially available micro optics in general are made of either glasses or polymers. Compared to polymeric micro optics, glass ones show less sensitivity to temperature, lower moisture uptake, less birefringence, but higher chemical inertness, higher optical transmittance, higher refractive index and higher Abbe number, so they are preferred in those applications with higher imaging performance requirements or harsher working conditions. Satisfactory glass micro optics products generally have features at the micro scale and are of high surface quality. Fabrication of these specified micro features on glass can be achieved by plasma etching [4], micro-milling [5,6], laserassisted micro machining [7] and micro hot embossing [8,9]. Among these, micro hot embossing is expected to be one of the most promising approaches for mass production, due to its high cost-efficiency, simplicity in tool design, high flexibility in process modification and

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high fidelity in pattern replication.

Micro hot embossing has become a mature open-mold replication technology for transferring microstructures from a master mold onto a thermoplastic polymer substrate [10], and involves four steps: heating, molding, cooling and demolding [11]. The embossing temperature is required to be above the glass transition temperature (𝑇𝑔) of the workpiece and maintained for a period of time during the molding stage, so the workpiece is more prone to viscoelastic deformation. Further, when being operated at appropriate temperature and pressure, this technology is applicable of embossing most amorphous materials, including glass. The normal approach for realizing such high temperature is by using electrical cartridge tubes, which requires the mold and workpiece to be heated simultaneously. As a result, the throughput of replication is limited by the high energy consumption and the long thermal cycle time. Therefore, countless attempts have been made to address these drawbacks by the replacement of the traditional bulk heating method with new rapid heating techniques such as infrared radiation (IR) heating [12], fluid-assisted heating [13], ultrasonic heating [14] and induction heating [15]. However, all these techniques have their own limitations. More specifically, IR heating is still energy-consuming; fluid-assisted heating is not suitable for embossing glass materials with high 𝑇𝑔 temperature; ultrasonic heating is not applicable to mold inserts with concave-structures; and induction heating cannot provide sufficient heat for embossing smallsize structures.

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Due to the extraordinary properties, graphene and graphene-based materials [16] have wide applications, such as batteries [17], ultracapacitors [18], transistors [19], water filters [20], gas sensors [21], solar energy conversion and storage devices [22–24], mold coatings [25] and film heaters [26]. In particular, Xie et al. [27] first found that a novel carbide-bonded graphene (CBG) networks offered the possibility of serving as a heat generator as well as a protective coating in the micro hot embossing process. By applying a small direct current voltage of less than 45 V, the CBG coating on silicon stampers could be heated to above the 𝑇𝑔 temperature of polymers, within tens of seconds. Besides, the localized rapid heating mode rendered a markedly reduced energy consumption and a high replication performance in transferring the features of microchannels and MLAs from a silicon mold insert onto the PMMA substrate. Later, Li et al. [28] validated the feasibility of utilization of the same heating technique in precision embossing microwells on infrared glass (As2S3) by a combined study involving experimentation and numerical simulation. Compared with IR heating in the glass molding process, the CBG-based localized rapid heating approach greatly shortened the molding cycle time and increased the replication fidelity, which was attributed to the concentration of heat on the target area of the glass blank and less thermal variation on the mold insert. It is noted that the successful fabrication of fine microstructures on thermoplastic polymers and infrared glasses was readily accomplished because of the low 𝑇𝑔 temperatures of less than 200 ℃. However, there appears to have been no further investigation of hot embossing microstructures on high-𝑇𝑔 amorphous materials, such as optical glass, by taking advantage of this CBG-based Joule heating technique, due to the higher requirements of power supply, electrode design and embossing parameter

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selection.

In this work, a tailor-made micro hot embossing device equipped with a modified CBG-based Joule heating system was employed to fabricate high-quality micro features on optical glass (PSK57) for the first time. The surface evolution of a 3×3 MLA feature was recorded for evaluating the form errors induced at different processing stages. The feasibility of the CBGassisted micro hot embossing process for the non-equilibrium thermal forming of optical glass was determined by evaluating the surface integrity of the embossed surfaces of the MLAs and calculating the replication fidelity. In addition, the residual stress inside glass replica was examined under polarized white light, and the imaging performance of the embossed glass MLA was tested by a standard optical system. Finally, the reproducibility of the proposed hot embossing technique was provided by carefully comparing the results of four glass replicas that were produced under the same condition.

2. Characteristics of CBG-based Joule heating By imprinting the intrinsic properties of pristine graphene [16], CBG networks exhibit superior electrical and thermal conductivities, in addition to low glass-adhesion and low surface friction coefficient [29], and thus it is able to serve as an electric heating film as well as a mold protective coating in the micro hot embossing of glass. Figure 1a illustrates the configuration of a CBG-based Joule heating system which consists of a quartz upholder, an intrinsic silicon substrate, a thin layer of CBG coating, two copper electrodes, a regulated power supply and

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several conductive leads. From the microscopic perspective, the CBG-based Joule heating is caused by the interactions between the charge carriers (usually electrons) and atoms in the lattice of conductive or semi-conductive materials. Once the power supply provides a specified potential difference to the electrodes at the both ends of the CBG coating, the corresponding electric field formed between the two terminals forces randomly moving electrons to drift towards the higher potential direction. During the drift movement, electrons continuously collide with atoms or other electrons (especially at high electron density) in a random fashion. Therefore, the drifting electrons keep losing partial kinetic energy in the successive collisions and then regaining the kinetic energy due to the presence of the applied electric field. As a result, the electric potential energy of the electrons provided by the power supply is finally converted into thermal energy for conductive heating of the glass blank.

In micro hot embossing, the form accuracy and surface finish of glass replica are predominantly influenced by the processing temperatures. To achieve precise temperature control of a CBGbased Joule heating system, the heating characteristics of CBG coated intrinsic silicon was investigated in our previous study [30]. At low temperature, the CBG coating [29] is a carbon material with a comparatively low resistivity, while the intrinsic silicon substrate is an “insulator” due to the extremely low concentration of the charge carriers (i.e., electrons in the conduction band and holes in the valence band). Therefore, most of the current flows through the CBG coating, whereas the passage of current in the intrinsic silicon substrate is negligible, as seen in Figure 1b. However, as the negative temperature coefficient of resistance for intrinsic

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silicon is lower than that of CBG, the resistance of the intrinsic silicon substrate decreases more rapidly than the CBG coating as the temperature increases. Consequently, both the CBG coating and intrinsic silicon substrate contribute to the total resistance in the intermediate temperature range. However, at high temperature, the intrinsic silicon substrate rather than CBG coating is preferred for the transport of electrons, attributed to its considerably lower resistance.

