Multi-Repeated Projection Lithography for High-Precision Linear Scale Based on Average Homogenization Effect

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1 sensors Article Multi-Repeated Projection Lithography for High-Precision Linear Scale Based on Average Homogenization Effect Dongxu Ren *, Huiying Zhao, Chupeng Zhang, Daocheng Yuan, Jianpu Xi, Xueliang Zhu, Xinxing Ban, Longchao Dong, Yawen Gu Chunye Jiang State Key Laboratory for Manufacturing Systems Engineering, Xi an Jiaotong University, Xi an , China; (H.Z.); (C.Z.); (D.Y.); (J.X.); (X.Z.); (X.B.); (L.D.); (Y.G.); (C.J.) * Correspondence: rendongxu313@126.com; Tel.: Academic Editor: Vittorio M. N. Passaro Received: 29 February 2016; Accepted: 11 April 2016; Published: 14 April 2016 Abstract: A photo method for manufacturing an incremental linear scale using projection is presented. method is based on average homogenization effect that periodically superposes light intensity locations pitches in mask to make a consistent energy distribution at a specific wavelength, from which accuracy a linear scale can be improved precisely using average pitch step distances. method s oretical is in 0.01 µm for a periodic mask a 2-µm sine-wave. intensity models in focal include rectangular grating on mask, static positioning, lens focal, which affect pitch uniformity less than in common linear scale projection splicing process. It was analyzed confirmed that increasing repeat exposure number a single stripe could improve accuracy, as could adjusting exposure spacing to achieve a set proportion black white stripes. According to experimental results, effectiveness photo method is confirmed to easily realize a pitch accuracy 43 nm in any 10 locations 1 m, whole length accuracy linear scale is less than 1 µm/m. Keywords: projection ; linear scale; linear displacement sensor; method; average homogenization effect 1. Introduction Linear scale is an indispensable component linear displacement sensors is defined as grating structure that is printed on a metal or glass substrate material by photo or mechanical scribing. It is key technology for precision displacement measurements, which are widely used in ultra-precision machining equipment, ultra-precision measuring instruments, semiconductor manufacturing equipment, where dem for position accuracy is always increasing. To improve accuracy linear scale, several processing methods have evolved, such as mechanical ruling [1], ion-beam etching [2], nanoimprinting, UV optical. However, mechanical ruling ion-beam etching primarily produce diffraction gratings, which require deep grooves strict shapes that can produce non-ideal curved gratings [3]. roller subdivision 2PI s fer challenges to nanoimprinting for high-precision grating; a special rotating exposure to roller mold fabrication was analyzed to fabricate gratings in a large area [4]. Projection is a UV optical technique that presents a solution to Sensors 2016, 16, 538; doi: /s

2 Sensors 2016, 16, issues associated precision resolution; this paper will review a method for manufacturing a high-precision linear scale. Sensors performance 2016, 16, 538 a projection system is characterized by three major parameters: 2 17 resolution, depth focus, overlay accuracy [5]. When system configuration is invariable, that presents quality a solution to grating issues lines associated will only beprecision restricted byresolution; focusing accuracy this paper will photoresist review resolution, a method for manufacturing inaccuracy a high-precision grating lines linear include scale. s, rotational skew s performance a projection system is characterized by three major parameters: mask, mask feature placement s. resolution, depth focus, overlay accuracy [5]. When system configuration is In linear scale projection, in addition to above problems, main factors that invariable, quality grating lines will only be restricted by focusing accuracy affectphotoresist accuracy resolution, include inaccuracy static grating dynamic lines include positioning accuracy, s, rotational parallelism focal skew s photoresist mask, mask onfeature scale, placement s. uniformity light intensity distribution. Several methods In linear have scale adopted projection, principlein addition splicingto toger, above inproblems, which patterns main factors are adjacent that printed affect accurately accuracy on wafer at an include accurate distance, static such dynamic as positioning step--repeat accuracy, method [6], single-step parallelism method [7], focal step--scan photoresist method on [8,9], scale, where x- uniformity y-direction light intensity positioning accuracies distribution. are notseveral high. methods hexagonal have adopted seamless scanning principle exposure splicing method toger, behaves in which advantage patterns for fabrication are adjacent large area printed grating accurately than stitching on wafer exposure at an accurate method distance, in steppers such as [10], adjacent step--repeat hexagonal method [6], single-step method [7], step--scan method [8,9], where x- y-direction scans overlap partially integrated doses from successive scans produce uniform exposure over positioning accuracies are not high. hexagonal seamless scanning exposure method behaves whole panel, however, we adopt adjacent quadrangular scans overlap by integer times pitch advantage for fabrication large area grating than stitching exposure method in steppers [10], oretically, adjacent hexagonal pitch s scans are overlap homogenized partially by integrated doses exposure from successive scans position produce grating on uniform mask. exposure influence over whole panel, however, processes we adopt methods adjacent on quadrangular accuracy scans overlap sby in linearinteger scale projection times pitch oretically, has been pitch rarely s reported. are homogenized by exposure To resolve position se grating issues, on a mask. influence photo processes method methods anon average homogenization accuracy effect s that in can linear improve scale projection accuracy has linear been scales rarely is reported. proposed in this paper. light To intensity resolve se function issues, a focal photo accuracy method expression an average linear scale homogenization effect that can improve accuracy linear scales is proposed in this paper. are given to describe operating principles ory proposed method. influences light intensity function focal accuracy expression linear scale are internal pitch s in mask on accuracy are simulated analyzed. It is given to describe operating principles ory proposed method. influences verified that re is a proportional relationship between grating strip repetitions internal pitch s in mask on accuracy are simulated analyzed. It is accuracy. verified that integer re times is a pitch proportional relationship exposurebetween spacing distance grating is strip achieved repetitions that can adjust proportion accuracy. black white integer stripes. times pitch defocus s exposure caused spacing bydistance a skewis focus achieved that or tilt photoresist can adjust onproportion scale areblack reduced white homogenized. stripes. defocus s caused by a skew focus or tilt photoresist on scale are reduced homogenized. 2. Photo Principle 2. Photo Principle fundamental principles projection for a high-precision linear scale are illustrated fundamental in principles 1. focal is projection calibrated by for a high-precision lens linear system scale to ensure are illustrated a high-precision in 1. grating focal pattern in is calibrated photoresist by. Divergent lens light a certain system to ensure a high-precision grating pattern in photoresist. Divergent light a wavelength from pulsed xenon lamp passes through concave lens into a parallel light, which certain wavelength from pulsed xenon lamp passes through concave lens into a parallel light, irradiates grating pattern on mask to make it accurately projected on photoresist by which irradiates grating pattern on mask to make it accurately projected on photoresist by lens. lens. 1. Scheme 1. Scheme proposed proposed projection, including including (a) conceptual (a) conceptual drawing n time exposure; (b) light intensity distribution exposure drawing n time exposure; (b) light intensity distribution distances. exposure distances.

