有限元方法模拟电流导线作用下铁磁流体化学机械抛光  

Simulation of Ferrofluid Chemical Mechanical Polishing under the Action of Current Conductors Using Finite Element Method

作　　者：向涛 李明军[1] XIANG Tao;LI Mingjun(School of Mathematics and Computing Science,Xiangtan University,Xiangtan 411100,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411100

出　　处：《工业技术创新》2023年第2期10-19,共10页Industrial Technology Innovation

基　　金：国家自然科学基金项目(项目编号:11971411);湖湘高层次人才聚集工程—创新团队项目(项目编号:2019RS1060)。

摘　　要：化学机械抛光(CMP)是半导体行业中十分有效的晶片平面化工艺,但CMP机制研究亟待深入。构建了直角坐标系下的铁磁流体CMP雷诺方程模型,使用边界处理灵活、有效解决奇点问题的有限元方法对模型进行了数值模拟,考察了电流导线产生的非均匀磁场和抛光参数对CMP过程中晶片表面压力分布的影响。研究发现:电流导线产生的非均匀磁场使得靠近电流导线一边的晶片表面出现负压区域,与已有文献结果相一致;当磁场强度在一定范围内时,晶片表面的高压区域会随着磁场强度的增大而远离电流导线;晶片中心抛光液膜厚、倾角、仰角等抛光参数对由磁场压力引起的载荷和力矩都有一定影响,在铁磁流体CMP过程中应适当选取。Chemical Mechanical Polishing(CMP)is a very effective wafer planarization process in the semiconductor industries,but the CMP mechanism needs to be further studied.A Reynolds equation model of ferrofluid CMP in the rectangular coordinate system was established,and the finite element method with flexible boundary treatment and effective solution to singularity problem was used to simulate such a model.The influence of non-uniform magnetic field generated by the current conductor and polishing parameters on the pressure distribution on the wafer surface during the CMP process was investigated.Findings:the non-uniform magnetic field generated by the current conductor makes a negative pressure region appear on the wafer surface near the current conductor,which is consistent with the results of the existing literatures;when the magnetic field intensity is within a certain range,the high pressure region on the wafer surface will be far away from the current conductor with the increase of the magnetic field intensity;the polishing parameters,such as the film thickness of polishing solution in the wafer center,inclination angle and elevation angle,have certain influence on the load and torque caused by the magnetic field pressure,and should be properly selected in the ferrofluid CMP process.

关 键 词：铁磁流体 化学机械抛光(CMP) 雷诺方程 电流导线 负压区域 

分 类 号：TH117[机械工程—机械设计及理论]