Apart from intrinsic silicon substrates, carbide-bonded graphene (CBG) films can also be uniformly deposited on doped silicon and fused silica substrates under certain processing conditions. However, CBG coated intrinsic silicon wafer shows the best heating performance in hot embossing process (see Section 1 in supplementary information). Figure 1c plots the temperature dependence of the total resistance for CBG coated intrinsic silicon under various initial input voltages, which were obtained by conducting heating experiments complied with specified procedures [30]. The black curve represents the temperature dependence in the cooling stage, whereas the rest indicate temperature dependence in the heating stage. Based on the experimental results, a schematic of the temperature dependence of total resistance of CBG coated intrinsic silicon in the heating and cooling stages is provided in Figure 1d. It is seen that with the increase of temperature, the total resistance of the CBG coated silicon decreases slowly at low temperatures (from room temperature of ~22 ℃ to 𝑇𝐵), and then experiences a sharp fall until the current limiting mechanism is triggered at temperatures ranging from 𝑇𝐶 to 𝑇𝐷, followed by stabilizing at a specific value (precisely, with inconspicuously linear dips). In order to determine the temperature dependence of resistance for CBG coated intrinsic silicon in the cooling stage, the power supply is turned off as soon as the temperature reaches 𝑇𝐸. Indeed, the resistance finally drops back to

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its initial value at room temperature. However, the resistance returns along a path (blue curve) distinct from the original path (red curve) as the temperature drops. This unusual property of CBG coated intrinsic silicon deserves further investigation, as a better understanding of the electrical and thermal properties of the heating elements is necessary for the optimization of the heating strategy for the CBGbased Joule heating system.

Figure 1. (a) Configuration of CBG-based Joule heating system. (b) Schematic of the current flow inside CBG coated silicon wafer at low and high temperatures. (c) Temperature dependence of resistance for CBG coated intrinsic silicon under various initial input voltages, which was determined by conducting heating experiments in a vacuum chamber with a vacuum pressure of 5 Pa. The resistance in cooling stage (see black curve) was automatically measured by a high-precision ohmmeter. (d) Schematic of temperature dependence of total resistance of CBG coated intrinsic silicon in heating and cooling stages.

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3. Design and development of CBG-assisted micro hot embossing tool The procedures for the development of the micro hot embossing tool using the CBG-based Joule heating system are shown in Figure 2. Firstly, the microstructures were fabricated on the bare intrinsic silicon wafer by using single point diamond turning (SPDT). The machined silicon mold insert was then placed in a chemical vapor deposition (CVD) device for growing the CBG networks. Finally, the CBG coated silicon mold insert was assembled in a micro hot embossing device for implementing heating and molding.

Figure 2. Schematic of development of micro hot embossing tool using CBG-based Joule heating. (a) Bare intrinsic silicon wafer and optical microscopy (OM) image of a specific area on its surface. (b) Silicon mold insert and OM image of the machined microstructures on its surface. (c) CBG coated silicon mold insert and OM image of CBG coating on the cavities. (d) Tailor-made micro hot embossing device and the CBG-based heating tool.

3.1 Micro-structuring of silicon mold insert The selection of the mold material is essential for achievement of the desired deformation of glass blanks in the micro hot embossing processes. Basically, the selected mold materials must withstand extremely harsh conditions, such as ultrahigh temperature, repeated mechanical loading and oxidation. In addition,

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suitable mold materials are supposed to allow the microstructures to be readily processed on their surfaces. The commonly used mold materials are ceramics (e.g., tungsten carbide, fused silica [28] and glassy carbon [31]) or metals (e.g., nickel and hardened steel). However, monocrystalline silicon exhibits better machinability and an extremely fine finished surface, as compared with ceramic materials, and shows relatively lower thermal expansion coefficient than that of most metallic materials. Besides, the intrinsic silicon substrate is a key component for the CBG-based Joule heating system, due to its unusual electrical properties. Furthermore, compared with other substrates such as ceramic crucibles, glass fibers, quartz, silicon wafers, TiO2/SiO2 treated steel, nickel, Al2O3, etc., the CBG coating on the silicon substrate has fairly low surface roughness and friction coefficient [29]. Hence, single crystal silicon was finally employed as the mold insert material for hot embossing of optical glass in this study.

Microstructures on the silicon mold can be obtained by electrochemical wet stamping [32], metal-assisted chemical etching [33,34], laser-assisted micromachining [35], and SPDT [36– 38], among which SPDT is a robust and reliable approach for the surface micro-structuring of silicon, with high geometric freedom, low surface roughness and few chemical or physical hazards. Therefore, SPDT was adopted to fabricate the MLA features on the (111) crystal face of a monocrystalline silicon wafer for hot embossing. As shown in Figure 3, the fabrication process started from the design of the surface geometry of MLA for the single-crystal silicon stamper. For a typical gapless rectangular plano-concave MLA on the mold insert, the thickness of silicon workpiece was 1 mm, the width and length of MLA features were 3 mm and 3 mm respectively, the curvature

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radius and dimple depth of a single lenslet 0.5 mm and 1.8 μm respectively, and the pitch between neighboring lenslets 60 μm. These feature sizes of MLA were designed with reference to the specifications of commercial lenses. The designed surface geometry of the MLA was then inputted into the computer-aided manufacturing (CAM) system, and sag data information was used to check the accuracy of the surface. Based on the workpiece material and surface geometry, analysis was performed to determine the optimum tool radius, the required sweep on the tool and the minimum required tool clearances. Once the analysis was completed, a tool path was generated by taking account of the tool radii, rake angles and the tool orientations.

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Figure 3. Process chain for fabrication of plano-concave MLAs on silicon mold insert.

Normally, cutting brittle materials like single crystal silicon will cause severe wear of the diamond tool and fractures on the machined surfaces [39,40]. To mitigate such damage, the cutting thickness in our tool path planning approach was set to be about 100 nm, where single crystal silicon undergoes plastic deformation [41]. During the work, the spindle of the diamond turning machine was not rotated, while the diamond tool was able to move along three axes. In this case, the dimple surface of MLA was generated by ductile broaching layer by layer using the nose edge of the diamond tool, instead of enveloping through multiple tool paths. Further, the diamond cutter was specially selected to have a nose radius that almost equaled the curvature radius of the designed dimple surfaces. Therefore, the machined surface profiles perpendicular to the cutting direction were highly sensitive to the instantaneous cutter contact line (CCL) between the nose edge and workpiece. However, as the tool nose radius and feed rate no longer affect the kinematic surface roughness of machined surface, the obtained MLA on silicon substrate normally shows an extremely high surface finish.

