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Abstract
A lateral thickness distribution control model for magnetron sputter-deposited coatings was established using shadow masks. The sputtering yield distributions were investigated in detail, particularly the variation trend from straight to curved tracks, based on the erosion profiles of rectangular targets. On this basis, a mathematical model for a planetary rotation system was established to simulate the thickness distribution of coatings on different substrates, including flat, spherical, and aspherical shapes, accurately. A shadow mask with multi-Gaussian outlines was proposed, and the coating thickness was effectively controlled according to specific distribution requirements by optimizing the profile parameters of the masks using a genetic algorithm. Flat and ellipsoidal substrates were used to prepare Mo and Si monolayer coatings to verify the effectiveness of this model. Although the diameters of the substrates were close to the lengths of the rectangular targets, the results showed that uniform coatings were obtained on the flat substrate, whereas the ellipsoidal substrate exhibited high-precision gradient coatings, with maximum deviations below 0.5%, which proved the validity of this approach.
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1 Introduction
Magnetron sputtering offers the advantages of a high sputtering atomic energy, stable sputtering rate, high coating packing density, and smooth coating surface, and has been widely used in coating production [1–6]. However, controlling the lateral thickness of a coating deposited by magnetron sputtering is more difficult than controlling those formed by thermal evaporation and ion beam sputtering. A magnetron sputtering target is the surface source, and the sputtering yield distribution of the target typically presents a complex distribution profile [7–9]. In addition, the distance between the target and substrate is often very short, and as a result, the coating thickness at different positions of the substrate depends on the sputtering distribution of the target material, which makes it difficult to numerically simulate the coating thickness distribution accurately [10,11]. Without controlling the uniformity, a coating on a flat substrate is usually thick at the center, and the thickness gradually decreases toward the edges [12]. This limits the size and number of coating elements that can be produced in a single coating run. For curved optics, the coating thickness should increase from the center to the edge according to a specific lateral gradient trend with an increasing incident angle [13]. In this case, the desired thickness distribution cannot be achieved without effectively controlling the thickness. Therefore, controlling the lateral thickness distribution is essential for coatings prepared by magnetron sputtering.
Three methods are generally used to control the distribution of the thickness of a coating deposited by magnetron sputtering. In the first method, the magnetic field distribution is changed by changing the shape of the magnet below the target, thereby improving the uniformity of the sputtering yield distribution [14–16]. However, the areas that can be improved by this method are typically severely limited, and it cannot be applied to different specific thickness distributions. The second method uses the variable revolution speed control technique of the substrate to control the thickness distribution. However, in this method, the control capacity of the revolution speed profile and positioning accuracy of the substrate rotating system should be high [17–20]. In the third method, a shadow mask is inserted between the substrate and the target to control the lateral thickness of the coating by selectively blocking the deposition plume, and thus, this method has the advantages of convenient production, low cost, portable disassembly, and flexible use [21–25]. However, in most studies on thickness control for planetary rotation magnetron systems, which are widely used in the current coating manufacturing industry, the substrates are significantly smaller than the targets, and the corrected areas and amplitudes are limited [19–22]. Furthermore, shadow masks are usually designed based on semi-quantitative analysis and few studies have introduced optimization methods for shadow masks in combination with the complex sputtering yield distribution of the target in detail. In addition, in curve optics, aspherical surfaces are often treated as approximately spherical contours for simplification, and thus the accurate numerical expression for aspherical surfaces in these studies has not been mentioned. Therefore, it is worth seeking a universal procedure that considers the target sputtering characteristics and obtains the desired thickness distribution for magnetron-sputtered coatings on large substrates with flat or complex curved surfaces.
In this paper, we propose a model for planetary rotation magnetron sputtering systems using shadow masks to control lateral coating thickness distributions. The erosion profiles of rectangular magnetron targets were measured, and the detailed target sputtering characteristics were investigated. Accordingly, a thickness distribution control model was established in combination with the target sputtering yield distribution that could be applied to substrates with different shapes, including flat, spherical, and aspherical surfaces, with the help of a universal surface function. We developed a fixed-position shadow mask with multi-Gaussian outlines, which was found to be suitable for coating thickness distribution control over a large size range on multiple types of substrates, benefiting from its higher level of freedom for optimization. Using a genetic algorithm, the outlines of the masks can be optimized automatically. To verify this approach, we corrected the thicknesses of Mo and Si monolayer coatings on flat and curved substrates, whose sizes were similar to those of the targets. By optimizing the shapes of the shadow masks using this model, the coating thickness distributions were effectively controlled according to their specific requirements, and the maximum deviations were below 0.5%.
