Study on Optical Property of Fabricating Free-form Micro-optical Element by Varying Dose Exposure Method

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1 Key Engineering Materials Online: ISSN: , Vol. 55, pp doi:1.48/ 13 Trans Tech Publications, Switzerland Study on Optical Property of Fabricating Free-form Micro-optical Element by Varying Dose Exposure Method Yanjun Sun 1,a, Yanbing Leng,b, Zhe Chen 3,c, Lianhe Dong 4,d 1,,3,4 Changchun University of Science and Technology 789 Weixing Road, Changchun, Jilin, P.R.China 13 a custsun@16.com, b custleng@yahoo.com, c cz9368@163.com, d custdong@16.com Keywords: Free-form; Varying Dose Exposure; Micro-Lens Array; Lithography Abstract. Free-form lens is a special element with non-rotating body and aspheric structure. The surface can t be expressed by stationary analytic formula, and generally it expressed by discrete list point. Free-form lens can distribute light intensity freely,and control light angle, optical path difference etc. Specific light spot is formed in illumination surface, meanwhile the light energy utilization ratio is improved greatly. There are two kinds of methods about Free-form fabrication, and the first kind of method is that free-form is grinded by a small grinding head,which is controlled by computer; its disadvantage is low precision, high waster rate,especially for optical material; The second kind fabricating method is that multi-degree-of-freedom single-point diamond turning equipment; its disadvantage is that plenty of sub-micron crack formed when brittle material fabricated. In addition, micro-lens array element can t be fabricated by the two kinds of methods. In allusion to the feature of free-form without stationary analytic formula,which varying dose exposure lithography method for free-form micro-optical element is presented for free-form microlens and array. The method is from the theory that the relation between different exposure energy and different developing depth, adopting laser direct writing equipment free-form photoresist structure is formed in material surface, then the free-form photoresist structure is transfered on the substrate by ion etching method. Any surface figure can be fabricated by controlling every point laser energy for this method, and surface roughness can t be effected because ion etching belongs to nanofabrication. In this paper, that low Distribution of light amplitude and relation of between exposure energy and exposure time was analysised on base of optical propagation theory and mathematical model of light distribution law was built and simulated by computer program.the results indicate that light energy distributes in accordance with specific law; the exposure depth increases with exposure time. The experiment of exposure and developing finished, used the BOL- 5 laser direct writing system in Changchun University of Science and technology,american Futurrex6A photoresist, 41nn He-Ne laser device, 5 NaOH developing solution. The experimental data coincide with simulation result via comparative analysis. Meanwhile,a set of free-form micro-lens array testing system was established and focal spot shape,energy distribution,focal distance,f parameter were tested about the micro-lens array. 1. Introrduction Free-form lens is a special element with non-rotating body and aspheric structure. The surface can t be expressed by stationary analytic formula; generally it expressed by discrete list point. Optical systems composition of lens, prism, mirror, traditional optical elements, light energy high loss in the Field of special light distribution. Free-form lens can distribute light intensity freely, and controlling light angle, optical path difference, specific light spot is formed in illumination surface, meanwhile the light energy utilization ratio is improved greatly. [1] There are two kinds of methods about Free-form fabrication, the first kind method is that freeform is grinded by a small grinding head, the grinding head is controlled by computer, and obtained free-form by controlling every point pressure and time. Its disadvantages are low precision, high waster rate,especially for optical material; [] The second kind fabricating method is that multidegree-of-freedom single-point diamond turning equipment, and its disadvantage is that plenty of All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-1/5/16,3:4:47)