Besides, it is known

that an excessive Z-axis acceleration induced at the sharp-edge boundaries among the lenslets in the continuous slow tool servo (STS) cutting mode may introduce dynamic errors to the machine tool [38]. Therefore, a segment STS cutting method was adopted, which required the lenslets in one row to be machined in two steps. The planned tool path was post-processed in order to generate numerical control codes for the SPDT which was subsequently performed on a computer numerical control (CNC) ultra-precision lathe (Moore Nanotech 350FG), with the

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machining parameters listed in Table 1. Table 1. Machining conditions for diamond turning of MLAs on single-crystal silicon. Machining parameters Depth of cut t0 (𝜇𝑚) Spindle rotation rate C (rpm) Feed rate f (𝜇𝑚/𝑟𝑒𝑣) Cutting speed V𝑐 (mm/s) Cutting atmosphere Tool material Nose radius (mm) Cutting tool Rake angle (°) Relief angle (°)

Values 0.1 0 60 45 (rough cut); 10 (finish cut) Compressed air coolant Single-crystal diamond 0.5 -25 10

In SPDT, errors always exist, due to tool decentering, tool wear, machine-tool vibration [42] and recovery of the residual stress during cutting. Especially, the surface integrity of the MLA using the tool path planning method proposed in this article is extremely sensitive to the tool wear. Therefore, it is technically impossible to obtain absolutely perfect surfaces by SPDT. The quality of a diamond turned surface can be inspected by either stylus type instruments or optical interferometric instruments. Stylus instruments suffer from unbearably long measurement time when conducting areal surface topography, and the measured surface may be damaged by scratches induced by the conispherical diamond tips. Hence, the Zygo Nexview 3D optical surface profiler was preferentially employed to conduct non-contact surface measurements of the silicon mold inserts. In practice, the silicon mold inserts possessing adequate surface quality would be directly passed to the subsequent coating process; otherwise, one or multiple compensation processes would be required to keep the surface finish and form accuracy at an acceptable level. In the compensation process, the difference between the measured surface profile and the designed surface profile was calculated for the generation of modified profile

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data for re-planning of the tool path positions [43].

3.2 Chemical vapor deposition of CBG coating Mold-glass adhesion is a serious problem in the hot embossing of optical glass, especially when silicon is selected as the mold material, since chemical bonds are readily formed between the silicon mold and glass blank at elevated temperature. In this study, an isolated layer of CBG film is deposited on the silicon mold insert for suppressing the glass adhesion formation as well as enhancing the tribological properties for the silicon mold insert. The deposition of the CBG coating on the silicon mold insert was realized by using CVD, with procedures referring to a previous patent [44]. Considering the complexity of preparation of GP-SO3H nanopapers [45], acetylene was selected as the main carbon source instead. The silicon source was still solid polydimethylsiloxane (PDMS) with a purity of 99.8%. Prior to the coating process, the silicon mold insert and PDMS were placed in a quartz tube furnace with a diameter of 5.08 cm (2’’) and a length of 0.6 m, as seen in Figures 4a and 4b. A typical process for deposition of CBG coating on silicon mold insert is provided in Figure 4c. The air in the tube was first evacuated by a vacuum pump and then purged by inert Argon gas at a flow rate of 1000 SCCM for 10 minutes, followed by decreasing the flow rate to 530 SCCM. After that, the temperature of quartz tube was heated up at a rate of 20 ℃/min. As soon as the temperature reached the suitable coating temperature of 950 ℃, acetylene was introduced at 50 SCCM, together with the inert gas flow. The tube temperature was held at 950 ℃ for 50 minutes, and then cooled down to the room temperature. Finally, the treated silicon wafer was taken out from the quartz

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tube, and washed with water and acetone for the removal of any ash on the surface, followed by being dried in a vacuum oven at 100 ℃ for 12 hours.

Figure 4. (a) Setup, (b) device and (c) process for deposition of CBG coating on silicon mold insert.

The bonding structure of the deposited carbon film was determined by a combined analysis of X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy. From the overall XPS survey spectrum in Figure 5a, carbon, oxygen and silicon were three main elements in the CBG coating, with atomic concentrations of 73.48%, 20.89% and 5.62% respectively. Figure 5b shows the C1s spectrum, in which the C=C and C-C bonds are located at 284.4 eV and 284.8 eV respectively. In this case, the sp2/sp3 ratio is estimated to be 1.4, indicating that the CBG coating is mainly composed of sp2 carbon sites. Moreover, the C-Si bond appears at a binding energy of 283.7 eV, and the C-Si-O bond is at 285.5 eV. The weak peak near 286.7 eV is

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assigned to the C-O bond, which implies that the surface of the CBG coating is slightly oxidized due to exposure to the air. A far left peak appearing at 288.3 eV is assigned to the C-O-Si-O-C bond. From the Si2p spectrum in Figure 5c, the binding energies of C-Si, C-Si-O and C-O-SiO-C bonds are located at 103.0 eV, 103.6 eV and 104.3 eV respectively.

Raman spectroscopy is widely used to distinguish ordered and disordered carbon structures because of its ability to distinguish between different bonding types and domain sizes [46]. Usually, the Raman spectra of amorphous carbon films are characterized by a D peak centered around 1360 cm-1 and a G peak in the range between 1500 to 1630 cm-1. The D peak is attributed to the breathing mode of the sp2 atoms in the rings or to some sp3 carbon atom matrices, and this mode only becomes active in the presence of disorder. Whereas, the G peak is due to the bond stretching of all pairs of sp2 atoms in both the rings and chains. The Raman spectrum of the CBG coating on the silicon, which was collected by using a 488-nm laser, exhibits a D peak at around 1377 cm-1 and a G peak near 1594 cm-1, as shown in Figure 5d. The area ratio of D and G bands (𝐴𝐷 𝐴𝐺) is roughly 1.92, and the full width at half maximum (FWHM) of G peak is about 105.76 cm-1. The significantly high position of G peak, relatively high 𝐴𝐷 𝐴𝐺 and notably low FWHM of G peak imply that the CBG coating is dominated by the sp2 content. Therefore, the result of Raman spectroscopy confirms that of XPS analysis. As suggested by previous studies [47,48], the carbon films dominated by sp2 sites exhibit low internal stress, high load bearing capacity and excellent tribological properties. Furthermore, the existing sp3 sites give rise to the high toughness in the CBG coating. Consequently, the CBG film is a

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suitable protective coating for improving the embossing performance and prolonging the lifetime of the silicon mold inserts.

