Multivariable control of multizone chemical mechanical polishing

Abstract

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 60×3 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 60×3 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.