A statistical model for material removal prediction in polishing

This paper develops analytically a statistical model for predicting the material removal in mechanical polishing of material surfaces (MS). The model was based on the statistical theory and the abrasive–MS contact mechanisms. The pad-MS and pad-abrasive-MS interactions in polishing were characterised by contact mechanics. Two types of active abrasive particles in the polishing system were considered, i.e., Type I – the particles that can slide and rotate between the pad and MS, and Type II – those embedded in the pad without a rigid body motion. Accordingly, the material removal is considered to be the sum of the contributions from the two types of abrasive interactions. It was found that the mechanical properties and microstructure of the polishing pad and polishing conditions have a significant effect on the material removal rate, such as the porosity and elastic modulus of the pad, polishing pressure, volume concentration of abrasives, particle size, pad asperity radius and pad roughness. It was also found that different types of active particles contribute quite differently to the material removal. When the mean particle radius is small, the material removal is mainly due to the Type II particles, but when the mean particle radius becomes large, the Type I particles remove more materials. The model predictions are well aligned with experimental results available in the literature and can be used for the material removal prediction in chemo-mechanical polishing if a proper treatment of the chemical effect is introduced.     

磁射流抛光时几种工艺参数对材料去除的影响

研究了磁射流抛光时几种工艺参数对材料去除的影响。首先介绍了磁射流抛光的原理和实验装置,然后从实验出发研究了磁射流抛光中材料的去除。利用标准的磁流变液进行了一系列定点抛光实验。重点研究了冲击角、工作距离、射流速度和磁场强度对抛光区形状和去除量的影响,获得了相应的关系曲线。运用计算流体力学方法分析了材料去除机理。为进一步研究磁射流抛光的各种参数的最佳匹配,实现磁射流抛光的数控加工奠定了基础。     

液体喷射抛光技术材料去除机理的有限元分析

实验研究了液体喷射抛光技术的材料去除量分布特征,并利用有限元分析方法,分析了抛光头(液体柱)与工件表面相互作用时流场的分布特点。实验结果及计算机模拟的结果表明,材料去除量与射流碰撞工件后流体沿工件表面的速度有关,即材料去除量的分布与抛光液在工件表面速度场的分布有关,速度分布最大的边缘部分,材料去除量最大;相互作用区外,速度逐渐减小,材料去除量也随之渐少。该现象说明,抛光液中磨料粒子的径向流动对工件产生的径向剪切应力是材料去除的关键。     

A study of material removal amount of sapphire wafer in application of chemical mechanical polishing with different polishing pads

The study mainly explores the fabrication mechanism for fabricating sapphire wafer substrate, by using chemical mechanical polishing (CMP) method. A slurry containing the abrasive particles of SiO₂ is used to contact with the sapphire substrate polish and to produce chemical reaction for removal of sapphire wafer substrate when CMP method is used. The study observes the changes of the removal amount of sapphire wafer substrate when the pattern-free polishing pad and hole-pattern polishing pad are used under different down forces, polishing velocities, abrasive particle sizes and slurry concentrations. Employing regression analysis theory, the study makes improvement of the equation of material removal rate (MRR) to be the material removal height per 30 minutes (MRRh), and develops a compensation parameter C_rv of the error caused by the volume concentration of slurry. The results of experimental analysis show that under a certain down force, if the polishing velocity is greater, the material removal amount will be greater. Generally speaking, the material removal amount of hole-pattern polishing pad is greater than that of pattern-free polishing pad. As to the relationship between abrasive particle size and slurry concentration, when particle size is smaller, the volume concentration of slurry will be higher, and the number of abrasives for polishing wafer will be greater. As a result, a better material removal depth can be acquired. Through the above analytical results, considerable help is offered to the polishing of sapphire wafer.     

Modeling and simulation of material removal in planarization process

In planarization processes, material removal analysis is essential to the estimation of the wear rate and non-uniformity. A model that describes the material removal of a pad with rough surface grinding by using abrasive grains is developed. A collection of micro-contact spots is identified and the deformation approach is subsequently calculated. Elastic-plastic theory and the wear model are used to construct the expression for the magnitude of material removal as a function of the indentation depth. First, the indentation depth of micro-contact spots in the asperity of the pad and the deformation of the flat part of pad are obtained by using elastic-plastic theory. Then, the material removal caused by individual micro-contacts is calculated with the help of wear theory. Finally, the macroscopic wear volume is found by summing the volumetric wear of each individual micro-contact. Moreover, the pad dressing process is introduced to demonstrate the developed model for material removal. A parametric study is conducted to explore the influence on the material removal results and the planarization interfacial phenomena of operational parameters. These parameters compose of the applied down force, rotational speed of dresser, and the density of abrasive grains. The results provide a detailed picture of the interface phenomena and yield an insight into the physical effects of the operating parameters in the planarization processes.     