2 Lateral thickness distribution control model with shadow masks
2.1 Basic model
To control the lateral thickness distribution of magnetron sputtering coatings accurately and efficiently, a mathematical model was established, based on MATLAB software, for a planetary rotation magnetron system with rectangular targets. Figures 1(a) and 1(b) show the top and axonometric views of the geometric configuration of the model, respectively. A Cartesian coordinate system (X, Y, Z) was established, wherein the Z-axis coincided with the central axis of the vacuum chamber and revolution axis of the rotation system. A concave substrate with a clear aperture of CA was placed at the center of the substrate mount, followed by the mount for horizontal planetary rotation. The CA plane of the substrate was at the same height H as that of the mounted planet, and a similar configuration was applied for a flat or convex substrate. Herein, R is the revolution radius, θ is the revolution angle, ω1 is the revolution speed, ω2 is the spin speed, and ω2 >> ω1.
Fig. 1. (a) Top view and (b) axonometric view of a planetary rotation magnetron sputtering system with a concave substrate.
${S(}{{x}_{S}}{,}{{y}_{S}}{,}{{z}_{S}}{)}$ is a surface element of the substrate, which has an initial spin angular γ. r is the horizontal distance from S to the spin axis of rotation, h is the vertical distance from S to the CA plane, and $\mathrm{\vec{n}}$ is the normal vector from S to the substrate surface. When the substrate performs planetary rotation, the motion trajectory of element S can be expressed as
Then, the normal vector $\mathrm{\vec{n}}$ at S to the substrate surface is
A rectangular target plane with dimensions d × e (d ≥ e) lies on the XY plane, and the Y-axis coincides with the symmetry axis of the short side of the target plane. The horizontal distance between the center of the target plane and the revolution axis is R, which is equal to the revolution radius of the substrate. T (xT, yT, 0) denotes the surface element of the target, and $\overrightarrow {{TS}} $ represents the vector from T to S with a length of ρ. The angle between the vector $\overrightarrow {{TS}} $ and the Z-axis, and that between the vectors $\overrightarrow {TS} $ and $\vec{n}$ are α (namely, sputtering angle) and β (i.e., deposition angle), respectively. The deposition of a coating over a surface from a source was simplified as an illumination case. At some point, the coating thickness ${t}$ of the surface element S of the substrate, which is attributed to the surface element T of the target, can be expressed as [17,26]:
In Eq. (5), ${U}$ is a constant, and m is the sputtering characteristic parameter of the target material. For the geometrical configurations shown in Fig. 1, the expression can be converted to coordinate geometry:
The radial thickness distribution was considered to examine the coating layer deposition process. The difference of the circumferential thickness is negligible because ω2 >> ω1. When the revolution angle θ of the substrate changes from θ1 to θ2, the calculated coating thickness ${{t}_{c}}({r} )$ of the surface element S can be expressed as the integral of the contribution of each element of the target surface within the motion trajectory as
In Eq. (9), $\textrm{Tar}({{x, y}} )$ is the sputtering yield distribution function of the target, which describes the different contributions of the sputtering material at different positions on the target. E(r, γ, θ, x, y) is the self-shadow function, which describes the self-shadow effect for some strongly curved substrates. For a convex substrate, when the deposition angle β is larger than 90°, the coating cannot be deposited, and E(r, γ, θ, x, y) is 0; otherwise E(r, γ, θ, x, y) is 1. For a concave substrate, when the vector $\overrightarrow {{TS}} $ passes though the clear aperture CA, E(r, γ, θ, x, y) is 1; otherwise the coating cannot be deposited, and E(r, γ, θ, x, y) is 0. M(r, γ, θ, x, y) is the shadow mask function, which describes the shapes of shadow masks and their selectively blocking effect. Thus, a basic thickness distribution control model was established that can be applied to different substrate shapes, including flat, spherical, and aspherical surfaces.
