Material removal rate has greatly relied on the distribution of shear stress and dynamic pressure on the workpiece surface in hydrodynamic effect polishing (HEP). Fluid dynamic simulation results demonstrate that the higher rotation speed and smaller clearance will cause the larger material removal rate. Molecular dynamic (MD) calculations show the bonding energy of Si-O in the silicon-oxide nanoparticle is stronger than that in the quartz glass, and therefore the atoms can be dragged away from the quartz glass surface by the adsorbed silicon-oxide nanoparticle. The deep subsurface damage cannot be efficiently removed by HEP due to its extremely low removal rate. However, the subsurface damaged layer can be quickly removed by ion beam figuring (IBF), and a thinner layer containing the passivated scratches and pits will be left on the surface. The passivated layer is so thin that can be easily removed by HEP process with a low material rate under the large wheel-workpiece clearance. Combined with the IBF process, the subsurface damage and surface scratches have been efficiently removed after the HEP process. Meanwhile there are not obvious duplicated marks on the processed surface and the surface roughness has been improved to 0.130nm rms, 0.103nm Ra.
© 2014 Optical Society of America
The development of modern optics and microelectronic requires the components with extremely high surface quality [1, 2]. Large and grand-scale integration has put high requirements on the wafer surface roughness. Modern shortwave optics and high energy laser optics requires the surface with ultralow roughness. Surface roughness, referred to high-spatial frequency roughness, can easily cause wide-angle scattering and result in a loss or decreasing the image quality and reflectivity of the surface [3, 4]. Ultrasmooth surface calls for extremely low surface roughness. As one of the promising technologies for next generation lithography, extreme ultraviolet lithography requires that the mirror substrate have to be fabricated with a roughness of about 0.1nm . Surface/subsurface damage (SD) can be easily induced in the traditional contact machining process in which the material is mainly removed by the mechanical effect. Defects such as scratches and cracks are hidden below the surface under the effect of redeposition . Laser damages are often initiated by SD, and even a low level of defects can considerably reduce the lifetime of optical components .
To achieve the ultrasmooth surface, the material removal unit should be at the atomic level. Defects are unavoidably caused by the traditional lap polishing process with contact mode. Until now researchers have done widely studies on the ultrasmooth polishing technique. Ultrasmooth surface has been achieved by float polishing [8, 9], elastic emission machining [10, 11], micro-jet polishing  and hydrodynamic effect polishing (HEP) . All these methods are non-contact polishing processes and their material removal rates are extremely low. Material can be removed with high efficiency by physical sputtering effect in the ion beam figuring (IBF) process. No subsurface damages are induced in IBF process because no mechanical force is applied on the workpiece surface [13, 14]. Nanoparticles in the slurry are reactive with the atoms on the workpiece surface in HEP, and the impact is so lightly that only elastic deformation occurs on workpiece surface. Within elastic deformation no defects are caused in the polishing process. However, the main problem of HEP is that the material removal rate is too low to removal the SD effectively when the SD is deep. In this paper, an ultrasmooth and defect-free surface was quickly fabricated by the HEP process combined with the IBF process. We present an efficient way to fabricate the ultrasmooth surface with HEP.
2. 2. Hydrodynamic effect polishing (HEP)
The schematic diagram of HEP is illustrated in Fig. 1. The semi-spherical polishing wheel is composed of a metallic core and a wearable polymer shell with certain elasticity. The polishing wheel and the workpiece are all submerged into the nanoparticle slurry, and the distance between the wheel and workpiece surface is about micrometers or tens of micrometers. The HEP system is mounted on an ultra-precision numerical controlled multi-axis platform system.
There will be a hydrodynamic lubricant film between the wheel and workpiece when the wheel rotates at a certain speed. Nanoparticles interact and form a linkage with the workpiece surface under the effect of the dynamic pressure. With the action of the flow shear stress, nanoparticles are transported to separate from the workpiece surface leading to breaking the bonding force between the workpiece surface and subsurface-layer atoms. The material removal rate MR, determined by the dynamic pressure and shear stress, can be expressed as :
Here τ and P denote the shear stress and dynamic pressure on the workpiece surface respectively, and C and C1 are positive constants related with the material properties. From Eq. (1) we can see the material removal rate increases with the shear stress and dynamic pressure if the shear stress is large enough to break the bonding energy of the workpiece surface atoms. The distributions of shear stress and dynamic pressure on the workpiece surface are mainly determined by the rotation speed ω and the clearance h between the wheel and workpiece surface, as shown in Fig. 1(a). Three-dimensional fluid dynamic simulation was introduced to investigate the relationships. The radius of the semi-spherical wheel is 40mm. Figure 2 shows the maximum shear stress and dynamic pressure affected by the rotation speed. For the same clearance, the shear stress and dynamic pressure linearly increase as one and second orders with the rotation speed respectively, as shown in Fig. 2.