Effect of interfacial friction force on material removal in full aperture continuous polishing process

Full aperture continuous polishing using pitch lap is a key process of finishing large flat optical workpiece. The friction force of the workpiece and pitch lap interface significantly affects material removal. In this work, the friction force was determined by a measurement system that uses force transducers to support the workpiece. Experimental and theoretical analyses have been carried out to investigate the evolution of friction force with polishing time and its effect on material removal. Our results show that the friction coefficient of the workpiece/lap interface decreases during polishing, which is due to surface smoothing of the viscoelastic pitch lap by loading conditioner. In addition, the spatial average and uniformity of material removal rate (removal coefficient) increases with the increase of friction coefficient, which is due to rough lap surface, provides more sharp asperities to charge the polishing particles.     

An experimental study on the correlation of polishing force and material removal for bonnet polishing of cobalt chrome alloy

Cobalt chrome alloys are the most extensively used biomaterials for manufacturing artificial prostheses, which need nanometer scale surface roughness and micrometer scale form tolerance to extend their lifespan in the tough environment of the human body. In order to machine bearing surfaces to sufficiently high accuracy, the way in which material is removed by the final finishing, such as bonnet polishing, must be completely understood. This study has experimentally investigated the influence of process parameters (precess angle, head speed, tool offset, and tool pressure) on the polishing forces as well as the material removal in bonnet polishing of a medical grade cobalt chrome alloy. Experimental results indicate that normal force increases with the increase in the precess angle, head speed and tool offset, but varies only slightly with the variation of the tool pressure. Tangential force increases with the increase in the precess angle and tool offset while it shows little variation with the change of the head speed and tool pressure. It is concluded that both normal force and tangential force can contribute to the material removal rate, but tangential force is found to be more correlated with the width of the influence function while normal force has a stronger correlation with the maximal height of the influence function.     

An integrated material removal model for silicon dioxide layers in chemical mechanical polishing processes

The material removal rate in CMP processes obeys Preston's equation, which can be expressed as a linear function of the applied areal power density under usual operating conditions. However, some experimental results have shown a nonlinear relationship between the CMP material removal rate and the applied areal power density, suggesting non-Prestonian behavior under certain operating regimes. Although the material removal rate is caused by the coupled effect of both mechanical and chemical actions in actual CMP processes, the treatment of the chemical action as a mere supplementary means of softening the surface makes it difficult to explain this non-Prestonian behavior. In this work, we propose an integrated material removal model for silicon dioxide during CMP based on a multiscale mechanical abrasion model coupled with the slurry chemical diffusion effects. The synergetic effects on the material removal mechanism due to both mechanical and chemical actions are incorporated in the model, and the total material removal rate is predicted by accounting for both effects. Consequently, the non-Prestonian behavior often shown in silicon dioxide CMP may be explained using the proposed model. The validity of the model is supported by comparing the predicted material removal rates with experimental values available in the literature.     

An empirical approach to explain the material removal rate for copper chemical mechanical polishing

In this paper, an empirical expression was deduced based on the experimental data for material removal rate of copper chemical mechanical polishing. The parameters of this expression includes the initial chemical corrosion rate(MRR₀), the corrosion inhibition efficiency(k) and the mechanical abrading rate(MRR_M). The deduced empirical expression revealed that under certain slurry systems, the corrosion inhibition efficiency may always keep unchanged, which may be useful to characterize the inhibition properties of different inhibitors.     

光学玻璃磁性复合流体抛光应力与材料去除率的实验研究

根据光学玻璃元件超精密加工技术的需求,研究自旋转式和行星旋转式磁性复合流体(MCF)抛光的应力分布和材料去除率。首先,设计可实现自旋转和行星旋转抛光装置,搭建抛光实验平台;然后,进行自旋转式和行星旋转式MCF抛光实验,通过自行设计抛光应力分布测试实验分析了两种抛光方式的应力分布规律;最后,通过定点抛光实验,对抛光前后的工件表面轮廓进行检测,计算并分析两种抛光方式的材料去除率。实验结果表明,立式的两种抛光方式,正应力均明显大于剪切应力,工件外侧受到的剪切应力大于中心受到的剪切应力,行星式抛光的材料去除率明显大于自旋转式抛光的材料去除率。     

Modeling the material removal rate in ultrasonic machining of titanium using dimensional analysis

Titanium is known as the metal of the future because of its excellent combination of properties such as high strength-to-weight ratio, low thermal conductivity, and high corrosion resistance. Machining of titanium, however, is considered as cumbersome with the conventional manufacturing practices, and there is a critical need of developing and establishing cost-effective methods of machining. This investigation is focused on exploring the use of ultrasonic machining, a nontraditional machining process for commercial machining of pure titanium (American Society for Testing and Materials grade-I) and evaluation of material removal rate under controlled experimental conditions. The optimal settings of parameters are determined through experiments planned, conducted, and analyzed using Taguchi method. An attempt has been made to construct a micro-model for prediction of material removal rate in ultrasonic machining of titanium using dimensional analysis. The predictions from this model have been validated by conducting experiments. The microstructure of the machined surface under different experimental conditions has been studied using scanning electron microscopy. A relation was established between the mode of material removal and the energy input rate corresponding to the different process conditions.     

