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Article Theoretical and Experimental Study on Hot-Embossing of -Microprism Array without Online Cooling Process

Manfeng Hu 1,2, Jin Xie 2,*, Wei Li 1 and Yuanhang Niu 2 1 School of Mechatronic Engineering and Automation, Foshan University, Foshan 528225, China; [email protected] (M.H.); [email protected] (W.L.) 2 School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China; [email protected] * Correspondence: [email protected]; Tel.: +86-20-222-36-407

 Received: 2 October 2020; Accepted: 29 October 2020; Published: 31 October 2020 

Abstract: Optical glass-microprism arrays are generally embossed at high temperatures, so an online cooling process is needed to remove thermal stress, but this make the cycle long and its equipment expensive. Therefore, the hot-embossing of a glass-microprism array at a low strain rate with reasonable embossing parameters was studied, aiming at reducing thermal stress and realizing its rapid microforming without online cooling process. First, the flow-field, strain-rate, and deformation behavior of glass microforming were simulated. Then, the low-cost microforming control device was designed, and the silicon carbide (SiC) die-core microgroove array was microground by the grinding-wheel microtip. Lastly, the effect of the process parameters on forming rate was studied. Results showed that the appropriate embossing parameters led to a low strain rate; then, the trapezoidal glass-microprism array could be formed without an online cooling process. The standard deviation of the theoretical and experimental forming rates was only 7%, and forming rate increased with increasing embossing temperature, embossing force, and holding duration, but cracks and adhesion occurred at a high embossing temperature and embossing force. The highest experimental forming rate reached 66.56% with embossing temperature of 630 ◦C, embossing force of 0.335 N, and holding duration of 12 min.

Keywords: hot-embossing; microprism array; optical glass; numerical simulation

1. Introduction An optical glass- array has excellent micro-optical properties, and it is widely used in microfluidic chips [1], imaging [2], optical communication [3], solar-cell substrates [4], and other fields. For example, the glass microlens can be compactly integrated with a charge-coupled-device (CCD) to form a Shack –Hartmann sensor for measurement [5]. By employing a ¬ glass-microlens array integrated with subwavelength structures, the power-conversion efficiency of solar cell can be improved by 8.5% [6]. Refractive microlens arrays fabricated on the glass slide can reduce beam divergence and increase transmission [7]. Moreover, it was demonstrated that the glass can work in strong acid and high-temperature conditions in which other materials cannot be used [8]. Due to its high glass-transition temperature and brittle fracture, it is difficult to precisely process a glass microlens [9]. Glass microgrooves are fabricated by using ion etching [10], ultrafast laser pulses [11], and micromilling technology [12]. However, most are relatively expensive and time-consuming. Compared to these fabrication methods, hot embossing is a net-shape approach for fabricating fine and high-precision microstructures on a glass substrate [13].

Micromachines 2020, 11, 984; doi:10.3390/mi11110984 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 984 2 of 13

The dimensional accuracy of hot embossing depends on the precision of the die core [14], so research was carried out on core processing technology. Picosecond laser micromachining was used to fabricate a microcircular hole array on the steel die-core surface, but its machining accuracy was unknown [15]. The accuracy of the selective laser melting manufacturing of a metallic microstructured core was studied, but it had dimensional deviation [16]. Focused-ion-beam milling could produce high-surface-quality microstructures, but it had low processing efficiency [17]. Steel core micropits could also be prepared by chemical etching, but etching reagents easily pollute the environment [18]. Moreover, rectangular microchannels were milled on the aluminum tool surface, but it was easy to generate milling marks [19]. Microgrinding technology is an effective method for processing difficult-to-machine materials, but the effect of processing SiC die core has not been studied [20]. The hot embossing of glass microlens is challenging, so some related process studies were conducted [21,22]. The effect of the width of the die V-groove on the curvature and filled area of the molding glass microlens were investigated, but the influence of process parameters has not been studied [23]. The glass Fresnel was embossed with consideration of the process parameters, and indicated that the glass preform was easy to break under excessive molding force at low molding temperature [24]. Similarly, it was also revealed that the glass protrusion crack was generated at high imprinting pressure [25]. As a result, the crack affects the service life and performance of glass microstructures [26]. Therefore, it is necessary to optimize the process parameters. Generally, the hot-embossing glass-microlens cycle is long due to its long cooling time to eliminate thermal stress [27]. A hexagonal-microlens array was fabricated via a precise thermal–mechanical embossing process, but the time of the glass-embossing process reached 138 min with cooling time of 88 min [28]. Refractive lens and diffractive gratings were developed, but the total time of hot embossing lasted about 250 min, including the cooling time of 120 min [29]. However, online cooling reduces efficiency, and water-cooling devices make the high-precision ultrathin glass-molding-process apparatus complex and expensive [30]. Theoretically, the hot-embossing process of a microprism array under different mold temperature, pressure, and holding-time levels was simulated by DEFORM software [31]. Finite-element analysis was also designed to evaluate the deformation behavior during hot-embossing processes [32,33]. Stress evolution in the cooling process was also simulated through finite-element simulation [34]. However, most of them are about polymer-microforming simulation, and there are few studies on the analysis of flow behavior, deformation, and strain rate during the hot embossing of glass microlenses [35]. In this paper, a hot-embossing method with low strain rate is proposed to realize the fabrication of a glass microlens array at low cost without an online cooling process. First, flow-field distribution, strain-rate change, and material-deformation process in the microforming process were simulated. Then, the microforming control device of the hot-embossing glass microlens was designed, and the grinding-wheel microtip was applied to fabricate a microgroove array on the surface of the SiC die core. Lastly, the effect of the process parameters on forming rate was studied.