3 Sensors 2016, 16, When irradiation time reaches a set value t at a certain position, a complete exposure process is completed. Meanwhile, electrical control system triggers pulsed xenon lamp power f, motion control system drives grating substrate to a distance (S 1, S 2,..., S n ) relative to lens in one direction. Following periodic operation process, light intensity eventually is superimposed at positions to achieve averaging. 3. ory 3.1. Fundamental ory Because lens numerical aperture, lens distortion, optical vignetting effect, pitch on mask accuracy will cause projection light intensity pattern s on photoresist. light intensity at positions can be expressed as: $ I 1 pxq, x P r0, L 1 s & I pxq % I 2 pxq, x P rs 1, L 2 ` S 1 s I 3 pxq, x P rs 1 ` S 2, L 1 ` S 1 ` S 2 s. n 1 ř I n pxq, x P S i, L n ` n 1 j ř S i i 1 i 1 (1) where L n is nth projection length on photoresist (when projection lens reduction ratio is 0.25, mask length is 4L), I n pxq is nth projection light intensity, S i is spacing distance between ith position (i 1)th position, S i mp ` i, m is integer pitch number exposure spacing distance, p is ideal pitch linear scale, i is ith spacing distance. To better explain exposure dose distribution projection, assume re are km = n 1 pitches on mask I ij pxq is jth period light intensity ith position exposure, k is repeat exposure number each pitch, kmp = 4L. exposure dose is defined as light intensity multiplied by exposure time [11]. sum expression exposure dose under se conditions can be expressed as: Part B: $ ř D m0 pxq 1 I ij px ` i q t & % i 1 ř D 2m0 pxq 2 I ij px ` i q t i 1. ř D km0 pxq k I ij px ` i q t subject to j pk 1q m ` m 0 pi 1q m, m 0 P r1, ms. Part C: $ D km`m0 pxq k`1 ř I ij px ` i q t & % i 1 i 2 D pk`1qm`m0 pxq k`2 ř D n pk 2q`m0 pxq. i 3 n pk 2qm`k 1 ř i n pk 2qm I ij px ` i q t I ij px ` i q t (2) (3)

4 Sensors 2016, 16, subject to j pk 1q m ` m 0 pi pn pk 2q mqq m, m 0 P r1, ms. Part D: nř D n pk 1qm`m0 pxq I ij px ` i q t i n k`1 nř $ & D n pk 2qm`m0 pxq I ij px ` i q t % D n m`m0 pxq. i n k`2 n ř i n 1 I ij px ` i q t subject to j pk 1q m ` m 0 pi pn 1qqm, m 0 P r1, ms. As shown in 2a, re is a critical point in process exposure development technology where exposure energy is higher than threshold dose, after which resist chromium coating will be washed away to form black white stripes, i.e., when [12]: D n pxq ą D t (5) threshold critical is energy line that intersects D pxq function surfaces to form cross-points x i, corresponding to difference between two adjacent x coordinates is width black white grating strips; formula can be expressed as: p 1 i x ˇ i ˇX 1 rd i pxq D t s (6) where x is function root value D i pxq D t p 1 i is difference between function root value also is pitch formed by. From Equations (2) (4), 2, it can be seen that energy amplitude distribution Part B Part D is incremented or decremented as process ends; only energy curve distribution Part C is suitable for accuracy analysis. n, oretical this point can be written as: p 1 i p1 i p (4) x i ˇˇX 1 rd i pxq D t s p ˇˇˇˇˇX 1 «n pk 2qm`k 1 ř x i i n pk 2qm I ij px ` i q t D t ff p (7) where p 1 i is between ideal pitch pitch formed by projection. Obviously, average value n exposure doses D n pxq is smaller than maximum MaxrD n pxqs: n pk 2qm`k 1 ÿ i n pk 2qm I ij px ` i q t ă Max ki ij px ` i q t (8) n, accuracy comparison two methods is given by: p 1 i ă Max r p is (9) subject to i P r1, ns. Equations (8) (9) show that average s are accumulated homogenized regularly from position energies in projection, which are smaller than maximum s respect to same position energy in common projection. Thus, grating accuracy will be improved.