2 13 Advances in Optics Manufacture sub-micron crack formed when brittle material fabricated. According to the feature of free-form without stationary analytic formula, which varying dose exposure lithography method for free-form micro-optical element is presented for free-form micro-lens and array. [3] The method is from the theory that the relation between different exposure energy and different developing depth,adopting laser direct writing equipment free-form photoresist structure is formed in material surface, then the free-form photoresist structure is transfered on the substrate by ion etching method. Any surface figure can be fabricated by controlling every point laser energy for this method,and surface roughness can t be effected because ion etching belongs to nanofabrication..the Principles Fabricating The principle of making spherical micro-lens through laser writing mutative does method is shown in Fig.1.We coat thick photoresist on the surface of base materials, which is shown in Fig.1(a).According to the photo-chemica principles of laser and photoresist film, we accomplish the mutative does exposure towards different positions of adhesive layer by means of controlling laser beam residence time in different positions and the motion trails on X,Y and Z axis, which is shown in Fig.1(b). [4] In order to dissolve the exposed adhesive film, we put the exposed adhesive film into developer, which is shown in Fig.1(c).Later, we accomplish the transfer from adhesive film surface structure to base materials by means of ion beam etching which is shown in Fig.1(d).From the above process, to study the distributing rules of the energy in adhesive film layer in the process of exposure and to grasp the principles and rules of photo-chemistry after sensitive material exposure are the keys to achieve micro-lens array structure. (a) (b) (c) (d) Fig 1: The principle of fabricating Free-form micro-lens array through laser writing vary does method 3.Mathematical Model Of Exposure Spatial Distribution 3.1 Light amplitude distribution Aiming at improving solar energy homogenization, the slender light beam that is generated through laser device should be expanded, and then focused. The light amplitude distribution expanded is [5] U( r) = exp( r )/ ω (1) Expanded light beam goes through photolithograph objective and the light spot amplitude distribution on the focal plane is exp a iπρr / λ f G( ρr,) = U ( r) πrj ( πrρr / λ f ) dr iλ f () In the formula, ω is Gaussian beam radius, f is objective focal distance, a is clear aperture radius, pr is focal plane radial coordinate. As we can see in Formula (1) and (), the ratios of incident Gaussian beam aperture and clear aperture have direct influences on the light intensity distribution of focal point writing. If the clear aperture is constant, light beam truncation will be more serious along with the magnifying of incident light beam diameter. In order to make deep seated photoresist sensitive, focal plane needs to be put into the adhesive layer. The light-field distribution in the photoresist layer affects exposure. If we neglect reflection, the light amplitude distribution in the adhesive layer is [6]

3 Key Engineering Materials Vol a π exp iπλ( f + δ ) ρ πδr U ( ρ, z) = U ( r)exp i J ( πρr) rdr iλ( f + δ ) λf ( f + δ ) In Formula (3), p is frequency spectrum plane radius, ρ r is the radial radius of defocus plane, δ is defocusing-amount, δ is the distance between focal point and the upper surface of adhesive layer.δ can be either positive value or negative value. When the base is made of materials with high refractive index, we should consider the effects of reflected light. Assuming Z stands for the distance from reflected light to the upper surface of adhesive layer, d stands for the thickness of adhesive layer, Formula (3) can be changed into (3) Z π exp iπλ( f + δ + ) ρ U( ρ, z) = U ( r)exp i ( f ) U Z πλ + δ + + ρ + iλ( f δ ) n + + n n d Z λ 1 3. Exposure changing rules following length In the condition that we have known the light amplitude distribution in adhesive layer, assuming exposed light beam is perpendicular to the surface of substrate, we can use Lambert-Beer law to describe photo-chemical reaction Z deep in the adhesive layer like Formula (5). I( zt, ) = I( zt, ) [ am 1 1( zt, ) + am ( zt, ) + am 3 3( zt, )] (5) z In Formula (5), L (z, t) is the light intensity Z deep in the adhesive layer at the time of t, a1, a and a3 are absorbing constants. The decomposition rate after solar energy absorption of adhesive layer that is Z deep is (4) M1( zt, ) = M1( zt, ) I( ztc, ) t So we can get the relation between depth and exposure (6) t M( zt, ) = M( z,)exp C I( z, τ) dτ (7) It represents the exposure energy Z deep at the time of t, and we can record it as E(z, t).assuming the ordinary density is 1,we can get de( zt, ) M( zt, ) = exp [ CE( zt, )], I( zt, ) = (8) dt After integrals with respect to t direct at Formula (7), we can get I( zt, ) z Substituting Formula (8) into Formula (9), we can get t t dτ = I( z, τ) [ AM( z, τ) + B] dτ (9) E( zt, ) A = { exp [ CE( zt, )] 1 } BE( zt, ) z C Formula (1) stands for the spreading rules of exposure E following Z at the time of it. (1) 4.The Computer Emulation Of Photoresist Exposure According to the former mathematical model, we emulate the exposure effects in the photoresist by computer. We choose quadrupling optical writing objective, 5mm focal distance,.1 numerical aperture and 1mm optical pass diameter. We select American Futurrex6A photoresist. The depth of coated adhesive layer is 4µm.We choose He-Cd gas laser which has good homochromatism and the wavelength is 41m.We adopt Gaussian beam and exposure ratio A is.6,b is.8,c is.1.from Formula (4); [7] the light distribution in emulation adhesive film is shown in Fig.(). Light