Figure 5. (a) Overall XPS survey spectrum, (b) C1s spectrum, (c) Si2p spectrum and (d) Raman spectrum of CBG coating on silicon mold insert.

3.3 Assembly of micro hot embossing tool The tailor-made micro hot embossing device consists of a vacuum chamber, a marble stand, a Z shaft driven by a step motor, as shown in Figure 6a. The vacuum pressure is monitored by a vacuum gauge, and can reach as low as 5 Pa. Figure 6b illustrates the configurations inside the vacuum chamber, where the CBG coated silicon stamper is mounted on the upper mold holder which is movable along the Z axis. Highly elastic silicone rubber is sandwiched between the lower mold holder and pedestal, in order to compensate for some non-parallelism between the

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bottom face of mold insert and the top face of the glass wafer. The force sensor was placed outside chamber for eliminating impacts from the high temperature. Moreover, a piece of lowemissivity tin foil paper was attached to the inner wall of the vacuum chamber for the reduction of heat loss, though it was not shown in the figure.

Based on our previous work [30], higher input voltages result in higher heating rates of CBGcoated silicon wafer in the initial state. Moreover, the resistance of CBG-coated silicon wafer after the excitation temperature is roughly stabilized, and the stabilized resistance is closely related to the current limiting threshold. That is to say, the maximum input power at elevated temperature is strongly dependent on the rated current of the power supply. Therefore, the CBGbased Joule heating system is equipped with a regulated power supply with high rated voltage and current of 100 V and 30 A for maintaining desirable heating performance for glass hot embossing.

From the assembly of the modified CBG-based Joule heating system in Figure 6c, the underlying fused silica is used to separate the conductive CBG coated silicon mold insert from the metallic mold holder. Two soft copper ribbons, shown in the inset at the right top corner, serve as electrodes. A fixation system is specially developed to clamp the electrodes and the CBG-coated mold insert together on the mold holder, as seen in Figure 6d. The preloaded clamping force on the cover plate can be adjusted by screwing the nuts. The flexibility of copper ribbons, combined with the optimization of the clamping force, can ensure a good contact

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between the electrodes and CBG coating, and prevent the breakage of brittle mold insert due to thermal expansion.

Figure 6. (a) Assembly of the tailor-made micro hot embossing device. (b) 3D model of the configuration inside the vacuum chamber. (c) Assembly of the modified CBG-based Joule heating tool. (d) Fixation configuration for the CBG coated mold insert.

4. Materials and methods 4.1 Glass preform and mold insert The crown glass, P-SK57, exhibits excellent optical properties, such as high transmittance, desirable refractive index and low index-dispersion. Besides, it has relatively low values of glass transition and softening points (𝑇𝑔 = 493 ℃ and 𝑇𝑠 = 593 ℃ respectively) in the optical glass genre, which is especially designed for precision molding. Therefore, P-SK57

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glass was selected as the preform material in the micro hot embossing experiment. The material properties of P-SK57 glass, such as thermal expansion coefficient, specific heat [49], viscoelastic thermorheological simple (TRS) behavior [50], glass-to-mold sticking force [51] and refractive index drop [52] have been intensively investigated by previous studies. The PSK57 glass balls purchased from Schott Corporation were shaped into glass wafers by employing a commercial Toshiba glass molding machine (GMP-311). The resulting glass wafers used for hot embossing had a thickness of ~1.975 mm, a diameter of ~13.25 mm and a low Sq value of ~5 nm.

Figure 7. (a) Dimensions of CBG coated silicon stamper used for micro hot embossing experiment. (b) Cross-sectional view of CBG coated silicon mold insert under SEM. (c) SEM image of a typical 3×5 MLA on bare silicon mold insert, and the 3×3 MLA (framed by a red square) which has been measured in advance of the deposition of CBG coating. (d) Surface defects on the CBG coated silicon mold insert.

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The CBG coated silicon mold insert (see Figure 7a) can serve not only as an effective heating element but also a stamper for embossing. The stamper had a width of 20 mm, a length of 30 mm, a substrate thickness of 1 mm and a coating thickness of ~60 nm, which was determined from the SEM image of its cross-section (see Figure 7b). In a typical 3×5 MLA on a bare silicon mold insert (See Figure 7c), only the 3×3 MLA which is framed by a red square has been measured in the 3D optical surface profiler in advance of the deposition of the CBG coating. From the SEM image in Figure 7d, there are two main types of surface flaws (i.e., microfractures and ridges) existing on the micro-structured surface of the CBG coated silicon mold insert. The microfractures which consist of numerous tiny cracks were caused by brittle mode cutting when the instantaneous cutting depth was in excess of the critical cutting thickness of single-crystal silicon [40], while the ridges were generated due to the presence of the fracture wear on the cutting edge of the diamond tool.

4.2 CBG-assisted glass hot embossing process The CBG-assisted hot embossing process includes five stages, namely presetting, heating, embossing, cooling and demolding, as shown in Figure 9. Initially, the pre-shaped P-SK57 glass wafer after cleaning treatment is carefully placed on a copper cylinder inside the hot embossing device, as seen in Figure 8a. The upper mold insert is moved downward, leaving a gap of about 2 mm for avoiding contact with the glass wafer. The small gap enables the upper surface of glass wafer to be radiatively heated during the heating stage, so that the temperature difference between the mold insert surface and glass wafer surface can be somewhat minimized before the

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embossing step. Since the embossing temperature of optical glass is higher than 550 ℃, it is necessary to apply a vacuum to the chamber for the removal of air, thus protecting the mold from oxidization at such elevated temperatures. Nitrogen is introduced afterwards for further purging the system, followed by applying the vacuum again.

Figure 8. (a) Setup of micro hot embossing experiment. (b) The CBG coated silicon mold insert of heating state. (c) Embossed optical glass replica with desired MLA features.

In the next stage, a direct current is applied to both ends of the CBG coating for electric heating. As the resistance of CBG coated silicon is relatively high at room temperature, a fairly high voltage of 100 V is supplied for initiating the Joule heating system. When the surface temperature of the CBG coated silicon reaches the excitation point, where the resistance decrease exponentially [30], a power-control heating strategy is adopted for the adjustment of temperature. Although the heat loss increases significantly at high temperature, a steady high heating rate of 2.25 ℃/s is remained. When the upper mold temperature reaches 565 ℃, the embossing stage is started by directly moving the upper mold into contact with the glass blank. After that, a constant force is applied to the glass blank by feedback control of the position speed and direction. At this temperature range, the glass blank is viscoelastic and is readily deformed, so that it is able to fully fill the cavity of the mold insert by holding the upper mold

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in place for a few seconds.

