Grey forecasting run-to-run control system in copper chemical mechanical polishing

Abstract

In this paper, an online grey forecasting run-to-run control system was proposed with the integration of run-to-run control system, recursive least-squares (RLS) algorithm, and grey forecasting model (GFM). One of the objectives of this study is to explore the possibility and feasibility of applying GFM to run-to-run control system in copper chemical mechanical polishing. Under the condition of limited experiment data, GFM is excellent at estimating and forecasting error of the next batch online. To keep the process under control, the controllers are then employed to adjust the process parameters in order to compensate the error. In addition, the RLS algorithm is used to construct dynamically a system estimation matrix for the purpose of stating precisely the relationship between process quality and process parameters, and to consequently improve processing performances. From the computer simulation and the experiment results, the proposed new method developed in this study was able not only to confine the processing performances' error within the range of 5% but also to supplement, when the process parameters are saturated, the control capability through adjusting other unsaturated process parameters, thus maintaining good processing performances

Fuzzy predictive R2R control to CMP process

“…Material removal rate (MRR) defined removal amount of a single wafer in a single run is an important goal of CMP. According to Preston equation, in order to response to MRR drift, shift, pad aging and other factors for real-time CMP environment, without considering the impact of polishing time, nonlinear CMP process model is formed as follows [13][14][15]:…”

“…For nonlinear characteristic of CMP process, intelligence and statistics based the controllers have been presented. The neural network controller [4,[11][12][13][14], a grey predictive model and recursive least square based controller [15], a d-EWMA controller based on recursive Least squares and real coded genetic algorithm[ [16], and a CMP process predivtive model based on Bayesian analysis and statistical regression modeling [17] are proposed.…”