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.     

磨粒流研抛伺服阀阀芯喷嘴的冲蚀磨损分析

为了研究固液两相磨粒流对伺服阀阀芯喷嘴的研抛性能,从冲蚀磨损的角度对比分析了不同磨粒硬度下的磨粒流研抛效果。利用计算流体力学方法,求解分析了磨粒流研抛伺服阀阀芯喷嘴时流场中的冲蚀磨损特性,采用电子显微镜以及扫描电镜仪检测伺服阀阀芯喷嘴零件经磨粒流研抛前后的表面粗糙度和表面形貌。实验结果表明:采用碳化硅磨粒和白刚玉磨粒加工后的伺服阀阀芯喷嘴主干通道、交叉孔以及小孔区域的粗糙度分别由1.1μm、0.823μm、0.743μm降低为0.735μm、0.721μm、0.571μm和1μm、0.747μm、0.696μm。在本试验中碳化硅磨粒的加工效果优于白刚玉磨粒,即具有高磨粒硬度的磨粒研抛效果好。检测结果显示,磨粒流研抛技术可有效改善伺服阀阀芯喷嘴的表面质量;提高磨粒硬度可提高磨粒流的研抛效果;伺服阀阀芯喷嘴的交叉孔以及小孔区域的表面质量要高于主干通道的表面质量。     

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.     

Modeling the effects of abrasive size, surface oxidizer concentration and binding energy on chemical mechanical polishing at molecular scale

No conclusive results have been proposed for the influence of the abrasive particle size on the material removal during the chemical mechanical polishing (CMP). In this paper, a mathematical model as a function of abrasive size and surface oxidizer concentration is presented for CMP. The model is proposed on the basis of the molecular-scale removal theory, probability statistics and micro contact mechanics. The influence in relation to the binding energy of the reacted molecules to the substrate is incorporated into the analysis so as to clarify the disputes on the variable experimental trends on particle size. The predicted results show that the removal rate increases sub-linearly with the abrasive particle size and oxidizer concentration. The model predictions are presented in graphical form and show good agreement with the published experimental data. Furthermore, variations of material removal rate with pressure, pad/wafer relative velocity, and wafer surface hardness, as well as pad characteristics are addressed. Results and analysis may lead further understanding of the microscopic material removal mechanism from molecular-scale perspective.     

Abrasive removal depth for polishing a sapphire wafer by a cross-patterned polishing pad with different abrasive particle sizes

The paper establishes a new theoretical model for abrasive removal depth for polishing a sapphire wafer using chemical mechanical polishing with a polishing pad that has a cross pattern. The theoretical model uses binary image pixel division to calculate the pixel polishing times. An abrasive contact model for single-pixel multiple abrasive particles, to estimate the contact force between a single abrasive particle and the wafer, is then established. When the contact force is calculated, it is possible to calculate the abrasive depth of a single abrasive particle on the surface of the sapphire wafer. Using this theoretical model, carring a numerical simulation with a slurry of the same concentration, but with different abrasive particle diameters, determines the removal volume and average abrasive removal depth at each pixel position and the surface condition of the wafer. The simulation result is also compared with experimental data, in order to verify that the new model is feasible.     

硅晶片化学机械抛光材料去除机制与模型

通过分析软质层的形成、作用以及纳米磨料的自身变形对材料去除的影响,改进了CMP过程的接触力学模型;分析了纳米磨料自身变形量对磨料嵌入硅晶片基体材料的深度的影响,以及纳米磨料硬度对抛光表面粗糙度的影响。结果表明：软质层的存在增加了单个纳米磨料所去除材料的体积,且对基体材料有保护作用,减小了纳米磨料嵌入基体材料的深度;纳米磨料的自身变形抵消了纳米磨料嵌入基体材料的切削深度,从而也决定了抛光表面的粗糙度;纳米磨料的自身变形量与纳米磨料的硬度有关,硬度低的纳米磨料自身变形量大,因而切削深度小,抛光后表面的粗糙度值低。     

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.     

Surface roughness modeling in chemically etched polishing of Si (100) using double disk magnetic abrasive finishing

Abstract

The present paper focuses on proposing a new method for determining the surface roughness of chemically etched polishing of Si (100) using double disk magnetic abrasive finishing (DDMAF). Based on chemical etching in KOH solution Vicker’s hardness of Si (100) at different concentration of KOH was determined in context to chemical etching phenomenon. A mathematical relationship was established to relate Vicker’s hardness of Si (100) as a function of the concentration of KOH. The penetration depth of abrasive particle into Si (100) workpiece was determined considering viz; the normal force acting on the abrasive particle under the influence of magnetic flux density and Vicker’s hardness of etched Si (100). The other modeling variables such as wear constant, penetration area of the abrasive particle into Si (100) workpiece which is dependent on the penetration depth of abrasive particle was modified in terms of magnetic flux density and concentration of KOH. The process parameters such as working gap, abrasive mesh number and the rotational speed of the primary magnet were also considered in modeling the surface roughness. The results of surface roughness obtained by the model were also experimentally validated. The theoretical and experimental findings agreed well with each other.     