4 134 Advances in Optics Manufacture amplitude distribution spreads a little following depth. As is shown in Fig (3), the broad curve stands for the relation emulation curve of exposure depth and time. Exposure depth increases following time and gradually becomes saturated. The slender curve represents the ideal curve changing linearly. Fig : Light distribution law in photoresist film 5. Experiment Research Fig 3: Exposure depth changing rules following time The research of using laser writing mutative does exposure method to make micro-lens array can be divided into several steps:1substrate treatment. We should deal with the pollutions on the surface, enhancing the adhesive force of photoresist and substrate. coating photoresist. We use centrifugation to coat PR1-1A positive photoresist µm on the quartz surface.3 roast. We put coated substrate into the environment that is 9 and baked it for minutes. Then, we make it cool naturally and remove the volatile matters in the photoresist.4mutative does exposure. We put the coated substrate on the work table of laser writing system. The laser writing system is BOL5 compound coordinate laser writing system that is developed together by Changchun University of Science and Technology and Harbin Institute of Technology, exposuring sensitive adhesive layer through the movement of work table and exposure system controlling programs. [8] 5 development. In the temperature of, we get photoresist micro-lens array by using developing solution matched with photoresist to develop substrate. That photoresist films are the same kind and have the same thickness, which developed during the experiment. After each exposure, they are developed in the alkaline solution, the density of which is 5%. And then, they are tested their depth under atomic force microscope. The results are shown in Table 1.The curve that Table 1 describes shown in Fig.4.Compared with Fig.3 and Fig 4, the experimental curve basically depends on the rules of emulation curve. Analytically, a few prominent points are led by exposure and development parameter controlling errors during the experiment. [9] 6ion etching. Because the mechanical ability and optical property of photoresist micro-lens are bad, we need to use ion etching to transfer micro-lens pattern to the surface of quartz substrate. We adopt ICP81 inductively coupled plasma etcher. Etching gas is a mixture of Ar and CF4; etching speed is 5.6nm/min; ion beam current density is 1mA/cm and ion-beam energy is 5eV.In order to ensure the effects of device side walls, we apply incident angle. In the experiment, the free-form micro-lens array micro effects are shown in Fig.5. Table 1 Relation between exposure time and depth exposure time exposure depth exposure time exposure depth