2. Numerical Simulation

2.1. Simulation Model of Hot Embossing of Glass-Microprism Array The simulation model of a hot-embossing glass-microprism array is shown in Figure1. The die core was sized as 1.5 0.4 0.25 mm, and its surface was covered by microgrooves with angle θv × × of 120◦ and height hv of 145 µm. The size of the glass substrate contacting with the microgroove was 1.5 0.25 0.25 mm. Both sides of the substrate were considered as symmetrical boundaries. × × The sparse solver was adopted, and the simulation time step length was set as 1 s. Moreover, preheating time and holding duration were given as 8 and 10 min, respectively. The sliding friction coefficient was regarded as 0.08. Simulation-environment temperature T, holding duration t, and Micromachines 2020, 11, x 3 of 12

During the hot embossing of a glass-microprism array, the relationship between plastic flow . stress σ , temperature T, strain ε , and strain rate ε is given in the following equation [36]:

. σεε= (1) f (,,T ) Because there was no heat source inside the material, the temperature change in the hot-embossing process satisfied the simplified heat-balance equation: ∂∂∂TT ρck= [] ∂∂ ∂ (2) txx, where c is specific heat; and ρ, T, and k are density, temperature, and heat conductivity, respectively [37]. Because the cross-section of the die-core microgroove was triangular, the cross-sectional area Micromachines 2020, 11, 984 3 of 13 of the microprism is given as S1; then, the forming rate during the forming process could be defined as embossing force F were set as 560–710 ◦C, 8–12η min,= and 0.335–0.835 N, respectively. DEFORM software 2/()Shd1 vv (3) was adopted to carry out simulation research.

Figure 1. SimulationSimulation model model of of hot-embossing hot-embossing glass-microprism glass-microprism array: array: (a) (physical-theorya) physical-theory model; model; (b) (formationb) formation of rate-calculation of rate-calculation principle. principle.

2.2. MaterialDuring theProperties hot embossing of a glass-microprism array, the relationship between plastic flow stress . σ, temperature T, strain ε, and strain rate ε is given in the following equation [36]: The substrate material was K9 optical glass with transformation temperature Tg of 560 °C and the . softening point Tf of 714 °C. Transformationσ temperature= f (ε, ε, T) Tg means that the optical glass begins to (1)be transformed from its solid state into a plastic state, and softening point Tf indicates the temperature whereBecause the glass there becomes was no heat obviously source insidesoftened the material,and deforms the temperature at its own change weight in [38]. the hot-embossing The thermal processconductivity satisfied and thespecific simplified heat of heat-balance the K9 optical equation: glass were 5 W/(m·K) and 2100 J/(kg·K), respectively. The die-core material was SiC, which has high wear, temperature, and oxidation resistance. The thermal ∂T ∂ ∂T conductivity and specific heat of the opticalρc glass= were[k 77.5], W/(m·K) and 670 J/(kg·K), respectively. (2) The material properties of the die core and the∂t K9 ∂opticalx ∂x glass substrate are listed in Table 1. whereTablec is specific 2 shows heat; flow and stressρ, T, andσ fork theare density,K9 optical temperature, glass, which and was heat adjusted conductivity, to be respectively consistent with [37]. our previousBecause theexperiments, cross-section and of set the as die-core the initial microgroove parameters was in the triangular, simulation. the This cross-sectional showed that area flow of . ε thestress microprism σ increased is givenwith increasing as S1; then, strain the forming rate rate, and during decreased the forming with increasing process couldtemperature be defined T. as

Table 1. Material propertiesη = 2ofS 1die/( hcorevdv )and K9 optical glass [38]. (3)

Thermal Young’s 2.2. Material PropertiesDensity Specific Heat Poisson’s Material Conductivity Modulus (kg/m3) (J/(kg·K)) Ratio The substrate material was K9 optical(W/(m·K)) glass with transformation temperature(GPa)T g of 560 ◦C and the softeningSiC die point core Tf of 714 3.02 ◦×C. 10 Transformation3 77.5 temperature Tg 670means that the optical 192 glass begins0.142 to be 3 transformedK9 optical glass from its 2.41 solid × 10 state into a plastic5 state, and softening 2100 point Tf indicates 79.2 the temperature0.211 where the glass becomes obviously softened and deforms at its own weight [38]. The thermal conductivity and specific heat of the K9 optical glass were 5 W/(m K) and 2100 J/(kg K), respectively. · · The die-core material was SiC, which has high wear, temperature, and oxidation resistance. The thermal conductivity and specific heat of the optical glass were 77.5 W/(m K) and 670 J/(kg K), respectively. · · The material properties of the die core and the K9 optical glass substrate are listed in Table1.

Table 1. Material properties of die core and K9 optical glass [38].

