Lens of Controllable Optical Field with Thin Film Metallic Glasses for Uv-leds References and Links Optical Film for Led with Triangular- Pyramidal Arrayusing Size-reducible Embossing Method, "

In the exposure process of photolithography, a free-form lens is designed and fabricated for UV-LED (Ultraviolet Light-Emitting Diode). Thin film metallic glasses (TFMG) are adopted as UV reflection layers to enhance the irradiance and uniformity. The Polydimethylsiloxane (PDMS) with high transmittance is used as the lens material. The 3-D fast printing is attempted to make the mold of the lens. The results show that the average irradiance can be enhanced by 6.5~6.7%, and high uniformity of 85~86% can be obtained. Exposure on commercial thick photoresist using this UV-LED system shows 3~5% dimensional deviation, lower than the 6~8% deviation for commercial mercury lamp system. This current system shows promising potential to replace the conventional mercury exposure systems. Fluorescence image excited by a scanning UV-LED light, " Opt. Rev. UV enhanced substrate conformal imprint lithography (UV-SCIL) technique for photonic crystals patterning in LED manufacturing, " Microelectron. Three dimensional metal pattern transfer for replica molded microstructures, " Appl. Fast freeform reflector generation usingsource-target maps, " Opt. A novel LED lighting module using patternable design concept for underwater illumination, " " Status and future of high-power light-emitting diodes for solid-state lighting, " J. Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source, " Opt. Design of high-efficient freeform LED lens for illumination of elongated rectangular regions, " Opt. Mechanical properties of ZrCuTi thin lm metallic glass with high content of immiscible tantalum, " Surf. Correlation between reflectivity and resistivity in multi-component metallic systems, " Appl.


Introduction
Traditional fluorescent lamps are mainly applied on the exposure machines.In addition to the environmental pollution, UV (Ultraviolet) radiation is emitted around which may cause radiation leakage, that results in the unnecessary energy consumptions and overall declines in UV radiant intensity.LED (light emitting diode) could be used in much wider application in the near future because of small volume and mercury (Hg) free.Also, the blue or near-UV high brightness light emitting diodes (HB-LEDs) has high energy conversion efficiency, and the UV-LED has longer life term compared with traditional fluorescent lamps.This UV-LED chips are capable of emitting radiation at a wavelength of 390 nm.Therefore, UV-LED lamp starts replacing the traditional fluorescent Hg lamp.The cost of lithography process can be decreased and the efficiency can be enhanced [1,2].Lithography with different exposure systems such as lamps and UV-LEDs was demonstrated to compare the advantages with each other [3,4].
The UV-LED used in this work can be approximated to a Lambertian emitter, whose UV irradiance of half intensity angle is around 60 degree.Undoubtedly, a uniform circular illumination cannot be ensured when the LED light source is used for light illumination systems [5].Thus, the secondary optical designs are becoming the most important issues in directly lighting applications.Huang et al. [6] studied lens curve design.There are two main methods to design a freeform surface for uniform illumination: PDE (partial differential equation) method and MPO (multi-parameter optimization) method [7][8][9][10][11].
In this paper, lens design and fabrication for a uniform UV irradiance over the target with thin film metallic glasses (TFMG) can enhance the reflection at the UV wave band of UV-LED.TFMG is coated around the lens.The TFMG are materials of amorphous metal alloy, with high glass forming ability, corrosion resistance, high hydrophobicity, low surface roughness, good protective coatings and unique characteristics.Application examples of bulk metallic glasses (BMG) have been extended to much valuable fields.Liu et al. [12] studied the fabrication of triangular-pyramidal metal molds using BMG master molds with micro structures by thermal imprint process.By alloying minor addition of Al and Ag into Zr-based MG, the thermal stability and homogeneity could be further enhanced to satisfy the requirement of sputtering target [13].In study [14], the reflectance of Al-based TFMG in UV wavelength is more stable than general alloys with the same ingredient, even higher than pure metals with high reflection rate.
In this study, conventional Hg exposure system was compared with UV-LED device, which is schematically shown in Fig. 1.The UV-LED exposure system was established to reduce the radiation leakage and increase the energy efficiency for energy saving.First, according to the law of the conservation of energy and law of refraction, the irradiation at the target plane was investigated.Second, the UV-LED packaged with Polydimethylsiloxane (PDMS) lens coated with Al-based TFMG was designed to improve the serious decay of reflectance at UV wave band.Third, the PDMS lens was molded by 3-D fast printing method.The distribution of the UV irradiance such as irradiance and uniformity was analyzed by FRED commercial software.The exposure system of UV-LED was used to expose AZ4620.The result shows this UV-LEDs system has potential to replace the commercial mercury lamp exposure system for the micro-electronic photolithography such as print circuit board industry.