In the cooling stage, a low initial cooling rate needs to be set to minimize the thermal stress of glass replica. However, due to the consideration of potential impact of the electric field on the surface quality of the thermally ionized glass replica at elevated temperature, the power supply, in practice, is immediately turned off after the embossing point, that is, there is no annealing treatment. At relatively low temperature (~210 ℃), the upper mold is moved upward for demolding, and the nitrogen is introduced for faster cooling. The molded glass lens is taken out for quality assessment when the temperature is lower than 60 ℃.

By reviewing relevant studies [53–57] and conducting a series of tentative experiments, appropriate parameters were assigned to the glass hot embossing process, as listed in Table 2. In the embossing experiments, the surface temperature of the CBG coating was measured by a K-type thermocouple directly attached to the CBG film (see Figure 6c). Another K-type thermocouple was used to monitor the temperature variation of the upper mold holder. The input voltage and current signals as well as temperature signals were recorded in a multichannel data acquisition device (Graphtec midi logger GL240). In addition, the pressing force was determined by a force sensor located on the Z shaft outside the vacuum chamber. Table 2. Critical parameters for hot embossing experiment Parameters Stamper material Preform material Mold insert feature Embossing temperature (℃) Embossing pressure (Pa)

Values CBG coated silicon mold insert P-SK57 glass wafer Rectangular, plano-concave MLA ~565 ~4.35 × 104

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Holding time (s) Cooling rate when annealing (℃ 𝑠) Demolding temperature (℃) Embossing cycle time (s) Energy consumption per cycle (J)

~1 Naturally cooling in vacuum ~210 ~600 ~12076

Figure 8b illustrates the CBG coated silicon mold insert being heated at an elevated temperature of more than 500 ℃. Microstructures were successfully imprinted on the surface of P-SK57 glass wafer, as seen in Figure 8c. The glass hot embossing process has been recorded by a video (see Visualization 1), and the histories of the experimental parameters (i.e., force, temperature, resistance and power) are plotted in Figure 9. Particularly, the resistance was derived from the input voltage divided by current, while the power was calculated by multiplying the voltage by the current. The continuously decrease of packing force during the period between the embossing point and the demolding point can be ascribed to the stress relaxation of glass. It is noted that the temperature of the upper mold holder was always less than 80 ℃, though the surface temperature of the CBG coating was nearly 565 ℃. This can prevent the tool from the negative impacts exerted by the uneven distribution of the thermal stress during the hot embossing process. Furthermore, the high efficiency of CBG-assisted localized rapid hot embossing was experimentally corroborated. Only 10 minutes were needed to complete one mold cycle, and the energy consumption was fairly low, of ~12076 J, which was simply determined by the integral of power with respect to time.

- 24 -

Figure 9. Histories of experimental parameters during micro hot embossing process.

5. Results and discussions 5.1 Evolution of MLA surfaces at different processing stages The measured surface of MLA on the embossed glass replica is presumed to be always distinct from its design surface due to the existence of form error, which is composed of machining error of the bare mold insert, error induced by the non-uniform thickness of the mold coating, embossing error as well as measurement error. Therefore, the form characterization of a particular 3×3 MLA feature (see Figure 7c) was carried out from the bare silicon mold insert to the embossed glass replica, so that the form errors induced by different surface treatments can be evaluated. A standard iterative closest point (ICP) matching algorithm [58] was used for the registration of two distinct surfaces, which is a necessary prerequisite to the form error

- 25 -

evaluation of discretely structured surfaces like MLA.

The design surface of the 3×3 MLA in Figure 10a was simulated by MATLAB software, with individual lenslets denoted as L𝑚𝑛, where m=1, 2, 3 and n=3, 4, 5. Figures 10b-10d illustrate the measured surfaces of MLA on the bare mold insert, coated mold insert and embossed glass replica respectively. These measured surface data were acquired from Zygo Nexview 3D optical surface profiler. The surface topography of the bare silicon wafer (see Figure 10e) implies an ultra-fine surface finish of the silicon workpiece. By subtracting the measured surface of the bare mold insert from the design surface after fine ICP registration, the areal error map representing the machining error of the bare silicon mold insert is visualized in Figure 10f. The areal error maps in Figures 10g and 10h, which can indicate the coating induced error and embossing error respectively, are obtained in a similar way. The mean deviations from corresponding ideal geometrical surfaces were also calculated for MLA surfaces on the CBG coated silicon mold insert and embossed glass replica, and are plotted in Figures 10i and 10j.

Height parameters, especially the parameters 𝑆𝑎 (arithmetic average (AA) value), 𝑆𝑞 (rootmean-square (RMS) value) and 𝑆𝑧 (maximum peak-to-valley (PV) value) are widely used for the characterization of form errors of freeform surfaces. These three parameters are defined as Sa  Sq 

1 z  x, y  dxdy A  A 1 z 2  x, y  dxdy A  A

(1)

S z  S P  SV  max z  x, y   min z  x, y  A

A

- 26 -

where SP and SV are maximum peak height and maximum valley height respectively, A the measured surface area, and z(x,y) the ordinate values. The three parameters for each areal error map in Figures 10f-j were calculated on the basis of Equation 1, and are given in the topleft corner of the error maps. It is noted that the PV values of all areal error maps are considerably high. This is due to the outliers generated in certain regions of measured surfaces where pits and micro-fractures are located.

In Figure 10f, the AA and RMS values are 63.2 nm and 87.3 nm respectively, both of which are modestly low. Furthermore, for the sub-regional 2×2 MLA which is composed of lenses L14, L15, L24 and L25, the RMS error is calculated to be approximately 30 nm after ICP registration with the design surface. Such a low machining error is benefitted from the tool path planning algorithm. In the situation where the chuck is non-rotational, and the surfaces of MLA are generated by a STS broaching, the surface roughness formation is unlikely to be caused by the spindle rotation speed and the tool feed rate. Instead, the factors that can influence the surface generation of a diamond turned silicon mold insert include the surface flaws brought in by improper operations, the surface inhomogeneity of the workpiece, incorrect assembly of workpiece and vacuum chuck, geometric errors and irregularities of tool tips, dynamic errors of SPDT machine and surface recovery of machined surface. The effect of the above-mentioned causes on the machined surface can be determined by using a multi-spectrum analysis [59] of the primary surface profiles of individual lenslets. Form characterization of MLAs on bare mold insert can be seen in Section 2 in supplementary information.

