Mechanism and Simulation of Removal Rate and Surface Roughness During Optical Polishing of Glasses

Glass optics with ultra‐low roughness surfaces (<2 Å rms) are strongly desired for high‐end optical applications (e.g., lasers, spectroscopy, etc.). The complex microscopic interactions that occur between slurry particles and the glass workpiece during optical polishing ultimately determine the removal rate and resulting surface roughness of the workpiece. In this study, a comprehensive set of 100 mm diameter glass samples (fused silica, phosphate, and borosilicate) were polished using various slurry particle size distributions (PSD), slurry concentrations, and pad treatments. The removal rate and surface roughness of the glasses were characterized using white light interferometry and atomic force microscopy. The material removal mechanism for a given slurry particle is proposed to occur via nano‐plastic deformation (plastic removal) or via chemical reaction (molecular removal) depending on the slurry particle load on the glass surface. Using an expanded Hertzian contact model, called the Ensemble Hertzian Multi‐gap (EHMG) model, a platform has been developed to understand the microscopic interface interactions and to predict trends of the removal rate and surface roughness for a variety of polishing parameters. The EHMG model is based on multiple Hertzian contacts of slurry particles at the workpiece–pad interface in which the pad deflection and the effective interface gap at each pad asperity height are determined. Using this, the interface contact area and each particle's penetration, load, and contact zone are determined which are used to calculate the material removal rate and simulate the surface roughness. Each of the key polishing variables investigated is shown to affect the material removal rate, whose changes are dominated by very different microscopic interactions. Slurry PSD impacts the load per particle distribution and the fraction of particles removing material by plastic removal. The slurry concentration impacts the areal number density of particles and fraction of load on particles versus pad. The pad topography impacts the fraction of pad area making contact with the workpiece. The glass composition predominantly impacts the depth of plastic removal. Also, the results show that the dominant factor controlling surface roughness is the slurry PSD followed by the glass material's removal function and the pad topography. The model compares well with the experimental data over a variety of polishing conditions for both removal rate and roughness and can be extended to provide insights and strategies to develop practical, economic processes for obtaining ultra‐low roughness surfaces while simultaneously maintaining high material removal rates.     

Nanoscratching of Optical Glass Surfaces Near the Elastic–Plastic Load Boundary to Mimic the Mechanics of Polishing Particles

The nanomechanical deformations on glass surfaces near the elastic–plastic load boundary have been measured on various glasses by nanoscratching using an atomic force microscope (AFM) to mimic the mechanical interactions of polishing particles during optical polishing. Nanoscratches were created in air and aqueous environments using a 150‐nm radius diamond‐coated tip on polished fused silica, borosilicate, and phosphate glass surfaces; the topology of the nanoscratches were then characterized by AFM. Using load ranges expected on slurry particles during glass polishing (0.05–200 μN), plastic‐type scratches were observed with depths in the nm range. Nanoscratching in air generally showed deeper & narrower scratches with more pileup compared to nanoscratching in water, especially on fused silica glass. The critical load needed to observe plastic deformation was determined to range from 0.2–1.2 μN for the three glasses. For phosphate glass, the load dependence of the removal depth was consistent with that expected from Hertzian mechanics. However, for fused silica and borosilicate glass in this load range, the deformation depth showed a weak dependence with load. Using a sub‐T_g annealing technique, material relaxation was observed on the nanoscratches, suggesting that a significant fraction of the deformation was due to densification on fused silica and borosilicate glass. Repeated nanoscratching at the same location was utilized for determining the effective incremental plastic removal depth. The incremental removal depth decreased with increase in number of passes, stabilizing after ~10 passes. In water, the removal depths were determined as 0.3–0.55 nm/pass for fused silica, 0.85 nm/pass for borosilicate glass, and 2.4 nm/pass for phosphate glass. The combined nanoscratching results were utilized to define the composite removal function (i.e., removal depth) for a single polishing particle as a function of load, spanning the chemical to the plastic removal regimes. This removal function serves as an important set of parameters in understanding material removal during polishing and the resulting workpiece surface roughness.     

Molecular beam epitaxy-grown PbSnTe-PbEuSeTe buried heterostructurediode lasers

Buried heterostructure (BH) PbSnTe-PbEuSeTe lasers with a PbSnTe active layer were fabricated for the first time using a two-stage molecular beam epitaxy (MBE) growth procedure. Lasers with 4-μm-wide and 0.65-μm-thick buried Pb_0.961Sn_Sn0.039Te active layer and Pb_0.985Eu_0.015Se_0.02Te _0.98 cladding layers were grown. Continuous wave (CW) operating temperature of 175 K was measured with CW threshold currents of 1.6 mA (20 K), 13.6 mA (80 K), and 195 mA (160 K). Single-mode operation with 3.0-cm^-1-mode tuning was measured at 1639.8 cm ^-1 emission     