Figure 3 shows the maximum shear stress and dynamic pressure affected by the clearance under the same rotation speed. The shear stress decreases quickly when the clearance increases, and the influence becomes very weak when the clearance increases to 40μm, as shown in Fig. 3(a). The magnitude of the dynamic pressure is almost at the same level when the clearance changes, as shown in Fig. 3(b). Previous work has demonstrated that the clearance has no influence on the magnitude of dynamic pressure but great effect on its distribution . From the above analysis, we should select the proper rotation speed and clearance to get the effective material removal in the polishing process.
3. Material removal mechanism for silicon-oxide nanoparticle
Nanoparticles, which have strong chemisorption due to their high specific area, are employed as the polishing medium in HEP process. On the other hand, inverse gas chromatography experiments indicate there are lots of reactive sites on the workpiece surface . Once these two surfaces come close to each other, the workpiece surface atoms and nanoparticle atoms will react with each other forming a Si-O-R (R represents nanoparticle atoms) linkage. When the nanoparticles are transported to separate by the shear stress, Surface atoms will drag away from the surface [16–18]. Only if the strength of O-R bond is stronger than that of Si-O, the quartz tetrahedron will remain bonded to the nanoparticle surface leading to material removal. However the silicon-oxide nanoparticle has the same element composition with that of quartz glass, and how the material removal occurs is still unknown. Silicon-oxide nanoparticle deviates from the normal stable structure due to the lack of oxygen atoms, and its molecular formula is SiOx with x ranging from 1.2 to1.6 or 1.18 to 1.83 [19–21]. To investigate the difference of the structure due to lack of oxygen atoms in [SiO4] structure, first-principles molecular dynamic (MD) simulations was employed. The cluster models are Si2O7H6, Si2O6H5 and Si2O5H4, which have the same number of Si atoms but different oxygen atoms. Figure 4 shows the stable structures of different cluster models by MD calculation.
Simulation results show the angle of Si-O-Si bond becomes larger with the decrease of oxygen atoms. Su et al.  has found that the angle of Si-O-Si is in the range of 120þ to 180þ in [SiO4] structure and the Si-O bond strengh has the following relationship with the angle of Si-O-Si:
Here φ denotes the angle of Si-O-Si. From Eq. (2) we can easily calculate the relative strength of Si-O bond. Table 1 shows the angle of Si-O-Si and the relative strength of Si-O bond in different structures. The strength of Si-O bond becomes stronger as the decrease of the oxygen atoms. Due to the lack of oxygen atoms in silicon-oxide nanoparticles, we can conclude that the average angle of Si-O-Si is larger than that in quartz glass, and thus the Si-O bond is stronger than that in the quartz glass. That is why effective material removal rate can be obtained when silicon-oxide nanoparticles are applied as the polishing medium in HEP.
Figure 5 shows the material removal rate of the silicon-oxide nanoparticle slurry with concentration of 20wt.% at different wheel-workpiece clearance when the wheel rotation speed is 200rpm. It is clearly demonstrated from the experiment results that material removal is at the atomic level per second and the removal rate non-linearly decreases as the clearance which agrees well with the fluid dynamic simulation results shown in Fig. 3. No obvious material removal occurs when the clearance is more than 60μm that means the shear stress is not large enough to overcome the binding energy of the surface atoms. According to the analysis of Fig. 2 and Fig. 3, effective material removal will surely occur when the rotation speed is larger than 200rpm and the clearance is under 40μm, if silicon-oxide nanoparticles are employed as the polishing medium in HEP process.
