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subsurface damage using atmospheric pressure plasma processing
Applied Surface Science 382 (2016) 260–267
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Modeling study on the surface morphology evolution during removing the optics surface/subsurface damage using atmospheric pressure plasma processing Qiang Xin, Xing Su, Bo Wang ∗ Center for Precision Engineering, Harbin Institute of Technology, Harbin, 150001, PR China
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Article history: Received 29 February 2016 Received in revised form 13 April 2016 Accepted 24 April 2016 Available online 26 April 2016 Keywords: Optics Level set method Surface/subsurface damage Surface formation
a b s t r a c t Plasma processing has been widely reported as an effective tool in relieving or removing surface/subsurface damage induced by previous mechanical machining process. However, the surface morphology evolution during removing the damage using plasma processing is rarely reported. In this research, this procedure is studied based on experiments and robust numerical models developed on the basis of Level Set Method (LSM). Even if some unique properties of plasma etching are observed, such as particle redistribution, the dominant role of isotropic etching of plasma processing is verified based on experiments and 2D LSM simulations. With 2D LSM models, the damage removal process under various damage characteristics is explored in detail. Corresponding peak-to-valley roughness evolution is investigated as well. Study on morphology evolution is also conducted through the comparison between experiments and 3D LSM computations. The modeling results and experiments show good agreement with each other. The trends of simulated roughness evolution agree with the experiments as well. It is revealed that the plasma processing may end up with a planar surface depending on the damage characteristics. The planarization procedure can be divided into four parts: crack opening and pit formation; pit coalescing and shallow pits subsumed by deep ones; morphology duplicate etching; and finally a planar and damage free surface. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Surface/subsurface damage is inevitably induced into the optics using traditional mechanical machining methods. These damages, especially the micro-cracks, are regarded as the leading factor in lowering the strength and laser damage threshold of optical components [1,2]. When irradiated by high-energy laser, even the expansion of a few flaws in the optics could restrain the lifetime of the component [3]. Techniques in eradicating these damages have long been the research interests of scientists. Plasma processing has been recognized as a solution in mitigating or removing these damages in optics [4]. This chemical method also has other superiorities in optical fabrication such as deterministic optical surface machining owing to its near Gaussian-shaped material removal function [4,5], and high potential in manufacturing complex shaped optical surfaces [6] as well as meter scale optics [7]. Therefore, considerable studies have been devoted to develop this technique. Different
∗ Corresponding author. E-mail address: [email protected] (B. Wang). http://dx.doi.org/10.1016/j.apsusc.2016.04.157 0169-4332/© 2016 Elsevier B.V. All rights reserved.
types of plasma processing have been developed in fulfilling various optical manufacturing demands, such as Plasma Jet Machining [7], Reactive Atom Plasma Technology [8], Plasma Chemical Vaporization Machining [9], Plasma Assisted Chemical Etching [10] and Atmospheric Pressure Plasma Processing [11]. Understanding the surface formation using these plasma methods can help us in determining the location of the plasma methods in an optical fabrication chain, as well as in optimizing the fabrication chain to reduce the fabrication time and production costs. Consequently, researchers have been devoting to study on the surface formation using plasma processing. Jin et al. reported an experimental study on the surface morphology and chemistry evolution of fused silica surface using Atmospheric Pressure Plasma Processing (APPP) [11]. Xin et al. studied the surface formation and morphology evolution of ground fused silica parts using APPP as well. Their results indicated some similarities between the plasma method and the isotopic wet chemical etching, and the surface formation resulted from removing the surface/subsurface damage [4]. Research on surface smoothing mechanism was basically reported by Zarowin using a model based on differential surface evolution equations. A simple sinusoidal profile was used as an initial
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Fig. 1. The selected evolution of etched micro-cracks with various material removal depths: (a) 1 m; (b) 8.8 m; (c) 19.3 m. (d) Cross section profiles for the etched pits with material removal depths: A 1 m; B 3.6 m; C 5.5 m; D 7.1 m; E 8.8 m; F 10 m; G 15.6 m; H 19.3 m. (e) Schematic drawing of the etchant particle redistribution and the formation of micro-trenches (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
input for the 2D profile evolution model and a fundamental explanation on the surface smoothing mechanism was provided [12]. For surface formation in removing damage using isotropic etching, the research of Spierings showed that cusp-like surface structure was originated from surface flaws in wet chemical etching [13,14]. Wong et al. reported experimental and theoretical studies on the effect of the damage characteristics on the peak-to-valley roughness (RPV ) evolution with wet chemical etching [15,16]. Yet, not many studies theoretically focus on the surface formation and evolution process during removing surface/subsurface damage using plasma processing. In this paper, we demonstrate the dominate role of isotropic etching using APPP. A 2D level set method (LSM) model is then applied to simulate the development of two microcracks under isotropic etching, and the results are compared with the experiments to verify the demonstration. Moreover, the 2D surface profile developments considering the influences of different micro-crack characteristics are explored. Finally, 3D morphology
evolution is investigated and compared with the experimental results during removing the damage. 2. Numerical modeling method and experimental setup LSM, introduced by Osher and Sethian [17], has been widely applied in tracking the interface evolution such as fluid mechanics, combustion, computer vision, crystal growth, and etching [18,19]. This method is a robust numerical technique for tracking the evolving interfaces and providing accurate geometric properties. The interface, either a 2D profile or 3D surface, is embedded as a zero level set of a higher-dimensional function. The motion of the interface is governed by an externally generated velocity field. The corresponding level set equation for APPP processed interface is t = Vn |∇ |
Fig. 2. Comparison between the experiments and modeling results (a) the surface profiles, (b) the big pit depth.
