A micro-contact and wear model for chemical–mechanical polishing of silicon wafers

A micro-contact and wear model for chemical–mechanical polishing (CMP) of silicon wafers is presented in this paper. The model is developed on the basis of elastic–plastic micro-contact mechanics and abrasive wear theory. The synergetic effects of mechanical and chemical actions are formulated into the model. A close-form equation of material removal rate from the wafer surface is derived relating to the material, geometric, chemical and operating parameters in a CMP process. The model is evaluated by comparing the theoretical removal rates with those experimentally determined. Good agreement is obtained for both chemically active and inactive polishing processes. The model reveals some insights into the micro-contact and wear mechanisms of the CMP process. It suggests that the removal rate is sensitive to the particle concentration in the slurry, more sensitive to the applied load and operating speed and most sensitive to the surface hardness and slurry particle size. The model may be used to study the effects of different materials, geometry, slurry chemistry and operating conditions on CMP processes.     

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.     

A model to simulate surface roughness in the pad dressing process

Pad dressing, which is one of the most important planarization processes, is widely used in CMP. The estimation of surface roughness under various machining parameters (such as dressing force, diamond density of the dresser, rotational speed of the dresser, different machining paths, etc.) is essential to the pad dressing process. In this study, 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. The deformation of the pad is obtained by using elastic-plastic theory, and 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. A parametric study is conducted to explore the influence on the surface roughness results and the pad dressing interfacial phenomena of operational parameters. The results reveal that a rapid initial improvement followed by a leveling off, manifesting a saturation effect. Moreover, the model shows that a higher dressing force with a dresser speed close to the pad speed and a moderate translation speed increase the material removal rate corresponding with a lower surface roughness dressing.     

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.     

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 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.     

软性粒子抛光石英玻璃的材料去除机理

基于阿伦尼乌斯原理和分子振动理论,分析了软性抛光粒子、石英玻璃和抛光垫之间的弹性与超弹性接触,研究了用软性粒子抛光石英玻璃的材料去除机理。基于理论研究进行了大量的抛光试验,建立了软性粒子抛光石英玻璃的材料去除率模型。理论计算与试验结果表明:在石英玻璃化学机械抛光中,材料的去除主要由抛光粒子与石英玻璃的界面摩擦化学腐蚀作用来实现;单个抛光粒子压入石英玻璃的深度约为0.05nm,且材料去除为分子量级;石英玻璃表层的分子更易获得足够振动能量而发生化学反应实现材料的去除;抛光压力、抛光液中化学试剂种类和浓度以及石英玻璃试件与抛光盘的相对运动速度决定了软性粒子抛光石英玻璃的材料去除率大小。     

一种基于非晶层粘性流动的机械化学抛光模型

通过分析单个微纳米磨粒滑动接触的分子动力学模拟的研究结果，提出了在典型的机械化学抛光（CMP）过程中芯片表面材料的去除应为表面非晶层物质粘性流动所致的新观点。基于这种机理，应用微观接触力学和磨粒粒度分布理论建立了一种新的表征CMP过程材料去除速率的数学模型。模型中引入了一个表征单个磨粒去除芯片表面非晶层能力的比例系数k，k综合反映了磨粒的机械作用、抛光液对芯片表面的化学作用和芯片的材料特性。通过实验验证发现该模型的理论预测值与实验测定值十分吻合。     

Effects of particle size, polishing pad and contact pressure in free abrasive polishing

The objective of this research is to better understand the mechanisms of material removal in the free abrasive polishing process. Experiments were carried out to understand the effects of particle size, polishing pad and nominal contact pressure on the wear rate and surface roughness of the polished surface. A theoretical model was developed to predict the relationship between the polishing parameters and the wear rate for the case of hard abrasive particles sandwiched between a soft pad and a workpiece (softer than the abrasive particles). Experimental results and theoretical predictions indicate that the wear rate increases with an increase in particle size, hardness of polishing pad and nominal contact pressure, and with a decrease in elastic modulus of the polishing pad. Surface roughness increases with an increase in particle size and hardness of polishing pad, and nominal contact pressure has little effect on the roughness. A dimensionless parameter, wear index which combines all of the preceding parameters, was introduced to give a semi-quantitative prediction for the wear rate in free abrasive polishing. It is also suggested that when polishing hard material, in order to achieve a high materials removal rate and a smooth surface, it is preferable to use diamond as the polishing particles because of their high deformation resistance.     

