Model-based control for chemical-mechanical planarization (CMP)

The research described in this tutorial paper involves an effort for physical modeling and model-based sensing and control of CMP systems. A dynamic model of a rotational CMP process is developed, as well as simulation software. This dynamic model is used for feedback control design based on in-situ thickness measurements, as well as run-to-run control using in-line metrology. Simulation results of open-loop, feedback control, and combined feedback and run-to-run control are presented and compared. A multivariable LQ (linear quadratic) feedback controller was designed and showed improvement of Within-Wafer-Non-Uniformity (WIWNU) at the end of a run in simulation over existing open-loop control of a CMP process. It also showed the possibility of using feedback control as a means of end-pointing the CMP process. Furthermore, a run-to-run (R2R) controller was designed and simulated. Additional improvement of WIWNU and tracking a desired average wafer thickness was obtained, showing the merits of a combined feedback/ run-to-run control process.