Density Thermal Conductivity Specific Heat Young’s Modulus Material Poisson’s Ratio (kg/m3) (W/(m K)) (J/(kg K)) (GPa) · · SiC die core 3.02 103 77.5 670 192 0.142 × K9 optical glass 2.41 103 5 2100 79.2 0.211 × Micromachines 2020, 11, 984 4 of 13

Table2 shows flow stress σ for the K9 optical glass, which was adjusted to be consistent with our previous experiments, and set as the initial parameters in the simulation. This showed that flow stress Micromachines 2020, 11, x . 4 of 12 σ increased with increasing strain rate ε, and decreased with increasing temperature T. Table 2. Flow stress σ for K9 optical glass. Table 2. Flow stress σ for K9 optical glass. . . ε 503 °C 603 °C 703 °C 803 °C ε/T /T 503 ◦C 603 ◦C 703 ◦C 803 ◦C −5 −7 0.0001 967 100 1.42 × 10 5 2.98 × 10 7 0.0001 967 100 1.42 10− 2.98 10− 0.01 96,760 10,000 1.42 × 10×−3 3 2.98 × 10−5× 5 0.01 96,760 10,000 1.42 10− 2.98 10− × −3× 11 9,676,000 9,676,000 1,000,000 1,000,000 0.142 0.142 2.98 ×2.98 10 10 3 × − 3. Experiment and Measurement 3. Experiment and Measurement

3.1.3.1. Microgrinding Microgrinding of of Core Core Microgrooves Microgrooves TheThe scheme scheme of of microgrinding microgrinding SiC SiC die die core core is isshow shownn in inFigure Figure 2.2 The. The SiC SiC die die core core was was sized sized as 30 as ×30 30 ×30 10 mm,10 mm the, resin-boned the resin-boned #3000 #3000 wheel wheel was was adopte adoptedd to tomicrogrind microgrind microgrooves microgrooves on on the the die die core, core, and× microgroove× angle θv and depth hv were designed to be 120° and 145 μm, respectively. For form and microgroove angle θv and depth hv were designed to be 120◦ and 145 µm, respectively. For form microgrinding, wheel speed N, speed rate vf, and cutting depth a were set as 2400 rpm, 500 mm/min, microgrinding, wheel speed N, speed rate vf, and cutting depth a were set as 2400 rpm, 500 mm/min, andand 55µ m,μm, respectively. respectively. After After the cumulativethe cumulati cuttingve cutting depth had depth reached had 140 reachedµm, finish 140 microgrinding μm, finish microgrinding was carried out for 5 times, and feed rate vf and cutting depth a were changed to 100 was carried out for 5 times, and feed rate vf and cutting depth a were changed to 100 mm/min and mm/min1 µm, respectively. and 1 μm, respectively.

FigureFigure 2. 2. SchemeScheme of of microgrinding microgrinding SiC SiC die die core. core. 3.2. Experiment Setup of Hot-Embossing Glass-Microprism Array 3.2. Experiment Setup of Hot-Embossing Glass-Microprism Array The experiment setup of the hot-embossing glass-microprism array is shown in Figure3. The experiment setup of the hot-embossing glass-microprism array is shown in Figure 3. A A high-temperature furnace was used to heat the die core and optical glass substrate in the hot-embossing high-temperature furnace was used to heat the die core and optical glass substrate in the experiment (see Figure3a). The temperature sensor could detect temperature in the furnace in real hot-embossing experiment (see Figure 3a). The temperature sensor could detect temperature in the time, and the maximal heating temperature of the furnace could reach 1200 ◦C. The console adopted an furnace in real time, and the maximal heating temperature of the furnace could reach 1200 °C. The intelligent proportional-integral-derivative (PID) digital-display controller that could protect overload console adopted an intelligent proportional-integral-derivative (PID) digital-display controller that and short circuit. could protect overload and short circuit. Moreover, a small control device for hot-embossing glass-microprism array was designed and placed in the furnace. Figure 3b shows the magnified view of the experimental scene of the hot-embossing glass-microprism array, and Figure 3c shows the schematic diagram of the principle of the hot-embossing glass-microprism array. First, a K9 optical glass substrate with a size of 15 × 15 × 1 mm was placed on the movable substrate stage and moved to the work station. Then, the die core was placed on the support plate with a central hole; due to the limitation of the limit block around, the mold core could only move up and down on the support plate, not horizontally. The die

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core was moved over the substrate by rotating the rotary handle to control the relative movement between screw and screw nut. The substrate passed through the central hole of the support plate and closely contacted with the die core, as the height of the substrate was greater than the thickness of the support plate. Lastly, the hot-embossing force was adjusted by controlling the gravity of the loading block above the die core; the substrate was separated from the die core and sent out of the work station at the end of hot embossing.

MicromachinesExperimental2020, 11, 984parameters were set as embossing temperature T of 560–710 °C, holding duration5 of t 13of 8–12 min, and embossing force F of 0.335–0.835 N.

FigureFigure 3.3. ExperimentExperiment setup of hot-embossi hot-embossingng glass-microprism glass-microprism array: array: (a) ( ahigh-temperature) high-temperature furnace; furnace; (b) (bmagnified) magnified view view of ofexperimental experimental scene scene of of hot-embossing hot-embossing glass-microprism array; ((cc)) schematicschematic diagramdiagram ofof principle principle of of hot-embossing hot-embossing glass-microprism glass-microprism array. array.