磨粒对ADZ复合陶瓷材料磨损性能的影响

采用块 -块摩擦磨损试验机在不同磨粒的 5 %NaOH泥浆中 ,对氧化铝增强四方氧化锆多晶陶瓷材料 (ADZ)的磨损性能进行了研究。研究结果表明尖锐磨粒对ADZ复合陶瓷材料磨损的影响要比球形磨粒严重的多 ,磨料硬度是影响陶瓷材料磨损率的重要因素 ,磨损率随磨粒硬度的提高而增大。在不同形状的SiO2 磨粒的泥浆中ADZ陶瓷材料的主要磨损机理为塑性变形和微犁削。在高硬度Al2 O3磨料的泥浆中ADZ陶瓷材料磨损表面以断裂机制占主导地位。     

微通道反应器沟槽底面的磨料水射流抛光研究

针对燃料电池微通道反应器的沟槽底面抛光技术难题,开展磨料水射流沟槽抛光仿真与试验研究.采用FLUENT软件,对不同工艺参数下沟槽底部剪切力分布进行了数值模拟;根据仿真结果进行316L不锈钢材料的单沟槽抛光工艺试验,检测分析不同抛光参数下单沟槽底面形貌、材料去除率以及表面粗糙度的变化规律;根据单沟槽底面几何精度和表面粗糙...     

基于修正Preston方程的百页轮抛光材料去除深度建模

由于百页轮具有一定的柔性,故实际材料去除深度与名义抛光深度不一致,直接影响抛光效率及表面质量的控制。基于Hertz弹性接触理论建立了抛光接触区抛光压力和切削速度分布函数,并依据修正的Preston方程建立了材料去除深度模型,据此确定了影响材料去除深度的关键抛光工艺参数(磨粒粒度、主轴转速、百页轮变形量和进给速度),获得了百页轮抛光接触区的材料去除深度分布规律和关键抛光工艺参数对材料去除深度的影响规律。最后,通过模拟仿真和抛光实验验证了所建模型和影响规律的正确性,结果表明,该模型可以较好地预测百页轮柔性抛光的材料去除深度。     

单晶硅同质互抛实验研究

以材料的去除率和表面粗糙度为评价指标设计对比实验,验证了硬脆材料互抛抛光的可行性,得到了抛光盘转速对硬脆材料互抛的影响趋势和大小。实验结果表明：当抛光压力为48 265 Pa（7 psi）、抛光盘转速为70 r/min时,自配抛光液互抛的材料去除率为672.1 nm/min,表面粗糙度为4.9 nm,与传统化学机械抛光方式的抛光效果相近,验证了硬脆材料同质互抛方式是完全可行的;互抛抛光液中可不添加磨料,这改进了传统抛光液的成分;采用抛光液互抛时,材料去除率随着抛光盘转速的增大呈现先增大后减小的趋势,硅片的表面粗糙度随着抛光盘转速的增大呈先减小后增大的趋势。     

纳米聚集氧化硅固定磨料抛光布的抛光特性

针对传统磨料的固定磨料抛光布容易在加工表面产生划伤,以及材料去除效率低等问题,提出了采用微米级球形聚集氧化硅粒子的固定磨料抛光布。将纳米聚集氧化硅粒子添加到抛光布中,用pH为10.5的碱性水溶液替代传统的抛光液,进行了Si基板的的抛光加工试验。与传统采用不规则形状天然氧化硅及球形熔融氧化硅固定磨料抛光布进行了比较,得到了纳米聚集氧化硅的固定磨料抛光布的加工特性,并讨论了它的基本参数对加工特性的影响。实验得到了与现行纳米抛光液(重量百分比为3%,pH=10.5)相同的材料去除率,加工表面粗糙度降低了约30%。与传统不规则形状天然氧化硅磨料抛光布相比,纳米聚集氧化硅抛光布的磨料为球形,弹性系数仅为其1.4%~60%,因此不易划伤抛光表面。与熔融氧化硅抛光布相比,纳米聚集氧化硅抛光布在pH为10.5的碱性水溶液中磨料表面可吸附的[-OH]离子提高了25倍,使得液相化学去除作用增大至去除率的70%以上。另外,随着纳米聚集氧化硅的微米粒径的增大,固定磨料抛光布的纳米级加工表面粗糙度几乎不变,但对前加工面表面粗糙度的去除能力明显增大,表现出微米粒径效应。     

Predicting the Material Removal in Polishing: The Applicability of Two Types of Statistical Models

This article develops two statistical rough surface models to investigate the material removal rate in surface polishing. Model I implies that the contact between two surfaces is equivalent to that between a composite surface and a plane; but Model II is without the equivalent surface concept. The prediction differences of the two models were first investigated with the aid of contact mechanics. The analysis shows that the relative error of the predictions by the two models could be minimized by considering the interactions between asperities, and that this error increases with the separation of the mean planes, but decreases with the asperity density, asperity radius and standard deviation of the asperity height. By extending the models to study the material removal rate in polishing, it was found that asperity interaction is an important factor in a statistical modelling of polishing, and that with a given separation of the reference planes of the pad and workpiece surfaces, the material removal rate increases with the volume concentration of abrasive particles and varies with the pad roughness. The study also showed that the microstructure of a polishing pad has a significant effect on the material removal rate of a polishing.     