- 27 -

Figure 10. Form characterization of the 3×3 MLA. (a) Design surface. Measured surfaces on

- 28 -

(b) bare silicon mold insert, (c) CBG-coated silicon mold insert and (d) embossed glass replica. (e) Surface topography of the bare silicon wafer, which shows a sub-nanometer surface finish. Areal error maps which represent the differences between (f) the measured surface of bare mold insert and design surface, (g) the measured surfaces on coated mold insert and bare mold insert, (h) the normalized surfaces on embossed replica and coated mold insert, (i) the measured surface on coated mold insert and design surface, and (j) the normalized surface on embossed replica and design surface.

The areal error map in Figure 10g is obtained by subtracting the bare mold surface from coated mold surface. The calculated AA and RMS values are extremely low, at 4.5 nm and 6.7 nm respectively. Although the dinky deviation between two surfaces cannot directly demonstrate the uniform thickness of the CBG coating on the silicon mold insert, it is sufficient to indicate that the MLA shape is insensitive to the CBG coating treatment. The insensitivity of the surface roughness of silicon wafer to the CBG coating has also been demonstrated in our previous study [30]. These insensitivities can account for the similarity in textures of the primary surfaces for the bare mold insert (see Figure 10f) and CBG coated mold insert (see Figure 10i).

Figure 10h indicates the deviation between the normalized surfaces of the embossed replica and the coated mold insert. The considerably low AA and RMS values demonstrate the fine replication fidelity of the MLA features produced by using the CBG-assisted hot embossing technique, which will be discussed in detail in the next section. A bunch of peaks occurring in

- 29 -

lenslets L33 and L34 correspond to the micro bubbles, which are easily formed at the edges of the glass replica samples during hot embossing. Due to the higher thermal expansion coefficient of the optical glass than that of CBG coated silicon, the form shrinkage is larger for the glass replica in the cooling process; thus the deviation values are mostly positive. By registration of the normalized surface of the embossed replica and the design surface, the areal error map is obtained, as seen in Figure 10j. Due to the formation of micro bubbles on the embossed replica, its PV value is relatively higher than that in Figure 10i. However, its AA and RMS values are comparably lower, which means that the embossed replica has a higher form accuracy than that of the coated mold insert. A possible explanation is that the feature sizes of the coated mold surface are higher than those of the design surface, and the form error of the coated mold insert is thus partially compensated by the form shrinkage of the embossed replica during surface transferring.

5.2 Form evaluation of embossed glass MLAs To successfully realize specific functions (e.g., homogenizing the light emitters and enhancing the light collection efficiency), the PV form error for a typical microlens is required to be less than λ/4, where λ is the wavelength of incident light (in default conditions, λ=546.07 nm). Therefore, the acceptable PV error or irregularity of lenslets is below 136 nm. In addition, the total integrated scattering (TIS) of an optical surface is mostly dependent on the RMS surface roughness, which is described by

 4 S q  TIS      

2

(2)

- 30 -

Therefore, the surface roughness 𝑆𝑞 for single lenslet needs to be controlled at < 9.7 nm, in order to minimize the optical scattering to an acceptable level of 5% for most optical systems.

Form characterization was conducted for a 3×6 MLA situated in the central region, where the best surface integrity occurs. Figures 11a and 11b are surface topographies of the 3×6 MLA features on coated mold insert and glass replica respectively. By subtracting the surface of glass replica from the normalized surface of mold insert, the deviation map is obtained (see Figure 11c), with the mean deviation being fairly low, about 8.89 nm. Figure 11d suggests that the mean deviation for a single lenslet can be even lower and reach 2.1 nm. This low deviation is attributed to the concentration of heat on the target area of the glass blank, the less thermal variation and the enhanced tribological properties of the mold insert. It is evident from Figures 14c and 14d that most lenslets have satisfied the minimum requirements of form accuracy and surface finish, indicating the desired surface integrity of embossed MLA. However, a few lenslets failed to meet the surface finish requirement, which is attributed to the poor surface quality of mold insert or the surface defects introduced during hot embossing.

- 31 -

Figure 11. Areal surface measurements of 3×6 MLA on (a) coated mold insert and (b) embossed glass replica. Both surface topographies of MLAs on mold insert and glass replica have been processed by removal of tilt and fixing the minimum value to zero. (c) Deviation between measured surfaces of mold insert and measured surface of glass replica after normalization. (d) Deviation map of a single lenslet L13.

Further form characterization was implemented for glass lenslet L13, which had a surface topography as shown in Figure 12a. The extracted surface profile data at four equally spaced radial sections are compared in Figure 12b. These profiles appear to be quite identical to each other, demonstrating the excellent axial symmetry of the embossed glass microlens.

- 32 -

Figure 12. Form characterization of lenslet L13. (a) Raw measured surface. (b) Surface profiles at four equally spaced radial sections.

5.3 Replication fidelity of embossed micro features Micro hot embossing is a widespread replication technology that allows the micro features to be manufactured on optical glass by reproducing the surface geometry of mold insert, in the presence of heat and external pressure [60]. In order to quantify the replication fidelity of the CBG assisted embossing process, the AA value for the deviation of surface profiles between MLA features on the glass replica and mold insert (δAA), transfer ratio of curvature radius (TRRc), transfer ratio of surface modulation depth (TRh), transfer ratio of PV form error (TRPV) and transfer ratio of RMS surface roughness (TRRMS) [61] for single lenslet were introduced. Typically, the AA profile deviation, curvature radius transfer ratio and surface modulation depth transfer ratio are employed to assess the replication capability at the micro scale, while the PV transfer ratio and RMS transfer ratios indicate the replication capability at the nanoscale.

- 33 -

Figure 13. Comparison between three line scans of the 3×6 MLA on CBG coated silicon mold insert and optical glass replica. The surface profiles have been normalized.