Moreover,Figure 3 shows a small that control the experiment device for setup hot-embossing of the hot-embossing glass-microprism glass-microprism array was array designed was andsimple, placed cheap, in theand furnace. compact Figurecompared3b shows with that the of magnified the precision view glass-molding of the experimental machine scene (Guangdong of the hot-embossingHUST Industrial glass-microprism Technology Research array, and Institute), Figure3 cwhich shows involves the schematic an numerical diagram control of the principle- system, ofheating, the hot-embossing bending, and glass-microprismannealing and cooling array. stages First,, a a chamber, K9 optical anglass entrance substrate and exit with mechanism, a size of 15and 15ancillary1 mm facilitieswas placed such onas water-cooling the movable substrateand nitrogen-transport stage and moved devices to the [30]. work station. Then, × × the die core was placed on the support plate with a central hole; due to the limitation of the limit block around,3.3. Processing the mold of Hot-Emboss core coulding only Glass-Microprism move up and down Array on the support plate, not horizontally. The die core was moved over the substrate by rotating the rotary handle to control the relative movement The history of the hot-embossing glass-microprism array is shown in Figure 4. The whole between screw and screw nut. The substrate passed through the central hole of the support plate and process included preheating, holding, and demolding stages. The initial temperature of the closely contacted with the die core, as the height of the substrate was greater than the thickness of the substrate was at room temperature T0 = 20 °C, and it was preheated for about 5–10 min to achieve support plate. Lastly, the hot-embossing force was adjusted by controlling the gravity of the loading set embossing temperature T, which was greater than Tg but less than Tf because the glass was in block above the die core; the substrate was separated from the die core and sent out of the work station viscoelastic state in this interval. Substrate and die core were separated after holding duration t, and at the end of hot embossing. the substrate was then cooled in air offline, while the die core was kept at a high temperature the Experimental parameters were set as embossing temperature T of 560–710 C, holding duration t entire time. Therefore, the die core did not undergo a cooling process, and it could◦ avoid repeatedly of 8–12 min, and embossing force F of 0.335–0.835 N. switching on and off the power of the high-temperature furnace. This was different from the process Figure3 shows that the experiment setup of the hot-embossing glass-microprism array was simple, cheap, and compact compared with that of the precision glass-molding machine (Guangdong HUST Industrial Technology Research Institute), which involves an numerical control - system, heating, bending, and annealing and cooling stages, a chamber, an entrance and exit mechanism, and ancillary facilities such as water-cooling and nitrogen-transport devices [30]. Micromachines 2020, 11, 984 6 of 13

3.3. Processing of Hot-Embossing Glass-Microprism Array The history of the hot-embossing glass-microprism array is shown in Figure4. The whole process included preheating, holding, and demolding stages. The initial temperature of the substrate was at room temperature T0 = 20 ◦C, and it was preheated for about 5–10 min to achieve set embossing temperature T, which was greater than Tg but less than Tf because the glass was in viscoelastic state in this interval. Substrate and die core were separated after holding duration t, and the substrate was then cooled in air offline, while the die core was kept at a high temperature the entire time. Therefore, the die core did not undergo a cooling process, and it could avoid repeatedly switching Micromachines 2020, 11, x 6 of 12 on and off the power of the high-temperature furnace. This was different from the process of a ofhot-embossing a hot-embossing glass glass microlens microlens with with an online an online cooling cool stageing stage reported reported in other in studiesother studies [39]. In [39]. this In paper, this paper,embossing embossing temperature temperatureT, holding T, holding duration durationt, and embossing t, and embossing force were force set were as 560–710 set as◦ C,560–710 8–12 min,°C, 8–12and 0.335–0.835min, and 0.335–0.835 N, respectively. N, respectively.

FigureFigure 4. 4. HistoryHistory of of hot-embossing hot-embossing glass-microprism glass-microprism array. array.

4.4. Results Results and and Discussion Discussion

4.1.4.1. Theoretical Theoretical Analysis Analysis of of Microfor Microformingming Glass-Microprism Glass-Microprism Array Array Process TheThe flow-field flow-field distribution distribution of of th thee microforming glass glass substrate substrate is is shown in Figure 55.. InIn thethe simulation,simulation, hot-embossing parameters parameters were were set set as as holding holding duration duration tt ofof 10 min, embossing temperature T of 630 °C,◦C, and embossing force force FF of 0.555 N. When the die-core tip entered the material, the the molten molten glassglass material material first first flowed flowed downward downward from from the the substrate substrate (see (see Figure Figure 55a),a), and thenthen turnedturned thethe flowflow directiondirection toward toward the the microgroov microgroovee cavity, cavity, forming forming a vortex a vortex at att =t 4= min4 min (see (see Figure Figure 5b).5 b).Flow Flow rate rate in the in formingthe forming process process was wasvery verysmall, small, and andthe maximal the maximal velocity velocity of 0.17 of μ 0.17m/sµ appearedm/s appeared at t = at 7t min= 7 (see min Figure(see Figure 5c). Then,5c). Then,flow rate flow decreased rate decreased to about to 0.1 about μm/s 0.1 at t µ= m10/s min at t (see= 10 Figure min (see5d). FigureIt can be5d). deduced It can thatbe deduced the flowthat behavior the flow of the behavior molten of polymer the molten larg polymerely determines largely the determines shape of the glass shape microprism, of the glass andmicroprism, the polymer and theflowing polymer into flowing the microcavity into the microcavity of the die of core the dieis conducive core is conducive to the toformation the formation of a glass-microprismof a glass-microprism array. array.

