Multivariable Control of Multi-zone Chemical Mechanical Polishing

Abstract

The modeling and multivariable control of the multi-zone chemical mechanical polishing (CMP) is 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 non-square multi variable control problem. Thus, a 60x3 steady-state gain matrix is obtained followed by finding dynamic elements according to the gas holdup in each chamber. As a result of the non-square system, it is not possible to keep all 60 outputs at their set points using only 3 inputs. The singular value decomposition (SVD) is used to design a non-square feedback controller. The proposed control system is test on incoming wafers with different surface profiles. Results show that achievable performance can be maintained using the proposed SVD controller