A model for chemical-mechanical polishing of a material surface based on contact mechanics

A new contact-mechanics-based model for chemical-mechanical polishing is presented. According to this model, the local polish rate is controlled by the pressure distribution between features on the wafer and the polishing pad. The model uses an analysis based on the work by Greenwood to evaluate this pressure distribution taking into account pad compliance and roughness. Using the model, the effects of pattern density, applied down-force, selectivity, pad properties, etc. on the evolution of the wafer surface can be readily evaluated. The interaction between individual pad asperities and the wafer pattern is investigated in detail. It is shown that the pressure distribution between an asperity and the wafer surface is discontinuous at edges of features that have different nominal polish rates and that this pressure discontinuity dominates the polish rate and dishing of narrow features.The model is implemented as an algorithm that calculates the evolution of the profile of a set of features on the wafer during the polishing process. The model can be applied to chemical-mechanical polishing used for oxide planarization, metal damascene or shallow trench isolation.     

Characterization and Control of Residual Stress and Curvature in Anodically Bonded Devices and Substrates with Etched Features

While anodic bonding is commonly used in a variety of microelectromechanical systems (MEMS) applications, devices and substrates that incorporate this processing technique are often subjected to significant residual stress and curvature that create post-processing and reliability issues. Here, using an anisothermal anodic bonding procedure, residual stresses and the resulting wafer curvature in these structures are controlled by varying the initial bond temperatures of the silicon and Pyrex wafers independently. Residual stresses are quantified by measuring bulk wafer curvature and, locally, stress concentrations are measured using infrared photoelasticity accompanied by 3-D thermomechanical finite element analysis. Based on the good agreement between numerical predictions and experimental results, this process can be used to determine the bulk post-bond wafer curvature and to reduce the likelihood of structural failure at these sites, by changing the residual stresses from tensile in nature, which may drive initiation and growth of cracks, to compressive, which can suppress such failures.     

X射线衍射法测量碳化硅单晶的残余应力

为了准确评估晶体的质量、提高器件的使用性能,本文围绕单晶碳化硅材料残余应力方面开展了相关研究工作.首先通过对原有的多重线性回归分析方法加以改进,推导出适用于求解六方晶系单晶碳化硅试样所处应力状态的相关理论.其次,采用该方法对沿着[1010]取向生长的6H-SiC单晶片进行了残余应力检测,同时选用{214}晶面族作为测量衍射面.最后,探究了来源于不同晶面组数的数据进行计算时对残余应力测量结果的影响.结果显示:采用多重线性回归分析方法可以实现单晶6H-SiC的面内残余应力的测定;当给定无应力晶面间距d;的精确值时,该应力结果的误差高于选用5组以上(hkl)晶面数计算得到的残余应力结果的误差;如果d;未知,则随着参与应力计算的晶面组数的增加,平面残余应力的误差结果会逐渐降低并趋于平稳.这表明实验测定的残余应力结果具有较高的精度.另外,为了保证实验测得的应力结果的可靠性,应该选用六组及以上衍射面数通过多元回归分析方法来求解单晶碳化硅试样所处的残余应力状态.     

X射线衍射法测量碳化硅单晶的残余应力

为了准确评估晶体的质量、提高器件的使用性能,本文围绕单晶碳化硅材料残余应力方面开展了相关研究工作.首先通过对原有的多重线性回归分析方法加以改进,推导出适用于求解六方晶系单晶碳化硅试样所处应力状态的相关理论.其次,采用该方法对沿着[1010]取向生长的6H-SiC单晶片进行了残余应力检测,同时选用{214}晶面族作为测量衍射面.最后,探究了来源于不同晶面组数的数据进行计算时对残余应力测量结果的影响.结果显示:采用多重线性回归分析方法可以实现单晶6H-SiC的面内残余应力的测定;当给定无应力晶面间距d;的精确值时,该应力结果的误差高于选用5组以上(hkl)晶面数计算得到的残余应力结果的误差;如果d;未知,则随着参与应力计算的晶面组数的增加,平面残余应力的误差结果会逐渐降低并趋于平稳.这表明实验测定的残余应力结果具有较高的精度.另外,为了保证实验测得的应力结果的可靠性,应该选用六组及以上衍射面数通过多元回归分析方法来求解单晶碳化硅试样所处的残余应力状态.     