5 Sensors 2016, 16, Sensors 2016, 16, Imaging process using a photoresist. (a) sum exposure dose under condition ( = 2. Imaging process using a photoresist. (a) sum exposure dose under condition = ); (b) scale grating formed by developing threshold. (S 1 = S 2 = S n = P); (b) scale grating formed by developing threshold Mask Error Model 3.2. Mask Error Model mask pattern for linear scale is uniform rectangular stripes. Letting N be mask pattern for linear scale is uniform rectangular stripes. Letting N be largest diffraction order that passes through lens, using dense space diffraction largest diffraction order that passes through lens, using dense space diffraction pattern pattern Euler s orem, light intensity image is [13]: Euler s orem, light intensity image is [13]: ( ) = +2 Nÿ 2 (2 / ) (10) I i pxq ˇ ` 2 a j cos p2πjx{pq (10) ˇa0 ˇ where where p is is pitch, pitch, a is DC component, is diffraction order. For case equal 0 is DC component, j is diffraction order. For case equal lines lines spaces, spaces, diffraction diffraction order order amplitudes amplitudes become: become: = sin ( / ) pjπw{pq a (11) j (11) jπ In In precise precise or or ultra-precise ultra-precise manufacturing manufacturing process process for for grating grating mask, mask, micron- micron- or or nanometer-level nanometer-level s s are are inevitable inevitable among among pitches, pitches, which which does does not not meet meet even even spacing spacing requirements requirements multi-slit multi-slit Fraunher Fraunher diffraction. diffraction. According to to analysis analysis Fourier Fourier optical optical transfer transfer function, function, image image light light intensity intensity is is equivalent equivalent to to sum sum frequency harmonics; n, n, projection projection image image intensity intensity separate separate pitches pitches can can be be approximated approximated as as a single-slit single-slit Fourier Fourier harmonic harmonic expression, expression, finally, finally, can can be be written written as: as: «ff p 1 = (, ) = i x i ˇ ˇX 1 k`i 1 ř I m px, p i q t D t p m i» fi = x i ˇ ˇX 1 k`i 1 ř ř ˇ `+2 2 N 2 (12) a j cos (2 / p2πjx{p i q ) t = D t fl p m i ˇa0 j 1 ˇ j Exposure Repeated Number Model 3.3. Exposure Repeated Number Model Because resist corrosion threshold to energy required is constant, when exposure time t is setbecause to a constant resist value, corrosion exposure threshold number to energy is inversely required proportional is constant, towhen light intensity; exposure n, time t relationship is set to a constant can be expressed value, as: exposure number is inversely proportional to light intensity; n, relationship can be expressed as: D constant pxq ki k1 pxq t (13) subject to k P 1, n 1, where I k1 pxq is light ( ) intensity, = corresponding ( ) to repeated number (13) k. maximum average subject to [1, energy ], where repeated exposure numbers can be expressed as: ( ) is light intensity, corresponding to repeated number k. maximum average energy repeated exposure numbers can be expressed as:

6 Sensors 2016, 16, Max řk`i 1 m i Im k1 pxqt k j ă Max řk`i 2 m i Im pk 1q1 pxqt k 1 j ři`1 ă ă Max m i I21 m pxqt 2 j ă ř i m i Im 1 pxq t (14) subject to i, k P 1, n 1. average has same law, so maximum average energy repeated exposed number can be written as: Max p 1 i prn kq ă Max p 1 i prn k 1q ă ă Max p 1 i prn 2q ă Max p 1 i prn 1q (15) subject to i P 1, n 1, where RN represents repeated number. It reflects influence repeated exposure number on accuracy Spacing Distance Model exposure interval distance is considered as an integer multiple a pitch in proposed projection method, which does not accurately reflect photo process. In actual process, existence positioning s dem for compensation will produce submicron nanometer for exposure interval distance, which need to be discussed because y have a great influence on accuracy. Thus, we intend to describe sum expression exposure dose non-integral pitch s: $ & % D n k`2 pxq D n 1 pxq D n pxq D 1 pxq k ř m 1 D 2 pxq k`1 ř D n k`1 pxq nř m n k`2 n ř m n 1 n ř m n m 2. nř I m px pq t I m px pq t m n k`1 I m px pq t ` I m px pq t 1ř m 1 I m px pq t. I m px pq t ` k 2 ř I m px pq t I m px pq t ` k 1 ř m 1 m 1 I m px pq t where ` p p represent positive deviation negative deviation spacing distance, respectively. 4. Simulation average homogenization effect proposed method has proven oretically that several micro/nano s have little effect on projection accuracy; simulations are carried out as follows Influence Mask Errors To study impact pitch on accuracy, three types s are introduced into simulation: (1) sum sinusoid pitch on mask is equal to zero; (2) sum increasing pitch on mask is more than zero; (3) sum decreasing pitch on mask is less than zero. (16)

7 Sensors 2016, 16, shows relative light intensity relationship between a mask s, an ideal mask out s, projection method. maximum intensity amplitude projection method is smaller than or two. Assuming parameter threshold intensity is 0.25, linear grating can be formed as in 4, which shows developing results function s. Sensors 2016, 16, Sensors 2016, 16, Relative light intensity relationship between a mask s, an ideal mask out 3. Relative light intensity relationship between a mask s, an ideal mask out s, s, projection method. (a) Sinusoid pitch on mask; (b) Increasing 3. Relative pitch projection light intensity on mask; relationship (c) Decreasing method. between pitch (a) a mask on Sinusoid mask. pitch s, an ideal on mask; (b) out Increasing s, projection method. (a) Sinusoid pitch on mask; (b) pitch on mask; (c) Decreasing pitch on mask. Increasing pitch on mask; (c) Decreasing pitch on mask. 4. Developing results function s. Zones 1, 2 3 are formed from intensity, mask s, ideal mask respectively in (a c) 4. Developing results function s. Zones 1, 2 3 are formed from 4. Developing 3. (a) Grating results sinusoid pitch ; function (b) Grating s. increasing Zones 1, pitch 2 ; 3 are (c) formed Grating from intensity, mask s, ideal mask respectively in (a c) intensity decreasing pitch. 3. (a) Grating, sinusoid pitch mask ; (b) Grating s, increasing ideal pitch mask; respectively (c) Grating in (a c) decreasing 3. (a) Grating pitch. sinusoid pitch ; (b) Grating increasing pitch ; (c) Grating 5 shows pitch comparison a mask s in projection decreasing pitch.. When 10 pitch s red thread were sinusoidally distributed at 5 shows pitch comparison a mask s in projection maximum peak-valley value 2 µm, maximum blue thread would be 0.01 µm. When 10 pitch s red thread were sinusoidally distributed at method, linear scale precision was increased maximum peak-valley value 2 µm, maximum blue thread would be 0.01 µm by 99.5%. Meanwhile, by comparing influence proposed method on pitch type, method, linear scale precision was increased while pitch red thread was set to a linear increasing function distribution or linear by 99.5%. Meanwhile, by comparing influence proposed method on pitch type, decreasing function distribution at maximum 0.9 µm, maximum blue while pitch red thread was set to a linear increasing function distribution or linear thread was reduced to 0.28 µm 0.27 µm, respectively, by proposed method, decreasing function distribution at maximum 0.9 µm, maximum blue linear scale precision was increased by 68.9% 70%, respectively. thread was reduced to 0.28 µm 0.27 µm, respectively, by proposed method, linear scale precision was increased by 68.9% 70%, respectively. 5 shows pitch comparison a mask s in projection. When 10 pitch s red thread were sinusoidally distributed at maximum peak-valley value 2 µm, maximum blue thread would be 0.01 µm method, linear scale precision was increased by 99.5%. Meanwhile, by comparing influence proposed method on pitch type, while pitch red thread was set to a linear increasing function distribution or linear decreasing

