Optimization of Thickness Uniformity Distribution on a Large-Aperture Concave Reﬂective Mirror and Shadow Mask Design in a Planetary Rotation System

Article Optimization of Thickness Uniformity Distribution on a Large-Aperture Concave Reﬂective Mirror and Shadow Mask Design in a Planetary Rotation System

Gang Wang 1,* , Yunli Bai 1, Jing Zhao 1, Li Wang 1, Jiyou Zhang 2 and Yuming Zhou 2

1 Beijing Institute of Space Mechanics & Electricity, 104 Youyi Road, Beijing 100094, China; [email protected] (Y.B.); [email protected] (J.Z.); [email protected] (L.W.) 2 Optical Ultraprecise Processing Technology Innovation Center for Science and Technology Industry of National Defense (Advanced Manufacture), 104 Youyi Road, Beijing 100094, China; [email protected] (J.Z.); [email protected] (Y.Z.) * Correspondence: [email protected]

Abstract: Improving the spatial resolution of remote sensing satellites has long been a challenge in the field of optical designing. Although the use of large-aperture reflective mirrors significantly improves the resolution of optical systems, controlling the film thickness uniformity remains an issue. The planetary rotation system (PRS) has received significant attention owing to the excellent uniformity of the coating applied to the large-aperture reflective mirror. However, the development of the PRS remains hindered by a lack of research on its properties and the design method of the shadow mask. To address this, we performed a theoretical analysis of the distribution of film

thickness and uniformity in the PRS, which is impacted by parameters of geometric conﬁguration in the vacuum chamber. We present a ﬁlm thickness expression based on Knudsen’s law and the

Citation: Wang, G.; Bai, Y.; Zhao, J.; geometric configuration of the vacuum chamber that incorporates an additional shading function. Wang, L.; Zhang, J.; Zhou, Y. Moreover, the variation of uniformity in the standard and counter PRSs was elucidated by changing Optimization of Thickness the location of the evaporation source. Finally, a fixed-position shadow mask, which was obtained Uniformity Distribution on a by theoretical design, allows the nonuniformity of the concave reflective mirror (with a 700 mm Large-Aperture Concave Reflective aperture) to reduce from 2.43% to 0.7%, highlighting the importance of initial shape design. Mirror and Shadow Mask Design in a Planetary Rotation System. Coatings Keywords: planetary rotation system; film thickness uniformity; geometric configuration; shadow 2021, 11, 140. https://doi.org/ mask 10.3390/coatings11020140

Academic Editor: Chen Tei-Chen Received: 7 December 2020 1. Introduction Accepted: 20 January 2021 Published: 27 January 2021 With the development of commercial aerospace, there is an increasing demand for high-resolution remote sensing images. These high-resolution images are taken by remote

Publisher’s Note: MDPI stays neutral sensing satellites. To provide the requisite resolution, large-aperture reflective mirrors are with regard to jurisdictional claims in a critical component of the optical systems in remote sensing satellites [1]. Maintaining published maps and institutional affil- the uniformity in film thickness is a prerequisite in the fabrication of these large-aperture iations. reflective mirrors because a lack of uniformity in film thickness can result in a shift of the characteristic wavelength from the center to the edge over the surface [2]. Moreover, a nonuniformity in the film thickness reduces the surface accuracy of the reflective mirror, subsequently degrading the imaging quality of the optical system. Typically, these large reflective mirrors are coated with a film of uniform thickness, for which uniformity is Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. obtained using a simple rotation system with a fixed-position uniformity mask [3]. For This article is an open access article instance, Villa and colleagues researched the film thickness distribution using extended distributed under the terms and evaporation sources [4] and designed shadow masks to provide large-area coatings on conditions of the Creative Commons flat, spherical reflective mirrors [5]. The emission characteristics of evaporation sources Attribution (CC BY) license (https:// were summarized by Aaron and Charles [6]. Film thickness distributions of the flat plate, creativecommons.org/licenses/by/ spherical surface and planetary substrate holders of evaporation sources were investigated 4.0/). by Kotlikov and Prokashev [7]. However, with the gradual increase in the aperture of

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reflective mirrors, achieving film thickness uniformity has become more challenging. In recent years, the planetary rotation system (PRS) has gained popularity because it can obtain better uniformity than simple rotation for large-aperture reflective mirrors [8]. Fur- thermore, a reflective mirror that has no holes in the center can be deposited using the PRS, which extends the application of this system. Despite these considerable advantages, the widespread application of the PRS is still restricted owing to the revolution–rotation path of the reflective mirror in the PRS. The reflective mirrors execute not only the revolution around the center of the vacuum chamber but also rotation around the center of the planets. Therefore, optimizing the uniformity and design of the initial shape of the shadow mask are important issues in current research on the PRS. To date, considerable research has been conducted to explore the properties of the PRS. Recently, Oliver and coworkers have exploited the uniformity in the PRS, including but not limited to: (i) measuring the impacts on nonuniformity due to planetary gearing [9]; (ii) applying a stationary mask to correct thickness nonuniformity [10]; (iii) investigating the impact of deposition rate on the thin-film thickness and uniformity [11]; (iv) the occurrence of film thickness deviation caused by errors in planetary design and fabrication, such as angular errors and source-to-mirror distances [12]; (v) describing the analysis of film thickness and uniformity in the PRS for different numbers of planetary revolutions during a given layer, thereby certifying that greater film uniformity and nominal-thickness control can be achieved via higher planetary motion speeds because more revolutions per layer are realized [13]. Meanwhile, Liu and Kong demonstrated a simple and straightforward routine for the theoretical design of the shadow masks used to prepare uniform coatings on spherical reflective mirrors in a standard PRS [14]. Wang and Fu reviewed the methods and simulation for improving thin film uniformity in physical vapor deposition, covering characteristic aspects of evaporation sources, projection/mask effects on film thickness distribution, as well as geometric and rotational influences from apparatus configurations [15]. Although these studies have provided valuable contributions with respect to achieving uniformity in the PRS, there are still several challenges that have yet to be resolved: (i) the film thickness distribution in cases where the vapor molecules are obscured by the external profile of the reflective mirrors; (ii) the relationship between the position parameters (e.g., the vapor source position and the reflective mirror height) and the film thickness distribution; (iii) shadow mask design that accounts for complicated paths. To solve the above issues, we made a deeper exploration of the uniformity of a large-aperture concave reflective mirror in the PRS based on previous studies. In this paper, we demonstrate the impact of the film thickness distribution using simulations in which the evaporated molecules from the evaporator source are obscured by the reflective mirror. Furthermore, the impact of the evaporation source position on the uniformity is explored for both the standard and counter PRSs. This prompted an investigation of the impact of the number of planetary revolutions and the height of the reflective mirror on the film uniformity. Finally, we propose a method for designing the shadow mask that considers complicated paths. This paper will guide future studies on the optimization of the vacuum chamber geometric configuration, such as the revolution and rotation methods as well as the height of reflective mirrors. Moreover, the proposed method can be used for effectively designing the initial shape of the shadow mask, considerably reducing the number of experiments.

