Principal components and optimal feature vectors of EUVL stochastic variability: applications of Karhunen-Loève expansion to efficient estimation of stochastic failure probabilities and stochastic metrics

Abstract

Karhunen-Loève Expansion (KLE) is a generalization of Principal Component Analysis (PCA) to random fields and random processes, providing optimal basis functions to represent random stochastic variability most accurately, ensuring the minimal mean square approximation error. Application of KLE to EUVL stochastic modeling is proposed and illustrated on examples of stochastic failure probabilities calculation (tip-to-tip pinching probability for metal layers and "via missing" probabilities for the via layers), providing the insight into the mechanisms of stochastic variability in EUVL.