Figure 5. Flow-field distribution of microforming glass substrate. (a) flow-field distribution at t = 0 min; (b) flow-field distribution at t = 4 min; (c) flow-field distribution at t = 7 min; (d) flow-field distribution at t = 10 min.

Micromachines 2020, 11, x 6 of 12 of a hot-embossing glass microlens with an online cooling stage reported in other studies [39]. In this paper, embossing temperature T, holding duration t, and embossing force were set as 560–710 °C, 8–12 min, and 0.335–0.835 N, respectively.

Figure 4. History of hot-embossing glass-microprism array.

4. Results and Discussion

4.1. Theoretical Analysis of Microforming Glass-Microprism Array Process The flow-field distribution of the microforming glass substrate is shown in Figure 5. In the simulation, hot-embossing parameters were set as holding duration t of 10 min, embossing temperature T of 630 °C, and embossing force F of 0.555 N. When the die-core tip entered the material, the molten glass material first flowed downward from the substrate (see Figure 5a), and then turned the flow direction toward the microgroove cavity, forming a vortex at t = 4 min (see Figure 5b). Flow rate in the forming process was very small, and the maximal velocity of 0.17 μm/s appeared at t = 7 min (see Figure 5c). Then, flow rate decreased to about 0.1 μm/s at t = 10 min (see Figure 5d). It can be deduced that the flow behavior of the molten polymer largely determines the shape of the glass microprism, andMicromachines the polymer2020, 11 ,flowing 984 into the microcavity of the die core is conducive to the formation7 of of 13a glass-microprism array.

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Figure 6 shows the strain-rate and deformation change of the microforming glass substrate. The change of strain-rate is shown in Figure 6a. The strain-rate of the glass material was very small, the strain-rate of the polymer at the tip of the die-core microgroove tip was larger than that of other Figure 5. Flow-field distribution of microforming glass substrate.a (a) flow-field distributiont at t = 0 positions, andFlow-field maximal distributionstrain-rate ofin microforming the hot-embossing glass substrate. process ( )was flow-field only 0.0011 distribution−s. It can at = be0 mindeduced; min;(b) flow-field (b) flow-field distribution distribution at t = 4 at min; t = (c4) min; flow-field (c) flow-field distribution distribution at t = 7 min; at (td =) flow-field7 min; (d distribution) flow-field from Equation (1) and Table 2 that a small strain-rate means small thermal stress, so a hot-embossing distributionat t = 10 min. at t = 10 min. glass-microprism array may be realized through an offline air-cooling process instead of online coolingFigure and6 annealingshows the to strain-rate remove thermal and deformation stress, which change can ofsave the about microforming 12–30 min glass of cooling substrate. and Theannealing change time, of strain-rate compared is with shown cooling in Figure and6 annealinga. The strain-rate the glass of preform the glass and material mold was from very 560 small, °C to theroom strain-rate temperature of the with polymer a cooling at the rate tip of of 0.25–0.75 the die-core °C/s microgroove[40]. tip was larger than that of other The change of temperature field and deformation is shown in Figure 6b. Afters preheating, the positions, and maximal strain-rate in the hot-embossing process was only 0.0011− . It can be deduced fromtemperature Equation of (1) the and glass Table substrate2 that a reached small strain-rate about 600 means °C, which small was thermal slightly stress, lower so a than hot-embossing that of the glass-microprismdie core (630 °C) arraybecause may the be thermal realized conductivity through an o offfl inethe air-coolingglass substrate process was instead lower ofthan online that cooling of the anddie core. annealing As for to the remove deformation thermal stress,of glass which material, can save the aboutsubstrate 12–30 material min of was cooling first and squeezed annealing into time, the cavity of the core microgroove, and a microprism array was then formed in the microgroove cavity. compared with cooling and annealing the glass preform and mold from 560 ◦C to room temperature This process was similar to that of the microforming polymer microlens array reported in [41]. with a cooling rate of 0.25–0.75 ◦C/s [40].

Figure 6.Figure (a) Strain-rate 6. (a) Strain-rate and (b) anddeformation (b) deformation changes changes of microforming of microforming glass substrate. glass substrate.

4.2. MicrogroundThe change Die of temperatureCore field and deformation is shown in Figure6b. After preheating, the temperature of the glass substrate reached about 600 C, which was slightly lower than that of the The microground die core is shown in Figure 7. The◦ photo of the die core is shown in Figure 7a; die core (630 C) because the thermal conductivity of the glass substrate was lower than that of the it is shown that◦ some continuous microgroove arrays were machined on the surface of the die core. die core. As for the deformation of glass material, the substrate material was first squeezed into the Average total depth hv and width dv of the microgroove were 145.15 μm and 0.50 mm, respectively cavity of the core microgroove, and a microprism array was then formed in the microgroove cavity. (see Figure 7b). The SEM morphology of the microgrooves on the die-core surface is shown in This process was similar to that of the microforming polymer microlens array reported in [41]. Figure 7c; the microground die-core microgroove surface was relatively smooth with a roughness of 0.15 μm. Angle θv of the microgroove was 118°, compared with the designed angle of 120° and forming angle error of 1.7%. The radius of the microgroove tip was 9.93 μm, which was mainly caused by the wear of the grinding-wheel tip during the machining process (see Figure 7d).