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Fig. 3. Surface profile evolutions with periodical cracks with LDs (a) 0.5 m, (b) 1 m and (c) 2 m. (d) RPV for 2D models (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
where t represents a versatile and time dependent level set function for 2D profile or 3D surface. Vn is the velocity along the surface normal direction. As a relatively mature method, the interface equations of LSM can be solved using various libraries and tools [20,21]. To build the LSM model for APPP, the driving force and its basic characteristics are necessary to be understood. To get an insight into these characteristics, experiments were conducted using an in-house developed inductively coupled plasma processing system. The detailed experimental setup and results can be found from our previous study [4]. For completeness of this work, the experiments are briefly described. Electric power with 27.12 MHz inductively coupled radio frequency was supplied to the plasma via the load coil through an impedance matching box. Ar/CF4 mixtures were used to generate high density reactive plasma and process fused silica samples under atmospheric pressure. For better comparison between the modeling results and the experiments, the initial conditions for LSM model and experimental details are described in subsequent corresponding sections. 3. Results and discussion 3.1. Modeling verification of the isotropic etching of APPP Evolution of two common cracks and their coalescence procedure were in situ investigated to get the characterizations for the driving force of APPP and for the subsurface crack evolution. These experiments were conducted on a polished fused silica sample with a reactant gas flow of 2 sccm and input power of 900 W. About 1 m in depth was etched away from the surface to make sure the Bielby layer was removed and the healed cracks were opened. Therefore, the micro-cracks could be viewed by the microscope (OLS 3000, Olympus Co., Japan). The sample was then etched and observed layer by layer with a removal depth of ∼2 m at each step. Fig. 1(a)–(d) shows the selected experimental images of the etched pits, and the cross section profiles measured along the red lines of the experimental results [4]. Fig. 1(e) is the drawing of the etchant particle redistribution and the formation mechanism of micro-trenches based on the experimental surface profiles. From the experimental results as shown in Fig. 1(d), microtrenching is observed in the bigger etched pit from its cross-section profiles B to D. The micro-trench formation is the combined effects
of the redistribution of reactive particles [22] together with the sidewall angles [23] as illustrated in Fig. 1(e). The redistribution of etchant particles might play some dominant roles in quick opening of the subsurface cracks, because the crack walls are too close to each other at the beginning. Yet, after material of several micrometers in depth is removed, the micro-trenches disappear as illustrated in the profiles F to H in Fig. 1(d). One possible reason for this is the disappearance of side wall (thick lines shown in Fig. 1(d)) as the etching advancing in the normal direction of the surface. The other reason for this is that the distance between the walls is too large for re-emitted particles to reach the other side under atmospheric pressure. Thus, after the crack is fully opened, the etching which is induced by particle redistribution is less pronounced. It can be noted that the bottoms of the pits (profiles E to H in Fig. 1(d)) are almost parallel to each other, this indicates that the isotropic etching starts to come into play. Because the particle redistribution is less obvious, especially after the micro-cracks are widely opened, this effect can be ignored to simplify the LSM model. Hence, the model would only take the isotropic etching effect into consideration, which means that the substrate material is etched away uniformly in all directions, and the etching velocity advances along the surface normal direction. To verify the accuracy of the LSM model, 2D etched pit profile evolution is investigated and compared with the experimental results. The profile of etch pits, shown in Fig. 1(d) line A, is used as the initial input surface profile in the model to compute the etched pit evolution. Fig. 2 is the comparison of the experimental surface profiles and depths with the simulation results. The experimental profile results are illustrated using thin lines in Fig. 2(a). The simulation results are represented using thick lines with the same colors. The criteria to evaluate the simulation results depends on whether the pit edges are matched with the experiment ones, as the black lines illustrated in Fig. 2(a). The modeling profiles for small pit agree well with the experimental results. But for the big pit, all the experimental profile bottoms are smaller than the computations. This can be explained through the depth evolution curve of the pit and the particle redistribution shown in Figs. 1(e) and 2(b). The depth points on the curve in Fig. 2(b) are obtained at the center of the bigger pit cross section profiles. An obvious reduction at the beginning can be noticed, which indicates that a shallow advance of depth right after the crack is opened. This is also resulted from the etchant particle redistribution. Most of the particles are bounced from one side wall
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Fig. 4. The SEM results for the plasma etched surfaces with various material removal depths: (a) 0 m, (b) 20.6 m, (c) 45.3 m, (d) 95.2 m, (e) 164.6 m, (f) 300 m, and (g) the corresponding RPV and RMS evolution measured by AFM.
to the other side as illustrated in Fig. 1(e). This leads to the reduction of the particles that could reach to the pit bottom, and brings about the bump at the bottom. Due to the weakened particle redistribution effect as aforementioned, after this reduction, the depths keep constant in the following procedure as shown in Fig. 2(b). In computing the 2D profile evolution, the surface line A in Fig. 2(a) is used as the initial profile for the LSM model. The depth of the profile line A is the deepest one. For isotropic etching computation, the etch depth keeps constant and it is as same as the initial profile as shown in Fig. 2(b). Therefore, the simulation depths are deeper than the experimental ones. All the computed profile bottoms are slightly lack behind of the experimental ones as shown in Fig. 2(a). But from Fig. 2(a) line G and H, the etched profiles are almost parallel to each other and to the computing results. Moreover, the depth data in Fig. 2(b) are almost parallel to each other except the first point. All these indicate that isotropic etching of APPP comes into play, and the pits begin to evolve under the driving force which is normal to the surface.
