Nonnegative Matrix Factorization for Binary Data to Extract Elementary Failure Maps from Wafer Test Images

Abstract

We introduce a probabilistic variant of nonnegative matrix factorization (NMF) applied to binary datasets. Hence we consider binary coded images as a probabilistic superposition of underlying continuous-valued basic patterns. An extension of the well-known NMF procedure to binary-valued datasets is provided to solve the related optimization problem with nonnegativity constraints. We demonstrate the performance of our method by applying it to the detection and characterization of hidden causes for failures during wafer processing. Therefore, we decompose binary coded (pass/fail) wafer test data into underlying elementary failure patterns and study their influence on the quality of single wafers.