2.2 Sputtering characteristics of the targets
To calculate the thickness distribution accurately using this model, the sputtering yield distribution of the target $\textrm{Tar}({{x, y}} )$ and the sputtering characteristic parameter of the target material m should first be known because they combine to determine the sputtering characteristics of the deposited particles. In this study, a planetary rotation DC magnetron system with rectangular Mo (200 × 85 × 6 mm) and Si (220 × 90 × 6 mm) targets was used to fabricate the coatings. Rectangular targets are widely employed in industrial coating-deposition processes. However, because of the particularity of the magnetic field distribution, target utilization is reduced. In most studies on thickness correction using shadow masks or variable motion speed profiles, the sputtering yield distribution of a rectangular target is treated as a Gaussian-type distribution along a race track with two straights and two semicircular curves, and the yield is identical along the entire track [7,20]. Nevertheless, because of the difference in magnetic field distribution in the straight and curved regions, the sputtering yield may differ between the two regions and affect the coating thickness distributions [9,14]. Consequently, in order to simulate the thickness distributions accurately, it is worth investigating the complex sputtering yield distribution in detail, particularly for the rectangular targets used in this study, which do not have large aspect ratios.
Figures 2(a) and 2(b) show photographs of the Mo and Si targets, respectively, after a period of use. Erosion ditches such as race tracks were observed on both the targets. This indicates that the sputtering yield distributions were nonuniform across the target surfaces, and the sputtering rates were higher along the tracks. To obtain an accurate sputtering yield distribution and refine the control model, the erosion profiles of the two targets were characterized using a coordinate measuring machine (CMM; Xi’an AEH LEGEND). The maximum erosion depths were 1.391 and 2.475 mm for the Mo and Si targets, respectively. The depth information was positive and normalized, as shown in Figs. 2(c) and 2(d). For the Si target, cracks easily emerged, and the crack region (blue rectangular region shown in Fig. 2(b)) was difficult to measure via the CMM. The coordinate information of this region is replaced with that of the symmetrical region, as shown in Fig. 2(d). The geometric configuration of the erosion trace is more distinct in the CMM profile and can be treated as a race track with two straight and two semicircular curves. The maximum depth was located at the centerline along the race track. However, along the centerline of the racetrack, the depth of the curved track was significantly smaller than that of the straight track. This indicates that the sputtering yield was lower in the curved region, which may be due to the lower magnetic field intensity around this region.
Fig. 2. Photographs of a (a) Mo target and (b) Si target. Erosion profiles of the (c) Mo target and (d) Si target measured by a CMM.
To perform a more distinct numerical analysis of the erosion profiles, a two-dimensional coordinate system (A, B) using the center of the target as the origin point and curve C (from the straight midpoint to the curve midpoint along the centerline of the racetrack) was established, as shown in Figs. 2(a) and 2(b). The cross profiles of the erosion tracks were analyzed first, and the relative depth distributions along direction A for the Mo and Si targets are shown in Fig. 3(a) and 3(b), respectively. The measured erosion depths are similar to Gaussian distributions, which can be fitted to Gaussian curves. Subsequently, the variation in erosion rate from straight to curved along the racetrack was evaluated. Figures 3(c) and 3(d) show the relative depth along curve C as a function of the corresponding projection distance in direction B for the Mo and Si targets, which describes the maximum depths of the Gaussian-type cross section at different positions along the race track. Here, direction B, rather than direction C, was treated as the abscissa because of its higher suitability in the mathematical model. In the straight region, the depth exhibits little variation and can be treated as approximately constant. However, in the curved region, the erosion depth in the Mo and Si targets clearly decreased, from ∼100% to 74.7% and ∼100% to 84.4%, respectively, from the end of the straight track to the apex of the curved track. Furthermore, this variation trend can be fitted as part of a Gaussian curve, which means that the maximum sputtering yield along the centerline of the curved track can be approximated as a Gaussian distribution.
Fig. 3. Relative depths of the (a) Mo and (b) Si targets along direction A. Relative depths of the (c) Mo and (d) Si targets along the curve C as functions of the corresponding projection distance in direction B.
The target sputtering yield distribution function Tar(x, y) was established based on the analysis of the erosion profiles, as shown in Eq. (10,11). The sputtering yield race track includes two straight lines of length L and two semicircular curves of radius Rc. The cross profile of the racetrack followed a Gaussian distribution, including an amplitude function Q(y) and standard deviation parameter s1. Q(y) represents the maximum sputtering yield of the Gaussian-type cross-section at different positions along the race track. In the straight region, Q(y) is a constant ${{Q}_{0}}$. In the curved region, Q(y) is the product of the constant ${{Q}_{0}}$ and a normalized Gaussian function, including a position parameter ${u}$ and standard deviation parameter s2, which describes the variation trend of the sputtering yield along the curved track.