3.2. 2D modeling study on the surface profile evolution 2D LSM simulations are carried out to study the crack characteristics, such as depth and lateral distance (LD) between cracks, on the surface formation. The simulations were performed with 10 m long surface profile. Cone cracks, as the bigger pit in profile line A shown in Fig. 2(a), were used in the models to simulate the subsurface cracks. Periodical cone cracks with 0.4 m, 0.7 m, and 1 m in depth were used in the simulations. The LDs between the cracks were set as 0.5 m, 1 m and 2 m, and crack opening (as illustrated in Fig. 2(a) profile line A) with 0.04 m was used in the models. The profiles evolved with the normal velocity of 0.25 m/unit time (m/ut). The processing time with arbitrary unit (a.u.) ranged from 0 a.u. to 36 a.u. with an interval of 1 a.u. The obtained results are shown in Fig. 3(a)–(c). The solid black lines denote the boundary development between the pits formed by 0.4 m cracks and 0.7 m cracks, the solid blue lines represent for boundary development between pits formed by 0.7 m cracks and 1 m cracks, the dash-dotted blue lines denote the bound-
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Fig. 5. Top views for the plasma etched surfaces with various processing time (a.u.): (a) 0; (b) 0.2; (c) 0.4; (d) 0.6; (e) 0.8; (f) 1; (g) 1.2; (h) 2 and (i) 5 (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
ary between pits formed by 0.7 m cracks and themselves, and the dash-dotted red lines represent for boundary between pits formed by 1 m cracks and themselves. The corresponding RPV for Fig. 3(a)–(c) is calculated for each profile as shown in Fig. 3(d). Fig. 3(a)–(c) shows the surface profile evolutions under different damage characteristics. As can be seen from the figures, pits are resulted from the opening of the cracks under isotropic etching. Cusps are then formed when pits begin to coalesce with the adjacent one. When linking these cuspidal points, boundary development lines could be obtained as shown in the figures. For the boundary lines between cracks with different depths (solid lines), these lines shrink toward the small pits and disappear finally. This means that the small pits are swallowed up by the bigger ones. At the same time, a new boundary line is formed between the bigger pits. The new boundary lines continue to shrink until the pits with similar depths meet each other, and a vertical boundary line is then formed as illustrated by the dash-dotted lines in Fig. 3. If the vertical line is not formed by the coalescing of deepest pits, they will disappear finally as the blue dash-dotted lines showing in Fig. 3 (a) and (b), because the pit swallow-up procedure is still going on. This procedure will continue until the deepest pits meet each other, and finally form a vertical boundary line as the red dashdotted lines show. These vertical lines indicate that the boundaries of the pits do not change while more material is wiped off. And the surface begins to copy the previous surface morphology, which can be seen from the lines in the red rectangular boxes of Fig. 3(a) and (b). This phenomenon reveals that the isotropic etching might result in a morphology duplicate etching.
Fig. 3(d) shows the RPV evolution with various LD values. For LD equals to 0.5 m, the first point on the RPV evolution curve is identical to the largest crack depth, 1 m. And a slight decrease of RPV can be noticed at the second point. The reason for this is that the cracks open with the speed of 0.25 m/ut, and the LD between cracks is 0.5 m, where we should take the crack openings (0.04 m) into account. Therefore, the peaks of magenta line in Fig. 3(e) decrease a little faster. For the other two curves, the horizontal stages at the beginning are because the pits are still isolated from each other and the depths are as same as the crack depths. With increment of the LDs, the lengths of horizontal stages increase as well. The reason is shown in Fig. 3(b) and (c): the larger the LDs are, the more difficult the platforms at the beginning profiles to be eliminated, namely, for the pits to get close to each other. Therefore, more time is needed for RPV curves with large LDs to wipe out the horizontal stage. And kink points are also observed on the curves. The kink points imply that the farthest pits are getting closed and begin to coalescence with each other. In addition, the prominent effects of LD in RPV evolution and its evolution agree well with the conclusion of isotropic wet chemical etching [15]. As for the final values of the RPV , even if the damages are equivalent in the three simulations, small LD, namely a high density of cracks, makes the pits more easy to merge mutually, and results in a quickly convergence of the roughness to a better surface quality. Accordingly, small LDs lead to a better surface quality than larger LDs when using the same processing parameters as the RPV shown in Fig. 3(d). From results of Fig. 3, it is concluded that the final surface is out of damage, more specifically a crack-free surface. The results
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Fig. 6. Side views for the plasma etched surfaces with various processing time (same as Fig. 5) and (j) the corresponding RPV evolution for 3D LSM simulation results (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
reveal the basic crack removal mechanism using plasma processing: pits grow larger and merge with one another. Meanwhile, some small/shallow pits are subsumed by the big/deep ones as more material is removed. 3.3. 3D modeling study on the surface formation and morphology evolution To verify the analyses and further prove the damage removal mechanism using plasma processing, 3D LSM simulations are implemented. In addition, the morphology comparison is performed between the experiments and simulation results. The experiments were conducted on grinded samples to investigate the surface morphology evolution [4]. The samples were processed with the material removal rate of ∼0.45 m/s. Time was varied to
get different material removal depth. Fig. 4 presents the surface texture evolutions which were measured by Field Emission Scanning Electron Microscope (SEM, Quanta 200, FEI Co., America), and the corresponding RPV and root mean square roughness (RMS) were measured by AFM (Brucker Vecco Dimension 3100, Veeco Inc., USA) before and after plasma processing. For the surface texture before plasma processing, shown in Fig. 4(a), cracks and scratches might be filled with abrasive products or healed after mechanical machining. The fillings and closures result in a relatively smooth surface with RMS of 100 nm as presented in Fig. 4(g) point a. And the big RPV value for point a is resulted from some singular deep cracks that are not fully healed or filled by the abrasives. After ∼20 m material was removed, the hidden defects were opened and led to a rougher surface as shown in Fig. 4(b) and (g) point b. As processing proceeded, small pits
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Fig. 7. Schematic drawing of plasma processing procedure.