Study of temperature distributions in wafer exposure process

 During the exposure process of photolithography, wafer absorbs the exposure energy, which results in rising temperature and the phenomenon of thermal expansion. This phenomenon was often neglected due to its limited effect in the previous generation of process. However, in the new generation of process, it may very likely become a factor to be considered. In this paper, the finite element model for analyzing the transient behavior of the distribution of wafer temperature during exposure was established under the assumption that the wafer was clamped by a vacuum chuck without warpage. The model is capable of simulating the distribution of the wafer temperature under different exposure conditions. The flowchart of analysis begins with the simulation of transient behavior in a single exposure region to the variation of exposure energy, interval of exposure locations and interval of exposure time under continuous exposure to investigate the distribution of wafer temperature. The simulation results indicate that widening the interval of exposure locations has a greater impact in improving the distribution of wafer temperature than extending the interval of exposure time between neighboring image fields. Besides, as long as the distance between the field center locations of two neighboring exposure regions exceeds the straight distance equals to three image fields wide, the interacting thermal effect during wafer exposure can be ignored. The analysis flow proposed in this paper can serve as a supporting reference tool for engineers in planning exposure paths. Received on 11 October 2000 / Published online: 29 November 2001     

Nano-tribological study on a super-hydrophobic film formed on rough aluminium substrates

A novel super-hydrophobic stearic acid (STA) film with a water contact angle of 166^o was prepared by chemical adsorption on aluminum wafer coated with polyethyleneimine (PEI) film. The micro-tribological behavior of the super-hydrophobic STA monolayer was compared with that of the polished and PEI-coated Al surfaces. The effect of relative humidity on the adhesion and friction was investigated as well. It was found that the STA monolayer showed decreased friction, while the adhesive force was greatly decreased by increasing the surface roughness of the Al wafer to reduce the contact area between the atomic force microscope (AFM) tip and the sample surface to be tested. Thus the friction and adhesion of the Al wafer was effectively decreased by generating the STA monolayer, which indicated that it could be feasible and rational to prepare a surface with good adhesion resistance and lubricity by properly controlling the surface morphology and the chemical composition. Both the adhesion and friction decreased as the relative humidity was lowered from 65% to 10%, though the decrease extent became insignificant for the STA monolayer. The project supported by the National Natural Science Foundation of China (50375151, 50323007, 10225209) and the Chinese Academy of Sciences (KJCX-SW-L2)     

超声瑞利波测试材料表面载荷应力的实验研究

实验研究了利用超声瑞利波传播特性测试材料表面应力的方法.在测试过程中采用回振法测声速,以分辨应力作用引起声速的徽小变化;并设计夹具实现探头与试样之间的稳定耦合和弹性接触,精简了实验机构,提高了实验精度.研究结果表明,在应力作用下,平行和垂直于应力方向传播的瑞利波发生了相应的变化:应力较小时,声速随应力变化较快;随着应力...     

核-壳结构PS/CeO_2复合磨料的制备及其氧化物化学机械抛光性能

以无皂乳液聚合方法制备的聚苯乙烯(PS)微球为内核,硝酸铈为铈源,六亚甲基四胺为沉淀剂,采用液相工艺制备了PS/CeO2复合颗粒.利用XRD、TEM、SAED、FESEM、EDAX等手段,对所制备样品的物相结构、形貌、粒径大小和元素成分组成进行表征.将所制备的复合磨料用于硅晶片热氧化层的化学机械抛光,用AFM观察抛光表面的微观形貌,并测量表面粗糙度.结果表明,所制备的PS/CeO2复合颗粒具有核-壳结构,呈近似球形,粒径在250～300nm,PS内核表面被粒径在5～10nm的CeO2纳米颗粒均匀包覆,壳层的厚度为10～20nm.抛光后的硅热氧化层表面在5μm×5μm范围内粗糙度Ra值和RMS值分别为0.188nm和0.238nm,抛光速率达到461.1nm/min.     

基于分子量级的化学机械抛光界面动力学模型研究

考虑抛光液/芯片的相界面氧化剂浓度和芯片氧化薄膜缺陷对材料去除机理的影响,提出化学机械抛光(CMP)中材料去除机理的量级估算方法,应用化学动力学及传质学等理论估算氧化薄膜的扩散深度量级和生成速率,采用纳米压痕仪模拟单个磨粒在芯片表面的压痕作用,应用线性回归方法分析载荷70 nN下,磨粒压入芯片的深度量级为10-11 m.结合模型估算,证实了CMP材料去除机理为单分子层去除机理.结果表明,减小氧化膜厚度可以提高材料去除率,估算结果与他人试验结果相吻合.为进一步研究CMP单分子层材料去除机理提供了理论依据.     