An analytical model of the material removal rate between elastic and elastic-plastic deformation for a polishing process

This paper develops an analytical model for the material removal rate during specimen polishing. The model is based on the micro-contact elastic mechanics, micro-contact elastic-plastic mechanics and abrasive wear theory. The micro-contact elastic mechanics between the pad-specimen surfaces used the Greenwood and Williamson elastic model. The micro-contact elastic-plastic mechanics between specimen and particle, as well as the micro-contact elastic mechanics between particle and pad, are also analyzed. The cross-sectional area of the worn groove in the specimen is considered as trapezoidal area. A close-form solution of material removal rate from the specimen surface is the function of average diameter of slurry particles, pressure, the specimen/pad sliding velocity, Equivalent Young’s modulus, RMS roughness of the pad, and volume concentration of the slurry particle.     

Effect of wafer size on material removal rate and its distribution in chemical mechanical polishing of silicon dioxide film

Chemical mechanical polishing (CMP) is a semiconductor fabrication process. In this process, wafer surfaces are smoothed and planarized using a hybrid removal mechanism, which consists of a chemical reaction and mechanical removal. In this study, the effects of wafer size on the material removal rate (MRR) and its uniformity in the CMP process were investigated using experiments and a mathematical model proposed in our previous research; this model was used to understand the MRR and its uniformity with respect to wafer size. Under constant process conditions, the MRR of a silicon dioxide (SiO₂) film increased slightly along with an increase in wafer size. The increase in MRR may be attributed to the acceleration of the chemical reaction due to a rise in process temperature. Based on the results obtained, the k and α values in the mathematical model are useful parameters for understanding the effect of wafer size on the MRR and its distribution under a uniform, relative velocity. These parameters can facilitate the prediction of CMP results and the effective design of a CMP machine.     

Prediction of the surface roughness and material removal rate in chemical mechanical polishing of single-crystal SiC via a back-propagation neural network

Chemical mechanical polishing (CMP) is a common method for realising the global planarisation and polishing of single-crystal SiC and other semiconductor substrates. The strong oxidant hydroxyl radicals (·OH) generated by the Fenton reaction can effectively oxidise and corrode the SiC substrate, and are thus used to improve the material removal rate (MRR) and surface roughness (Ra) after polishing of SiC during CMP. Therefore, it is necessary to study the material removal mechanism in detail. Based on the modified Preston equation, the effects of the CMP process parameters on the MRR and Ra after polishing of SiC and their relationship were studied, and a prediction model of the CMP process parameters, MRR, and Ra after polishing was also established based on a back-propagation neural network. The MRR initially increased and then decreased, and the Ra after polishing initially decreased and then increased, with increasing FeSO₄ concentration, H₂O₂ concentration, and pH value. The MRR continuously increased with increasing abrasive particle size, abrasive concentration, polishing pressure, and polishing speed. However, the Ra continuously decreased with increasing abrasive particle size and abrasive concentration, increased with increasing polishing pressure, and initially decreased and then increased with increasing polishing speed. The established prediction model could accurately predict the relationship between the process parameters, MRR and Ra after polishing in CMP (relative prediction error of less than 10%), which could provide a theoretical basis for CMP of SiC.     

Material removal characteristics of full aperture optical polishing process

Precision surfaces of optical grade have been in great demand for various applications such as high-power laser systems, astronomical reflecting telescopes glass mirrors, folding mirrors of avionics displays, reflectors, guides for transmission of hot and cold neutron beams for neutron exploration setups, electronic substrate, display covers and substrates for biomedical imaging and sensing, etc. Generation of such surfaces has been a challenge; particularly the polishing operation of optical fabrication process is quite critical which determines the final surface quality. To achieve the required optical surface parameters, a good control and systematic understanding of polishing process and its parameters are required. However, the conventional or full aperture optical polishing process still depends on operator's skills to achieve the target surface quality. To exploit the process to the extent, it is must to have a scientific understanding of material removal behavior of the polishing process, which will lead to the process becoming deterministic. This article has attempted to address this issue. Authors have summarized different material removal theories and discussed various mathematical models as proposed by researchers so far. Attempt has been made to come up with knowledge gaps which are required to be bridged in future.     

随动压力分布下的非球面抛光去除函数

考虑去除函数对数控小工具抛光光学元件精度的影响,提出了如何根据需要加工的非球面参数以及抛光盘参数得到最优去除函数的方法。由于计算非球面上去除函数的核心是准确获得抛光盘与镜面间的动态压力分布,本文提出利用有限元法仿真抛光盘与非球面间的压力分布,并结合经典Preston方程与行星运动模型来得到非球面不同位置处的去除函数。基于随动压力分布模型,分析了沥青盘抛光非球面时在不同抛光位置处去除函数的变化。在曲率半径为1 000mm的球面上进行了去除函数验证实验。结果表明:基于本文理论得到的去除函线型更接近实际情况,皮尔逊系数达到了0.977。本文提出的方法可以方便地调整加工位置来得到相应的压力分布,实现去除函数的优化,对提高加工效率与精度有实际指导意义。