2. Theory This study considers a geometric conﬁguration identical to that of the commercially available ZZS-2500 coating plant (Chengdu Modern South-vacuum Equipment Co., Ltd., Chengdu, China). As illustrated in Figure1a, this coating plant comprises a PRS carrying four mirror holders within a 2500 mm diameter vacuum chamber. Different from the planetary solar system, in PRS, the mirror holder rotates around the axis of rotation while revolving around the center of the vacuum chamber. The geometrical conﬁguration is illustrated schematically in Figure1b. Coatings 2021, 11, 140 3 of 15 Coatings 2020, 10, x FOR PEER REVIEW 3 of 15

(a) (b)

FigureFigure 1. (a 1.) Schematic(a) Schematic diagram diagram of the of thevacuum vacuum chamber. chamber. (b) Geometric (b) Geometric configuration conﬁguration of the of thevacuum vacuum chamber. chamber.

AsAs shown shown in in Figure Figure1b, 1b, the theZ -axisZ-axis is is in in the the center center of of the the vacuum vacuum chamber, chamber, and and we we designateddesignated the the evaporator evaporator source source as as aa flatflat surfacesurface described by the the coordinates coordinates (a, (a, b, b, 0). 0). In Inaddition, addition, ds ds represents represents a apoint point on on the the surface surface of of the the concave concave reflective reflective mirror; mirror; f and f and s are s areunit unit vectors vectors normal normal to tothe the surfaces surfaces of ofthe the ev evaporatoraporator source source and and the the reflective reflective mirror, mirror, re- respectively;spectively; RR(620(620 mm) denotes the the radius radius of of the the planet planet orbit; orbit; 𝜌ρ isis the the radial radial position position of ofa apoint point on on the the planet, planet, and and ΨΨ is isthe the angular angular position position of ofthe the planet planet in inits itsorbit. orbit. In each In each sim- simulation,ulation, the the planet planet begins begins at atan an orientation orientation of of ψψ = =0; 0;thus, thus, the the path path of of the the point point ds ds can can be beexpressed expressed as as [16]. [16]. x = R · cos Ψ + ρ · cos(K · Ψ) (1) xR=⋅cos Ψ+⋅ρ cos() K ⋅Ψ (1) y = R · sin Ψ − (−1)Mρ · sin(K · Ψ) (2) M =⋅ Ψ−−()ρ ⋅ (1 ⋅Ψ ) yRK sin 1 sin 2 (2) z = H − RoC − RoC2 − ρ2 (3) 1 22 where K (217/37) is the ratio of thezH number=− RoCRoC of teeth −() on the−ρ solar2 and planet gears; H is the(3) height of the top of the concave reflective mirror; RoC indicates the radius of curvature, andwhereM is usedK (217/37) to distinguish is the ratio between of the thenumber standard of teeth and on counter the solar PRSs and (1 forplanet standard gears; andH is 0the for counter).height of the According top of the to concave Knudsen’s reflective laws [ 17mirror;], the filmRoC thicknessindicates atthe point radius ds of can curva- be determined using the following semiempirical equation: ture, and M is used to distinguish between the standard and counter PRSs (1 for standard and 0 for counter). According to Knudsen’s(cos φ laws)n · cos [17,θ the film thickness at point ds can be determined using the following semiempiricalt = C equation: (4) r2 ()cosφ n ⋅ cosθ where C is a constant; n is the numbert of= termsC in the series depending on the evaporator(4) source, and r is the distance between evaporatorr source2 and point ds. The cosφ and cosθ terms can be expressed as [4]. where C is a constant; n is the number of terms in the series depending on the evaporator source, and r is the distancef · betweenr evaporatorz source and point ds. The cosϕ and cos ϕ = = (5) cosθ terms can be expressed as| f ||[4].r| h i 1 (x − a)2 + (y − b)2 + z2 2 ⋅ ϕ ==fr z cos 1 fr 1 (5) M 222 2 −r · s ρ cos(KΨ)(x − a) + (−()()xa1)−+−+ρ sin( ybKΨ)(b − zy) + z RoC2 − ρ2 2 cos θ = =  (6) |−r||s| h i 1 − 2 + − 2 + 2 2 1 RoC (x a)M (y b) z 22 −⋅rs ρρcos()()()KxaΨ−+− 1 sin ()() KbyzRoC Ψ−+() − ρ2 cosθ == Then, the thickness− ofrs the point ds undergoing N revolutions can be obtained1 by integrating(6) RoC()() x−+−+ a22 y b z2 2 the angular position: 

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1 n ( )( − ) + (− )M ( )( − ) + 2 − 2 2 Z 2πN z ρ cos KΨ x a 1 ρ sin KΨ b y z RoC ρ thickness = C · n+3 dΨ (7) 0 h i RoC (x − a)2 + (y − b)2 + z2 2

For concave reflective mirrors, the evaporation molecules are sometimes prevented from arriving at the surface owing to the outer contour of the reflective mirror being obscured. As shown in Figure2, at a certain moment, the shaded part on the surface can accumulate the molecules, but the blank part is obscured by the element. This shading effect can affect the film thickness distribution. Referring to Figure2, h denotes the height of the clear aperture (CA) of the reflective mirror and T indicates the intersection of r and the CA. The coordinates (xT, yT, zT) of point T on the straight line can be expressed as [17].

 (x−a)h  xT = z + a,  ( − )  y = y b h + b T z , (8) 1 2  2 2 2  zT = h = H − RoC − RoC − ρmax .

Next, the distance between T and the center of the reﬂective mirror, with the coordinates (R cos Ψ, R sin Ψ, h), can be calculated as [17]. q 2 2 d = (xT − R cos Ψ) + (yT − R sin Ψ) (9)

According to the geometric relationship, the molecules can arrive at the surface when point T falls within the CA. Otherwise, no molecules which are evaporated from the evaporator source accumulate at the surface. Therefore, the shading function can be deﬁned as [17]. ( 1, d < 1 CA, S = 2 1 (10) 0, d ≥ 2 CA.

Then, Equation (7) must be modiﬁed as follows [17]: 1 n ( )( − ) + (− )M ( )( − ) + 2 − 2 2 Z 2πN z ρ cos KΨ x a 1 ρ sin KΨ b y z RoC ρ thickness = C · S · n+3 dΨ (11) 0 h i RoC (x − a)2 + (y − b)2 + z2 2

For a concave reflective mirror with a radius of 350 mm, the film thickness distribution can be calculated for a source coordinate (in centimeters) of (−800, −300, 0) and a vapor–plume exponent of n = 2 in the counter rotation system. The film thickness in the center of the planet (ρ = 0 mm) was normalized to 1, yielding the results shown in Figure3. For the distance spanning the planet’s center to 347 mm along the radius, the uniformity of the film thickness is significantly better than in the 347–350 mm range. We defined the edge of the surface as a non-uniform area, in which the film thickness is reduced drastically compared to the center of the surface, for example, as demonstrated for the 347–350 mm range in Figure3. However, irrespective of adjustments to the geometric configuration parameters, the non-uniform region covers only 3–5 mm according to the simulation results. Although it is clear that the obscuring of the outer contour has a great impact on the film thickness at the edge of the surface, the non-uniform area is nearly negligible because the edge area usually does not require coating for large-aperture reflective mirrors. Consequently, in the following analysis and discussion, the non-uniform region is not afforded further consideration. Coatings 2021, 11, 140 5 of 15

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Figure 2. Schematic diagram illustrating the outer contour shielding of the reflective mirror. Figure 2. SchematicSchematic diagramdiagram illustratingillustrating thethe outerouter contourcontour shieldingshielding ofof thethe reﬂectivereflective mirror.mirror.

