基于灰色模型的CMP过程免疫预测R2R控制

Grey model based immune predictive R2R control of CMP process

针对化学机械研磨(chemical mechanical polishing,CMP)过程非线性、时变、产品质量不能在线测量的特性,为了提高CMP过程R2R(Rum-to-Run)控制的精度,提出了一种基于灰色模型和克隆选择免疫算法的CMP过程R2R预测控制器GI-PR2R。通过离线测量获得历史批次少量数据,构建CMP过程的在线灰色GM(1,N)预测模型,解决了复杂CMP过程难以建立精确数学模型的难题提高了预测模型的精度。通过基于克隆选择免疫算法的CMP过程预测控制的滚动优化,避免了基于导数的优化技术易陷入局部最优的问题,进而提高了控制精度。仿真结果表明,CMP过程GIPR2R控制器的控制精度优于EWMA(exponentially weighted moving average)方法,有效抑制了过程漂移,减小了不同批次间产品的差异,材料去除率(material removalrate,MRR)的均方根误差在总批次与控制目标不同这2种情况下分别降低了18.09%和16.84%。

Aiming at the characteristics of nonlinearity, time-varying and impossibly of in-situ measurement of chem- ical mechanical polishing （CMP） process, and in order to improve the Run-to-Run （R2R） control accuracy of CMP process, this paper proposes a CMP process R2R predictive controller named GIPR2R based on grey model and don- al selection algorithms. A GM （ 1 ,N） grey predictive model is constructed using the sparse data of historical batches of CMP process, which solves the difficult problem of constructing accurate mathematical model for complicated CMP process and improves the prediction accuracy. The rolling horizon optimization of predictive control is achieved using clonal selection immune algorithm, so the problem that derivative-based optimization technology is easy to fall into lo- cal optimum is solved and the control precision is improved. Simulation results illustrate that the performance of GI- PR2R controller is better than that of EWMA method, and the process drifts and shifts are suppressed significantly, the variation in various runs of products is decreased, and the RMSEs of material removal rate （MRR） for different runs and different targets are reduced by 18.09% and 16.84% , respectively.