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。     

Estimating the mechanical properties of polyurethane-impregnated felt pads

Chemical mechanical polishing (CMP) is an essential process in semiconductor fabrication. The results of CMP process are determined with the selection of consumables and process parameters. The polishing pad transports the slurry to the interface between the polishing pad and wafer and obtains material removal planarity. The mechanical properties of the polishing pad should be studied to analyze the material removal mechanism of CMP because polishing pad deformation is directly related to material removal rate and its uniformity. Various studies have investigated the stress distribution of the CMP process by using the elastic modulus and Poisson’s ratio of the polishing pad. However, these aspects of polishing pad have not been fully elucidated. In this study, we estimated the mechanical properties of commercial polyurethane-impregnated felt pads by comparing the experimentally measured compressive deformation amounts with finite element analysis results.     

A mixed elastohydrodynamic lubrication model with layered elastic theory for simulation of chemical mechanical polishing

Mixed elastohydrodynamic lubrication (mixed EHL) model has been successfully used to study phenomena in chemical mechanical polishing (CMP) process. However, in various mixed EHL simulation frameworks, a polishing pad's deformation cannot correctly be described by adopted models for pad deformation such as elastic half-space model and Winkler elastic foundation model. Thus, a more accurate model for pad deformation is needed, since this is the prerequisite for an accurate prediction of contact pressure and material removal rate, which is critical for improvement of polishing quality. In this paper, a layered elastic theory, which is frequently used to calculate flexible pavement response to truck loading, is introduced into the mixed EHL model. It is found that this theory has a similar accuracy to the traditional 3D finite element method for calculating the pad deformation. However, its computational cost is much lower, which is especially important for accurate and efficient simulation of mechanical behavior and material removal rate (MRR) in CMP. In order to highlight benefits of the proposed theory, simulations are carried out based on three different pad deformation models with the mixed EHL model. The pad deformation behavior is found to have a significant influence on the final simulation results, especially the MRR prediction. By comparing the different simulation models, the proposed layer elastic theory is found to be an optimal model for describing the polishing pad deformation behavior in CMP and can provide accurate simulation results on contact pressure distribution and the material removal rate.     

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。     

Water-jet-assisted diamond disk dressing characteristics of CMP polishing pad

This paper presents an experimental investigation of the dressing characteristics of a porous polishing pad using a combination of water-jet dressing (WJC) and traditional diamond disk dressing (DDC). The WJC and DDC dressing mechanisms were integrated in order to improve the dressing efficiency. The pad recovery test was performed. In this test, the real-time friction force was determined, scanning electron microscope images were obtained, and the dressed surface topography after prolonged operation without conditioning was examined. The pad cut rate and the rate of removal of the copper substrate by the polishing process were investigated by comparing the results of the WJC?+?DDC, only DDC, and only WJC methods. The experimental results showed that although the WJC can remove the slurry residue from the pad surface and consumes less pad material, it cannot remove the glazed layer formed as a result of plastic deformation, which contributes to the low material removal rate. On the other hand, DDC can remove the glazed layer of the pad and restore the pad asperities; however, a few residual chips still remain on the sides of the pores or inside the pores. WJC?+?DDC cannot only remove the embedded slurry particulates and the glazed layer, but also remove the slurry residue accumulated on the pad surface and restore the pad asperities. In addition, the chip residues in the pores, created by the diamond grit, are completely removed by the WJC?+?DDC conditioning process; the removal of the chip residue helps in obtaining the highest material removal rate. In summary, WJC?+?DDC can be used as an effective pad conditioning method.     