8 Sensors 2016, 16, function distribution at maximum 0.9 µm, maximum blue thread was reduced to 0.28 µm 0.27 µm, respectively, by proposed method, linear scale precision was increased by 68.9% 70%, respectively. Sensors 2016, 16, Sensors 2016, 16, Pitch comparison a mask s in projection 5. Pitch comparison a mask s in projection. projection pattern pitch mask is set respectively. as (a) ( ) = ( ) projection + ; (b) ( ) pattern = + ; pitch (c) ( ) = +. mask is set respectively as (a) p i pxq 5. Asin Pitch pωxq `comparison p; (b) p i pxq a mask Kx ` p; s (c) pin i pxq projection Kx ` p.. Referring to projection 3 5, in pattern comparison pitch mask phase mask is set respectively projection Referring as (a) to ( ) intensity, s = ( ) 3when + ; 5 in (b) curvature comparison ( ) = + ; pitch (c) phase curve ( ) = +. was positive mask in projection 5, phase intensity, when curvature intensity pitch was fset curve to wasleft positive in in3; on or 5, h, phase when curvature Referring to pitch 3 curve 5, was in comparison negative in 5, phase phase mask projection intensity was fset to left in 3; on or h, when intensity, intensity was when fset curvature to right in pitch 3. curve was positive in 5, phase curvature pitch curve was negative in 5, phase It can be seen from se intensity simulations was that fset to proposed left in projection 3; on or h, process when can intensity was fset to right in 3. reduce curvature influence pitch mask pitch curve was on negative accuracy in linear 5, scale. phase It can be seen intensity from se was fset simulations to right thatin proposed 3. projection process can reduce influence 4.2. Influence It can be mask seen Repeated pitch from Exposure se onsimulations Number accuracy that linear proposed scale projection. process can reduce influence mask pitch on accuracy linear scale Influence To analyze Repeated influence Exposure Number repeated exposure number grating positions on 4.2. accuracy Influence Repeated Exposure projection Number, 10 repetitions three types To functions analyze were applied influence to simulation repeated exposure using number light intensity, grating strips, grating positions pitch s. on accuracy three To analyze graphs (a c) influence projection s repeated 6 8, correspond exposure to 10each number or. repetitions three grating types positions on functions accuracy projection, 10 repetitions three types were applied to simulation using light intensity, grating strips, pitch s. three functions were applied to simulation using light intensity, grating strips, pitch s. graphs (a c) s 6 8 correspond to each or. three graphs (a c) s 6 8 correspond to each or. 6. Relative light intensity comparison 10 repeat grating; numbers represent repetitions proposed method. (a)relative intensity sinusoid pitch ; (b) Relative intensity increasing pitch ; (c)relative intensity decreasing pitch. 6. Relative light intensity comparison 10 repeat grating; numbers represent 6. Relative light intensity comparison 10 repeat grating; numbers represent repetitions proposed method. (a)relative intensity sinusoid pitch ; (b) Relative repetitions intensity increasing proposed pitch method. ; (c)relative (a) Relative intensity intensity decreasing sinusoid pitch pitch. ; (b) Relative intensity increasing pitch ; (c) Relative intensity decreasing pitch.