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4.2. Microground Die Core The microground die core is shown in Figure7. The photo of the die core is shown in Figure7a; it is shown that some continuous microgroove arrays were machined on the surface of the die core. Average total depth hv and width dv of the microgroove were 145.15 µm and 0.50 mm, respectively (see Figure7b). The SEM morphology of the microgrooves on the die-core surface is shown in Figure7c; the microground die-core microgroove surface was relatively smooth with a roughness of 0.15 µm. Angle θv of the microgroove was 118◦, compared with the designed angle of 120◦ and forming angle Micromachineserror of 1.7%. 2020 The, 11, radius x of the microgroove tip was 9.93 µm, which was mainly caused by the wear8 of of12 Micromachinesthe grinding-wheel 2020, 11, x tip during the machining process (see Figure7d). 8 of 12

Figure 7. Microground die core: (a) photo of SiC die core; (b) surface profile; (c) SEM morphology of FiguremicrogroovesFigure 7. MicrogroundMicroground on die-core die die surface; core: core: ( (aa )() dphoto photo) angle of of θ SiC SiCv and die die radius core; core; R( (bb of)) surface surface die-core profile; profile; microgroove ( (cc)) SEM SEM tip. morphology of of microgrooves on die-core surface; (d) angle θv and radius R of die-core microgroove tip. microgrooves on die-core surface; (d) angle θv and radius R of die-core microgroove tip. 4.3. Photograph and Profile of Glass-Microprism Array 4.3.4.3. Photograph Photograph and and Profile Profile of of Glass-Microprism Glass-Microprism Array The photograph and profile of the glass-microprism array are shown in Figure 8. Processing parametersTheThe photograph were set and andas profile embossingprofile of theof glass-microprismth temperaturee glass-microprism of array 630 arearray°C, shown holdingare inshown Figure duration in8. ProcessingFigure of 8.10 Processing parametersmin, and parameterswereembossing set as embossingforcewere ofset 0.555 as temperature embossingN. The experiment of temperature 630 ◦C, holdingshow ofed 630 durationthat °C, the holding ofglass-microprism 10 min, duration and embossing of array 10 min,could force and be of embossinghot-embossed0.555 N. The force experiment with of a 0.555surface showed N. roughne The that experiment thess of glass-microprism 85 nm; show a photographed that array the of could thglass-microprisme bemicroformed hot-embossed glass-microprism array with could a surface be hot-embossedarrayroughness is shown of 85with in nm; Figure a asurface photograph 8a. roughne ofss the of microformed 85 nm; a photograph glass-microprism of the microformed array is shown glass-microprism in Figure8a. array is shown in Figure 8a.

Figure 8. PhotographPhotograph and and profile profile of of glass-microprism glass-microprism array: array: (a) (photoa) photo of glass-microprism of glass-microprism array; array; (b) Figurecross-sectional(b) cross-sectional 8. Photograph profile profile ofand glass-microprism of profile glass-microprism of glass-microprism array array (embossing (embossing array: temperature, (a) temperature, photo of 630glass-microprism 630 °C; ◦holdingC; holding duration, array; duration, ( 10b) cross-sectional10min; min; embossing embossing profile force, force, of 0.555 glass-microprism 0.555 N). N). array (embossing temperature, 630 °C; holding duration, 10 min; embossing force, 0.555 N). Moreover, thethe cross-sectionalcross-sectional profileprofile ofof thethe glass-microprismglass-microprism array array is is shown shown in in Figure Figure8b; 8b; height heighth hand and widthMoreover, widthd of d the theof microprism thecross-sectional microprism were profile 45were and of 50045 the andµm, glass- respectively.500 microprismμm, respectively. According array is According toshown Equation in Figureto (3), Equation forming 8b; height rate(3), hforming and width rate ηd was of thecalculated microprism to be 50%.were The 45 shapeand 500 of theμm, microprism respectively. was According approximately to Equation trapezoidal, (3), formingwhich was rate consistentη was calculated with simulationto be 50%. Theanalysis shape (seeof the Figure microprism 6b). Therefore, was approximately this proves trapezoidal, that the whichglass-microprism was consistent array with could simulation be molded analysis without (see online Figure cooling, 6b). Therefore, and molding this proves efficiency that wasthe glass-microprismsignificantly improved array compared could be with molded the mi withoutcro-hot-embossing online cooling, time ofand 138 molding min in [28]. efficiency was significantly improved compared with the micro-hot-embossing time of 138 min in [28]. 4.4. Theoretical and Experimental Forming Rates of Microprism Array 4.4. Theoretical and Experimental Forming Rates of Microprism Array The theoretical and experimental forming rates of the glass-microprism array are shown in FigureThe 8. theoreticalTheoretical and values experimental were in good forming agreement rates ofwith the the glass-microprism experimental values, array areand shown standard in Figuredeviation 8. Theoreticaland difference values were were controlled in good within agreement 7% and with 12%, the respectively. experimental values, and standard deviationWhen and embossing difference temperature were controlled and force within were 7% 630and °C 12%, and respectively. 0.335 N, respectively, forming rate η increasedWhen with embossing an increase temperature in holding and duration force were t (see 630 Figure °C and 9a). 0.335 Forming N, respectively, rate was increased forming to rate 66.56% η increased with an increase in holding duration t (see Figure 9a). Forming rate was increased to 66.56%

