Modeling and Control of Chemical Mechanical Polishing(3/3)
Date Issued
2004
Date
2004
Author(s)
余政靖
DOI
922214E002032
Abstract
In this work, the control of a new type of chemical mechanical polishing (CMP), multi-zone CMP, is explored. Unlike the typical single zone configuration, the wafer carrier is divided into three zones in the radial position and different pressure can be applied to each zone. For the Applied Materials three-zone CMP, the copper thickness across the radial position is measured with an in-situ sensor. The measurement is converted to 59 data points along 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, and we focus on the multivariable control of this 59x3 process. First, a two-level factorial design is carried out on all three pressures followed by the least square regression to find the steady-state gain matrix. Incorporated with the gas holdup dynamics, we have a 59x3 process transfer function matrix with the same first order dynamics in each column. Second, the singular value decomposition (SVD) is used to design the non-square feedback controller. Next, a diagonal PI controller (3x3) is designed and the controller outputs in the principle input directions (3x1) are computed. Finally, these controller outputs are transformed to the true inputs (3 pressures) to the process. This SVD controller can be implemented using standard software with little difficulty. The proposed control system is test on incoming wafers with different surface profiles. Results show that achievable performance (least square results) can be maintained using the proposed SVD controller.
Publisher
臺北市：國立臺灣大學化學工程學系暨研究所
Type
report
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