Convergent Pad Polishing of Amorphous Silica

A new method of optical polishing termed “Convergent Polishing” is demonstrated where a workpiece, regardless of its initial surface figure, will converge to the lap shape in a single iteration. This method of polishing is accomplished by identifying the phenomena that contribute to non-uniform spatial material removal, and mitigating the non-uniformity for each phenomenon (except for the workpiece-lap mismatch due to the workpiece surface shape). The surface mismatch at the interface between the workpiece and lap causes a spatial and time varying pressure differential which decreases with removal, thus allowing the workpiece to converge to the shape of the lap. In this study, fused (amorphous) silica workpieces are polished using ceria slurry on various polyurethane pads. Polishing parameters were systematically controlled to prevent various sources of non-uniform material removal which include: (i) moment force, (ii) viscoelastic lap relaxation, (iii) kinematics, (iv) pad wear, and (v) workpiece bending. The last two are described herein. With these mitigations, removal uniformity has been demonstrated to within 1.0 μm over the surface after 83 μm of material removal corresponding to a within workpiece non-uniformity (WIWNU) of <1.2%. Also, convergence has been demonstrated down to 0.18 ± 0.04 μm peak-to-valley flatness on 100 mm-sized workpieces.     

Chemistry and Formation of the Beilby Layer During Polishing of Fused Silica Glass

The chemical characteristics and the proposed formation mechanisms of the modified surface layer (called the Beilby layer) on polished fused silica glasses are described. Fused silica glass samples were polished using different slurries, polyurethane pads, and at different rotation rates. The concentration profiles of several key contaminants, such as Ce, K, and H, were measured in the near surface layer of the polished samples using Secondary Ion Mass Spectroscopy (SIMS). The penetration of K, originating from KOH used for pH control during polishing, decreased with increase in polishing material removal rate. In contrast, penetration of the Ce and H increased with increase in polishing removal rate. In addition, Ce penetration was largely independent of the other polishing parameters (e.g., particle size distribution and the properties of the polishing pad). The resulting K concentration depth profiles are described using a two‐step diffusion process: (1) steady‐state moving boundary diffusion (due to material removal during polishing) followed by (2) simple diffusion during ambient postpolishing storage. Using known alkali metal diffusion coefficients in fused silica glass, this diffusion model predicts concentration profiles that are consistent with the measured data at various polishing material removal rates. On the other hand, the observed Ce profiles are inconsistent with diffusion based transport. Rather we propose that Ce penetration is governed by the ratio of Ce–O–Si and Si–O–Si hydrolysis rates; where this ratio increases with interface temperature (which increases with polishing material removal rate) resulting in greater Ce penetration into the Beilby layer. Calculated Ce surface concentrations using this mechanism are in good agreement to the observed change in measured Ce surface concentrations with polishing material removal rate. These new insights into the chemistry of the Beilby layer, combined together with details of the single particle removal function during polishing, are used to develop a more detailed and quantitative picture of the polishing process and the formation of the Beilby layer.     

Influence of partial charge on the material removal rate during chemical polishing

A partial charge-based chemical polishing model has been developed, which can serve as metric for describing the relative polishing material removal rate for different combinations of slurries and workpieces. A series of controlled polishing experiments utilizing a variety of colloidal polishing slurries (SiO₂, CeO₂, ZrO_2, MgO, Sb₂O₅) and optical materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂-Al₂O₃-P₂O₅-Li₂O glass ceramic (Zerodur); and glasses of SiO₂:TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅-Al₂O₃-K₂O-BaO (Phosphate)] was performed and its material removal rate was measured. As previously proposed by Cook (J Non-Cryst Solids. 1990;120:152), for many polishing systems, the removal rate is governed by a series of chemical reactions which include the formation of a surface hydroxide, followed by condensation of that hydroxyl moiety with the polishing particle, and a subsequent hydrolysis reaction. The rate of condensation can often be the rate limiting step, thus it can determine the polishing material removal rate. By largely keeping the numerous other factors that influence material removal rate fixed (such as due to particle size distributions, interface interactions, pad topography, kinematics, and applied pressure), the material removal rate is shown to scale exponentially with the partial charge difference (δ_wp-s) between the workpiece and polishing slurry particle for many of the slurry-workpiece combinations indicating that condensation rate is the rate limiting step. The partial charge (δ) describes the equilibrium distribution of electron density between chemically bonded atoms and is related to the electronegativity of the atoms chemically bonded to one another. This partial charge model also explains the age-old experimental finding of why cerium oxide is the most effective polishing slurry for chemical removal of many workpieces. Some of the slurry-workpiece combinations that did not follow the partial charge dependence offer insight to other removal mechanisms or rate limiting reaction pathways.     

