Combined Run-to-Run and Lqg Control of a 12-Inch Rtp Equipment

A combined run-to-run (R2R) and LQG control method has been proposed for rapid thermal processing (RTP) equipments for run-wise improvement together with real-time multivariable control of the temperature uniformity over the wafer. The standard LQG objective was modified to include a quadratic penalty term for input deviation from a bias value which is updated by the R2R control. The proposed method has been applied to a commercial 12-inch rotating RTP equipment which has ten circular groups of tungsten-halogen lamps and four pyrometers for manipulation and real-time measurements of wafer temperatures. Multivariable LQG control was evaluated under wafer rotation and found to show a quite accurate control performance. For testing the combined control technique, a wafer that has eight thermocouples (TC's) attached along the radical direction has been employed without wafer rotation considering the TC temperatures as the post-run uniformity measurements. Experiments obviously showed that the temperature uniformity is improved as the run number increases.