The deviation map in Figure 11c indeed provides a picture of the departure of the embossed surface from the surface of the mold insert. To be more intuitive, three line scans of MLA surface in different rows on the stamper and embossed features are compared in Figure 13, and the differences between two surface profiles at various line scans are also plotted. Normally, the difference is linearly associated with the height of the mold. However, due to the surface shrinkage of the embossed replica, larger differences seem to not occur on positions with larger heights. The AA profile deviation is described by

 AA 

1 n replica mold  za  za n a 1

(3)

- 34 -

where zreplica is the ath sampling height of glass replica, and zmold is the ath inversely a a normalized height of mold insert. δAA, 1, δAA,

2

and δAA,

3

representing AA profile deviation

at row 1, row 2 and row 3 are calculated to be 11.1 nm, 7.3 nm and 7.4 nm respectively. Hence, the average AA profile deviation is determined to be 8.6 nm, revealing that a fairly low form error is introduced during this CBG-assisted hot embossing. It is noted that the AA profile deviation in the first row is higher than that in the other two rows, which can be attributed to the higher average height of the former profile. Interestingly, the deviation profile in each row resembles the cross-sectional profile of a Fresnel lens, because of the replica surface shrinkage.

The transfer ratios of the curvature radius, surface modulation depth, PV form error and RMS surface roughness for single lenslet are simply defined as

| Rcreplica  Rcmold | TRRc  1  Rcmold | h replica  h mold | TRh  1  h mold | S replica  S mold | TRPV  1  z mold z Sz TRRMS  1 

(4)

| S qreplica  S qmold | S qmold

where Rc, h, Sz and Sq are the curvature radius, surface modulation depth, PV form error and RMS surface roughness for single lenslets respectively, and the superscript (i.e., replica or mold) indicates the location of the measured single lenslet features.

- 35 -

Figure 14. Transfer ratios of (a) curvature radius, (b) surface modulation depth, (c) PV form error and (d) RMS surface roughness for single lenslets. The statistics in the yellow area (see Figure 15) outside the circular aperture of microlens are ignored when calculating the surface modulation depths, curvature radii, PV form errors and RMS surface roughness. Four repeated measurements of the same MLA were conducted for obtaining the mean value and error bars.

From Figures 14a and 14b, the transfer ratios of curvature radius and surface modulation depth are above 98.8%, indicating the remarkably excellent replication capability of the proposed hot

- 36 -

embossing technique at the micro scale. It is also noted that the lenslets on glass replica usually have larger curvature radii but lower surface modulation depths, compared with those on the mold insert. This is result from that the shrinkage of glass preform is higher than that of CBGcoated silicon mold insert during the cooling stage.

By removing the best-fitted spherical form of the lenslet features, the PV values and RMS surface roughness were determined. Figures 14c and 14d compare the resulting PV and RMS values of lenslet features on the mold insert and glass replica, and plot the corresponding PV and RMS transfer ratios. As the PV value of the glass lenslets is sensitive to the defects induced during hot embossing, occasionally the calculated PV transfer ratios are relatively low. However, the RMS transfer ratios are usually higher than 0.85 (see Figure 14d). Compared with the mold insert, the embossed glass lenslets sometimes have a higher surface finish, resulting from the incomplete filling of the surface defects (e.g., pits, cracks and ridges) on the mold insert. Besides, it is evident from Figure 15 that the roughness information (i.e., roughness textures) of the lenslets on glass replica is almost identical to that on the mold insert. More comparative results can be found in Figures S3 in supplementary information, which validates the capability of CBG-assisted micro hot embossing technique for achieving fine replication at the nanoscale. Therefore, fabrication of the mold inserts with considerably high surface integrity is critical to the successful embossing of high-quality MLAs.

- 37 -

Figure 15. Comparison of the roughness information of lenslets on mold insert and glass replica. The surface roughness maps are extracted by subtracting the best-fit surfaces from the normalized surfaces of single lenslets on mold insert or glass replica. The heights of yellow areas outside the circular aperture of microlens are set to be zero, and the yellow areas are ignored when calculating the roughness parameters.

5.4 Residual stress in the embossed glass replica Satisfying the geometric requirements is insufficient to ensure that the embossed glass optical component functions well. Optical properties of the embossed glass replica also need to be measured. For example, the residual stress inside the glass lens can result in refractive index variation, light path deviation, light intensity change and even structural distortion. Therefore, the amount of the internal residual stress is a significant criterion for evaluating the imaging quality of glass optical components. The thermally induced residual stress inside the embossed glass replica was visualized by the use of plane polarized white light (Strainoptics PS-100-SF

- 38 -

Polarimeter), together with the raw glass ball and glass wafer pre-shaped by GMP311, as seen in Figure 16. The photoelastic stress measurement results show that an unsatisfactory residual stress exists inside the glass replica, which can be ascribed to the lack of an annealing stage in the hot embossing process. However, the residual stress can be easily eliminated by annealing post-treatment. Considering that the additional annealing treatment may alter the form of MLA features on glass replica, the surface topographies of a 3×6 MLA features before and after annealing treatment are compared. We find that the annealing treatment has negligible effects on the form accuracy of the embossed surface, though the surface topography is altered slightly (see Figure S5 in supplementary information).

Figure 16. Comparison of different components under polarized white light. (a: raw glass ball, b: glass wafer pre-shaped by GMP311, c: hot embossed glass replica before annealing treatment and d: hot embossed glass replica after annealing treatment.)

In practice, the cycle time of thermal annealing treatment can be reduced to less than 10 minutes by using high-performance heating vacuum chambers and implementing process optimization. Moreover, usually more than 10 pieces of embossed glass replicas can be treated together in

- 39 -

one batch. In this case, the exact time including the annealing step for fabricating a glass MLA is about 11 minutes. Hence, a high efficiency of the whole production process can be ensured. 5.5 Imaging test of the MLA replica The imaging quality of the embossed glass MLA was tested by using the Optikos QC Bench, as shown in Figure 17a, and the measurement arrangement is provided in Figure 17b. The spectral range of the fiber optic light source is from 400 nm to 900 nm. In order to mimic the practical use, no band-pass filter was added in the testing system. The diameter of the selected pinhole was 400 μm, which was modestly small. Consequently, high spatial frequencies in the image plane of the beam can be filtered. The spatially filtered white light beam was collimated and then passed through the glass MLA, forming spot array in its focal plane. An objective lens (×10) was added behind the glass MLA for magnifying the spot array. Finally, the magnified spot array was detected by the CCD camera (see Figure 17c). The uniformly bright circular shape of the spots demonstrates satisfactory imaging performance of the embossed glass MLA. Particularly, the 3×3 spot array framed by the yellow dotted square corresponds to the 3×3 MLA which has been discussed in Section 5.1. In this test, the effective front focal length of MLA was estimated to be 0.86 mm. In practice, the glass MLA can be compactly integrated with the CCD camera to form a Shark Hartmann sensor for wavefront measurement.