Considering that there were errors in the CMM measurement and that the magnetic field and plasma around the target would have a secondary effect on the sputtering yield distribution of the source in the horizontal direction [8,16], the parameters L, Rc, s1, u, and s2 in the function $\textrm{Tar}({\textrm{x, y}} )$ were not directly derived from the erosion profiles via CMM. Instead, these parameters, together with the sputtering characteristic parameter m were reversed by simultaneously fitting the calculated thickness and the experimentally measured thickness of the coatings on flat substrates with several heights without thickness control, which was thought to be more effective in improving the simulation accuracy of this model. Three flat substrate holders (φ200 mm in diameter) were mounted on the magnetron system at three different heights (H = 77, 87, and 97 mm). To fabricate the Mo and Si monolayer coatings, silicon wafers and fused silica samples (φ10 mm in diameter) were evenly distributed in these holders along the radial direction. The diameter of the coating chamber was 1300 mm and the revolution radius R was 340 mm. The substrates swept across the target at a constant revolution speed ω1 (0.5 rpm) and spin speed ω2 (500 rpm) for several rounds. The coating thickness was evaluated via grazing incidence X-ray reflectivity (GIXRR) measurements using a PANalytical Empyrean diffractometer with Cu-Kα (0.154 nm) radiation and a X’Pert Reflectivity software [27,28]. The inversion was based on the least-squares method using a genetic algorithm, and the merit function is described as
Figures 4(a) and 4(b) show the experimentally measured and calculated relative thickness distributions of the Mo and Si coatings, respectively. The calculated results fit well with the experimental data, indicating that the thickness distribution can be accurately simulated using this model. Figures 4(c) and 4(d) show the reverse sputtering yield distributions of the Mo and Si targets. The sputtering parameters are listed in Table 1. From the straight track to the apex of the curved track, the reverse yield decreases from 100% to 73.5% and to 85.4% for the Mo and Si targets, respectively. These variations were consistent with the trends derived from the CMM erosion profiles, corresponding to the assumption that the quantitative proportions of sputtering particles at the corresponding positions were constant during the coating process.
Fig. 4. Measured and calculated relative thickness distributions of the (a) Mo and (b) Si coatings. Sputtering yield distributions of the (c) Mo and (d) Si targets.
Table 1. Reversed sputtering parameters.
2.3 Shadow mask design
Once the sputtering characteristics of a target are determined, the lateral thickness distribution of the coatings on a certain substrate can be controlled according to the specific distribution requirements by optimizing the shape of the shadow masks. The absolute thickness could then be controlled by adjusting the revolution speed or number. The horizontal-plane shadow mask was fixed directly above the target and selectively blocked sputtering particles from moving toward the substrate. A projection algorithm was used to determine the shadow mask function M(r, γ, θ, x, y). If the height of the mask is ${{H}_{m}}$, then the coordinates of point G on the vector $\overrightarrow {{TS}} $ with the same height are
If the point G is inside the mask range, then M(r, γ, θ, x, y) = 0, and the sputtered particles are blocked by the mask. Otherwise, M(r, γ, θ, x, y) = 1, and the sputtered particles continue to move toward the substrate.
To obtain the desired masks more efficiently, an initial shape was essential to make the merit function achieve effective convergence rapidly. Several types of shadow masks with different initial shapes such as parabolic, hyperbolic and gaussian types were tried. Finally, a type of mask with multi-Gaussian outlines was found to be more suitable for coating thickness distribution control over a large size range on multiple types of substrates, benefiting from its higher level of freedom for optimization. Figure 5 shows a schematic of a typical multi-Gaussian shadow mask. The size of 300 × 300 mm was used to provide a larger tolerance to improve the control effect. The mask profiles are defined as follows:
3 Coating thickness distribution control experiments and results
After the mathematical model was established, the thickness distribution control of the coatings on flat and curved substrates was carried out using the magnetron system mentioned above to evaluate the effectiveness of this approach. As shown in Eq. (16), the maximum thickness distribution deviation for the evaluation is defined as the maximum absolute value of the difference between the calculated or experimental relative thicknesses and the desired relative thicknesses at each radial position. The thickness of the coating at the center (${{r}_\textrm{1}}{ = \; 0}$) of the substrate was used for normalization.
