Maximum contributed component regression for the inverse problem in optical scatterometry

Scatterometry has been widely applied in microelectronic manufacturing process monitoring. As a key part in scatterometry, inverse problem uses scatter signature to determine the shape of profile structure. The most common solutions for the inverse problem are model-based methods, such as library search, Levenberg-Marquardt algorithm and artificial neural network (ANN). However, they all require a pre-defined geometric model to extract 3D profile of the structure. When facing the complex structure in manufacturing process monitoring, the model-based methods will cost a long time and may fail to build a valid geometric model. Without the assumption of the geometric model, model-free methods are developed to find a mapping between profile parameter named label Y and corresponding spectral signature X. These methods need lots of labeled data obtained from transmission electron microscopy (TEM) or cross-sectional scanning electron microscopy (XSEM) with time-consuming and highly cost, leading to the increase of production costs. To address these issues, this paper develops a novel model-free method, called maximum contributed component regression (MCCR). It utilizes canonical correlation analysis (CCA) to estimate the maximum contributed components from pairwise relationship of economic unlabeled data with few expensive labeled data. In MCCR, the maximum contributed components are used to guide the solution of the inverse problem based on the conventional regression methods. Experimental results on both synthetic and real-world semiconductor datasets demonstrate the effectiveness of the proposed method given small amount of labeled data.