Abstract 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.

中文翻译：

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一种用于化学机械抛光操作优化的两阶段聚类多任务学习方法

摘要 化学机械抛光的操作优化，设置适当的抛光时间，对于提高半导体制造工艺的生产效率非常重要。然而，通常基于 Run-to-Run 策略的操作优化方法并不适用于 CMP 的混合产品加工模式。此外，在该模式下，由于相应样本数量不足，很难对抛光时间进行建模。针对上述样本量较小的建模问题，本文提出了一种两阶段聚类多任务学习方法，其中提出的基于概率的任务聚类算法首先对相似的产品进行分组，使其对应的样本可以用于建模同时地。此后，在每个集群中，所提出的共享多任务学习（SMTL）算法为每种产品协同获得相应的模型，其中每个模型的参数向量是两部分的总和——共享部分和私有部分。在每个集群中，共享部分代表所有产品的共同特征，私有部分代表每种产品的特定特征。另外，在SMTL中，通过Accelerated Proximal Method构造并求解非光滑凸优化问题后，可以得到这两部分。实际工业数据集和其他两个数据集的数值模拟结果证明了所提出算法的有效性。