Figure 3. Normalized thickness distribution for the counter planet undergoing 37 revolutions of theFigureFigure planetary 3.3. NormalizedNormalized rotation.thickness thickness distributiondistribution forfor thethe counter counter planet planet undergoing undergoing 37 37 revolutions revolutions of of the planetarythe planetary rotation. rotation. For the distance spanning the planet’s center to 347 mm along the radius, the uni- 3. AnalysisFor the and distance Discussion spanning the planet’s center to 347 mm along the radius, the uniformity of the film thickness is significantly better than in the 347–350 mm range. We de- formity of the film thickness is significantly better than in the 347–350 mm range. We de- finedAccording the edge of to the the surface above as theory, a non-uniform we can research area, inthe which influence the film of thickness different is geometric reduced configurationsfined the edge of on the film surface thickness as a non-uniform uniformity in area, the PRS.in which Before the starting film thickness the research, is reduced the drastically compared to the center of the surface, for example, as demonstrated for the followingdrastically assumptions compared to must the becenter made: of the surface, for example, as demonstrated for the 347–350 mm range in Figure 3. However, irrespective of adjustments to the geometric con- 347–350 mm range in Figure 3. However, irrespective of adjustments to the geometric configuration(1) All analyses parameters, are simulated the non-uniform using Mathlab region covers software only (2016a, 3–5 mm MathWorks, according Natick, to the sim- MA, figuration parameters, the non-uniform region covers only 3–5 mm according to the sim- ulationUSA); results. Although it is clear that the obscuring of the outer contour has a great ulation results. Although it is clear that the obscuring of the outer contour has a great impact(2) The on PRS the isfilm moving thickness at a constant at the edge speed, of andthe thesurface, reflective the non-uniform mirror is horizontal area is duringnearly impact on the film thickness at the edge of the surface, the non-uniform area is nearly negligiblethe movement; because the edge area usually does not require coating for large-aperture re- negligible because the edge area usually does not require coating for large-aperture reflective(3) The mirrors. evaporation Consequently, rate is 0.1 in nm/s; the following analysis and discussion, the non-uniform flective mirrors. Consequently, in the following analysis and discussion, the non-uniform region(4) During is not afforded the coating further process, consideration. the characteristics of the evaporation source remain regionunchanged. is not afforded further consideration. 3. Analysis and Discussion 3.1.3. Analysis Impact of and Evaporation Discussion Source Position on Film Thickness Uniformity According to the above theory, we can research the influence of different geometric TheAccording paths described to the above by atheory, point undergoingwe can research a single the revolutioninfluence of of different the standard geometric and configurations on film thickness uniformity in the PRS. Before starting the research, the counterconfigurations PRS are on shown film thickness in Figure uniformity4. In a standard in the rotation, PRS. Before the revolutionstarting the and research, rotation the following assumptions must be made: arefollowing in the same assumptions rotation must direction be made: as shown by the red line, while the rotation direction of (1) All analyses are simulated using Mathlab software (2016a,MathWorks, Natick, revolution(1) All analyses and rotation are simulated are opposite using in Mathlab the counter software PRS, as(2016a,MathWorks, shown by the black Natick, line. MA, USA); MA, USA); (2) The PRS is moving at a constant speed, and the reflective mirror is horizontal (2) The PRS is moving at a constant speed, and the reflective mirror is horizontal during the movement; during the movement; (3) The evaporation rate is 0.1 nm/s; (3) The evaporation rate is 0.1 nm/s; (4) During the coating process, the characteristics of the evaporation source remain (4) During the coating process, the characteristics of the evaporation source remain unchanged. unchanged.

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3.1.3.1. ImpactImpact ofof EvaporationEvaporation SourceSource PositionPosition onon FilmFilm ThicknessThickness UniformityUniformity TheThe pathspaths describeddescribed byby aa pointpoint undergoingundergoing aa singlesingle revolutionrevolution ofof thethe standardstandard andand countercounter PRSPRS areare shownshown inin FigureFigure 4.4. InIn aa standardstandard rotation,rotation, thethe revolutionrevolution andand rotationrotation areare Coatings 2021, 11, 140 6 of 15 inin thethe samesame rotationrotation directiondirection asas shownshown byby thethe redred line,line, whilewhile thethe rotationrotation directiondirection ofof revolutionrevolution andand rotationrotation areare oppositeopposite inin thethe countercounter PRS,PRS, asas shownshown byby thethe blackblack line.line.

Figure 4. Paths in the standard and counter planetary rotation systems, as viewed from the top of FigureFigure 4.4. Paths in the standard and counter planetary planetary ro rotationtation systems, systems, as as viewed viewed from from the the top top of of the chamber. thethe chamber.chamber. The paths traversed by a point during 24 revolutions of the PRS are shown in Figure TheThe pathspaths traversedtraversed byby a a point point during during 24 24 revolutions revolutions of of the the PRS PRS are are shown shown in in Figure Figure5. 5. The geometric configuration is a 2500 mm vacuum chamber with a planetary gear ratio The5. The geometric geometric conﬁguration configuration is ais 2500 a 2500 mm mm vacuum vacuum chamber chamber with with a planetary a planetary gear gear ratio ratioK K of 217/37; the radius of the planet orbit R is 620 mm; the radial position of the point on ofK 217/37;of 217/37; the the radius radius of of the the planet planet orbit orbitRRisis 620 620 mm; mm; the the radial radial position position ofof thethe pointpoint onon the planet ρ is 350 mm and the height of the point is 1500 mm. It is apparent that the two thethe planetplanet ρρ isis 350350 mmmm andand thethe heightheight ofof thethe pointpoint isis 15001500 mm.mm. ItIt isis apparentapparent thatthat thethe twotwo paths are very different because the point pass tracks overlap much more at the edge for pathspaths areare veryvery differentdifferent becausebecause thethe pointpoint passpass trackstracks overlapoverlap muchmuch moremore atat thethe edgeedge forfor the standard PRS, whereas they overlap more in the center for the counter PRS. thethe standardstandard PRS,PRS, whereaswhereas theythey overlapoverlap moremore inin thethe centercenter forfor thethe countercounter PRS.PRS.

(a) (b) (a) (b) Figure 5.5. Paths described by a pointpoint atat ρρ == 350350 mmmm inin thethe systemsystem withwith aa 217/37217/37 gear ratio and a solar radius of 620 mm Figure 5. Paths described by a point at ρ = 350 mm in the system with a 217/37 gear ratio and a solar radius of 620 mm undergoing 24 revolutions in (a) standard planetary rotation and (b) counter planetary rotation. undergoingundergoing 2424 revolutionsrevolutions inin ((aa)) standardstandard planetary planetary rotation rotation and and ( b(b)) counter counter planetary planetary rotation. rotation. Moreover, therethere isis a a difference difference in in the the uniformity uniformity of of the the two two paths paths when when the the evaporation evapora- Moreover, there is a difference in the uniformity of the two paths when the evapora- tionsource source is at is the at samethe same location. location. Therefore, Therefor thee, influencethe influence of the of evaporationthe evaporation source source on theon tion source is at the same location. Therefore, the influence of the evaporation source on thefilm film uniformity uniformity should should be considered be considered for the for standard the standard and counter and counter PRSs. For PRSs. the For 0–350 the mm 0– the film uniformity should be considered for the standard and counter PRSs. For the 0– 350range, mm the range, relationship the relationship between the between film nonuniformity the film nonuniformity and the offset and of the the source offset position of the 350 mm range, the relationship between the film nonuniformity and the offset of the sourcefrom the position center offrom the the vacuum center chamber of the vacuum is shown chamber in Figure is sh6. own in Figure 6. source position from the center of the vacuum chamber is shown in Figure 6.

