指数比率局部保持投影健康状态监控方法及其半导体蚀刻过程应用

Health Monitoring Method Based on Exponential Ratio Locality Preserving Projections and Its Application in Semiconductor Etching Process

针对局部保持投影在监控半导体蚀刻过程时T^(2)统计量的缺陷,提出指数比率局部保持投影健康状态监控方法(exponential ratio locality preserving projections health monitoring method,ERLPP).将半导体数据通过统计模量方法展开为二维数据,利用局部保持投影将展开后数据投影到特征空间,首先确定特征空间中样本的第k近邻,称其为一步近邻;再确定第k近邻的前K近邻集,称其为二步近邻;最后通过一步近邻与二步近邻的指数比值运算构造统计量P.ERLPP方法不仅可以消除样本统计值的多模态特征并提高过程故障检测率,同时还可以在保持数据流形结构的前提下降低计算复杂度.通过数值例子与半导体蚀刻过程的仿真实验,并与主元分析、局部保持投影、邻域保持嵌入、k近邻规则等方法进行比较,测试结果验证了ERLPP方法的有效性.

Aiming at the defects of T^(2) statistics of local preserving projections(LPP)in monitoring the semiconductor etching process,a health monitoring method based on exponential ratio local preserving projections health monitoring method(ERLPP)is proposed.The semiconductor data are unfolded into two-dimensional data by statistics pattern analysis.LPP is used to project the unfolded data into the feature space.The k-th nearest neighbor of the sample in the feature space is obtained,which is called one-step neighbor,and then the K-nearest set of the k-th neighbor is obtained,which is called two-step nearest neighbor.Finally,the statistic P is constructed by the exponential ratio operation of one-step nearcst neighbor and two-step nearest neighbor.ERLPP method not only eliminates the multi-modal features of sample statistics and improves the process fault detection rate,but also reduce the computational complexity while maintaining the data manifold structure.Compared with principal component analysis,LPP,neighborhood preserving embedding,k-nearest neighbor rule and other methods in a numerical case and simulation of semiconductor etching process,the validity of the ERLPP method is verified.