5 Key Engineering Materials Vol Fig 4: Scatter diagram between exposure time and depth Fig 5: Free-form spherical micro-lens arrays 6. Test Of S Free-form Micro-lens Array 6.1 Surface type detection Because probe will hurt the surface of lens array slightly and then influence the optical properties, when we apply contact process,so we design to adopt indirect measurement method, which is a optical interference measurement. [1]The measurement principle is shown in Fig.6.Optical system is Twyman-Green interference light path. Collimated He-Ne laser beams gather in the sphere center of micro-lens through micro objective. The beams are reflected by curved surface. Surface type errors that carry micro-lens units return from the ordinary route, interfering with another referential light beam and forming interference fringes. From interference fringes, we can know the deviation between measurement unit micro-lens and normal micro-lens. Fig 6 :Interference system of measuring surface type schematic plot 6. Optical property test system The optical test system schematic are shown in Fig.7.The testing system includes He-Ne light source, expansion system, micro-lens adjusting bracket, micro objective, CCD sensor, image grabbing card and processing software etc. The exit light beams from laser device are expanded. And then they irradiate on a few numbered micro-lenses after passing through light-limited diaphragm (the aperture is 1µm).The spotlight focal of micro-lens are collected by CCD sensor after imaging through micro objective, and then we can do numerical analysis of focal image via computer. The system is easy to use. What s more, it can accurately measure pulse, continuous laser light beam diameter and power/energy. Also, it covers pretty broad wavelength range. Processing software can display, analyses and save measuring results. The design of modular mode makes the system an ideal instrument to achieve quality control of micro-lens array. The greatest advantage of the system is the high measure efficiency, that is, it can measure scores of or even hundreds of lenses at one time and we can directly see the measuring results.fig.8,fig.9 are the focal image and point spread function of free-form surface micro-lens.

6 136 Advances in Optics Manufacture Fig 7: Micro optical test system schematic Fig 8: Square micro-lens array focal image We fix micro objective and CCD and adjust micro-lens to a suitable position making micro-lens focal spot which has the largest light intensity distribution presented from CCD, and that is the focal spot imaging of micro-lens. The focal length of micro-lens is the difference of flexible shelf reading s1 and s.after measuring focal distance, we can get its F No. 7 Conclusion This article studies the optical properties of free-form spherical micro-lens array made via laser mutative does exposure, establishes the theory mode of light amplitude in the photoresist and verifies the academic mode through emulation technology and experimental methods. The results indicate that when laser transported in the photoresist, its energy spread nearly isn t influenced by depth and there is a certain curvilinear relationship between exposure depth and exposure time together with solar energy, which is the premise and basis of achieving the mutative dose production of free-form surface micro optical device. What is needed to say is that the solar energy of most laser writing device cannot be changed. Therefore, we can program to control laser movement trail and residence time on the photoresist surface so that we can accomplish mutative dose exposure. At the same time, the square micro-lens array test system set by means of optical system and CCD etc. offer a basis to ensure the quality and property of micro-lens array. References [1] L. L. Zhang, Y. C. Qu, W. J. Zhao, D. M. Reng and X. Y. Hu, Laser Phys.9, 8. []G.Guo,B.Sheng Research on laser direct writing system and its lithography properties, Proc. S PIE. 9. [3] Y.L. Han, D.S. Liu, X.P. Jiang, Sqare selffocu- sing lens array and its image,acta Photonica Sinica, 7. [4] W. H. Yan, J. Wu, P. Chen, J. T. Dou, C. Y. Pan, Y. M. Mu and J. M. Lu, Laser Phys. 9. [5] Y.J. Sun, Y.B. Leng, Study on antireflective relief periodic structure of sapphire infrared window. Infrared Technology, 1. [6] M. L. Siniaeva, M. N. Siniavsky, V. P. Pashinin, Ad. A. Mamedov, V. I. Konov and V. V. Kononenko, Laser Phys.5, 9. [7]SONKA M, HLAVAC V, BOYLE R.Image Processing, Analysis, and Machine Vision. Posts & Telecom Press, 3. [8] G.A.Cranch,G.M.H.Flockhart,and C.K.Kirken dall,ieee Sens.J.8, 8. [9] V.A.Sautenkov,Yu.V.Rostovtsev,and E.R.Eliel,Phys.Rev.A 78, 8. [1] F. Bai, Q. P. Wang, Z. J. Liu, X. Y. Zhang and W. J. Sun, Laser Phys.11, 1.

7 Advances in Optics Manufacture 1.48/ Study on Optical Property of Fabricating Free-Form Micro-Optical Element by Varying Dose Exposure Method 1.48/