On the increase of the controllability matrix rank in non-threaded run-to-run control

One of the levers for cycle time and cost reduction in the semiconductor industry is the use of all the available production tools as much as possible. In this paper, a modified Non-threaded Run-to-Run approach is proposed. This approach permits the control of the maximum possible number of equipment simultaneously. The idea is to model the entire system with all possible combinations (threads) in a novel state space representation (SSR) so that we can increase the rank of the controllability matrix. Due to its efficiency, especially with a SSR, a Kalman filter is used as an estimator for the Run-to-Run control purpose. The accuracy of the proposed method is tested using real data derived from the deposition area of STMicroelectronics foundry in Rousset.