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Figure 6. Theoretical nonuniformitynonuniformity overover the the radius radius of of the the planet planet from from 0–350 0–350 mm mm versus versus the the offset offset of theof the source source position position from from the the center center of theof the vacuum vacuum chamber. chamber.

InIn thethe countercounter PRS, PRS, the the nonuniformity nonuniformity of of the the film film thickness thickness decreases decreases gradually gradually as the as offsetthe offset of the of sourcethe source position position from from the centerthe center of the of vacuumthe vacuum chamber chamber increases. increases. However, How- theever, nonuniformity the nonuniformity of the of film the thickness film thickness does not does decrease not decrease until the until offset the of offset the sourceof the positionsource position exceeds exceeds 900 mm 900 in the mm standard in the standa PRS. Therd PRS. film thicknessThe film thickness distribution distribution is shown inis Figureshown7 in as Figure a function 7 as a of function the radius of the of the radius planet of betweenthe planet 0 between and 350 mm0 and in 350 the mm standard in the PRS.standard Simulations PRS. Simulations were performed were performed based on sourcebased coordinateson source coordinates (in millimeters) (in millimeters) of (a, 0, 0), withof (a, the0, 0), values with ofthe a values varying of from a varying 0–1200 from mm. 0–1200 mm.

Figure 7. Theoretical ﬁlmfilm thicknessthickness distributiondistribution asas aa functionfunction ofof thethe radiusradius ofof thethe planetplanet atat differentdiffer- H valuesent values of the of the offset offset of theof the source source position position from from the the center center of of the the vacuum vacuum chamber chamber (H ( H= 1500= 1500 mm, mm, R = 620 mm, n = 2). R = 620 mm, n = 2).

As shown in FigureFigure7 7,, the the film film thickness thickness decreases decreases gradually gradually over over the the surface surface of of the the reflectivereflective mirrormirror withwith thethe magnitudemagnitude ofof aa increasingincreasing fromfrom 0–8000–800 mm.mm. ThisThis behaviorbehavior waswas analyzed in greater depthdepth usingusing thethe polarpolar diagramdiagram shownshown inin FigureFigure8 8,, for for which which the the polar polar diameter represents the thickness of the pointpoint at 350350 mmmm alongalong thethe radiusradius ofof thethe planetplanet and the polar angle represents the angular position Ψ of of thethe planetplanet inin itsits orbit.orbit. TheThe areaarea enclosed byby thethe curvecurve cancan characterizecharacterize thethe filmfilm thicknessthickness duringduring thethe NN revolutions.revolutions.

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FigureFigureFigure 8. 8.8. Polar PolarPolar diagram diagramdiagram for forfor paths pathspaths described describeddescribed by byby a aa point pointpoint at atatρ ρρ= =350=350 350 mmmm withwithwith a aa 217/37 217/37217/37 gear gear ratio ratio and and aa solarsolarsolar radius radiusradius of ofof 620 620620 mm mmmm undergoing undergoingundergoing a aa single singlesingle revolution. revolution.revolution.

FigureFigureFigure9 9 9shows showsshows the thethe sum sumsum of ofof the thethe ﬁlm filmfilm thickness thicknesthicknesss at atat the thethe point pointpoint 350 350350 mm mmmm along alongalong the thethe radius radiusradius of ofof thethethe planetplanetplanet after afterafter 37 3737 revolutions, revolutions,revolutions, for forfor which whichwhich the thethe evaporation evaporationevaporation source sourcesource is is inis inin different differentdifferent positions. positions.positions. It isItIt apparentisis apparentapparent that thatthat the thethe ﬁlm filmfilm thickness thicknessthickness is isis much muchmuch greater greatergreater at atat the thethe coordinate coordinatecoordinate (0, (0,(0, 0, 0,0, 0) 0)0) of ofof the thethe source sourcesource positionpositionposition than thanthan that thatthat at atat the thethe coordinate coordinatecoordinate ( − ((−−900,900,900, 0, 0,0, 0) 0)0) for forfor angular angularangular positions positionspositions ranging rangingranging from fromfrom (− ((−−222πππ/3)/3)/3) tototo (2(2(2πππ/3)./3)./3).

FigureFigureFigure 9.9.9. PolarPolar diagramdiagram forfor for thethe the pathspaths paths describeddescribed described byby by aa poin apoin pointtt forfor for severalseveral several valuesvalues values ofof the ofthethe offsetoffset offset ofof thethe of the sourcesourcesource position positionposition from fromfrom the thethe center centercenter of ofof the thethe coating coatingcoating chamber chamberchamber between betweenbetween coordinates coordinatescoordinates of of (0,of (0,(0, 0, 0)0,0, to0)0) (toto− (900,(−−900,900, 0, 0, 0).0, 0).0). According to the above analysis, there are two locations of the evaporation source at whichAccordingAccording the surface toto of thethe the aboveabove reflective analysis,analysis, mirror therethere achieves areare twtw greateroo locationslocations uniformity. ofof thethe evaporationevaporation One is in the sourcesource center atat ofwhichwhich the vacuum thethe surfacesurface chamber ofof thethe for reflectivereflective the standard mirrormirror PRS achievesachieves and the greatergreater other uniformity. isuniformity. close to the OneOne chamber isis inin thethe wall centercenter for theofof thethe counter vacuumvacuum PRS. chamberchamber The source forfor in thethe the standardstandard center can PRSPRS even andand achieve thethe otherother uniformity isis closeclose belowtoto thethe 1%.chamberchamber However, wallwall thereforfor thethe are countercounter two problems PRS.PRS. TheThe that sourcesource are difficultinin thethe centercenter to overcome: cancan eveneven achieveachieve uniformityuniformity belowbelow 1%.1%. How-How- (1)ever,ever, It therethere is very areare inconvenient twotwo problemsproblems to thatthat fill film areare difficult materialsdifficult toto because overcome:overcome: the evaporation source is far from (1)(1) ItItthe isis very chambervery inconvenientinconvenient door. toto fillfill filmfilm materialsmaterials becausebecause thethe evaporationevaporation sourcesource isis farfar (2) fromfromGenerally, thethe chamberchamber two evaporation door.door. sources need to be placed in the vacuum chamber. Yet, if the two evaporation sources are placed in the center of the chamber, they will (2)(2) Generally,Generally, twotwo evaporationevaporation sourcessources needneed toto bebe placedplaced inin thethe vacuumvacuum chamber.chamber. contaminate each other during the coating process. Yet,Yet, ifif thethe twotwo evaporationevaporation sourcessources areare placedplaced inin thethe centercenter ofof thethe chamber,chamber, theythey willwillIn summary, contaminatecontaminate the eacheach optimal otherother solution duringduring thethe is that coatingcoating the process. twoprocess. evaporation sources are placed symmetrically, close to the chamber wall in the counter PRS. InIn summary,summary, thethe optimaloptimal solutionsolution isis thatthat thethe twotwo evaporationevaporation sourcessources areare placedplaced sym-symmetrically,metrically, closeclose toto thethe chamberchamber wallwall inin thethe countercounter PRS.PRS.