Radiation field
The radiation distribution of bare UV-LED is Lambertian distribution, whose radiation distribution was defined as cosine exponential function of angle θ.The UV radiant intensity function is expressed as Eq. ( 1).The UV radiant intensity as a function of angle θ from central axis is m (θ) cos (θ)  SO II (see Fig. 1), where I O is a constant intensity, I s is radiation source, and m value is determined by the half intensity angle 0.5 θ of UV-LED.The half intensity angle of the UV-LED is 60 degree, and the m value is 1.The radiation field function of UV-LED can be expressed as Eq.(2).Due to the poor directivity and uniformity of bare UV-LED, the geometric mapping of lens was calculated based on the uniform UV radiation target plane requirement.A uniform irradiation on the target plane can be obtained after the UV-LED emits through the asdesigned lens.The area of target plane is set as 60 mm × 60 mm, and the exposure distance is set as 50 mm.The UV radiation distribution on target plane is established, expressed as the functions of UV radiation intensity and irradiance angle.The definition of the unit of irradiation is watt per square centimeter.
The intensity distribution I s (θ) can be converted into a cumulative flux distribution Φ source by integrating the intensity along the emission angle θ of the source.The cumulative source radiant flux distribution is given by Eq. (3): where θ is the emission angle of source, θ' is the angle between the y axis and the radiation direction, and dΩ = 2  sinθdθ is a differential annulus-shaped solid angle.
The cumulative target UV radiant flux distribution is given by Eq. ( 4).
where y is the distance of the target plane (see Fig. 1) and y' is the distance between the UV-LED and the target plane.
Then the flux conservation between the source and the target can be written as Eq. ( 5), and the E t (y) is the prescribed target irradiance: arg ( ) ( )