Micromachines 2020, 11, 984 9 of 13

η was calculated to be 50%. The shape of the microprism was approximately trapezoidal, which was consistent with simulation analysis (see Figure6b). Therefore, this proves that the glass-microprism array could be molded without online cooling, and molding efficiency was significantly improved compared with the micro-hot-embossing time of 138 min in [28].

Micromachines4.4. Theoretical 2020 and, 11, x Experimental Forming Rates of Microprism Array 9 of 12 for holdingThe theoretical duration and t = experimental12 min, which forming was 3.5 rates times of the of glass-microprismthe forming rate arrayfor holding are shown duration in Figure t = 88. min.Theoretical This is valuesbecause were an increase in good agreementin holding withtime thefacilitated experimental the flow values, of the and molten-glass standard deviationmaterial into and thediff erencemicrogrooves. were controlled within 7% and 12%, respectively. FigureWhen embossing9b also shows temperature that the greater and force the wereembossing 630 ◦C force and 0.335was, the N, respectively,greater the forming forming rate. rate Thisη increased may be withbecause an increasethe external in holding force can duration accelerat (seete the Figure flow 9ofa). molten Forming glass rate and was improve increased filling to efficiency.66.56% for Forming holding durationrate was tabout= 12 min,50% for which embossing was 3.5 timesforce F of = the0.715 forming N, which rate was for holdingabout 1.25 duration times thatt = 8 for min embossing. This is because force F an = increase0.355 N. in However, holding time compared facilitated with the other flow hot-embossing of the molten-glass parameters, material embossinginto the microgrooves. force had little effect on the microforming glass-microprism array.

FigureFigure 9. TheoreticalTheoretical and and experimental experimental forming forming rates rates of of glass-microprism glass-microprism array: array: (a) ( aforming) forming rate rate η versusη versus holding holding duration duration t; t(;(b)b forming) forming rate rate η ηversusversus embossing embossing force force FF; ;((cc) )forming forming rate rate ηη versus embossingembossing temperature temperature T..

Moreover,Figure9b alsoforming shows rate that increased the greater in “S” the shape embossing with the force increase was, thein embossing greater the temperature; forming rate. it firstThis slowly may be increased, because the and external then sharply force can increa acceleratesed when the embossing flow of molten temperature glass and was improve higher filling than 610effi ciency.°C (see FormingFigure 9c). rate After was the about temperature 50% for embossing had exceeded force 650F = °C,0.715 theN, theoreti whichcal was result about showed 1.25 times that thethat forming for embossing rate of the force microprismF = 0.355 array N.However, could reach compared 80%, while with the otherK9 optical hot-embossing glass substrate parameters, cracked duringembossing the experiment. force had little This eff mayect on be the because microforming the higher glass-microprism the embossing temperature array. is, the higher the degreeMoreover, of melting forming and the rate higher increased the forming in “S” shaperate ar withe. However, the increase if the in temperature embossing temperature; were too high, it firstthe greaterslowly increased,the thermal and stress then accumulated sharply increased inside the when substrate embossing was, especia temperaturelly near was the higher tip of the than die-core 610 ◦C microgroove,(see Figure9c). as Aftershown the in temperatureFigure 6a. This had means exceeded that thermal-stress 650 ◦C, the theoretical accumulation result needs showed be precisely that the limited.forming rate of the microprism array could reach 80%, while the K9 optical glass substrate cracked Therefore, it can be deduced from the theoretical and experimental results that embossing temperature had the greatest influence on forming rate, and embossing force had the least influence. Under a certain external force, the higher the embossing temperature is, the stronger the fluidity of the viscous-flow-state glass material, and higher forming rate, but too-high embossing temperature lead to thermal-stress accumulation and brittle substrate cracks.

