A Two-stage Clustered Multi-Task Learning method for operational optimization in Chemical Mechanical Polishing

Operational optimization of Chemical Mechanical Polishing, which sets the proper polishing time, is very important for improving the production efficiency of semiconductor manufacturing processes. However, usual operational optimization methods based on Run-to-Run strategies have not been suitable for the mixed-product processing mode of CMP. Also, under the mode, it is very difficult to model the polishing time due to the insufficient number of the corresponding samples. In this paper, a Two-stage Clustered Multi-Task Learning method is proposed for the above modelling problem with small sample size, in which the proposed Probability-based Task Clustering algorithm first groups similar products so that their corresponding samples can be used for modelling simultaneously. After this, in each cluster, the proposed Shared Multi-Task Learning (SMTL) algorithm obtains the corresponding model for each kind of products cooperatively, in which the parameter vector of each model is the sum of two parts – the shared part and the private part. In each cluster, the shared part represents the common characteristics of all products and the private part represents the particular characteristics of each kind of products. Also, in SMTL, the two parts can be obtained after a non-smooth convex optimization problem is constructed and solved through the Accelerated Proximal Method. The results of numerical simulations on a practical industrial data set and the other two data sets demonstrate the effectiveness of the proposed algorithms. The proposed algorithms can also be used in other problems such as the modelling problems of key indexes of urban development and operation.