Detection of liquid–vapor–solid triple contact line in two-phase heat transfer phenomena using high-speed infrared thermometry

Heat transfer in complex physical situations such as nucleate boiling, quenching and dropwise condensation is strongly affected by the presence of a liquid–vapor–solid triple contact line, where intense energy transfer and phase change occur. A novel experimental technique for the detection of the liquid–vapor–solid line in these situations is presented. The technique is based on high-speed infrared (IR) thermometry through an IR-transparent silicon wafer heater; hence the name DEPIcT, or DEtection of Phase by Infrared Thermometry. Where the heater surface is wet, the IR camera measures the temperature of the hot water in contact with the heater. On the other hand, where vapor (whose IR absorptivity is very low) is in contact with the heater, the IR light comes from the cooler water beyond the vapor. The resulting IR image appears dark (cold) in dry spots and bright (hot) in wetted area. Using the contrast between the dark and bright areas, we can visualize the distribution of the liquid and gas phases in contact with the heater surface, and thus identify the liquid–vapor–solid contact line. In other words, we measure temperature beyond the surface to detect phases on the surface. It was shown that even small temperature differences (∼1 °C) can yield a sharp identification of the contact line, within about 100 μm resolution. DEPIcT was also shown to be able to detect thin liquid layers, through the analysis of interference patterns.     

纳米CeO2颗粒的制备及其化学机械抛光性能研究

以硝酸铈和六亚甲基四胺为原料制备出不同粒径的纳米CeO2粉体颗粒,将纳米CeO2粉体配制成抛光液并用于砷化镓晶片的化学机械抛光.结果表明,不同尺寸的纳米磨料具有不同的抛光效果,采用粒度8 nm的CeO2磨料抛光后微观表面粗糙度最低(0.740 nm),采用粒度小于或大于8 nm的CeO2磨料抛光后其表面粗糙度值均较高.通过简化的固-固接触模型分析,认为当粒度过小时,磨料难以穿透软质层,表现为化学抛光为主,表面凹坑较多,表面粗糙度较高;当粒度大于一定值时,随着磨料粒度增加,嵌入基体部分的深度加大,使得粗糙度出现上升趋势.提出当磨料嵌入晶片表面的最大深度等于或接近于软质层厚度时,在理论上应具有最佳的抛光效果.     

Loading effect on ACPD of a crack in ferromagnetic material

The loading effect on alternating current potential drop (ACPD) for a ferromagnetic material containing a two-dimensional surface crack was investigated under opening mode loading without shear (mode I). The change in potential drop due to load was obtained with and without a magnetic field around the specimen. To remove the magnetic field from the circumference of the specimen, a new measuring system using the characteristic of coaxial transmission line was made. When the magnetic field does not exist around the specimen, the change in potential drop with load is governed by the change in electromagnetic properties near the crack tip. The results obtained by using the new measuring system are the basis for an application of the ACPD technique to the experimental determination of the stress intensity factor, since they are independent of the arrangement of the measuring probe lines and the current supply lines. The relationship between the change in potential drop and the change in load is linearized by demagnetization. The change in potential drop per unit change in the stress intensity factor is independent of the crack length.     

Experimental investigation of micro-scale temperature transients in sub-cooled flow boiling on a horizontal heater

Surface temperature fluctuations that occur locally underneath departing bubbles in pool boiling are shown to result in local heat transfer coefficients ranging from 1 to 10 kW/cm². These estimates were reported in the literature involved both numerical and experimental approaches. Significantly higher heat fluxes are associated with flow boiling than pool boiling under similar conditions of wall superheat and liquid subcooling (e.g. at boiling inception and at critical heat flux). These enhancements are primarily caused by the convective transport, acceleration/distortion of the bubble departure process as well as the resultant potential enhancement of the local surface temperature fluctuations.In this study we measure the surface temperature fluctuations using temperature micro/nano-sensors fabricated on a silicon wafer during flow boiling on the silicon wafer which is heated from below. The silicon wafer is clamped on a constant heat flux type calorimeter consisting of a vertical copper cylinder with embedded cartridge heaters and K-type thermocouples. Micro/nano-thermocouples (thin film thermocouples or “TFT”) are fabricated on the surface of the silicon wafer. High speed data acquisition apparatus is used to record temperature data from the TFT at 1 kHz. A fluorinert was used as the test fluid (PF-5060, manufacturer: 3M Co.). The calorimeter and surface temperature measurement apparatus is housed in a test section with glass walls for visual observation. The liquid is pumped from a constant temperature bath to maintain a fixed subcooling during the experiments under steady state conditions. The transient temperature data from the FFT array during flow boiling on the silicon wafer is analyzed using fast Fourier transform (FFT). The FFT data is analyzed as a function of the wall heat flux and wall superheat. The number of temperature peaks in the FFT data is observed to increase with increase in wall heat flux and the peaks are found to cover a wider spectrum with peaks at higher frequencies with enhancement of heat flux. The surface temperature fluctuations, especially at small length and time scales, are perturbed potentially by the coupled hydrodynamic and thermal transport processes, resulting in enhanced local and global heat flux values. Boiling incipience condition and the flow boiling data are compared with correlations reported in the literature.     