The law of conservation of UV radiation energy
According to the law of conservation of energy, if a system is in an isolated environment without input or output of energy or mass, the total energy of the system is kept at constant.Therefore, at ideal conditions, if the influence of the UV radiation absorbance of lens material is a constant, the total energy of UV radiation is balanced before and after it passes through the lens, expressed as Eq. ( 3) and ( 4).The UV radiant intensity before it enters the lens is equal to the UV radiation power in the target plane as Eq. ( 5).
To calculate the free-form lens, the UV irradiance angle θ from 0þ to 90þis divided into k intervals (90/k), and the total power of each interval of the UV irradiance is equivalent to the total power of each interval after the UV radiation passes through the lens.Take the first interval for an example, the total irradiance over the target in the range from k = 0 to k = a on the target plane, where a = lens radius, as expressed in Eq. ( 6).The y distance corresponding to each interval can be calculated, and then the direction of refracted UV radiation can be obtained.
Therefore, the relationship of the energy between the UV radiation and target plane is correlated, so as to design the lens curvature of the optimal uniform radiation distribution.
When the UV radiation is transmitted one medium to another with different refractivities, the refraction of UV radiation occurs.The relationship between incident angle and refraction angle can be described by Snell's law.Equation ( 7) is the vector expression of refraction law, n 1 and n 2 are the refractivity index of the lens and air, respectively.I and O are the unit vectors of incident and refracted UV radiation, respectively, corresponding to each interval angle obtained from Eq. ( 5) which are substituted in the vector expression of Snell's law Eq.( 7).The corresponding normal vector N can be calculated.This normal vector N is the vertical vector of lens curve corresponding to interval angle, as shown in Fig. 2.
Fig. 2. The schematic diagram of normal vector corresponding to the incident UV radiation vector and refracted radiation vector.
After the UV radiation field function of UV-LED and target plane are determined, the refracted UV radiation vector corresponding to the incident UV radiation vector of each interval, as well as the corresponding normal vector can be obtained.This tangent vector T is the tangent vector of the as-designed curve of lens.The as-designed curve is constructed after all the tangent vectors were obtained.
As the interval from 0 to 90 degree is divided into k equal parts, there will be k + 1 points.As shown in Fig. 3, the height H of lens was determined after the position of point P 0 was set, and the intersection point of the tangent vector 0 T corresponding to point P 0 and the incident UV radiation vector 1 I corresponding to the next point are defined as point P 1 .The intersection point of the tangent vector 1 T corresponding to point P 1 and the incident UV radiation vector 2 I corresponding to the next point is defined as point P 2 .This process is iterated until the point P k is found.The curve of lens surface can be obtained by connecting all of points with smooth curve.More split intervals can obtain better resolution of curve.When the number (K) of intervals is set as 30, a freeform can be obtained as shown in Fig. 4. When the number of intervals increased to 300, a new profile is obtained.To verify the convergence, the intervals were increased from 400 to 1000.The result shows that the curves of K = 300, 400 and 1000 almost overlapped together, that means the convergence and integrability condition can be reached.

Parameters of UV-LED
In this study, the UV-LED is from NICHIA-NCSU275 UV-LED.The LED chip with packaged size is 3.5 × 3.5 × 0.88 (mm 3 ), the effective emitting area is 1.5 × 1.5 (mm 2 ) and the wavelength is 385 nm, as shown in Table 1.And the first lens profile is designed as 15 mm (see Fig. 6).Since the ratio of the lens radius of Lambertian profile to the width of LED is greater than 10, LED could be assumed to be a point source.The UV radiation intensity distribution of single UV-LED is shown in Figs. 5.The Lambertian distribution of a cosine function was observed.The total luminous power was 350 mW.

Simulation and fabrication of lens coated with TFMG
As the number of divided intervals is larger than 300, the data of vector corresponding to each interval and the intersection points are too massive.In this study, MATLAB ® [15] software was used to calculate and draw the curve of lens, and used Pro/E software ® [16] to draw the 3-D lens.Then, with the designed curve, simulation model of UV-LED coated with TFMG was developed using commercial optical software FRED ® [17] to analyze the optical field on target plane.

Design and construction of TFMG reflector
The UV radiation leaving the LED die at great θ angles (almost 90°) may fall out of the plane if there is not any coating reflector (see path B in Fig. 6).However, if there was applied a TFMG reflective coating at determined height around the lens then the UV radiation incident will be deviated in direction to target through the path A. This is one reason to add this coating.Others are scratch and corrosion resistance.When the UV-LED radiation passes through the first profile with Lambertian curve, the radiation without refraction is assumed.
Then the radiation propagates to the second curve, where the first refractive surfaces generate an irradiance on the target plane (for example, the optical path C in Fig. 6).The mapping process is simple and time-saving way to obtain this freeform lens curve with uniform irradiance distribution.In addition, considering the requirement of reflector, the lens is coated with TFMG due to its scratch resistance and corrosion resistance.This study analyzes various degrees angle (α) of TFMG reflector covering on lens surface, as shown in Fig. 7.