caused by shallow cracks were swallowed up by bigger ones. And the bigger pits grew larger and coalesced with one another (same as the procedure aforementioned in the 2D LSM model). This process causes the RPV and RMS to decrease in Fig. 4(g). For 3D LSM simulation, the cracks were randomly and discretely distributed on a 180 × 180 m2 rough surface. The RPV of the surface was 500 nm without consideration of the subsurface crack depths. The crack depths were 10 m, 20 m, 30 m and 50 m with amount of 200, 160, 120 and 80, respectively. Material removal time ranged from 0 a.u. to 5 a.u. with an interval of 0.2 a.u. and a normal removal rate of 25 m/ut. Figs. 5 and 6 present the selected modeling results. Fig. 5 is the top views of the morphology, and Fig. 6 is the side views of the results. The surface bottoms in the figures were adjusted so that the lowest points of the surfaces are zero. The highest point on the surface is denoted by light yellow and the lowest point by dark blue. It can be seen that in Fig. 5(b), because the opening speeds of the cracks are the same, sizes of the pits are almost identical. With the increase of etching time, pits begin to grow lager and overlap with each other. In Fig. 5(e), most of the shallow pits formed by 10 m and 20 m cracks are subsumed by the bigger ones. When the deepest pits start to merge with each other, the number of pits with small depth reduces. As these small pits finally disappear, the biggest adjacent pits, formed by 50 m deep cracks, begin to merge and the duplicate etching begins as shown in Fig. 5 (f)–(i). The experimental results of SEM in Fig. 4 and LSM modeling results in Fig. 5 give a comprehensive perception of the plasma processed surface advancing. Cracks and scratches might be filled with abrasive products or closed after mechanical machining. This makes the SEM inspection difficult, and a smooth surface is obtained as shown in Fig. 4(a). After some material is removed, the hidden defects are opened and can be observed by the SEM, and this lead to a rougher surface as RPV shown in Fig. 4(f). The big pits are resulted from deep cracks, the small ones are caused by shallow cracks in like manner, and most of the etched pits are roughly spherical as shown in Figs. 4 and 5(b). At this initial opening stage of the cracks, the crack density is high because the pit swallow-up procedure does not fully come into action. When pits increase in size, small pits are merged by larger pits. The borderlines, formed by the merging of pits, are straight lines as shown inside the yellow rectangular boxes of Fig. 4(b)–(d). These straight borderlines can also be observed at the modeling results from Fig. 5(b) to (i). Due to the depth differences of the simulate cracks, the pit boundaries for shallow pits are ambiguous in Fig. 5(b)–(e). Micrographs presented in Fig. 4(b)–(f) and Fig. 5(b)–(e) show that the etched pit density decrease sharply with more material removal. This is because pits grow larger and coalesce with one another. Meanwhile, some small/shallow pits are swallowed up by the big/deep ones as more and more material is removed. This merging procedure is more clearly shown in the modeling results from Fig. 5(b) to (e). As it can also be observed in Fig. 5(d) that the left pits are formed by the deepest cracks (50 m deep cracks). This is in accordance with the analyzations of the 2D profile evolution. From the comparison, it can be found that the modeling surface formation
and morphology evolution agree well with the experiments as presented in Figs. 4 and 5. The developments of damage depth could be found from the side views in Fig. 6, which could be obtained from y-axis direction of the corresponding images of Fig. 5. The peak-to-valley changes can be directly seen from the figures. Even during the morphology duplicate etching from Fig. 6(f) to (i), the RPV still declines and converges to a relatively planar surface. This is also illustrated by the corresponding points f, h and i in Fig. 6(j). This roughness development trend agrees with the experimental results in Fig. 4(g). In summary, the damage removal procedure can be separated into four parts: (a) crack opening and pit formation; (b) pit coalescing and shallow pits subsumed by deep ones; (c) morphology duplicate etching; and (d) a finally planarized surface without damage. The schematic drawing of this procedure is based on the 2D LSM simulation, and it is shown in Fig. 7. Considering the randomness of the damage, such as depth, density and distribution, during the planarization using APPP, some steps might occur at the same time or only last for a short time. For example, if the crack density is really high, the crack opening and the coalescing would happen simultaneously. Also, a planar surface might be obtained with less steps of morphology duplicate etching. In addition, the planar degree of final surface is governed by the characteristics of the damage and the depth of removed material. For surface with high density and similar depth damage, a planar surface can be easily obtained using plasma processing. 4. Conclusion In summary, particle redistribution is observed in plasma processing under atmospheric pressure, and it plays some effects on crack opening. Despite of this unique etching property of plasma, the dominate role of isotropic etching using APPP is verified based on the experiments and 2D LSM models. The 2D modeling results clearly show that the surface formation is resulted from pits growing larger and merging with one another. A novel phenomenon of isotropic etching, morphology duplicate etching, is observed in the modeling results. This phenomenon happens when cracks with similar depths merge with each other. Density of the damage has more significant effect on the roughness evolution than damage depth. According to the modeling results, a planar surface can be obtained from surface with high damage density. Also, it is revealed that the plasma processing may end up with a planar surface depending on the damage characteristics. Surface morphology evolution is then compared between 3D modeling and the experiments. The morphology evolutions show good agreement with each other. The trends of simulated roughness evolution agree with the experiments as well. This verifies the accuracy using LSM in modeling surface formation when removing the surface/subsurface damage. The damage removal capacity and mechanism of plasma processing are theoretically and experimentally proved in this work. The surface planarization procedure is summarized into four parts: crack opening and pit formation; pit coalescing and shallow pits subsumed by deep ones; morphology duplicate etching; and finally a planar and damage free surface. This work is helpful in understanding the surface formation using APPP and in determining the location of APPP in an advanced optical manufacturing chain. Acknowledgements This work was supported by grants from the National Natural Science Foundation of China (No. 51175123 and No. 51105112), and National Science and Technology Major Project (No. 2013ZX04006011-205).