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3.2.3.2.3.2. ImpactImpact ofof NumberNumber ofof PlanetaryPlanetary RevolutionsReRevolutionsvolutions ononon FilmFilmFilm ThicknessThicknessThickness UniformityUniformityUniformity OliverOliverOliver demonstrated demonstrated thatthat that thethe the differentdifferent different geargear gear rara ratiostiostios havehave have aa significantsignificant a significant effecteffect effect onon thethe on filmfilm the filmthicknessthickness thickness uniformity,uniformity, uniformity, whilewhile while thethe geargear the ratio gearratio ratiomustmust must bebe nonintegralnonintegral be nonintegral suchsuch thatthat such thethe that cycloidcycloid the cycloid tracedtraced tracedoutout isis no outno longerlonger is no longer aa closedclosed a closed path.path. path.However,However, However, thethe numbernumber the number ofof revolutionsrevolutions of revolutions alsoalso affects alsoaffects affects thethe uni-uni- the uniformity,formity,formity, asas evidencedevidenced as evidenced byby FigureFigure by Figure 10.10. Within Within10. Within 2020 revolutions,revolutions, 20 revolutions, thethe uniformityuniformity the uniformity ofof thethe of filmfilm the thick-thick- film thicknessnessness changeschanges changes drasticallydrastically drastically becausebecause because thethe pathpath the pathtravtraversedersed traversed byby aa bypointpoint a point changeschanges changes constantlyconstantly constantly withwith withthethe numbernumber the number ofof revolutions.revolutions. of revolutions. AfterAfter After moremore more thanthan than 2020 20 revolutions,revolutions, revolutions, thethe the uniformityuniformity uniformity ofof the the filmfilmfilm thicknessthicknessthickness stabilizes. stabilizes.stabilizes. Thus, Thus,Thus, it itit is isis necessary necessarynecessary to toto determine determinedetermine the thethe number numbernumber of ofof revolutions revolutionsrevolutions according accord-accord- toinging the toto filmthethe filmfilm thickness thicknessthickness and and depositionand depositiondeposition rate rate whenrate whenwhen measuring measuringmeasuring the uniformity. thethe uniformity.uniformity.

FigureFigureFigure 10.10. FilmFilmFilm thicknessthickness thickness uniformityuniformity uniformity versusversus versus thethe the numbernumber number ofof revolutionsrevolutions of revolutions inin thethe in countercounter the counter PRSPRS forfor PRSKK for== ρρ K217/37,217/37,= 217/37, nn == n 2,2,= R 2,R==R 620620= 620 mm,mm, mm,rangingrangingρ ranging fromfrom from 0–3500–350 0–350 mmmm mm andand and sosource sourceurce coordinatescoordinates coordinates ofof of ((−−900, (900,−900, −−300,300,−300, 0).0). 0).

3.3.3.3.3.3. ImpactImpact ofof thethe HeightHeight ofof thethe OpticalOptiOpticalcal ElementElementElement ononon FilmFilmFilm ThicknessThicknessThickness UniformityUniformityUniformity AnotherAnotherAnother variablevariable thatthat hashashas aaa significantsignificantsignificant effecteffecteffect ononon the thethe uniformity uniformityuniformity ofofof the thethe film filmfilm thickness thicknessthickness isisis thethethe heightheightheight ofofof thethethe opticalopticaloptical element. element.element. FigureFigureFigure 11 1111 shows showsshows thethethe relationshiprelationshiprelationship betweenbetweenbetween thethethe heightheightheight ofofof thethe optical optical elementelement element andand and thethe the filmfilm film thicknessthickness thickness unifunif uniformity.ormity.ormity. ItIt cancan It can bebe seen beseen seen fromfrom from FigureFigure Figure 1111 thatthat 11 thatthethe uniformityuniformity the uniformity ofof thethe of filmfilm the film thicknessthickness thickness decreasedecrease decreasesss graduallygradually gradually asas thethe as height theheight height ofof thethe of theopticaloptical optical ele-ele- elementmentment increasesincreases increases fromfrom from 800–1500800–1500 800–1500 mm.mm. mm. ThisThis This alsoalso also meme meansansans thatthat that thethe the differencedifference in in filmfilmfilm thicknessthicknessthickness decreasesdecreasesdecreases fromfromfrom thethethe centercentercenter ofofof thethethe surface surfacesurface tototo its ititss edge. edge.edge. However,However,However, after afterafter exceeding exceedingexceeding a aa height heightheight of ofof 150015001500 mm, mm,mm, the thethe uniformity uniformityuniformity of ofof the thethe film filmfilm thickness thicknessthickness no nono longer longerlonger changes changeschanges significantly. significantly.significantly.

FigureFigureFigure 11.11.11. FilmFilm thicknessthickness uniformity uniformityuniformity versus versusversus the thethe height heightheight of ofof the thethe optical opticaloptical element. element.element. The TheThe height heightheight represents repre-repre- thesentssents position thethe positionposition of the of topof thethe of toptop the of concaveof thethe concaveconcave optical opticaloptical element. element.element.

ToTo analyzeanalyze thethe relationshiprelationship betweenbetween thethe heightheight andand thethe uniformityuniformity ofof thethe filmfilm thick-thickness,ness, EquationEquation (4)(4) isis revisited.revisited. BothBoth coscosϕϕ andand coscosθθ rangerange fromfrom 00 toto 1.1. DisregardingDisregarding thethe evaporationevaporation sourcesource position,position, thethe squaresquare ofof thethe radiusradius rr cancan bebe expressedexpressed asas