4. Experimental procedure
4.1 Prepolished by IBF
An initial quartz glass surface was prepared by the traditional pitch lap polishing process. The initial surface has many micro-scratches, as shown in Fig. 6(a). It is well known that the material is removed by physical sputtering effect without subsurface damage for IBF method. It also possesses highly stable removal efficiency. To remove the subsurface damage, semi-part of the initial surface was prepolished by IBF with the removal depth of 500nm. The experiment was conducted in our newly self-developed IBF system (5 × 10−3Pa work pressure). The surface was etched using Ar+ ion beams with ion energy of 800eV, ion current of 25mA, and a normal incident angle. The volume removal rate is about 7.8 × 10−3mm3/min for quartz glass. For its high stable removal efficiency, the time of removal depth of 500nm for the area of 5mm × 5mm can be calculated about 1.6min. Surface erosion occurs after being prepolished by IBF and all the defects have enlarged and passivated, as shown in Fig. 7(a).
4.2 Fine polished by HEP
Contrast experiments were conducted to verify the HEP performance under different process conditions. The diameter of the semi-spherical wheel is 80mm. The silicon-oxide nanoparticle with average diameter of 20nm was selected. The polishing slurry with concentration of 20wt.% was prepared by deionized water and some dispersants. Four polishing areas on the sample surface were selected. One area was directly polished by HEP. The other three areas were uniformly prepolished by IBF with the uniform removal depth of 500nm, and then HEP was employed as the final polishing process under different process parameters. The process parameters are listed in Table 2. The sample surfaces before and after the polishing processes were observed by atomic force microscopy (AFM, Bruker’s Dimension Icon). The AFM scanning area of 10μm × 10μm with a resolution of 512 × 512 pixels and a scan rate of 1.0Hz was set to investigate the improvement of high spatial frequency roughness. The AFM images were flatten by the 3rd to remove the tilt and bow, and the analysis was conducted with no filtering.
5. Results and discussion
Figure 6 shows the AFM images of the surface before and after HEP process in experiment #1. There exists a degenerative layer containing micro plastic scratches, pits and bumpy structures on the initial lap prepolished surface, as shown in Fig. 6(a). After HEP process, the defects are almost removed and the surface becomes much smoother. The surface roughness has improved from 1.16nm rms, 0.918nm Ra to 0.227nm rms, 0.181nm Ra. Although the processed surface becomes smoother, the deep scratches in the subsurface layer and the degenerative layer around them can’t be removed clearly due to the low material removal rate in HEP process, as shown Fig. 6(b). What’s more, the turning ripples on the polishing wheel were greatly duplicated on workpiece surface under the hydrodynamic effect with the small wheel-workpiece clearance.
The IBF prepolished surface observed by AFM was shown in Fig. 7(a). The scratches and pits caused in the lap polishing have been enlarged during the IBF process, and meanwhile defect depth has been greatly depressed. A passivated layer with bumpy structures was established on the surface after IBF process. When HEP was employed on the IBF prepolished surface, all the defects and bumpy structures have been removed clearly. Although the processed surface quality has greatly improved, there still exits obvious polishing marks on the processed surface with wheel-workpiece clearance of 10μm, as shown in Fig. 7(b). By comparison, we can see that the polishing marks on the processed surface in Fig. 7(c) have been depressed at a certain extent. With a larger polishing clearance, the effect on turning ripples on wheel surface duplicated on the workpiece surface has been restrained. That is why the polishing marks have been weakened on processed surface when the wheel-workpiece distance increases to 25μm. Surface roughness has decreased with depression of the polishing marks. When the clearance reaches 30μm, the polishing marks are very inconspicuous and the surface becomes very smooth, as shown in Fig. 7(d). The section profile shows the peaks of the processed surface are at the same level with fluctuation within ± 0.3nm. The surface roughness has been improved to 0.130nm rms, 0.103nm Ra. Meanwhile, there are no obvious polishing marks on the processed surface. From Fig. 3 we can see the effect of shear stress influenced by the polishing clearance becomes weaker when the clearance becomes larger. Therefore, with the large wheel-workpiece clearance, the phenomenon of periodic turning marks on the wheel duplicated on the workpiece by the hydrodynamic effect has been greatly restrained.
The measured values of AFM provide only vertical information such as roughness. To obtain lateral information, power spectral density (PSD) analysis was performed. The isotropic 2D-PSD curves of the surface at different processed stages were shown in Fig. 8. By comparison, surface error in the spatial wavelength higher than 10μm has been improved when the initial scratches and pits were broadened by IBF process. Whenever the HEP was employed, the surface quality has been greatly improved. However, the surface quality is much better especially for the surface error in the spatial wavelength higher than 1μm when HEP was applied on the IBF preprocessed surface under the large wheel-workpiece clearance. Combined with the IBF process, the lap prepolished surface can be quickly transformed to ultra-smooth and defect-free surface by HEP process even if with large wheel-workpiece clearance.