9 Sensors Sensors 2016, 2016, 16, 16, Sensors 2016, 16, Developing results function s repeat number. Zone 1 to 10 are 7. Developing results function s repeat number. Zone 1 to 10 are formed from respective intensities repetitions proposed method. (a) formed from respective intensities intensities repetitions repetitions proposed proposed method. method. (a) Grating (a) Grating sinusoid pitch ; (b) Grating increasing pitch ; (c) Grating decreasing pitch Grating sinusoid sinusoid pitch ; pitch (b) ; Grating (b) Grating increasing increasing pitch ; pitch (c) Grating ; (c) Grating decreasing decreasing pitch. pitch.. 8. Pitch comparison repeat grating 8. Pitch comparison repeat grating numbers. projection pattern pitch s mask are set respectively numbers. projection pattern pitch s mask are are set set respectively as as (a) as (a) ( ) = ( ) + ; (b) ( ) = ( ) + ; (b) ( ) = + ; (c) ( ) = + ; (c) ( ) = +. (a) p i pxq Asin pωxq ` p; (b) p i pxq Kx ` p; (c) p i pxq ( ) = +. Kx ` p. shows relative light intensity comparison 10 repeat gratings. With an 6 shows relative light intensity comparison 10 repeat gratings. With an increase in number repetitions, when pitch is incrementally changed, light increase in in number repetitions, when when pitch pitch is incrementally is incrementally changed, changed, light intensity light intensity phase shifts to right; in contrast, when pitch is decreasing, light intensity phase intensity shifts phase to shifts right; to in contrast, right; in when contrast, pitch when is pitch decreasing, is decreasing, light intensity light phase intensity shifts phase shifts to left. maximum amplitude light intensity decreased. 7 shows to phase left. shifts to maximum left. amplitude maximum amplitude light intensity light decreased. intensity decreased. 7 shows developing shows developing results function s repeat number; 7a c are a results developing results function sfunction repeat s number; repeat 7a c number; are a sinusoidal 7a c function are sinusoidal function, linear increasing function, linear decreasing function,, sinusoidal linearfunction increasing, function linear, increasing linear function decreasing, function linear, respectively. decreasing function Zone 1 to, zone respectively. Zone 1 to zone 10 are formed from intensity repetitions 10 respectively. are formedzone from to intensity zone 10 are formed from repetitions intensity proposed method. repetitions proposed method. proposed method. 8 shows that maximum pitch is reduced an increase in repeated exposure 8 shows that maximum pitch is reduced an increase in repeated number. shows 8a shows that that maximumpitch sinusoidal is reduced decreased from an 2 increase µm to 0.01 in µm, repeated 8b exposure number. 8a shows that maximum sinusoidal decreased from 2 µm to 0.01 shows exposure that number. maximum 8a linear shows increasing that maximum decreased sinusoidal from 0.9 µmdecreased to 0.28 µm, from µm to c µm, 8b shows that maximum linear increasing decreased from 0.9 µm to 0.28 µm, shows µm, that 8b maximum shows that linear maximum decreasinglinear increasing decreased from 0.9 decreased µm to 0.27 from µm. 0.9 µm to 0.28 µm, 8c shows that maximum linear decreasing decreased from 0.9 µm to 0.27 µm. It can be 8c shows seen from that se maximum simulations linear that decreasing increasing decreased exposure from repetitions 0.9 µm to 0.27 grating µm. It can be seen from se simulations that increasing exposure repetitions grating stripsit will can reduce be seen pitch from s, se which simulations can promote that increasing improvement exposure repetitions accuracy proposed grating strips will reduce pitch s, which can promote improvement accuracy proposed projection strips will reduce pitch process. s, which can promote improvement accuracy proposed projection process. projection process Influence Spacing Distance Errors 4.3. Influence Spacing Distance Errors 4.3. Influence To accurately Spacing analyze Distance Errors influence spacing distance non-integral pitch s on, To accurately analyze influence spacing distance non-integral pitch s on To accurately ideal analyze intensity period influence was set to 20 spacing µm, distance spacing distances non-integral werepitch set tos 0.1 µm, on 0.2, ideal intensity period was set to 20 µm, spacing distances were set to ±0.1 µm,, µm, 0.3 ideal µmintensity symmetrically. period was set to 20 µm, spacing distances were set to ±0.1 µm, ±0.2 µm, ±0.3 µm symmetrically. ±0.2 µm, 9 ±0.3 shows µm symmetrically. relative light intensity comparison spacing distance s. phase 9 shows relative light intensity comparison spacing distance s. shows positive relative negative light intensity equivalence comparison is symmetrically spacing distributed distance relative s. to phase positive negative equivalence is symmetrically distributed relative to ideal phase intensity positive period. Assuming negative equivalence parameter threshold is symmetrically intensitydistributed 0.25, linear relative grating to ideal intensity period. Assuming parameter threshold intensity is 0.25, linear grating can ideal intensity period. Assuming parameter threshold intensity is 0.25, linear grating can

10 Sensors 2016, 16, Sensors 2016, 16, cansensors be formed 2016, 16, 538 as in 10, which shows that developing results correspond 10 spacing 17 distance be formed s. as in 10, which shows that developing results correspond spacing distance be formed s. as in 10, which shows that developing results correspond spacing distance s. 9. Relative light intensity comparison spacing distance s: (a) spacing 9. Relative light intensity comparison spacing distance s: (a) spacing distance 9. Relative is ±0.1 light µm; intensity (b) spacing comparison distance is ±0.2 µm; (c) spacing distance s: is (a) ±0.3 spacing µm. distance is 0.1 µm; (b) spacing distance is 0.2 µm; (c) spacing distance is 0.3 µm. distance is ±0.1 µm; (b) spacing distance is ±0.2 µm; (c) spacing distance is ±0.3 µm. 10. Developing results correspond spacing distance s (a) ±0.1 µm; (b) ±0.2 µm; (c) ± Developing µm. Zones 1, results 2, correspond 3 are formed from spacing intensity distance s a spacing (a) distance ±0.1 µm; (b) negative ±0.2 µm; 10. Developing results correspond spacing distance s (a) 0.1 µm; (b) 0.2 µm; deviation, (c) ±0.3 ideal µm. mask, Zones 1, 2, spacing 3 are distance formed from positive intensity deviation, a respectively. spacing distance negative (c) 0.3 µm. Zones 1, 2, 3 are formed from intensity a spacing distance negative deviation, ideal mask, spacing distance positive deviation, respectively. deviation, ideal mask, spacing distance positive deviation, respectively. Table 1. Simulation results unit (µm). Table 1. Simulation results unit (µm). Spacing Distance Table Simulation 19.8 results 19.9 unit 20 (µm) Spacing Pitch Distance Spacing Black Distance Pitch grating White Black Pitch grating Black White grating grating White grating It can be seen from se simulations that when threshold exposure dose is constant, spacing It can distance be seen s from se simulations ratio black that stripes when white threshold stripes are exposure inversely dose proportional, is constant, spacing pitch distance has s not been changed ratio in black Table stripes 1, which white will affect stripes are accuracy inversely proportional, half cycle pitch has not been changed in Table 1, which will affect accuracy half cycle