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Coatings 2020, 10, x FOR PEER REVIEW 10 of 15 To analyze the relationship between the height and the uniformity of the film thickness, Equation (4) is revisited. Both cosφ and cosθ range from 0 to 1. Disregarding the evaporation1 222=++ρρ +Ψ+−2 + 22 − ρ + − 22 − ρ source position,r R the square21 RoC() K of the radius ( H RoCr can ) be() RoC expressed 2 as() H RoC() RoC 2 (12) 1 2 = 2 + 2 + [( + ) ] + ( − )2 + 2 − 2 + ( − ) 2 − 2 2 r R ρ It2 RoCcan beK seen1 fromΨ ρ EquationH RoC (12) thatRoC the valueρ of r2 isH determinedRoC RoC by ρ andρ H . The influ-(12) 2 enceIt can of beH seenon fromr is much Equation greater (12) thatthan the that value of ρ of. Inr isaddition, determined 1/r byisρ aand monotonicallyH. The influence de- creasingof H on function.r is much Therefore, greater than as the that height of ρ. Inincreases, addition, the1/ influencer2 is a monotonically of ρ on the film decreasing thick- nessfunction. becomes Therefore, gradually as thesmaller height and increases, the film the thic influencekness from of ρ theon thecenter film to thickness the edge becomes of the surfacegradually tends smaller to be uniform. and the film In summary, thickness fromwe can the increase center tothe the height edge of the reflective surface tends mir- to rorbe to uniform. enhance In the summary, uniformity we of can the increase film thic thekness. height However, of the reflective increasi mirrorng the toheight enhance of the the reflectiveuniformity mirror of the excessively film thickness. not only However, fails to improve increasing thethe uniformity height of of the the reflective film thickness mirror butexcessively also increases not only the difficulty fails to improve of connecting the uniformity the reflective of the filmmirror thickness and the but plate. also increases theAlthough difficulty the of connecting film thickness the reflectivedistribution mirror is analyzed and the using plate. the theory in Section 2, the theoryAlthough still has some the film limitations: thickness distribution is analyzed using the theory in Section2, the (1)theory This stilltheory has only some applies limitations: to planar evaporation sources. However, in the actual (1)coating This theoryprocess, only as appliesthe film to planarmaterial evaporation decreases, sources. the shape However, of the inevaporation the actual coating sourceprocess, changes as the from film a materialflat surface decreases, to a spherical the shape shape. of the So evaporationactual results source will be changes differentfrom afrom flat simulation surface to aresults. spherical shape. So actual results will be different from (2) Thesimulation PRS has design results. and construction errors, for example, there is a title present (2)in theThe surface PRS has to designbe coated. and These construction errors wi errors,ll affect for the example, actual results, there isbut a titlethe sim- present in ulationthe surface process to does be coated. not include These error errors analysis. will affect the actual results, but the simulation process does not include error analysis. 4. Shadow Mask Design 4. Shadow Mask Design A stable geometric configuration was optimized, with a gear ratio of K = 217/37, a A stable geometric configuration was optimized, with a gear ratio of K = 217/37, a reflective mirror height of 1500 mm and an evaporation source location of (−900, −300, 0). reflective mirror height of 1500 mm and an evaporation source location of (−900, −300, Residual thickness nonuniformities can be removed via masking. There are multiple 0). Residual thickness nonuniformities can be removed via masking. There are multiple methodsmethods for for masking masking the the vapor vapor plume. plume. Fixed-position Fixed-position masking masking is isthe the simplest simplest method, method, requiringrequiring low low maintenance maintenance and and offering offering high high mechanical mechanical reliability. TwoTwo criticalcritical aspects aspects of ofthis this masking masking system system are are the the proper proper mounting mounting of of the the mask mask in in the the coating coating chamber chamber and and the theshape shape of of the the shadow shadow mask. mask. The The mask mask is is placed placed at at a a negative negativeY Y-axis-axis position, position, as as shown shown in inFigure Figure 12 12,, and and is is parallel parallel to to the the bottom bottom of of the the vacuum vacuum chamber. chamber. Furthermore, Furthermore, to to reduce reduce the theprojection projection of of the the mask mask on on the the surface surface of theof th reflectivee reflective mirror, mirror, the the vertical vertical distance distance between betweenthe mask the mask and theand reflective the reflective mirror mirror is restricted is restricted to a few to a millimeters. few millimeters.

Figure 12. Geometric configuration of the shadow mask and the reflective mirror as viewed from the Figure 12. Geometric configuration of the shadow mask and the reflective mirror as viewed from thetop top of of the the vacuum vacuum chamber. chamber. The thickness of the obscured film is determined by the shape of the shadow mask. The thickness of the obscured film is determined by the shape of the shadow mask. Therefore, the critical issue in the design of a shadow mask is the determination of the film Therefore, the critical issue in the design of a shadow mask is the determination of the thickness in the area of the shadow mask. To analyze the film thickness in a certain area, film thickness in the area of the shadow mask. To analyze the film thickness in a certain area, we need to start from the path. The path, describing a point at ρ = 350 mm in the

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Coatings 2020, 10, x FOR PEER REVIEW 11 of 15 we need to start from the path. The path, describing a point at ρ = 350 mm in the system withsystem a 217/37 with a gear217/37 ratio gear and ratio a solarand a radius solar radius of 620 mmof 620 undergoing mm undergoing a single a single revolution, revolu- is showntion, is shown in Figure in Figure13. The 13. path The passes path passes through through the shadow the shadow mask mask on three on three occasions. occasions. The pathThe path is complicated, is complicated, and we and cannot we cannot calculate calculate the thickness the thickness obscured obscured when thewhen point the passes point throughpasses through the shadow the shadow mask accurately. mask accurately. However, However, we can we make can reasonable make reasonable assumptions assump- to approximatetions to approximate the film the thickness film thickn obscuredess obscured by the shadow by the shadow mask: mask: (1)(1) WhenWhen the the film film is is sufficiently sufficiently thick, thick, the the film film thickness thickness at at the the points points with with equiva- equivalent lentradii radii is equal is equal in the in the reflective reflective mirror. mirror. (2)(2) TheThe film film thickness thickness obscured obscured by by the the shadow shadow mask mask is the is thesame same each each time time the point the point passespasses through through the the mask. mask.

Figure 13. Paths describeddescribed byby aa pointpoint at atρ ρ= = 350 350 mm mm for for a a system system with with a 217/37a 217/37 gear gear ratio ratio undergoing undergo- aing single a single revolution revolution and and intersecting intersecti theng shadowthe shadow mask mask three three times. times.

The ﬁlm thickness obscured by the shadow mask is denoted as t , which, at a certain The film thickness obscured by the shadow mask is denoted as tobob, which, at a certain radius, can be determined byby thethe followingfollowing formula:formula: 1 n ( )( − ) + (− )M ( )( − ) + 2 − 2 2 3π +α z ρ cos KΨ x a 1 ρ sin KΨ b y z RoC ρ 1 Z 2 M t = C · N · zKxaKbyzRoCn ρρcos()()()Ψ−+− 1 sin ()() Ψ−+()22d −Ψ ρ2 (13) ob 3π 3π n+3 −α +α h i 2 2 2 2 2 2 tCN=⋅⋅π RoC (x − a) + (y − b) + z d Ψ (13) ob 3 −α n+3 2 RoC()() x−+−+ a22 y b z 2 2 where α is the central angle of the shadow mask width relative to the center position of the vacuum chamber. The total ﬁlm thickness obscured by the shadow mask is three times Where α is the central angle of the shadow mask width relative to the center position of greater than t . The width of the shadow mask at a certain radius is a function of the the vacuum chamber.ob The total film thickness obscured by the shadow mask is three times obscured position and the central angle: greater than tob . The width of the shadow mask at a certain radius is a function of the

obscured position and the centralwidth angle:mask = (R − ρ) · K · α (14) width=−⋅⋅() Rρ K α According to Equations (13) and (14),mask the calculation process for the design of(14) the shadow mask can be divided into the following steps: According to Equations (13) and (14), the calculation process for the design of the (1)shadowaccording mask can to be Equation divided (7), into the the film following thickness steps: distribution is calculated at different radius positions in the reflective mirror; (1) according to Equation (7), the film thickness distribution is calculated at different (2) assuming that the edge width of the shadow mask is known, the film thickness radius positions in the reflective mirror; obscured by the shadow mask can be calculated by Equation (13); (3)(2) assumingthe film thickness that the edge that needswidth to of be the obscured shadow at mask different is known, radius the positions film thickness is calculated obscuredsequentially by the to obtainshadowtob mask; can be calculated by Equation (13); (4)(3) thethe film value thickness of α can that be obtainedneeds to be according obscured to at Equation different (13); radius positions is calcu-