Construction and Characterization of the TFMG reflector
In this study, the reflectivity of Al-based TFMG for UV radiation at wavelength of 385 nm is around 80%, as shown in Fig. 8. ABS resin mold was produced to cast PDMS (Polydimethylsiloxane) lens, which was formed rapidly by 3-D fast printing, as shown in Fig. 9 (a).The defects are low material strength and poor surface roughness.The average roughness of the mold is 1.12 μm.After grinded by sand paper, it can be less than 100 nm, as shown in Fig. 9 (b).The PDMS is a type of Si based organic polymer (PDMS Sylgard® 184, Dow Corning Corporation).It is nontoxic and nonflammable in general environment and it has superior radiation transmittance.The refraction index of PDMS is 1.43 at 385 nm and its measured UV transmittance in the range 350-950 nm was 85-90% (see Fig. 10).That is much higher than that of PMMA.The geometric shape of the reflector was constructed.That shows that PDMS is an appropriate material for lens at 385 nm (UV-A).Figure 11 shows a finished PDMS lens with height 30mm replicated by ABS mold.

Measurement method of uniformity
The nine point measurement method by American National Standards Institute (ANSI) was used to measure the uniformity [18], as expressed in Eqs. ( 8), ( 9) and (10).The measuring in M square (60 mm  60 mm in area) was divided into nine points U 1 to U 9 , as shown in Fig. 12.The maximum value U Max , minimum value U Min and average value U Avg of the nine points, as well as the ratio of positive ΔU + and ratio of negative ΔUwere obtained.The difference between the higher ratio and 1 is the uniformity:

Multiple UV-LEDs with lens
In terms of the time efficiency of exposure process, the power intensity of single UV-LED could take a long time to complete a general exposure process.Therefore, multiple UV-LEDs were used to shorten the exposure time.The arrangement of multiple UV-LEDs is shown in Fig. 13.The assembled PCBs have 1, 3, 4, 5, 6 and 7 UVA-LEDs in patterns or configurations shown in Figs.13(a)-13(h).An extra single UV-LED is put in the center of square, regular pentagon and regular hexagon respectively.Figure 14 is the radar map of UV radiation intensity distribution curve of 5-set UV-LEDs, and the total energy increases to five times of a single UV-LED.For the arrangement of the same bare UV-LED quantity, (4 + 1)-set was compared with 5set UV-LEDs.Their arrangements are shown in Fig. 13 (d) and (e), respectively.The result is shown in Fig. 15.5-set UV-LEDs have irradiance of 13.8mW/cm 2 and has uniformity of 73.4%.However, in terms of uniformity, the result shows 5-set UV-LEDs had better uniformity than (4 + 1)-set UV-LEDs by 1.2%.The figure also reveals that the more UV-LEDs, the higher irradiance.On the other hand, more UV-LEDs consume more energy and produce more heat.Thus we chose 5-set UV-LEDs as our design, which produces less heat.

Simulation of lens with TFMG reflector for 5-set UV-LEDs
The influence of TFMG reflector on the UV irradiance was characterized.The simulated UV irradiance of lens with TFMG was analyzed at different angles (α) (α shown in Fig. 7).When the α angle is 0 degree, it means the TFMG reflector covers the lens bottom only.As the α angle increases from 0þ to 50þ, the irradiance is increased accordingly, but the uniformity declines, as shown in Fig. 16.It reveals when the coverage of TFMG reflector is larger, more incident UV irradiance reflected to target plane.Therefore, when the TFMG reflector was coated of 50þ, the irradiance value is increased obviously to 5.8 mW/cm 2 , but the uniformity is decreased from 93% to 66%, corresponding to the covering angle of 40þ and 50þ.Angle 50þ shows the largest irradiance, but its uniformity is poorer.The uniformities of 0, 20 and 40 degrees are 95, 94 and 93%, respectively; and the irradiance are 4.5, 4.7 and 4.8 mW/cm 2 , respectively.In this study, PDMS lens coated with Al-based TFMG with angles of 0þ, 20þ and 40þ are characterized.