Nano particles’ behavior in non-Newtonian slurry in mechanical process of CMP

Thin fluid film is thought to be formed between the wafer surface and the pad asperity. Hydrodynamic pressure on the surface asperity is periodically generated when particles are passing through it. Fatigue fracture occurs under the effect of periodic pressure, and the fatigue begins from the top to the bottom of the asperity. The removal rate is calculated based on the energy-balance fracture theory. Particle size and its relative velocity are important parameters that affect the polishing effect. Using the multiphase model and the power–law viscosity model of the slurry, particle’s velocity and its distribution in the slurry are numerically calculated. The results indicate that the slurry film thickness needs to be in the same order of the particle size that the particle can generate effective hydrodynamic pressure to remove the asperity materials.     

Pad surface and coefficient of friction correlation analysis during friction between felt pad and single-crystal silicon

In wafer polishing pad surface plays a crucial role in the polishing process. With the increase of friction time between pad and wafer, the pad becomes flattened or glazed with particles clogging the pores of the pad and forming a layer of slurry residue and wafer particles, leading to changes of COF, material removal rates and higher defects on the wafer surface. Thus, this study aims to determine the correlation between pad surface deformation, slurry adhesive rate and Coefficient of friction (COF) during friction between felt pad and single -crystal silicon, to analyze the relationship between pad condition and COF. The real-time COF between felt pad and single-crystal silicon wafer are tested which are sorted in groups depending on various loads and oscillation frequencies and surfaces of felt pads measuring by Scanning electron microscope (SEM) are compared. The correlation between pad surface deformation and abrasive adhesion and COF is evaluated through analyzing the experiment results.

     

基于不同微观固体接触模型的轮轨表面变形特性分析

针对轮轨表面接触变形问题,采用不同的统计型微观固体接触模型,即Greenwood-Williamson （GW）模型,Chang-Etsion-Bogy （CEB）模型和Zhao-Maietta-Chang （ZMC）模型,研究轮轨接触表面变形特性。利用Newton-Raphson方法对微观固体接触模型公式进行求解,并同时求解间隙方程和载荷平衡方程。考虑不同粗糙度和不同塑性指数下各微观固体接触模型的压力分布情况,以及接触半径随载荷的变化情况。并将不同微观固体接触模型的结果和Hertz模型结果对比,结果表明弹塑性微观接触模型（CEB,ZMC）比弹性模型（GW）有着更小的接触压力以及更宽的接触半径,最大压力均小于最大Hertz接触压力,接触半径均大于Hertz接触半径。     

抛光垫特性对抛光中流体运动的影响分析

抛光垫表面特性能可大大改变抛光液的流动情况,从而影响化学机械抛光的抛光性能。考虑抛光垫粗糙度和孔隙等对抛光液流动的影响,提出了一个初步的晶片级流动模型,并用数值模拟方法研究了不同参数条件(载荷和速度的变化等)下抛光液的流动特征。计算结果表明增加外载荷将导致粗糙峰的磨损概率增加,增加剪切速率则提高了剪切应力,均可导致高材料去除率。模型能较好理解材料去除机制和输运,从而有助于对化学机械抛光机制的了解。     

CMP过程中抛光盘作用外力的影响因素分析

根据芯片/磨粒/抛光盘三体接触当量梁的弯曲假设,建立了更加准确合理的抛光盘作用在磨粒上的外力的理论模型,并通过实例对前人的模型和新模型进行对比.最后借用已有分子动力学模拟结果对理论模型进行验证.结果表明作用在单个磨粒上的外力与磨粒的直径、磨粒的浓度、抛光盘的弹性模量有关,理论计算值与分子动力学模拟结果基本一致.     

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.