Nanoplastic removal function and the mechanical nature of colloidal silica slurry polishing

The nanomechanical deformations on a broad range of optical material surfaces (single crystals of Al₂O₃ [sapphire], SiC, Y₃Al₅O₁₂ [YAG], CaF₂, and LiB₃O₅ [LBO]; a SiO₂–Al₂O₃–P₂O₅–Li₂O glass-ceramics [Zerodur]; and glasses of SiO₂:TiO₂ [ULE], SiO₂ [fused silica], and P₂O₅–Al₂O₃–K₂O–BaO [Phosphate]) near the elastic-plastic load boundary have been measured by nanoindentation and nanoscratching to mimic the nanoplastic removal caused by a single slurry particle during polishing. Nanoindenation in air was performed to determine the workpiece hardness at various loads using a commercial nanoindenter with a Berkovich tip. Similarly, an atomic force microscope (AFM) with a stiff diamond coated tip (150 nm radius) was used to produce nanoplastic scratches in air and aqueous environments over a range of applied loads (~20-170 μN). The resulting nanoplastic deformation of the nanoscratches were used to calculate the removal function (i.e., depth per pass) which ranged from 0.18 to 3.6 nm per pass for these materials. A linear correlation between the nanoplastic removal function and the polishing rate (using a fixed polishing process with colloidal silica slurry on a polyurethane pad) of these materials was observed implying that: (a) the polishing mechanism using colloidal silica slurry can be dominated by mechanical rather than chemical interactions; and (b) the nanoplastic removal function, as opposed to interface particle interactions, is the controlling factor for the polishing material removal rate. Furthermore, this correlation is consistent with the Ensemble Hertzian Multi-Gap (EHMG) microscopic material removal rate model described previously. The nanoplastic removal depth was also found to correlate to the measured nanoindentation hardness (H₁) of the optical material, scaling as H₁^−3.5. Two-dimensional (2D) finite element analysis simulations of nanoindentation showed a similar nonlinear dependence of plastic deformation with the workpiece material hardness. The findings of this study are used to determine an effective Preston coefficient for the material removal rate expression and enhance the predictive nature of the nanoplastic polishing rate for various materials utilizing their material properties.     

Prediction of Rockburst and Sudden Outburst Hazard on the Basis of Estimate of Rock-Mass Energy

A method is developed for estimating the outburst and rock burst hazard of coal seams and faces of mine workings on the basis of determination of rock-mass energy. It is approved in a number of mines located in the Kuznetsk Basin.     

Rear-Surface Laser Damage on 355-nm Silica Optics Owing to Fresnel Diffraction on Front-Surface Contamination Particles

Light intensity modulations caused by opaque obstacles (e.g., dust) on silica lenses in high-power lasers often enhance the potential for laser-induced damage. To study this effect, particles (10-250 mum) with various shapes were sputter deposited on the input surface and irradiated with a 3-ns laser beam at 355 nm. Although a clean silica surface damages at fluences above 15 J/cm(2), a surface contaminated with particles can damage below 11.5 J/cm(2). A pattern that conforms to the shape of the input surface particle is printed on the output surface. Repetitive illumination resulted in catastrophic drilling of the optic. The damage pattern correlated with an interference image of the particle before irradiation. The image shows that the incident beam undergoes phase (and amplitude) modulations after it passes around the particle. We modeled the experiments by calculating the light intensity distribution behind an obscuration by use of Fresnel diffraction theory. The comparison between calculated light intensity distribution and the output surface damage pattern showed good agreement. The model was then used to predict the increased damage vulnerability that results from intensity modulations as a function of particle size, shape, and lens thickness. The predictions provide the basis for optics cleanliness specifications on the National Ignition Facility to reduce the likelihood of optical damage.     

Influence of Temperature and Material Deposit on Material Removal Uniformity during Optical Pad Polishing

The effects of temperature and material deposit on workpiece material removal spatial uniformity during optical pad polishing are described. Round and square‐fused silica workpieces (25–265 mm in size) were polished on a polyurethane pad using ceria slurry under various conditions. Using a nonrotated workpiece on a rotating lap, elevated temperatures (as measured by IR imaging), due to frictional heating at the workpiece–lap interface, were observed having a largely radial symmetric profile (relative to the lap center) on both the workpiece and lap with a peak temperature corresponding to the workpiece center. A 3D steady‐state thermal model of the polishing process, which accounts for the frictional heating and effective heat transfer from various surfaces, quantitatively describes the observed thermal profiles. The temperature spatial uniformity, which affects the material removal spatial uniformity, can be significantly improved using a rotated workpiece and a specially designed compensating septum during polishing. Next, using a rotating workpiece and lap, the workpiece surface develops two types of mid‐range structure: (1) fine ripples (sub‐mm scale length) that run circumferentially with respect to the lap, which have been attributed to microscopic islands of slurry on the lap leading to radial material removal nonuniformities; and (2) a center depression (cm scale length) which has been attributed to nonlinear slurry & glass products buildup at a specific radial lap location. A polishing simulator model (called Surface Figure or SurF), which accounts for workpiece wear, pad wear, and now deposition on the pad, correctly simulates the preferential material deposit on the pad and the center depression structure developed on the workpiece. Strategies, such as time averaging through kinematics and diamond conditioning, for preventing both these nonuniformities are demonstrated.