(5) latedaccording sequentially to Equation to obtain (14), t theob ; width of the shadow mask is calculated at different radius positions for the reflective mirror. (4) the value of α can be obtained according to Equation (13); The following is a specific example to demonstrate the entire process of designing the (5) according to Equation (14), the width of the shadow mask is calculated at differ- shape of the shadow mask. The CA of the reflective mirror is 700 mm (i.e., the range of ρ is ent radius positions for the reflective mirror. The following is a specific example to demonstrate the entire process of designing the shape of the shadow mask. The CA of the reflective mirror is 700 mm (i.e., the range

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of ρ is 0–350 mm); the RoC is 1250 mm and the height of the element is 1500 mm. The coordinates0–350 mm); of the the RoC evaporation is 1250 mm source and the are height (−900, of − the300, element 0) and isn 1500= 2. mm.The film The coordinatesthickness distributionof the evaporation on the surface source of are the (− refl900,ective−300, mirror 0) and isn shown= 2. The in ﬁlm Figure thickness 14. distribution on the surface of the reﬂective mirror is shown in Figure 14.

Figure 14. 3D map of the film thickness distribution on the surface of the reflective mirror. Figure 14. 3D map of the film thickness distribution on the surface of the reflective mirror. As shown in Figure 14, the film thickness at the edge of the reflective mirror is 215.8 nm (ρ =As 350 shown mm) in and Figure the width14, the offilm the thickness shadow at mask the edge at the of edge the reflective is 16 mm. mirror According is 215.8 to nmEquation (ρ= 350 (13),mm) the and film the thickness width of obscured the shadow by the mask shadow at the mask edge is is 5.1 16 nm mm. and According the tob = 5.1/3 to

Equation= 1.7 nm, (13), with the Equation film thickness (14) yielding obscuredα as 0.005.by the After shadow being mask obscured, is 5.1 nm the thicknessand the t ofob the= 5.1/3film = at1.7 the nm, edge with of Equation the reflective (14) mirroryielding is α 210.7 as 0.005. nm. ThisAfter means being obscured, that the film the thickness thickness at ofother the film obscured at the radiusedge of locations the reflective should mirror also beis 210.7 nm. This Table means1 shows that the the film film thickness thick- nessdistribution at other obscured at different radius radii locations of the reflective should also mirror, be 210.7 as well nm. as Table the associated 1 shows the obscured film thicknessthicknesses distribution and widths at different of the shadow radii of mask. the reflective mirror, as well as the associated obscured thicknesses and widths of the shadow mask. Table 1. Film thickness distribution and the width of the shadow mask at different radius positions.

Table 1. Film thickness distribution and the width of the shadow mask at different radius positions. NO. Radius/mm Film Thickness/nm Obscured Thickness/nm tob/nm α Width/mm 1 0Film 230.9 Thick- Obscured Thick- 20.7 6.9 0.0138 100.3 NO. Radius/mm tob /nm Width/mm 2 50 225.4ness/nm ness/nm 14.7 4.9 0.0134 89.6 31 100 0 224.8 230.9 20.7 14 6.9 4.70.0138 0.0128 100.3 78.1 42 150 50 223.5 225.4 14.7 13.1 4.9 4.40.0134 0.0119 89.6 65.1 5 200 222.4 11.8 3.9 0.0107 52.7 3 100 224.8 14 4.7 0.0128 78.1 6 250 220.6 10 3.3 0.0092 40 74 300 150 218.4223.5 13.1 7.7 4.4 2.60.0119 0.0075 65.1 28.5 85 350 200 215.8222.4 11.8 5.1 3.9 1.70.0107 0.005 52.7 16 6 250 220.6 10 3.3 0.0092 40 7 300 218.4 7.7 2.6 0.0075 28.5 8 350 The215.8 initial shape of the5.1 shadow mask 1.7 is shown in Figure0.005 15a. According16 to the experiments, the final shadow mask is obtained by making two to three adjustments based on theThe initialinitial shape;shape of the the final shadow shape mask of the is shadow shown in mask Figure is shown 15a. According in Figure to15 b.the Once exper- the iments,shadow the mask final is shadow installed mask in the is obtained correct position, by making the remainingtwo to three nonuniformity adjustments based is reduced on theto initial less than shape; 1%. the Figure final 16 shapea,b shows of the the shad interferenceow mask diagramsis shown in of Figure the surface 15b. beforeOnce the and shadowafter the mask application is installed of the in thinthe correct film coating, position, respectively. the remaining It is observed nonuniformity that there is reduced is almost tono less variation than 1%. in theFigure surface 16a,b profile shows accuracy, the inte whichrference means diagrams that the of nonuniformitythe surface before of the and film afterthickness the application is controlled of the with thin high film precision. coating, respectively. It is observed that there is almost no variation in the surface profile accuracy, which means that the nonuniformity of the film thickness is controlled with high precision.

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(a) (a)

(b) (b)

FigureFigure 15. 15. (a) Initial((aa)) Initial Initial shape shape shape of the of of theshadow the shadow shadow mask. mask. mask. The Th shape Thee shape shapeis drawn is drawn is drawn by formulasby formulas by formulas 13 and13 and (13)14 and14 and and the (14) thedata anddata in theTable in Table data 1. Source: in1. TableSource: 1. Author’sSource:Author’s own Author’s own conception, conception, own conception,based based on MATLABon basedMATLAB on software. MATLAB software. (b) software. (Finalb) Final shape shape (b) of Final the of the shapeshadow shadow of mask. the mask. shadow According According mask. to According theto the experi- experi- to the ments,experiments,ments, the the final final the shadow ﬁnalshadow shadow mask mask maskis obtained is obtained is obtained by bymaking by making making two two to tothreetothree three adjustments adjustments adjustments based based based onon the onthe initialthe initial initial shape. shape. shape.

(a) (a)

Figure 16. Cont.

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(b)

FigureFigure 16. ( 16.a) Surface(a) Surface profile proﬁle before before coating. coating. (b) Surface (b) Surface profile proﬁle after after coating. coating.