As shown in Fig. 6(a), a flat substrate holder was used to simulate a flat substrate with a 200 mm clear aperture, which is close to the lengths of the targets in the coating system. Silicon wafers and fused silica samples (φ10 mm in diameter) were evenly distributed in the holder along the radial direction, 15 mm apart, to fabricate Mo and Si monolayer coatings, respectively. The substituted substrate was placed at a height H = 77 mm in the coating chamber and swept across the target at a constant revolution and spin speed for several rounds. Figure 6(b) shows the desired thickness distribution and the measured and calculated thickness distributions without controlling the Mo and Si coatings. For the flat substrate, the control goal is to obtain an identical coating thickness on the entire substrate, that is, obtaining perfect uniformity. However, without control, the thickness decreased more rapidly with the increasing radius for both the coating types. At the edge, the maximum thickness deviations were 21.08% and 20.68% for the Mo and Si coatings, respectively, indicating a significant deviation from the desired uniformity.
Fig. 6. (a) Flat substrate holder. (b) Desired coating thickness distribution; calculated and measured thickness distribution without control.
To achieve the desired uniformity, multi-Gaussian shadow masks were optimized and fabricated for the Mo and Si coatings. In the optimization process, the masks were fixed directly above the targets at a height ${{H}_{m}}$ = 67 mm, which was 10 mm lower than that of the substrates. Here the masks were placed as high as possible to avoid affecting the magnetic field and plasma above the targets, and 10 mm distance was retained for security reasons to prevent collisions between the substrates and the masks. Figures 7(a) and 7(b) show the geometric shapes of the shadow masks. The Mo and Si monolayer coatings were prepared with masks and the thicknesses were characterized using GIXRR as shown in Figs. 7(c) and 7(d). The physical thicknesses of Mo and Si coatings on different samples were 49.6–50.0 nm and 43.5–43.8 nm, respectively. Figures 7(e) and 7(f) show the desired thickness distributions, calculated and experimentally measured relative thicknesses with shadow masks, and thickness deviations for the Mo and Si coatings, respectively. The maximum thickness-distribution deviations are listed in Table 2. Within a radius of 100 mm, the calculated maximum deviations for the Mo and Si coatings were 0.18% and 0.19%, respectively. For the experimentally measured results, the maximum deviations were 0.40% and 0.46% for the Mo and Si coatings, respectively. Therefore, by utilizing shadow masks, the thickness uniformity was significantly improved for both types of coatings.
Fig. 7. Geometrical shapes of the shadow masks for the (a) Mo and (b) Si coatings on a flat substrate. Measured and fitted curves of GIXRR results for the (c) Mo and (d) Si coatings. Desired thickness distributions, relative thicknesses, and deviations with shadow masks for the (e) Mo and (f) Si coatings.
Table 2. Relative thickness deviations of the Mo and Si coatings on the flat substrate.
For curved substrates, coatings often require specific lateral thickness gradients from the center to the edge owing to the different incident angles at different positions. Therefore, the control of the coating thickness is more complex than that of flat substrates. In this study, a strongly concave ellipsoidal substrate with a 200 mm clear aperture was used to prepare coatings with specific thickness gradient distributions. Ellipsoidal elements are widely used in optical facilities, such as extreme ultraviolet photolithographic systems [29–33]. In general, light propagates from one focus to the element and then converges to another focus through reflection; therefore, the incident angle increases with increasing radius. A precision-machining substrate holder, as shown in Fig. 8(a), was used to simulate an ellipsoidal substrate. This profile can be expressed using Eq. (2), where ${a} = {1/118}{.31\; \textrm{m}}{\textrm{m}^{\textrm{ - 1}}}$, ${N} = { - 0}{.6}$, and ${CA} = {200\; \textrm{mm}}$. The height difference between the center and the edge is 45.8 mm, and the dip angle is 45° at the edge. The incident angle ranged from 0° at the center to 33.2° at the edge. Silicon wafers and fused silica samples (φ10 mm in diameter) were evenly distributed in the holder along the radial direction 15 mm apart and perpendicular to the normal direction at each position to fabricate the Mo and Si monolayer coatings, respectively. The substituted substrate was placed at a height H of 67 mm, 10 mm lower than that of the flat substrate due to the overhead space limitation of the substrate mount, and swept across the target at a constant revolution and spin speed for several rounds. Figure 8(b) shows the desired thickness distribution and the measured and calculated thickness distributions without controlling the Mo and Si coatings. The control goal is to obtain identical effective optical thickness ${{N}_{c}} \cdot {t(}{r_i}\textrm{)} \cdot \mathrm{cos\delta (}{r_i}\textrm{)}$ at different radius positions, where ${{N}_{c}}$ is admittance of the coating, ${t(}{r_i}{)}$ is the physical thickness, and $\mathrm{cos\delta (}{r_i}\textrm{)}$ is the cosine value of refraction angle. With an increase in the radius, the desired thickness distribution increased from 100% to 124.18% and 119.53% for the Mo and Si coatings, respectively. However, without control, the thickness deviated the desired distribution significantly with increasing radius. At the edges, the deviation reached the maximum values 28.46% and 21.34% for the Mo and Si coatings, respectively.