11 Sensors 2016, 16, It can be seen from se simulations that when threshold exposure dose is constant, spacing distance s ratio black stripes white stripes are inversely proportional, Sensors 2016, 16, pitch has not been changed in Table 1, which will affect accuracy half cycle signal. It is signal. necessary It is tonecessary adjust to threshold adjust threshold exposure dose; exposure n, dose; ratio n, black ratio stripes black white stripes stripes white can reach stripes can set value. reach set value Influence Influence Focal Focal Plane Plane Alignment Alignment Errors Errors To To analyze analyze influence influence focal focal s s on on proposed proposed projection projection accuracy, accuracy, accuracies accuracies slope slope s s were were introduced introduced into into simulation. simulation. focal focal in projection in projection includes includes slope slope focus depth focus. depth. slope slope reflects reflects parallelism parallelism between between focal focal movement movement grating, grating, focus focus depth depth reflects reflects relative relative position position overlap overlap focal focal grating grating photoresist photoresist ; ; two two s s play play an an important important role role in in accuracy. accuracy shows shows 3D 3D relative relative light light intensity intensity comparison comparison between between common common accuracies. accuracies. area area light intensity light intensity region region is 400 µm is 400 ˆ 400 µm µm. 400 µm. data acquisition data acquisition is completed is completed though though a CCD sensor, a CCD sensor, gray value gray value image is normalized image is normalized to form to relative form intensity. relative Three intensity. Three focus focus positions are positions selected by are selected Sum-Modulus-Difference by Sum-Modulus-Difference method(smd) [14], method(smd) which is image [14], which definition is evaluation image definition algorithm. evaluation intensity algorithm. image is inclined intensity in image x direction. is inclined in x direction D 3D relative relative light light intensity intensity comparison comparison between between common common accuracies. (a c) accuracies. are light (a c) intensities are light intensities focus s, which focus correspond s, which to (d f), correspond respectively, to (d f), for respectively, for.. 12 shows 2D relative light intensity comparison between common 12 shows 2D relative light intensity comparison between common accuracies. With an increase in focal accuracies. With an increase in focal, amplitude light intensity decreases; meanwhile, curvature, amplitude light intensity decreases; meanwhile, curvature rising rising or falling curve decreases simultaneously. Assuming parameter threshold intensity is or falling curve decreases simultaneously. Assuming parameter threshold intensity is 0.56, 0.56, linear grating can be formed as in 13, which shows that developing results linear grating can be formed as in 13, which shows that developing results correspond correspond spacing distance. spacing distance. It can be seen from se simulations that method can generate uniform It can be seen from se simulations that method can generate a uniform light intensity distribution. With decrease in precision, maximum peak value light intensity distribution. With a decrease in precision, maximum peak value light intensity will be reduced, uniformity light intensity is not changed, which greatly light intensity will be reduced, uniformity light intensity is not changed, which greatly increases requirements for sensitivity threshold accuracy photoresist. increases requirements for sensitivity threshold accuracy photoresist.

12 Sensors 2016, 16, Sensors 2016, 16, Sensors 2016, 16, D relative light intensity comparison between common 12. 2D relative light intensity comparison between common 12. 2D relative light intensity comparison accuracies. between blue common line represents light accuracies. blue line represents light intensity focal intensity focal, accuracies. red line represents blue line represents light intensity light, red line represents light intensity. intensity. focal (a) SMD = 1.00;, (b) SMD = 0.51; red (c) line SMD represents = light intensity (a) SMD = 1.00; (b) SMD = 0.51; (c) SMD = (a) SMD = 1.00; (b) SMD = 0.51; (c) SMD = Developing results corresponding to accuracies. Zones 1 2 are formed 13. from Developing intensity results corresponding to defocus accuracies. s, Zones respectively Developing results corresponding to accuracies. Zones 1 2 (a) are Grating formed corresponding from intensity to SMD = 1.00 ; (b) Grating corresponding to defocus SMD s, = 0.51 ; respectively. (c) Grating are formed from intensity defocus s, respectively. corresponding (a) Grating corresponding to SMD = to SMD = 1.00 ; (b) Grating corresponding to SMD = 0.51 ; (c) Grating (a) Grating corresponding to SMD = 1.00 ; (b) Grating corresponding to SMD = 0.51 ; (c) Grating corresponding to SMD = corresponding to SMD = Experiment Results Discussion 5. Experiment Results Discussion 5. Experiment Results Discussion 5.1. Experimental Setup 5.1. Experimental Setup 5.1. Experimental 14 Setup illustrates grating machine fabricated by Beijing Micro Nano Precision Mechanical 14 illustrates Co., Ltd. grating (BJJM, Beijing, China), machine fabricated collaboration by Beijing Xi an Micro Nano Jiaotong 14 illustrates grating machine fabricated by Beijing Micro Nano Precision University. Precision Mechanical It can achieve Co., a Ltd. precision (BJJM, grating Beijing, 1250 China), mm. in collaboration whole assembly is Xi an placed Jiaotong on an Mechanical Co., Ltd. (BJJM, Beijing, China), in collaboration Xi an Jiaotong University. It can isolated University. precision It can achieve foundation. a precision device grating works 1250 in mm. a room whole assembly temperature is placed stabilization an achieve environment. isolated a precision precision grating foundation mm. device works whole in assembly a room is placed temperature on an isolated stabilization precision foundation. environment. device works in a room temperature stabilization environment.

13 Sensors 2016, 16, Sensors 2016, 16, Sensors 2016, 16, grating machine machine consists consists four major four elements: major elements: a reduced a projection reduced projection exposure system, exposure a programmable grating system, a programmable illumination machine illumination system, consists an AC system, servo four rotary an major AC drive elements: servo system rotary a reduced drive porous system projection aerostatic guideways, exposure system, a fixed a programmable grating vacuum illumination system. system, an AC servo rotary drive system porous aerostatic guideways, a fixed grating vacuum system. porous aerostatic guideways, a fixed grating vacuum system Schematic Schematic diagram diagram for for experimental experimental setup. setup. 14. Schematic diagram for experimental setup shows shows that that machine machine body body a natural a granite natural bed granite in V bed in 2 direction direction 14 motion shows has that porous aerostatic guide machine rails body installed to a ensure natural smooth granite bed precision in motion has porous aerostatic guide rails installed to ensure smooth precision movement. An movement. direction An motion industrial has porous CCD aerostatic camera guide a rails laser installed interferometer to ensure are smooth used to align precision industrial CCD camera a laser interferometer are used to align projection movement. An projection industrial CCD camera process. a laser interferometer are used to align process. To To reduce reduce projection caused caused by by process. loss loss experimental experimental devices devices (See (See 15), 15), several several principles principles To reduce for for ultra-precision ultra-precision caused measurement measurement by loss processing processing experimental technology technology devices have have (See been been adopted: adopted: 15), several principles for ultra-precision measurement processing technology have been adopted: (1) Abbe criteria. (1) (1) Abbe criteria. (2) Abbe Ultra-precision porous criteria. aerostatic bearing technology. (2) (3) Ultra-precision Precision temperature porous sensor aerostatic compensation. bearing technology. (3) (4) Precision Pulse number temperature compensation. sensor compensation. (4) Pulse number compensation. 15. Photo experimental device. 15. Photo experimental device. 15. Photo experimental device. 16 shows flowchart linear scale based on projection 16 shows process, flowchart in which linear s scale should be determined, based on 16 shows flowchart linear scale based on compensation projection projection occurs to realize high process, accuracy in which s linear should scale by be changing determined, exposure compensation process, in which s should be determined, compensation distance occurs to occurs to realize repeat times, high adjusting accuracy workbench's linear scale movement by changing speed, exposure strengning distance realize high accuracy linear scale by changing exposure distance repeat uniformity repeat velocity times, in several adjusting cycles. workbench's movement speed, strengning times, adjusting workbench s movement speed, strengning uniformity velocity in uniformity velocity in several cycles. several cycles.