5. Conclusions5. Conclusions To investigateTo investigate and and exploit exploit the theuniformity uniformity of the of thefilm film thickness thickness in the in thePRS, PRS, we weused used simulationsimulation to study to study the film the thickness film thickness distribution. distribution. In this Inarticle, this we article, report we a reportclose rela- a close tionshiprelationship between between the uniformity the uniformity of the thin of thefilm thin thickness, film thickness, which affects which the affects surface the pro- surface file profileof the reflective of the reflective mirror, mirror, and the and geomet the geometricric configuration configuration in the vacuum in the vacuum chamber chamber by by using the film thickness distribution formula based on Knudsen’s laws. The impact of using the film thickness distribution formula based on Knudsen’s laws. The impact of the the evaporation source position on the film thickness uniformity was analyzed for both evaporation source position on the film thickness uniformity was analyzed for both the the standard and counter PRSs. According to the simulation results, the reflective mirror standard and counter PRSs. According to the simulation results, the reflective mirror achieves better uniformity when the source is offset from the center of the chamber in achieves better uniformity when the source is offset from the center of the chamber in the the counter PRS. Moreover, the number of planetary revolutions and the height of the counter PRS. Moreover, the number of planetary revolutions and the height of the reflec- reflective mirror also affect the uniformity. The above simulation analysis results can be tive mirror also affect the uniformity. The above simulation analysis results can be used used to determine suitable positions of the evaporation source and optical components to to determine suitable positions of the evaporation source and optical components to im- improve the uniformity of the film thickness. Furthermore, the developed model has been prove the uniformity of the film thickness. Furthermore, the developed model has been shown to be effective for designing suitable masks to correct thickness nonuniformities. shown to be effective for designing suitable masks to correct thickness nonuniformities. The viewpoint from the movement path proposed in this study potentially offers new The viewpoint from the movement path proposed in this study potentially offers new insights into the shadow mask design, which would effectively require a reduced number insightsof experiments. into the shadow In general, mask design, by adjusting which would the geometric effectively configuration require a reduced and installing number the of experiments.shadow mask, In thegeneral, nonuniformity by adjusting of thethe 700 geometric mm concave configuration reflective and mirror installing is reduced the to shadowless thanmask, 1%. the nonuniformity of the 700 mm concave reflective mirror is reduced to less than 1%. 6. Outlook 6. OutlookDespite these results, there are still some aspects that are not satisfactory. First, we did notDespite consider these the results, effect ofthere extended are still sources some as onpects the filmthat thicknessare not satisfactory. uniformity. First, Second, we the did calculationnot consider of the the effect film thickness of extended obscured sources by on the the shadow film thickness mask is notuniformity. sufficiently Second, accurate, the necessitatingcalculation ofthree the film to four thickness further obscured modifications by the of shadow the initial mask mask is not shape. sufficiently Third, with ac- the curate,development necessitating of remote three to sensing four further satellites, modifications off-axis reflective of the initial optical mask systems shape. are Third, gradually withreplacing the development coaxial reflective of remote optical sensing systems, satellites, so off-axis off-axis mirrors reflective will optical be widely systems used are in the graduallyfuture. replacing However, coaxial due to reflective the limited optical length systems, of the so article, off-axis we mirrors have not will studied be widely the film usedthickness in the future. uniformity However, distribution due to the for limite off-axisd length mirrors of inthe the article, PRS. we have not studied the film thicknessTherefore, uniformity we will improve distribution subsequent for off-axis studies mirrors of the in uniformitythe PRS. in three primary areas:Therefore, (1) an we improved will improve description subsequent of the impact studies of of extended the uniformity sources toin morethree accuratelyprimary fit areas:the (1) film an thicknessimproved distribution; description (2)of the the impa effectct of of a extended movable evaporationsources to more source accurately on the film fit thethickness film thickness distribution; distribution; (3) the accurate (2) the determinationeffect of a movable of the evaporation film thickness source obscured on the by the filmshadow thickness mask; distribution; (4) the research (3) the on accurate the distribution determination of film of thickness the film ofthickness the off-axis obscured mirror in by thethe shadow PRS. mask; (4) the research on the distribution of film thickness of the off-axis mirror in the PRS.

Author Contributions: Conceptualization, G.W.; methodology, G.W. and L.W.; software, G.W.; validation, Y.B. and J.Z.; formal analysis, G.W.; investigation, Y.Z.; resources, J.Z.; writing—original

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Author Contributions: Conceptualization, G.W.; methodology, G.W. and L.W.; software, G.W.; validation, Y.B. and J.Z. (Jing Zhao); formal analysis, G.W.; investigation, Y.Z.; resources, J.Z. (Jiyou Zhang); writing—original draft preparation, G.W.; writing—review and editing, G.W. and L.W. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data sharing not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Piegari, A.; Flory, F. Optical Thin Films and Coatings: From Materials to Application, 2nd ed.; Woodhead Publishing Limited: Philadelphia, PA, USA, 2018; pp. 695–717. ISBN 978-008-102-073-9. 2. Madsen, C.K.; Zhao, J.H. Optical Filter Design and Analysis: A Signal Processing Approach, 1st ed.; John Wiley & Sons: New York, NY, USA, 1999; pp. 95–154. ISBN 047-118-373-3. 3. Panteleev, G.V.; Zhuravlev, A.A.; Morshakov, V.V. Correcting mask for increasing the thickness uniformity of vacuum coatings. Sov. J. Opt. Technol. 1988, 55, 547–548. 4. Villa, F.; Pompa, O. Emission pattern of real vapor sources in high vacuum: An overview. Appl. Opt. 1999, 38, 695–703. [CrossRef] [PubMed] 5. Villa, F.; Martinez, A. Correction masks for thickness uniformity in large-area thin films. Appl. Opt. 2000, 39, 1602–1610. [CrossRef] [PubMed] 6. Aaron, H.P.; Charles, A.W. Expressions for the evaporation and condensation coefficients in the hertz-knudsen relation. Chem. Rev. 2016, 116, 7727–7767. [CrossRef] 7. Kotlikov, E.N.; Prokashev, V.N.; Ivanov, V.A.; Tropin, A.N. Thickness uniformity of films deposited on rotating substrates. J. Opt. Technol. 2009, 76, 100–103. [CrossRef] 8. Smith, D.J.; Staley, A.; Eriksson, R.; Algar, G. Counter rotating planetary design for large rectangular substrates. In Proceedings of the 41st Annual Technical Conference of the Society of Vacuum Coaters, Boston, MA, USA, 1998; pp. 193–196. 9. Oliver, J.B.; Talbot, D. Optimization of deposition uniformity for large-aperture National Ignition Facility substrates in a planetary rotation system. Appl. Opt. 2006, 45, 3097–3105. [CrossRef][PubMed] 10. Oliver, J.B. Analysis of a planetary-rotation system for evaporated optical coatings. Appl. Opt. 2016, 55, 8550–8555. [CrossRef] [PubMed] 11. Oliver, J.B. Impact of deposition-rate fluctuations on thin-film thickness and uniformity. Opt. Lett. 2016, 41, 5182–5185. [CrossRef] [PubMed] 12. Oliver, J.B. Impact of non-integer planetary revolutions on the distribution of evaporated optical coatings. Appl. Opt. 2017, 56, 1460–1463. [CrossRef] 13. Oliver, J.B. Impact of a counter-rotating planetary rotation system on thin-film thickness and uniformity. Appl. Opt. 2017, 56, 5121–5124. [CrossRef][PubMed] 14. Liu, C.; Kong, M.; Guo, C.; Gao, W.; Li, B. Theoretical design of shadowing masks for uniform coatings on spherical substrates in planetary rotation systems. Opt. Express 2012, 20, 23790–23797. [CrossRef][PubMed] 15. Wang, B.; Fu, X.; Song, S.; Chu, H. Simulation and Optimization of Film Thickness Uniformity in Physical Vapor Deposition. Coatings 2017, 8, 325. [CrossRef] 16. Sun, J.; Zhang, W.; Yi, K.; Shao, J. Optimization of thickness uniformity of coatings on spherical substrates using shadow masks in a planetary rotation system. Chin. Opt. Lett. 2014, 12, 053101. [CrossRef] 17. Holland, L. Vacuum Deposition of Thin Films; Wiley: New York, NY, USA, 1956.