General run-to-run (R2R) control framework using self-tuning control for multiple-input multiple-output (MIMO) processes

Abstract

During recent years, run-to-run (R2R) control techniques have been developed and used to control various semiconductor manufacturing processes. The R2R control methodology combines response surface modelling, engineering process control, and statistical process control. The main objective of such control is to manipulate the recipe to maintain the process output of each run as close to the nominal target as possible. The primary focus of this research is on the multiple-input multiple-output self-tuning control of R2R processes. A general control scheme is presented that can compensate for a variety of noise disturbances frequently encountered in semiconductor manufacturing. The controller can also compensate for various system dynamics, including autocorrelated responses, deterministic drifts, and varying process gains and offsets. Self-tuning controllers are developed to provide on-line parameter estimation and control. A recursive least squares algorithm is normally used to provide on-line parameter estimation to the controller. This type of control strategy used in the proposed self-tuning controller applies the principle of minimizing total cost (in the form of an expected off-target and controllable factors adjustment) to obtain a recipe for the next run. It is shown through the simulation study that even if the control model is non-linear, the self-tuning controller offers satisfactory control performance for R2R applications as compared with those of the control actions provided by the optimizing adaptive quality controller module. At last, a relevant application to chemical mechanical planarization in semiconductor manufacturing, a critical fabrication step involving two quality characteristics (removal rate and within-wafer non-uniformity), is used to illustrate the proposed controller. In this case study, a multivariate statistical process control technique via the Hotelling T 2 statistic is also used as a dead-band for further investigation.