To make the evaluation more reasonable, three different points on the sample surface are measured by AFM with the area of 10μm × 10μm before and after polishing. The rms values of surface roughness are listed in Table 3. The surface roughness has greatly decreased when a passivated layer formed on the IBF prepolished surface. Whenever the HEP was applied, the surface roughness has decreased. What’s more, lower surface roughness can be obtained with a larger polishing clearance.
Wang  has found the depth of the surface/subsurface layer is in the range of 100 to 500nm after the traditional lap polishing process. Based on this research, we proposed the schematic diagram of ultrasmooth and defect-free surface fabricated by HEP combined with the IBF process, as shown in Fig. 9. The subsurface damaged layer has been effectively removed by the IBF prepolished process with the average removal depth of 500nm, and no subsurface damages are induced by the physical sputtering effect due to no mechanical force applied on the surface, as shown in Fig. 9(b). During ion beam sputtering, a variety of surface processes are active that tend to roughen or smooth the prepolished surface. Surface erosion occurs leading to removal of near surface atoms, and ion arrival and related sputtering events are stochastic contributing to surface roughening at atomic length scale. On the other hand, ion irradiation generates directed or random fluxes of recoil atoms moving parallel to the surface, and the surface is smoothed . With the action of these two contradictive effects, the scratches on the initial surface have been greatly enlarged and passivated, and meanwhile depths of scratches have been greatly reduced after IBF. The passivated layer only exists on the top surface layer. The passivated layer is so thin that can be easily removed by the lower material removal rate in HEP even with a lower removal rate.
The movement of the near-surface slurry flow is nearly parallel to the workpiece surface . Hence the convex atoms have a larger probability of impacting with the nanoparticles. The wheel surface roughness is usually made at a sub-micrometer level. Compared with the polishing clearance, the coarse wheel surface has little effect on the distance to workpiece surface. To investigate the detail difference on the workpiece surface, the wheel surface is supposed to be ultra-smooth and the uneven workpiece surface has been enlarged. Figure 10 shows the simplified sketch of the polishing wheel on the rough surface at different positions. The distance from the wheel at convex parts is much smaller than that at other locations on the surface. So the shear stress of the convex parts on the rough surface is larger than that of the other parts. According to Eq. (1), we can conclude that material removal rate of the convex atoms is higher than that of the atoms at other locations. Thus the surface becomes much smoother when HEP process is applied, as shown in Fig. 9(c). On the other hand, the nanoparticle is lightly transported to contact with the workpiece surface under the action of the hydrodynamic effect. The impact is so weak that only elastic deformation occurs on the workpiece surface . Therefore no damages are induced in the HEP process. Combined with IBF process, an ultrasmooth and defect-free surface has been efficiently fabricated by HEP with the large clearance process parameters.
In this paper, material removal rate affected by the wheel rotation speed and wheel-workpiece clearance was investigated by fluid dynamic simulation. Simulation results demonstrate that higher rotation speed and smaller clearance will cause relative higher removal rate in HEP process. Silicon-oxide nanoparticles have the same composite elements as quartz glass with molecular formula of SiOx(x<2). First-principles molecular dynamic (MD) simulation was introduced to investigate its removal mechanism. It is clearly demonstrated from the simulation results that the strength of Si-O in the silicon-oxide nanoparticle is stronger than that in quartz glass due to its larger angle of Si-O-Si. So silicon atoms on the quartz glass are understood to be removed off by removing the adsorbed silicon-oxide nanoparticles. The removal mechanism of HEP means the machining efficiency is extremely low. Subsurface damage layer can’t be removed clearly in a short time when HEP is directly applied on the traditional lap prepolished surface. Material removal rate of IBF is very high compared with that of HEP, and the subsurface damage layer can be easily removed leaving a thin passivated layer on the top surface. Combined with the IBF preprocess, an ultrasmooth surface with roughness of 0.130nm rms, 0.103nm Ra is obtained by HEP process. No defects were left on the processed surface. Meanwhile, it is greatly restrained that periodic turning marks on the wheel are duplicated on the workpiece by the hydrodynamic effect with the large clearance.
This work was financially supported by the National Natural Science Foundation of China (No. 51305450 and No. 91023042) and National Basic Research Program of China (No. 2011CB013200).
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