14 Sensors 2016, 16, Sensors 2016, 16, Sensors 2016, 16, Flowchart linear scale based on process. 16. Flowchart linear scale based on process Pitch Accuracy 16. Flowchart linear scale based on process Pitch Accuracy This section will provide some experimental results to verify proposed projection This Pitch section Accuracy will size provide linear some scale experimental is 1100 mm results 12 mm to verify 2 mm, proposed nominal projection pitch is. 20 µm. Errors sizethis including section linear will scale pitch provide is 1100 some mm on ˆexperimental 12mask mm ˆ 2 mm, results to verify nominal were proposed introduced pitch is 20 projection into µm. Errors including. experiment, pitch size n on repeated linear mask scale exposure is 1100 mm number 12 mm were spacing 2 mm, introduced distance nominal into non-integral pitch experiment, is 20 pitch µm. nerrors s repeated were including considered exposure pitch to number reduce on spacing compensate mask distance non-integral s. were pitch introduced s17 were shows into considered two to reduce experiment, images pitch compensate accuracy n measurements. repeated exposure s. number 17a shows 17 spacing a CCD shows image distance two images pitch non-integral accuracy pitchon pitch accuracy measurements. s focal were that considered is projected 17a to shows reduce from a CCD a mask compensate image pitch s accuracy by projection on s. focal 17 that shows lens; is projected two fromimages maximum a mask pitch s is accuracy byµm, measurements. projection minimum 17a is shows lens; µm. a CCD maximum image 17b shows pitch is an accuracy image µm, on pitch accuracy that is scanned from linear scale, which is fabricated by projection minimum focal that is is projected µm. from 17b a mask shows an image s by pitch projection accuracy that is scanned lens; from based on mask s, minimum is 41 nm. 18 shows linear maximum scale, which is fabricated µm, by minimum is projection µm. 17b shows based an image on mask pitch accuracy measurement that is results scanned pitch from accuracy, linear which scale, which are chosen is fabricated from 10 by consecutive adjacent projection pitches s, minimum is 41 nm. 18 shows measurement results pitch accuracy, four arbitrary based positions on in mask linear s, scale. maximum minimum pitch is is 41 small nm. than 4318 nm, shows which average are chosen four from positions 10 consecutive is between adjacent µm pitches µm. four arbitrary positions in linear scale. measurement results pitch accuracy, which are chosen from 10 consecutive adjacent pitches maximum pitch is small than 43 nm, average four positions is between µm four arbitrary positions in linear scale. maximum pitch is small than 43 nm, average µm. four positions is between µm µm. 17. Image pitch accuracy measurement. (a) A CCD image pitch accuracy on focal projected from mask s by projection lens; (b) An image pitch accuracy 17. scanned Image from pitch accuracy linear measurement. scale, which (a) is fabricated A CCD image by pitch accuracy on projection focal 17. Image based pitch projected from on accuracy mask measurement. (a). (a) A CCD image pitch accuracy on focal s by projection lens; (b) An image pitch projected accuracy fromscanned mask from s linear byscale, projection which is fabricated by lens; (b) An image pitch projection accuracy scanned from based linear on scale, mask which (a). is fabricated by projection based on mask (a).

15 Sensors 2016, 16, Sensors 2016, 16, Sensors 2016, 16, pitch accuracy measurement 10 arbitrary positions in long, pitch is 18. pitch accuracy measurement 10 arbitrary positions in 1 m long, pitch is µm. µm Accuracy Accuracy a Linear Linear Scale Scale size size linear linear scale scale manufactured manufactured by by by projection projection method method is 1100 is is mm mm mm ˆ mm mm ˆ 2 mm, mm, basis basis material is is isfloat glass, coefficient linear linear linear expansion is is 7.68 is ˆ / C. / C. / C shows shows shows accuracy comparison two projection projection ; ; a linear linear scale scale that that is is fabricated fabricated from from first first is is corrected corrected compensated compensated to to fabricate fabricate anor anor linear linear scale scale using using a second second.. During During experiment, experiment, s s corresponding corresponding to to accurate accurate position, position, temperature temperature humidity humidity variation variation curves, curves, ground ground vibration, vibration, electrical electrical interference interference were were programmed programmed into into control control system system to to improve improve accuracy. accuracy. data data acquisition acquisition system system for for measurement measurement accuracy accuracy includes includes a Heidenhain Heidenhain ND ND display, display, MicroE1900 MicroE1900 series series reading reading head, head, dual-frequency dual-frequency laser interferometer, measurement measurement uncertainty is determined is determined to be U to = be 0.3 µm. 0.3 room µm. environment room environment temperature is temperature C, uncertainty is determined to be U = 0.3 µm. room environment temperature is is ± humidity C, C, is less humidity humidity than 75% is is less less RH. than than 75% 75% RH. RH Accuracy Accuracy comparison comparison two two projection projection,, a linear scale 19. Accuracy that is fabricated comparison from two first is projection corrected, compensated to fabricate a linear linear scale that is fabricated from first is corrected compensated to fabricate scale anor that linear is fabricated scale using from second first. is corrected compensated to fabricate anor anor linear scale using a second. linear scale using a second. 6. Conclusions 6. Conclusions This study presented projection method for manufacturing an This study presented a projection method for manufacturing an incremental linear scale. common linear scale projection splice process is replaced incremental linear scale. common linear scale projection splice process is replaced by average homogenization technique, which overlaps position pitches regularly. by average homogenization technique, which overlaps position pitches regularly. simulation experimental results were discussed, following conclusions were drawn: simulation experimental results were discussed, following conclusions were drawn: (1) (1) multi-repeat multi-repeat grating grating positions positions pitch pitch achieved achieved uniform uniform light light (1) intensity intensity multi-repeat distribution, distribution, which which realized realized grating homogenized homogenized positions pitch compensation compensation achieved a uniform whole whole length length light grating, grating, intensity making making distribution, it it so so which realized system system homogenized reduces reduces requirements requirements compensation mask mask accuracy. accuracy. whole length (2) (2) Increasing Increasing grating, making exposure exposure it so repetitions repetitions system grating grating reduces strips strips will will requirements reduce reduce pitch pitch mask s, s, accuracy. when when exposure exposure repetitions repetitions are are equal equal to to number number pitches pitches on on mask, mask, average average homogenization homogenization will will be be minimum minimum oretically. oretically.