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Modeling study on the surface morphology evolution during removing the optics surface/subsurface damage using atmospheric pressure plasma processing Qiang Xin, Xing Su, Bo Wang ∗ Center for Precision Engineering, Harbin Institute of Technology, Harbin, 150001, PR China
a r t i c l e
i n f o
Article history: Received 29 February 2016 Received in revised form 13 April 2016 Accepted 24 April 2016 Available online 26 April 2016 Keywords: Optics Level set method Surface/subsurface damage Surface formation
a b s t r a c t Plasma processing has been widely reported as an effective tool in relieving or removing surface/subsurface damage induced by previous mechanical machining process. However, the surface morphology evolution during removing the damage using plasma processing is rarely reported. In this research, this procedure is studied based on experiments and robust numerical models developed on the basis of Level Set Method (LSM). Even if some unique properties of plasma etching are observed, such as particle redistribution, the dominant role of isotropic etching of plasma processing is verified based on experiments and 2D LSM simulations. With 2D LSM models, the damage removal process under various damage characteristics is explored in detail. Corresponding peak-to-valley roughness evolution is investigated as well. Study on morphology evolution is also conducted through the comparison between experiments and 3D LSM computations. The modeling results and experiments show good agreement with each other. The trends of simulated roughness evolution agree with the experiments as well. It is revealed that the plasma processing may end up with a planar surface depending on the damage characteristics. The planarization procedure can be divided into four parts: crack opening and pit formation; pit coalescing and shallow pits subsumed by deep ones; morphology duplicate etching; and finally a planar and damage free surface. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Surface/subsurface damage is inevitably induced into the optics using traditional mechanical machining methods. These damages, especially the micro-cracks, are regarded as the leading factor in lowering the strength and laser damage threshold of optical components [1,2]. When irradiated by high-energy laser, even the expansion of a few flaws in the optics could restrain the lifetime of the component [3]. Techniques in eradicating these damages have long been the research interests of scientists. Plasma processing has been recognized as a solution in mitigating or removing these damages in optics [4]. This chemical method also has other superiorities in optical fabrication such as deterministic optical surface machining owing to its near Gaussian-shaped material removal function [4,5], and high potential in manufacturing complex shaped optical surfaces [6] as well as meter scale optics [7]. Therefore, considerable studies have been devoted to develop this technique. Different
∗ Corresponding author. E-mail address: [email protected] (B. Wang). http://dx.doi.org/10.1016/j.apsusc.2016.04.157 0169-4332/© 2016 Elsevier B.V. All rights reserved.
types of plasma processing have been developed in fulfilling various optical manufacturing demands, such as Plasma Jet Machining [7], Reactive Atom Plasma Technology [8], Plasma Chemical Vaporization Machining [9], Plasma Assisted Chemical Etching [10] and Atmospheric Pressure Plasma Processing [11]. Understanding the surface formation using these plasma methods can help us in determining the location of the plasma methods in an optical fabrication chain, as well as in optimizing the fabrication chain to reduce the fabrication time and production costs. Consequently, researchers have been devoting to study on the surface formation using plasma processing. Jin et al. reported an experimental study on the surface morphology and chemistry evolution of fused silica surface using Atmospheric Pressure Plasma Processing (APPP) [11]. Xin et al. studied the surface formation and morphology evolution of ground fused silica parts using APPP as well. Their results indicated some similarities between the plasma method and the isotopic wet chemical etching, and the surface formation resulted from removing the surface/subsurface damage [4]. Research on surface smoothing mechanism was basically reported by Zarowin using a model based on differential surface evolution equations. A simple sinusoidal profile was used as an initial
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Fig. 1. The selected evolution of etched micro-cracks with various material removal depths: (a) 1 m; (b) 8.8 m; (c) 19.3 m. (d) Cross section profiles for the etched pits with material removal depths: A 1 m; B 3.6 m; C 5.5 m; D 7.1 m; E 8.8 m; F 10 m; G 15.6 m; H 19.3 m. (e) Schematic drawing of the etchant particle redistribution and the formation of micro-trenches (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
input for the 2D profile evolution model and a fundamental explanation on the surface smoothing mechanism was provided [12]. For surface formation in removing damage using isotropic etching, the research of Spierings showed that cusp-like surface structure was originated from surface flaws in wet chemical etching [13,14]. Wong et al. reported experimental and theoretical studies on the effect of the damage characteristics on the peak-to-valley roughness (RPV ) evolution with wet chemical etching [15,16]. Yet, not many studies theoretically focus on the surface formation and evolution process during removing surface/subsurface damage using plasma processing. In this paper, we demonstrate the dominate role of isotropic etching using APPP. A 2D level set method (LSM) model is then applied to simulate the development of two microcracks under isotropic etching, and the results are compared with the experiments to verify the demonstration. Moreover, the 2D surface profile developments considering the influences of different micro-crack characteristics are explored. Finally, 3D morphology
evolution is investigated and compared with the experimental results during removing the damage. 2. Numerical modeling method and experimental setup LSM, introduced by Osher and Sethian [17], has been widely applied in tracking the interface evolution such as fluid mechanics, combustion, computer vision, crystal growth, and etching [18,19]. This method is a robust numerical technique for tracking the evolving interfaces and providing accurate geometric properties. The interface, either a 2D profile or 3D surface, is embedded as a zero level set of a higher-dimensional function. The motion of the interface is governed by an externally generated velocity field. The corresponding level set equation for APPP processed interface is t = Vn |∇ |
Fig. 2. Comparison between the experiments and modeling results (a) the surface profiles, (b) the big pit depth.