DYNAMIC RESPONSE OF THE CATENARY RISER IN DEEP-SEA MINING SYSTEMS 1)

基于有限元模型,模拟、分析深海采矿系统悬链线立管在海流和水面船运动约束下的动力响应。结果表明：悬链线立管的最大等效应力和最大位移随时间呈周期性变化,且存在半个周期的相位差;当水面船运动到最高点时,悬链线立管位移达到最大值。悬链线立管最大 等效应力和最大位移随水面船运动位移幅值的增加而增加,随运动周期的增加而减小。进一步对比发现,水面船运动位移和周期对立管等效应力的影响大于对其位移的影响。     

Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition

The traditional contour method maps a single component of residual stress by cutting a body carefully in two and measuring the contour of the cut surface. The cut also exposes previously inaccessible regions of the body to residual stress measurement using a variety of other techniques, but the stresses have been changed by the relaxation after cutting. In this paper, it is shown that superposition of stresses measured post-cutting with results from the contour method analysis can determine the original (pre-cut) residual stresses. The general superposition theory using Bueckner’s principle is developed and limitations are discussed. The procedure is experimentally demonstrated by determining the triaxial residual stress state on a cross section plane. The 2024-T351 aluminum alloy test specimen was a disk plastically indented to produce multiaxial residual stresses. After cutting the disk in half, the stresses on the cut surface of one half were determined with X-ray diffraction and with hole drilling on the other half. To determine the original residual stresses, the measured surface stresses were superimposed with the change stress calculated by the contour method. Within uncertainty, the results agreed with neutron diffraction measurements taken on an uncut disk.     

声程差与应力强度因子的关系

基于弹性状态下力对材料声折射率及试件厚度的影响,推导了含裂纹的试件受力前后,超声纵波经其前后表面反射及透射时声程的变化,得到了应力强度因子与声程差的关系,为通过声程差的变化确定裂尖应力强度因子打下了基础。     

硅晶体纳米压痕试验与应力场分析

采用纳米压入法测量了4种硅晶体的微压痕特性,讨论了加载过程与卸载过程的特征,分析了硅晶体的纳米压入测量结果,同时计算了硅晶体中的应力分布,计算结果表明,剪应力为硅晶体微薄片剥落失效的原因。     

Rayleigh waves emitted by a propagating crack in a strain-rate dependent elastic medium

A simple model was proposed for the interpretation of the non-circular form of the Rayleigh wavefronts emitted by a fast running crack in a plate. The surface deformation around the crack tip, due to the high stress concentration there, propagated as a surface wave after fracture of this zone. On the other hand, the moving singularity of the crack tip created a dynamic stress field of varying intensity with time all over the specimen. This dynamic stress field resulted in a significant change of the mechanical properties of a strain-rate dependent material and therefore it influenced the velocity of propagation of fracture-Rayleigh wavefronts. An analysis of this varying dynamic strain field explained the non-circular form of Rayleigh waves, accompanying the propagating crack. For the experimental evaluation of the K₁-factor the method of dynamic caustics was used in conjunction with the high-speed photography technique.     

基于微凸体接触压力分布的粗糙表面法向接触建模

提出一种考虑微凸体弹塑性接触变形影响的粗糙表面法向接触力学模型。采用有限元模拟微凸体弹塑性接触过程,分析不同塑性屈服条件对微凸体接触载荷和实际接触面积的影响。再根据微凸体接触面上压力分布的变化规律,将微凸体的接触状态分为完全弹性接触阶段、弹塑性接触阶段、完全塑性接触阶段。分析接触面压力变化规律对微凸体法向接触载荷-变形的影响,再利用GW模型的数理统计分析的方法得到粗糙表面的法向接触载荷。将本文提出的模型与完全弹性模型、CEB模型、ZMC模型、KE模型、JG模型进行对比,并且研究了塑性指数对粗糙面接触载荷-平均高度距离的影响。结果表明,本文提出的模型能够更好地描述微凸体法向接触载荷与接触变形的变化趋势,模型预测粗糙表面法向载荷与ZMC、KE模型具有较好的一致性;粗糙面接触载荷随着平均接触距离增加而减少,随着塑性指数的增加,不同模型预测的法向接触载荷差异逐渐增大。