- 40 -

Figure 17. (a) Photograph of the Optikos QC Bench. (b) The measurement arrangement. (c) The magnified spot array captured by the charge-coupled device (CCD) camera. 5.6 Reproducibility of the hot embossing technique To suit the practical mass-produced applications, the proposed CBG-assisted hot embossing technique is required to have fine reproducibility. Figure 18 shows four glass replica samples that were produced under the same embossing conditions (see Table 2). In particular, samples 1 and 2 were subjected to the annealing post-treatment after hot embossing, while samples 3 and 4 were not. Several days later, cracks were formed spontaneously inside the latter two samples due to the concentration of residual stress. Hence, the importance of the annealing posttreatment of the glass replica needs to be underlined once again.

Table 3 compares the curvature radius, surface modulation depth and RMS surface roughness of microlenses in the first row of the 3×6 MLA on these four samples for evaluating the reproducibility of the proposed hot embossing technique. It is found that the mean deviation and standard deviation of curvature radius for these four samples are not in excess of 0.825 μm and 1.043 μm respectively, which are fairly small when comparing with the average value of

- 41 -

the curvature radius. Similarly, for surface modulation depth, both deviation parameters are less than 3 nm, roughly 0.35% of the average value. The insignificant deviations in the curvature radius and surface modulation depth of microlenses demonstrate the excellent reproducibility of the proposed hot embossing technique for replicating micrometer-sized features. Since the RMS surface roughness of microlenses is in the few nanometer range, its value is highly sensitive to the surface imperfections, such as tiny pits generated during hot embossing process. But still, for the RMS surface roughness, both the mean deviation and the standard deviation are well controlled at below 0.7 nm in the four trails. Such reproducibility of the RMS surface roughness is acceptable, as a slight change of RMS surface roughness can hardly affect the optical function of the glass microlenses.

Figure 18. Photographs of four glass replica samples that were hot embossed under the same conditions. The dissatisfactory transparency of sample 1 is attributed to the incompletely removal of gold coating which was used for the SEM observation.

Table 3. The curvature radius, surface modulation depth and RMS surface roughness of the selected microlenses on the four glass replica samples. Lenslet no.

Curvature radius (μm)

L11

L12

L13

L14

L15

L16

Sample 1 Sample 2

518.6 518.7

516.5 516.2

514.8 515.7

512.8 513.6

513.2 513.5

515.4 516.4

Sample 3

519.8

516.1

515.0

515.0

515.3

518.3

Sample 4

518.7

514.8

514.1

513.2

513.8

516.8

Average value

518.95

515.90

514.90

513.65

513.95

516.73

- 42 -

Mean deviation

0.425

0.550

0.450

0.675

0.675

0.825

Standard deviation

0.492

0.652

0.570

0.829

0.808

1.043

Sample 1

834.0

845.0

840.1

853.5

847.8

854.6

Sample 2

835.2

846.5

838.8

851.7

853.6

852.0

Surface

Sample 3

830.3

844.4

836.4

854.2

846.3

851.3

modulation

Sample 4

832.2

847.0

838.9

851.0

846.8

854.1

depth (nm)

Average value

832.93

845.73

838.55

852.60

848.63

853.00

Mean deviation

1.675

1.025

1.075

1.250

2.488

1.350

Standard deviation

1.854

1.062

1.343

1.298

2.923

1.384

Sample 1

10.64

8.566

6.268

6.118

6.425

7.233

Sample 2

10.71

8.984

6.943

6.636

6.952

9.134

Sample 3

10.84

8.528

6.426

6.060

6.784

8.488

Sample 4

10.82

8.746

6.601

6.025

6.446

8.389

Average value

10.753

8.706

6.560

6.210

6.652

8.311

Mean deviation

0.077

0.159

0.213

0.213

0.216

0.539

Standard deviation

0.082

0.180

0.251

0.248

0.224

0.685

RMS surface roughness (nm)

6. Conclusions This article introduces the development of a tailor-made hot embossing device, involving micro-patterning of single crystal silicon, CVD-grown of CBG coating and assembly of the whole machine. By studying the surface evolution at different processing stages, it is found that the form error of the final glass MLA mostly originates from the machining error of the silicon mold insert, whereas a few elements of the form error are contributed by the CVD coating treatment and hot embossing. The surface metrology results suggest that the proposed nonequilibrium hot embossing technique has the capability of fabricating high-quality MLA with a form error of ~50 nm and a RMS surface roughness of ~7 nm. In addition, this technique shows notably fine replication of surface shapes at the microscale, as well as roughness information at the nanoscale. The mean deviation between the surfaces of MLAs on the mold insert and glass replica is usually around 15 nm. This low deviation is attributed to the concentration of heat on the target area of the glass blank, the less thermal variation and the

- 43 -

enhanced tribological properties of the mold insert. However, due to the lack of a slow cooling stage in the experimental design, the thermally induced residual stress inside the embossed glass replica is high. Fortunately, this residual stress can be easily eliminated without perceptible alteration of the surface form by an annealing post-treatment, and the annealed glass MLA shows satisfactory imaging performance. Finally, the excellent reproducibility of the proposed hot embossing technique is well demonstrated. In the future, more efforts will be made to deeply investigate the underlying mechanism for the fine replication performance of the CBG-assisted hot embossing technique, further optimize the process and extend its application in the processing of other amorphous materials, such as polymers, infrared glass and metallic glass.

Acknowledgements The authors appreciate Prof. C.F. Cheung's suggestions on surface matching for form evaluation of microlens arrays. The silicon mold insert was machined by The State Key Laboratory of Ultraprecision Machining Technology, Hong Kong, China. The chemical vapor deposition of carbide-bonded graphene coating on silicon mold inserts was implemented by Nanomaterial Innovation LTD, USA. This work was supported by Innovation and Technology Commission of Hong Kong Special Administrative Region (GHP/043/14SZ) and the Research Committee of the Hong Kong Polytechnic University (RUWD).

Appendix A. Supplementary data Supporting information associated with this article can be found in the online version.

- 44 -

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Highlights 

CBG films can serve as not only a protective mold coating but also a heating element.



CBG-based Joule heating is employed to glass hot embossing for the first time.



The embossed glass microlens arrays show high surface integrity and replication fidelity.



The proposed hot embossing technique is energy-saving and has low thermal cycle time.



The surface evolution of a typical MLA at different processing stages were studied.

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Graphical abstract

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