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Fig. 3. Surface profile evolutions with periodical cracks with LDs (a) 0.5 m, (b) 1 m and (c) 2 m. (d) RPV for 2D models (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
where t represents a versatile and time dependent level set function for 2D profile or 3D surface. Vn is the velocity along the surface normal direction. As a relatively mature method, the interface equations of LSM can be solved using various libraries and tools [20,21]. To build the LSM model for APPP, the driving force and its basic characteristics are necessary to be understood. To get an insight into these characteristics, experiments were conducted using an in-house developed inductively coupled plasma processing system. The detailed experimental setup and results can be found from our previous study [4]. For completeness of this work, the experiments are briefly described. Electric power with 27.12 MHz inductively coupled radio frequency was supplied to the plasma via the load coil through an impedance matching box. Ar/CF4 mixtures were used to generate high density reactive plasma and process fused silica samples under atmospheric pressure. For better comparison between the modeling results and the experiments, the initial conditions for LSM model and experimental details are described in subsequent corresponding sections. 3. Results and discussion 3.1. Modeling verification of the isotropic etching of APPP Evolution of two common cracks and their coalescence procedure were in situ investigated to get the characterizations for the driving force of APPP and for the subsurface crack evolution. These experiments were conducted on a polished fused silica sample with a reactant gas flow of 2 sccm and input power of 900 W. About 1 m in depth was etched away from the surface to make sure the Bielby layer was removed and the healed cracks were opened. Therefore, the micro-cracks could be viewed by the microscope (OLS 3000, Olympus Co., Japan). The sample was then etched and observed layer by layer with a removal depth of ∼2 m at each step. Fig. 1(a)–(d) shows the selected experimental images of the etched pits, and the cross section profiles measured along the red lines of the experimental results [4]. Fig. 1(e) is the drawing of the etchant particle redistribution and the formation mechanism of micro-trenches based on the experimental surface profiles. From the experimental results as shown in Fig. 1(d), microtrenching is observed in the bigger etched pit from its cross-section profiles B to D. The micro-trench formation is the combined effects
of the redistribution of reactive particles [22] together with the sidewall angles [23] as illustrated in Fig. 1(e). The redistribution of etchant particles might play some dominant roles in quick opening of the subsurface cracks, because the crack walls are too close to each other at the beginning. Yet, after material of several micrometers in depth is removed, the micro-trenches disappear as illustrated in the profiles F to H in Fig. 1(d). One possible reason for this is the disappearance of side wall (thick lines shown in Fig. 1(d)) as the etching advancing in the normal direction of the surface. The other reason for this is that the distance between the walls is too large for re-emitted particles to reach the other side under atmospheric pressure. Thus, after the crack is fully opened, the etching which is induced by particle redistribution is less pronounced. It can be noted that the bottoms of the pits (profiles E to H in Fig. 1(d)) are almost parallel to each other, this indicates that the isotropic etching starts to come into play. Because the particle redistribution is less obvious, especially after the micro-cracks are widely opened, this effect can be ignored to simplify the LSM model. Hence, the model would only take the isotropic etching effect into consideration, which means that the substrate material is etched away uniformly in all directions, and the etching velocity advances along the surface normal direction. To verify the accuracy of the LSM model, 2D etched pit profile evolution is investigated and compared with the experimental results. The profile of etch pits, shown in Fig. 1(d) line A, is used as the initial input surface profile in the model to compute the etched pit evolution. Fig. 2 is the comparison of the experimental surface profiles and depths with the simulation results. The experimental profile results are illustrated using thin lines in Fig. 2(a). The simulation results are represented using thick lines with the same colors. The criteria to evaluate the simulation results depends on whether the pit edges are matched with the experiment ones, as the black lines illustrated in Fig. 2(a). The modeling profiles for small pit agree well with the experimental results. But for the big pit, all the experimental profile bottoms are smaller than the computations. This can be explained through the depth evolution curve of the pit and the particle redistribution shown in Figs. 1(e) and 2(b). The depth points on the curve in Fig. 2(b) are obtained at the center of the bigger pit cross section profiles. An obvious reduction at the beginning can be noticed, which indicates that a shallow advance of depth right after the crack is opened. This is also resulted from the etchant particle redistribution. Most of the particles are bounced from one side wall
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Fig. 4. The SEM results for the plasma etched surfaces with various material removal depths: (a) 0 m, (b) 20.6 m, (c) 45.3 m, (d) 95.2 m, (e) 164.6 m, (f) 300 m, and (g) the corresponding RPV and RMS evolution measured by AFM.
to the other side as illustrated in Fig. 1(e). This leads to the reduction of the particles that could reach to the pit bottom, and brings about the bump at the bottom. Due to the weakened particle redistribution effect as aforementioned, after this reduction, the depths keep constant in the following procedure as shown in Fig. 2(b). In computing the 2D profile evolution, the surface line A in Fig. 2(a) is used as the initial profile for the LSM model. The depth of the profile line A is the deepest one. For isotropic etching computation, the etch depth keeps constant and it is as same as the initial profile as shown in Fig. 2(b). Therefore, the simulation depths are deeper than the experimental ones. All the computed profile bottoms are slightly lack behind of the experimental ones as shown in Fig. 2(a). But from Fig. 2(a) line G and H, the etched profiles are almost parallel to each other and to the computing results. Moreover, the depth data in Fig. 2(b) are almost parallel to each other except the first point. All these indicate that isotropic etching of APPP comes into play, and the pits begin to evolve under the driving force which is normal to the surface.