含污染物油润滑条件下的磨粒磨损研究

概述了含污染物油润滑条件下的磨损试验方法，分析了磨粒尺寸、磨粒含量；材料硬度和材料表面粗糙度等试验参数对含污染物油润滑条件下材料的磨损性能的影响，结果表明其磨损机理主要是点蚀、犁削和熔着磨损，并提出了解决措施。     

使用优化的固着磨料磨盘全口径加工碳化硅反射镜

为提高碳化硅非球面反射镜的加工质量,对加工中涉及的固着磨料工艺去除函数进行了研究。在早期的实验中测试了圆形丸片的去除函数,引入填充因子的概念来评价实验所获得的去除函数,定量获得了丸片结构与填充因子之间的关系。为了提高填充因子和磨盘的加工特性,根据圆形丸片的实验结果优化了磨头的结构并基于Matlab软件模拟了新型磨头的去除函数。在全口径范围考察了磨头工作的稳定性,并在相同加工参数条件下完成了固着磨料和散粒磨料的加工实验。为了对理论模拟和实验结果进行比较,引入结构相似度指数的概念来评价全口径反射镜去除量模拟结果与实验结果之间的相似程度。结果显示,实验得到的结构相似度指数达到了0.425 7,证明优化后的固着磨料磨头在大口径碳化硅反射镜加工方面极有应用前景。     

A novel polishing method for single-crystal silicon using the cavitation rotary abrasive flow

Traditional low-pressure abrasive flow polishing can produce highly smooth surfaces, but the efficiency of this method is too low for polishing of hard-brittle materials parts. This paper proposes a novel cavitation rotary abrasive flow polishing (CRAFP) method. The energy generated from the cavitation bubble collapse is used to increase the kinetic energy of the abrasive particles in the low-pressure abrasive flow and the motion randomness of the abrasive particles near the wall; thereby, the efficiency and quality of low-pressure abrasive flow polishing are improved. The CRAFP mechanism was first introduced, and then the characteristics of the CRAFP process were investigated using computational fluid dynamics (CFD)-based abrasive flow simulation. Subsequently, a single-crystal silicon wafer polishing test was carried outperformed to verify the validity of the CRAFP method. The polishing results were compared with those of the traditional low-pressure abrasive flow polishing method. After 8 h of polishing using the CRAFP method and the traditional low-pressure abrasive flow polishing method, the surface roughness of the workpiece decreased to7.87 nm and 10.53 nm, respectively. Furthermore, by starting at similar initial roughness values, the polishing time required to reduce the roughness to 12 nm was 3.5 h and 6 h, respectively. The experimental results demonstrated that CRAFP can satisfy the surface requirements of single-crystal silicon (R_a < 12 nm) and exhibit high polishing efficiency and good quality.     

Hydrodynamic analysis of chemical mechanical polishing process

Chemical Mechanical Polishing (CMP) refers to a material removal process done by rubbing a work piece against a polishing pad under load in the presence of chemically active abrasive containing slurry. The CMP process is a combination of chemical dissolution and mechanical action. The mechanical action of CMP involves hydrodynamic lubrication. The liquid slurry is trapped between the work piece (wafer) and pad (tooling) forming a lubricating film. For the first step to understand the mechanism of the CMP process, hydrodynamic analysis is done with a semiconductor wafer. Slurry pressure distribution, resultant forces and moments acting on the wafer are calculated in typical conditions of the wafer polishing, and then nominal clearance of the slurry film, roll and pitch angles at the steady state are obtained.     

GMR硬盘磁头自由磨粒抛光极尖沉降的研究

磁头表面极尖沉降(PTR)是影响硬盘存储密度的关键因素之一。采用修正环形浮动块研磨抛光机和自由磨粒抛光方式抛光GMR硬盘磁头,并用原子力显微镜测试磁头的PTR,抛光试验表明:PTR与抛光盘表面形貌参数、磨粒大小、抛光压力和抛光盘转速有关。抛光盘表面取合适的形貌参数可以获得小的PTR;磨粒越小,PTR越小;抛光压力越大,PTR越小;抛光盘转速越小,PTR越小。研究结果有助于优化抛光工艺,在获得最佳PTR的同时,兼顾效率与成本的因素。