Measurement of lens with TFMG reflector for 5-set UV-LEDs
PDMS lenses coated with TFMG at angles of 0°, 20° and 40° were compared theoretically and experimentally, respectively.The uniformity was measured using nine-point measurement.The uniformities for the three different covering angles are around 85~86%.As shown in Fig. 17

Exposure process
Exposure process of photoresist AZ4620 by the UV-LEDs exposure system with TFMG in this study was compared with that by conventional mercury lamp exposure machines.The UV-LED exposure system is shown in Fig. 18.The average output power of UV-LEDs with PDMS lens was 8 mW/cm 2 , whereas that of conventional mercury lamp exposure machines was 19 mW/cm 2 .In order to reach the same total output energy of exposure, the exposure time of UV-LEDs system combining PDMS lens with TFMG was set as 47 sec, whereas the exposure time of mercury lamp exposure machines is 20 sec.According to the exposure results shown in Fig. 19, the exposed products using mercury lamp exposure systems have dimensional deviation of 6~8%, compared with original mask design.When the UV-LEDs with the PDMS lens and Al-TFMG was used, the dimensional deviation was reduced to 3~5%, proving the feasibility of using this UV-LEDs exposure system.

Conclusion
By using the law of conservation of energy and Snell's law method, a free-form lens is designed in the study.The UV irradiance field on target plane in terms of UV irradiance angle, UV radiant intensity distribution can be calculated, which could be applied on the exposure system in the micro-electronic process such as print circuit industry.Al-based TFMG with 80% reflectance at the UV wave band is coated partially around the lens by multi-gun sputtering method, i.e., 0, 20 and 40 degrees, respectively.When the lens is coated with Al-based TFMG as reflector, the reflectance at UV wave band can be enhanced.In addition, the leakage of radiation at the large angle portions of lens can be reduced and concentrated to the target plane.The measurement result shows that with the Al-based TFMG reflective layer, the average irradiance can be enhanced by 6.5~6.7%, while the uniformity is 85~86%.With TFMG coating, multi UV-LEDs arrangements can improve not only the output power, but also improve the uniformity.It shows that the uniformity of 5-set UV-LEDs with annular arrangement can be applied to the exposure system.Although the exposure time of 5-set UV-LEDs exposure system is longer than that of conventional mercury lamp exposure system, exposure design with more UV-LEDs can improve this disadvantage.However, the thermal conduction issue of LEDs should be taken into consideration.The preliminary result reveals that the exposed samples by Hg lamp exposure systems have dimensional deviation of 6~8%.But when the UV-LEDs with the PDMS lens and Al-TFMG was used, the dimensional deviation was reduced to 3~5%.This UV-LED exposure systems show potential to replace commercial ones.

(Fig. 5 .
Fig. 5.The radar chart of UV radiant intensity distribution curve of single UV-LED.

Fig. 9 .
Fig. 9. (a) ABS resin mold fabricated by 3-D fast printing and (b) the roughness of the ABS mold is less than100 nm.

Fig. 16 .
Fig. 16.Simulated average irradiance and uniformity of PDMS lens with different coverage angle of reflective layer.
(a), the variation of uniformity is not significant and the irradiance values #200327 -$15.00USD Received 5 Nov 2013; revised 19 May 2014; accepted 21 May 2014; published 5 Jun 2014 (C) 2014 OSA lies on 7.5-8.0mW/cm 2 range.When PDMS lens with TFMG layer compared with lens without TFMG layer is increased obviously by 6.5~6.7%(see Fig. 17 (b)).In addition, the trends of measurement results show good agreements with simulation ones, as shown in Fig. 17.Because of the roughness of the ABS mold (see Fig. 9 (b)), it could make radiation random scattering that caused the measured uniformity in Fig. 17 (a) lower than the simulated one.In addition, the surface roughness at the large zenith angle with TFMG coating could result in the radiation scattering, which could make the irradiance on the target plane decrease.That would be why the simulated result underpredicted as shown in Fig. 17 (b).