3.2. 2D modeling study on the surface profile evolution 2D LSM simulations are carried out to study the crack characteristics, such as depth and lateral distance (LD) between cracks, on the surface formation. The simulations were performed with 10 m long surface profile. Cone cracks, as the bigger pit in profile line A shown in Fig. 2(a), were used in the models to simulate the subsurface cracks. Periodical cone cracks with 0.4 m, 0.7 m, and 1 m in depth were used in the simulations. The LDs between the cracks were set as 0.5 m, 1 m and 2 m, and crack opening (as illustrated in Fig. 2(a) profile line A) with 0.04 m was used in the models. The profiles evolved with the normal velocity of 0.25 m/unit time (m/ut). The processing time with arbitrary unit (a.u.) ranged from 0 a.u. to 36 a.u. with an interval of 1 a.u. The obtained results are shown in Fig. 3(a)–(c). The solid black lines denote the boundary development between the pits formed by 0.4 m cracks and 0.7 m cracks, the solid blue lines represent for boundary development between pits formed by 0.7 m cracks and 1 m cracks, the dash-dotted blue lines denote the bound-
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Fig. 5. Top views for the plasma etched surfaces with various processing time (a.u.): (a) 0; (b) 0.2; (c) 0.4; (d) 0.6; (e) 0.8; (f) 1; (g) 1.2; (h) 2 and (i) 5 (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
ary between pits formed by 0.7 m cracks and themselves, and the dash-dotted red lines represent for boundary between pits formed by 1 m cracks and themselves. The corresponding RPV for Fig. 3(a)–(c) is calculated for each profile as shown in Fig. 3(d). Fig. 3(a)–(c) shows the surface profile evolutions under different damage characteristics. As can be seen from the figures, pits are resulted from the opening of the cracks under isotropic etching. Cusps are then formed when pits begin to coalesce with the adjacent one. When linking these cuspidal points, boundary development lines could be obtained as shown in the figures. For the boundary lines between cracks with different depths (solid lines), these lines shrink toward the small pits and disappear finally. This means that the small pits are swallowed up by the bigger ones. At the same time, a new boundary line is formed between the bigger pits. The new boundary lines continue to shrink until the pits with similar depths meet each other, and a vertical boundary line is then formed as illustrated by the dash-dotted lines in Fig. 3. If the vertical line is not formed by the coalescing of deepest pits, they will disappear finally as the blue dash-dotted lines showing in Fig. 3 (a) and (b), because the pit swallow-up procedure is still going on. This procedure will continue until the deepest pits meet each other, and finally form a vertical boundary line as the red dashdotted lines show. These vertical lines indicate that the boundaries of the pits do not change while more material is wiped off. And the surface begins to copy the previous surface morphology, which can be seen from the lines in the red rectangular boxes of Fig. 3(a) and (b). This phenomenon reveals that the isotropic etching might result in a morphology duplicate etching.
Fig. 3(d) shows the RPV evolution with various LD values. For LD equals to 0.5 m, the first point on the RPV evolution curve is identical to the largest crack depth, 1 m. And a slight decrease of RPV can be noticed at the second point. The reason for this is that the cracks open with the speed of 0.25 m/ut, and the LD between cracks is 0.5 m, where we should take the crack openings (0.04 m) into account. Therefore, the peaks of magenta line in Fig. 3(e) decrease a little faster. For the other two curves, the horizontal stages at the beginning are because the pits are still isolated from each other and the depths are as same as the crack depths. With increment of the LDs, the lengths of horizontal stages increase as well. The reason is shown in Fig. 3(b) and (c): the larger the LDs are, the more difficult the platforms at the beginning profiles to be eliminated, namely, for the pits to get close to each other. Therefore, more time is needed for RPV curves with large LDs to wipe out the horizontal stage. And kink points are also observed on the curves. The kink points imply that the farthest pits are getting closed and begin to coalescence with each other. In addition, the prominent effects of LD in RPV evolution and its evolution agree well with the conclusion of isotropic wet chemical etching [15]. As for the final values of the RPV , even if the damages are equivalent in the three simulations, small LD, namely a high density of cracks, makes the pits more easy to merge mutually, and results in a quickly convergence of the roughness to a better surface quality. Accordingly, small LDs lead to a better surface quality than larger LDs when using the same processing parameters as the RPV shown in Fig. 3(d). From results of Fig. 3, it is concluded that the final surface is out of damage, more specifically a crack-free surface. The results
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Fig. 6. Side views for the plasma etched surfaces with various processing time (same as Fig. 5) and (j) the corresponding RPV evolution for 3D LSM simulation results (For interpretation of the references to color in the text, the reader is referred to the web version of this article).
reveal the basic crack removal mechanism using plasma processing: pits grow larger and merge with one another. Meanwhile, some small/shallow pits are subsumed by the big/deep ones as more material is removed. 3.3. 3D modeling study on the surface formation and morphology evolution To verify the analyses and further prove the damage removal mechanism using plasma processing, 3D LSM simulations are implemented. In addition, the morphology comparison is performed between the experiments and simulation results. The experiments were conducted on grinded samples to investigate the surface morphology evolution [4]. The samples were processed with the material removal rate of ∼0.45 m/s. Time was varied to
get different material removal depth. Fig. 4 presents the surface texture evolutions which were measured by Field Emission Scanning Electron Microscope (SEM, Quanta 200, FEI Co., America), and the corresponding RPV and root mean square roughness (RMS) were measured by AFM (Brucker Vecco Dimension 3100, Veeco Inc., USA) before and after plasma processing. For the surface texture before plasma processing, shown in Fig. 4(a), cracks and scratches might be filled with abrasive products or healed after mechanical machining. The fillings and closures result in a relatively smooth surface with RMS of 100 nm as presented in Fig. 4(g) point a. And the big RPV value for point a is resulted from some singular deep cracks that are not fully healed or filled by the abrasives. After ∼20 m material was removed, the hidden defects were opened and led to a rougher surface as shown in Fig. 4(b) and (g) point b. As processing proceeded, small pits
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Fig. 7. Schematic drawing of plasma processing procedure.
