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Multivariable control of multizone chemical mechanical polishing

机译:多区域化学机械抛光的多变量控制

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The modeling and multivariable control of the multizone chemical mechanical polishing (CMP) are studied in this work. For a three-zone CMP, the copper thickness across the radial position is measured with an in situ sensor and then the measurements are converted to 60 data points across the radial position. In the process control notation, these are the controlled variables and the manipulated variables are the three pressures applied to each zone. Therefore, this is a 60x3 nonsquare multivariable control problem. In the modeling phase, two-level factorial designs are carried out on all three pressures followed by the least square regression. Thus, a 60x3 steady-state gain matrix is obtained followed by finding dynamic elements according to the gas holdup in each chamber. The control objective is to maintain uniform surface profile using all three manipulated variables. As a result of the nonsquare system, it is not possible to keep all 60 outputs at their set points using only three inputs. The singular value decomposition (SVD) is used to design a nonsquare feedback controller. This SVD controller can. be implemented using standard software with little difficulty. The proposed control system was tested on incoming wafers with different surface profiles. Results show that attainable uniformity can be maintained using the proposed SVD controller. (C) 2004 American Vacuum Society.
机译:在这项工作中,研究了多区域化学机械抛光(CMP)的建模和多变量控制。对于三区CMP,使用原位传感器测量径向位置上的铜厚度,然后将测量值转换为径向位置上的60个数据点。在过程控制符号中,这些是控制变量,而操纵变量是施加到每个区域的三个压力。因此,这是一个60x3的非平方多变量控制问题。在建模阶段,对所有三个压力执行两级因子设计,然后进行最小二乘回归。因此,获得60x3的稳态增益矩阵,然后根据每个腔室中的气体滞留量找到动态元素。控制目标是使用所有三个调节变量来保持均匀的表面轮廓。作为非平方系统的结果,不可能仅使用三个输入将所有60个输出保持在其设定点。奇异值分解(SVD)用于设计非平方反馈控制器。这个SVD控制器可以。使用标准软件即可轻松实现。所提出的控制系统已在具有不同表面轮廓的晶圆上进行了测试。结果表明,使用建议的SVD控制器可以保持可达到的均匀性。 (C)2004年美国真空学会。

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