Fig. 8. (a) Concave ellipsoidal substrate holder. (b) Desired coating thickness distribution; calculated and measured thickness distribution without control.
To achieve the desired thickness gradients, multi-Gaussian shadow masks were optimized and fabricated for Mo and Si coatings on the ellipsoidal substrate. In the optimization process, the masks were fixed directly above the targets at a height ${{H}_{m}}$ = 57 mm, which was 10 mm lower than that of the substrates. Figures 9(a) and 9(b) show the geometrical shapes of the shadow masks for the Mo and Si coatings, respectively. The Mo and Si monolayer coatings were prepared with masks and the thicknesses were characterized using GIXRR as shown in Figs. 9(c) and 9(d). The physical thicknesses of different samples were 53.9 nm ∼ 64.4 nm for Mo coatings and 51.3 nm ∼ 59.5 nm for Si coatings, respectively. Figures 9(e) and 9(f) show the desired thickness distributions, calculated and experimentally measured relative thicknesses with shadow masks, and thickness deviations for the Mo and Si coatings, respectively. The maximum thickness-distribution deviations are listed in Table 3. Within a radius of 100 mm, the calculated maximum deviations of the Mo and Si coatings are 0.05% and 0.08%, respectively. The experimental results show maximum deviations of 0.40% and 0.30% for the Mo and Si coatings, respectively. Therefore, the thicknesses were effectively controlled according to the specific gradients, and the deviations were significantly reduced for both the Mo and Si coatings.
Fig. 9. Geometrical shapes of the shadow masks for the (a) Mo and (b) Si coatings on a concave ellipsoidal substrate. Measured and fitted curves of GIXRR results for the (c) Mo and (d) Si coatings. Desired thickness distributions, relative thicknesses, and deviations with shadow masks for the (e) Mo and (f) Si coatings.
Table 3. Relative thickness deviations of the Mo and Si coatings on the concave ellipsoidal substrate.
4 Conclusions
A coating thickness distribution control model for magnetron sputtering systems with rectangular targets using shadow masks was proposed. The erosion profiles of the targets were evaluated to deduce the regularities of sputtering yield distributions, particularly the variations from straight to curved tracks. Based on the results, a mathematical model that could accurately simulate the thickness distribution of the magnetron sputter-deposited coatings was established. Subsequently, a shadow mask with multi-Gaussian outlines was proposed, and the coating thickness was effectively controlled according to specific distribution requirements by optimizing the profile parameters of the masks using a genetic algorithm. To verify the feasibility of controlling thickness distributions using this model, Mo and Si monolayer coatings were developed to achieve a uniform thickness on a substituted flat substrate as well as specific thickness gradients on a substituted ellipsoidal substrate. Although the diameters of the substrates were close to the lengths of the rectangular targets, we obtained uniform coatings on the flat substrate and high-precision gradient coatings on the ellipsoidal substrate, with maximum deviations below 0.5%, which proved the validity of this model. Overall, the approach based on the model established in this study can be used to control coating thicknesses rapidly and automatically according to different distribution requirements and can be applied to substrates with different shapes, including flat, spherical, or aspherical surfaces, in a large range. Thus, the proposed method will be useful for manufacturing magnetron sputtering coatings.
Funding
Science and Technology Planning Project of Shanghai Municipal Science & Technology Commission (21DZ1100400); National Natural Science Foundation of China (61975215); Program of Shanghai Academic Research Leader (23XD1424100).
Acknowledgments
The authors express their appreciation to Tao Wang and Yun Cui for their assistance with sample preparation and X-ray reflectivity measurements, respectively.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the corresponding authors upon reasonable request.
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