caused by shallow cracks were swallowed up by bigger ones. And the bigger pits grew larger and coalesced with one another (same as the procedure aforementioned in the 2D LSM model). This process causes the RPV and RMS to decrease in Fig. 4(g). For 3D LSM simulation, the cracks were randomly and discretely distributed on a 180 × 180 m2 rough surface. The RPV of the surface was 500 nm without consideration of the subsurface crack depths. The crack depths were 10 m, 20 m, 30 m and 50 m with amount of 200, 160, 120 and 80, respectively. Material removal time ranged from 0 a.u. to 5 a.u. with an interval of 0.2 a.u. and a normal removal rate of 25 m/ut. Figs. 5 and 6 present the selected modeling results. Fig. 5 is the top views of the morphology, and Fig. 6 is the side views of the results. The surface bottoms in the figures were adjusted so that the lowest points of the surfaces are zero. The highest point on the surface is denoted by light yellow and the lowest point by dark blue. It can be seen that in Fig. 5(b), because the opening speeds of the cracks are the same, sizes of the pits are almost identical. With the increase of etching time, pits begin to grow lager and overlap with each other. In Fig. 5(e), most of the shallow pits formed by 10 m and 20 m cracks are subsumed by the bigger ones. When the deepest pits start to merge with each other, the number of pits with small depth reduces. As these small pits finally disappear, the biggest adjacent pits, formed by 50 m deep cracks, begin to merge and the duplicate etching begins as shown in Fig. 5 (f)–(i). The experimental results of SEM in Fig. 4 and LSM modeling results in Fig. 5 give a comprehensive perception of the plasma processed surface advancing. Cracks and scratches might be filled with abrasive products or closed after mechanical machining. This makes the SEM inspection difficult, and a smooth surface is obtained as shown in Fig. 4(a). After some material is removed, the hidden defects are opened and can be observed by the SEM, and this lead to a rougher surface as RPV shown in Fig. 4(f). The big pits are resulted from deep cracks, the small ones are caused by shallow cracks in like manner, and most of the etched pits are roughly spherical as shown in Figs. 4 and 5(b). At this initial opening stage of the cracks, the crack density is high because the pit swallow-up procedure does not fully come into action. When pits increase in size, small pits are merged by larger pits. The borderlines, formed by the merging of pits, are straight lines as shown inside the yellow rectangular boxes of Fig. 4(b)–(d). These straight borderlines can also be observed at the modeling results from Fig. 5(b) to (i). Due to the depth differences of the simulate cracks, the pit boundaries for shallow pits are ambiguous in Fig. 5(b)–(e). Micrographs presented in Fig. 4(b)–(f) and Fig. 5(b)–(e) show that the etched pit density decrease sharply with more material removal. This is because pits grow larger and coalesce with one another. Meanwhile, some small/shallow pits are swallowed up by the big/deep ones as more and more material is removed. This merging procedure is more clearly shown in the modeling results from Fig. 5(b) to (e). As it can also be observed in Fig. 5(d) that the left pits are formed by the deepest cracks (50 m deep cracks). This is in accordance with the analyzations of the 2D profile evolution. From the comparison, it can be found that the modeling surface formation
and morphology evolution agree well with the experiments as presented in Figs. 4 and 5. The developments of damage depth could be found from the side views in Fig. 6, which could be obtained from y-axis direction of the corresponding images of Fig. 5. The peak-to-valley changes can be directly seen from the figures. Even during the morphology duplicate etching from Fig. 6(f) to (i), the RPV still declines and converges to a relatively planar surface. This is also illustrated by the corresponding points f, h and i in Fig. 6(j). This roughness development trend agrees with the experimental results in Fig. 4(g). In summary, the damage removal procedure can be separated into four parts: (a) crack opening and pit formation; (b) pit coalescing and shallow pits subsumed by deep ones; (c) morphology duplicate etching; and (d) a finally planarized surface without damage. The schematic drawing of this procedure is based on the 2D LSM simulation, and it is shown in Fig. 7. Considering the randomness of the damage, such as depth, density and distribution, during the planarization using APPP, some steps might occur at the same time or only last for a short time. For example, if the crack density is really high, the crack opening and the coalescing would happen simultaneously. Also, a planar surface might be obtained with less steps of morphology duplicate etching. In addition, the planar degree of final surface is governed by the characteristics of the damage and the depth of removed material. For surface with high density and similar depth damage, a planar surface can be easily obtained using plasma processing. 4. Conclusion In summary, particle redistribution is observed in plasma processing under atmospheric pressure, and it plays some effects on crack opening. Despite of this unique etching property of plasma, the dominate role of isotropic etching using APPP is verified based on the experiments and 2D LSM models. The 2D modeling results clearly show that the surface formation is resulted from pits growing larger and merging with one another. A novel phenomenon of isotropic etching, morphology duplicate etching, is observed in the modeling results. This phenomenon happens when cracks with similar depths merge with each other. Density of the damage has more significant effect on the roughness evolution than damage depth. According to the modeling results, a planar surface can be obtained from surface with high damage density. Also, it is revealed that the plasma processing may end up with a planar surface depending on the damage characteristics. Surface morphology evolution is then compared between 3D modeling and the experiments. The morphology evolutions show good agreement with each other. The trends of simulated roughness evolution agree with the experiments as well. This verifies the accuracy using LSM in modeling surface formation when removing the surface/subsurface damage. The damage removal capacity and mechanism of plasma processing are theoretically and experimentally proved in this work. The surface planarization procedure is summarized into four parts: crack opening and pit formation; pit coalescing and shallow pits subsumed by deep ones; morphology duplicate etching; and finally a planar and damage free surface. This work is helpful in understanding the surface formation using APPP and in determining the location of APPP in an advanced optical manufacturing chain. Acknowledgements This work was supported by grants from the National Natural Science Foundation of China (No. 51175123 and No. 51105112), and National Science and Technology Major Project (No. 2013ZX04006011-205).
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