4.5. Forming Defects during Hot-Embossing Glass-Microprism Array Process

Micromachines 2020, 11, 984 10 of 13 during the experiment. This may be because the higher the embossing temperature is, the higher the degree of melting and the higher the forming rate are. However, if the temperature were too high, the greater the thermal stress accumulated inside the substrate was, especially near the tip of the die-core microgroove, as shown in Figure6a. This means that thermal-stress accumulation needs be precisely limited. Therefore, it can be deduced from the theoretical and experimental results that embossing temperature had the greatest influence on forming rate, and embossing force had the least influence. Under a certain external force, the higher the embossing temperature is, the stronger the fluidity of the viscous-flow-state glass material, and higher forming rate, but too-high embossing temperature lead to thermal-stress accumulation and brittle substrate cracks. Micromachines 2020, 11, x 10 of 12 4.5. Forming Defects during Hot-Embossing Glass-Microprism Array Process Figure 10 shows the forming defects during the hot-embossing glass-microprism array process. Figure 10 shows the forming defects during the hot-embossing glass-microprism array process. When embossing temperature was close to the glass-softening point Tf of 714 °C, the sticky glass T debrisWhen embossingstuck to the temperature die-core microgroove was close totip the (see glass-softening Figure 10a). This point mayf of be 714 due◦C, to the the sticky high adhesion glass debris of glassstuck material to the die-core at high microgroove temperatures. tip As (see shown Figure in 10 Fia).gure This 10b, may brittle be duepits toand the debris high adhesionappeared of on glass the surfacematerial of at the high glass-microprism temperatures. As array, shown and in the Figure brittle 10b, pits brittle were pits circular and debris in the appeared middle onand the irregular surface atof the glass-microprismedge of the glass array,microstructure, and the brittle which pits may were have circular been in caused the middle by uneven and irregular thermal at stress, the edge as theof the reference glass microstructure, reported that excessive which may forming have been stress caused and residual by uneven stress thermal induce stress, the growth as the reference of glass crackingreported [42]. that Therefore, excessive formingit is very stress important and residual to control stress the induceappropriate the growth embossing of glass temperature cracking and [42]. embossingTherefore, itforce. is very important to control the appropriate embossing temperature and embossing force.

Figure 10. Forming defects during hot-embossing glass-microprism array process: ( (aa)) glass glass debris stickingsticking on on surface of die-core microgrooves; ( (bb)) brittle brittle pits pits and debris on glass-microprism array array

surfacesurface (embossing temperature 700 °C,◦C, holdin holdingg duration 10 min, embossing force 0.755 N).

5. Conclusions Conclusions (1) Theoretical-simulationTheoretical-simulation results results showed showed that that the the vortexlike vortexlike molten-glass molten-glass material material flowed flowed into intothe corethe corecavity cavity to form to form a trapezoidal a trapezoidal microprism microprism array. array. Appropriate Appropriate hot-embossing hot-embossing force force and temperaturetemperature led led to to small small strain strain rate, rate, which which meant meant that that thermal thermal stress stress was was low, low, and and the online coolingcooling process process may may not not have have been been needed, needed, reducing reducing hot-embossing hot-embossing time. time. (2) AA low-cost low-cost microforming microforming control control device device was was designed, designed, and and the the SiC SiC die-core die-core microgroove microgroove array array waswas microground microground by by the the grinding-wheel grinding-wheel microtip microtip.. Moreover, Moreover, the the trapezoidal trapezoidal microprism microprism array array waswas successfully successfully embossed embossed without without online online coolin coolingg processing, processing, and and the highest experimental formingforming rate rate reached reached 66.56% 66.56% with with a a holding holding duration duration of of 12 12 min. min. (3) TheoreticalTheoretical and and experimental experimental values values were were in in good good agreement agreement with with standard deviation and differencedifference of of 7% 7% and and 12%, 12%, respectively. respectively. Theoreti Theoreticalcal and and experimental experimental results results showed showed that thatthe formingthe forming rate rateof the of theglass-microprism glass-microprism array array increased increased with with increasing increasing holding holding duration, duration, embossingembossin force,force, andand embossing embossing temperature. temperature. (4) When embossing temperature and embossing force were high, the hot-melt glass material was stuck to the die-core microgroove surface, and the optical glass substrate cracked, which may have been caused by uneven thermal stress.

Author Contributions: conceptualization, M.H. and J.X.; methodology, M.H. and J.X.; validation, W.L. and Y.N.; formal analysis, M.H. and Y.N.; investigation, W.L.; resources, M.H. and W.L.; data curation, M.H. and Y.N.; writing—original-draft preparation, M.H.; writing—review and editing, M.H. and J.X.; supervision, W.L. and Y.N.; project administration, J.X.; funding acquisition, J.X. All authors have read and agreed to the published version of the manuscript.

Funding: This work was supported by the National Natural Science Foundation of China (51975219), the Guangdong Science and Technology Project (2020A0505100003), and the Natural Science Foundation of Guangdong Province (2020A1515010807), and the Fundamental Research Funds for the Central Universities

Acknowledgments: Thanks to all the fundings for the research of this paper.

Micromachines 2020, 11, 984 11 of 13

(4) When embossing temperature and embossing force were high, the hot-melt glass material was stuck to the die-core microgroove surface, and the optical glass substrate cracked, which may have been caused by uneven thermal stress.

Author Contributions: Conceptualization, M.H. and J.X.; methodology, M.H. and J.X.; validation, W.L. and Y.N.; formal analysis, M.H. and Y.N.; investigation, W.L.; resources, M.H. and W.L.; data curation, M.H. and Y.N.; writing—original-draft preparation, M.H.; writing—review and editing, M.H. and J.X.; supervision, W.L. and Y.N.; project administration, J.X.; funding acquisition, J.X. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (51975219), the Guangdong Science and Technology Project (2020A0505100003), and the Natural Science Foundation of Guangdong Province (2020A1515010807), and the Fundamental Research Funds for the Central Universities. Acknowledgments: Thanks to all the fundings for the research of this paper. Conflicts of Interest: The authors declare no conflict of interest.

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