16 Sensors 2016, 16, (2) Increasing exposure repetitions grating strips will reduce pitch s, when exposure repetitions are equal to number pitches on mask, average homogenization will be minimum oretically. (3) positioning projection motion system is considered to be one main factors affecting exposed distance interval, while developing threshold exposure dose is constant, which is inversely proportional to ratio black stripes white stripes, pitch is only slightly changed. It is necessary to adjust developing threshold exposure dose to make sure ratio black stripes white stripes can reach set value, which will directly affect accuracy half cycle signal. On or h, control system needs exposed distance interval to be written in control program, thus changing ratio black stripes white stripes achieve compensation. (4) simulation analysis results confirmed that light intensity became more uniformly distributed using. Increasing would reduce maximum peak value light intensity after proposed method; uniformity light intensity still was only slightly changed, which greatly increased requirements for sensitivity developing threshold accuracy photoresist. According to experimental results, when pitch was set to be 20 µm, process technique realized a pitch accuracy 43 nm in any 10 locations 1 m, accuracy whole grating was less than 1 µm/m. Meanwhile, when experimental conditions follow higher requirements i.e., first, choosing a fine projection lens adapted to a shorter wavelength, second, decreasing impact environmental conditions, such as improving temperature accuracy, reducing ground vibration, or constraints it can be applied to manufacture a nanoscale-precision linear scale, not just limited to results presented herein. Acknowledgments: This work has been supported both by National Science Technology Project China (No. 2011ZX ) Shaanxi province Technology Department Fund (No. 2014K07-09). Author Contributions: Dongxu Ren contributed to developing ideas this research. Dongxu Ren Huiying Zhao were involved in developing machine experimental setup, as well as drafting paper. Chupeng Zhang, Daocheng Yuan, Jianpu Xi Xueliang Zhu helped on oretical analysis experiment design, helped on data analysis. Xinxing Ban, Longchao Dong helped on measurement evaluation linear scale accuracy. Yawen Gu Chunye Jiang helped on monitor experimental parameters. Conflicts Interest: authors declare no conflict interest. References 1. Gerasimov, F.M. Use diffraction gratings for controlling a ruling engine. Appl. Opt. 1967, 6, [CrossRef] [PubMed] 2. Flam, A.J.; Bonnemason, F.; venon, A.; Lerner, J.M. blazing holographic gratings using ion-etching. Proc. SPIE 1989, 1055, Yu, H.; Li, X.; Zhu, J.; Yu, H.; Qi, X.; Feng, S. Reducing line curvature mechanically ruled gratings by interferometric control. Appl. Phys. B 2014, 117, [CrossRef] 4. Liu, H.; Shi, Y.; Yin, L.; Jiang, W.; Lu, B. Roll-to-roll imprint for high precision grating manufacturing. Eng. Sci. 2013, 11, Lin, B.J. Optical Present future challenges. Competes Rendus Phys. 2006, 7, [CrossRef] 6. Brunner, T.A. Pattern-dependent overlay in optical step repeat projection. Microelectron. Eng. 1988, 8, [CrossRef] 7. Larramendy, F.; Blatche, M.C.; Mazenq, L.; Laborde, A.; Temple-Boyer, P.; Paul, O. Microchannel-connected SU-8 honeycombs by single-step projection photo for positioning cells on silicon oxide nanopillar arrays. J. Micromech. Microeng. 2015, 25, 1 9. [CrossRef] 8. Bischf, J.; Henke, W.; Werf, J.V.D.; Dirksen, P. Simulations on step--scan optical. Proc. SPIE 1994, 2197,

17 Sensors 2016, 16, Williamson, D.M.; Mcclay, J.A.; Andresen, K.W.; Gallatin, G.M.; Himel, M.D.; Ivaldi, J.; Mason, C.; McCullough, A.; Otis, C.; Shamaly, J.; et al. Micrascan III: 0.25-µm resolution step--scan system. Proc. SPIE 1996, 2726, Ma, X.; Arce, G.R. Techniques in computational. In Computational Lithography; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2010; pp Jain, K.; Zemel, M.; Klosner, M. Large-Area High-Resolution Lithography Photoablation Systems for Microelectronics Optoelectronics Fabrication Jain. IEEE Proc. 2002, 90, [CrossRef] 12. Lawes, R.A. Manufacturing tolerances for UV LIGA using SU-8 resist. J. Micromech. Microeng. 2005, 15, [CrossRef] 13. Mack, C. Imaging Example: Dense Array Lines Spaces. In Fundamental Principles Optical Lithography: Science Micrabrication; John Wiley & Sons Ltd.: Chichester, UK, 2007; pp Chern, N.N.K.; Neow, P.A.; Ang, M.H. Practical issues in pixel-based autocusing for machine vision. IEEE ICRA 2001, 3, by authors; licensee MDPI, Basel, Switzerl. This article is an open access article distributed under terms conditions Creative Commons Attribution (CC-BY) license (

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