基于函数型数据分析的半导体生产过程监控

Monitoring of Semiconductor Manufacturing Process Based on Functional Data Analysis

提出一种基于函数型数据分析的非平稳生产状态下的多批次生产过程监控方法。引入函数型数据分析方法将三维数据中的每个变量沿时间方向进行函数拟合,从而将三维离散数据矩阵转化为二维函数矩阵。对各个变量曲线求取二阶导数,消除非平稳生产状态所导致的均值波动现象,增加建模的准确性。在此基础上,利用函数型主成分分析方法对各个变量的导数曲线进行特征提取,并使用基于权重的主成分融合方法,获得函数型主成分矩阵。利用支持向量数据描述方法对函数型主成分矩阵进行监控,并将其应用于工业半导体生产过程的监控中。结果表明,基于函数型数据分析的监控方法与传统方法相比,具有更低的漏检率,验证了新方法的有效性。

A monitoring method based on functional data analysis(FDA) is proposed to improve the quality of batch process in non-stationary condition. Each variable of the three-dimensional data is transformed into smooth functions by FDA method. After that, the three-dimensional data can be described as a two-dimensional matrix. In order to improve the accuracy of monitoring model, the second derivative of smooth functions is calculated to eliminate mean fluctuation caused by non-stationary manufacturing process. Features of the second derivative of each variable are extracted by functional principal component analysis(FPCA) to obtain FPCs. A model is built by the support vector data description method(SVDD) to monitor FPCs and the model is applied to an industrial semiconductor manufacturing process. The results show that the new monitoring method has the lowest missed rate compared with conventional methods, so the effectiveness of the proposed method is validated.