Regularized Autoencoder for The Analysis of Multivariate Metrology Data

Abstract

A new generation of metrology tools has been recently released to the market, allowing extensive characterization of semiconductor samples thanks to massive measurements. The resulting substantial growth of measurement sets in size and number of descriptors made the data analysis with the traditional statistical techniques laborious, being unable to consider all data simultaneously. In this work, we propose an analysis method applicable to the massive measurement sets based on a machine learning technique, called Autoencoder (AE). The performance of the original AE model has been boosted in this work thanks to its regularization, by imposing orthogonality of its internal representation and by training only half of the model weights while the second half is deduced. Practically, once the model is trained on the data set of interest, it is used to study relationships between input variables through the chart of the circle of correlations. In this chart, input variables are projected as vectors into the compression plane where the angular distance between them will express their degree of correlation. The representation of massive measurements data through a condensed simple chart that still shows complex interactions between variables is in fact very efficient and facilitating the interpretation of measurements themselves. The experimental validation of the proposed method has been done with measurements of Contact Hole (CH) patterns acquired on samples manufactured with 3 different exposure conditions (underexposure dose, nominal exposure dose, and overexposure dose). The proposed data analysis technique allowed us to clearly identify the impact of the process conditions on patterns characteristics, such as their eccentricity, their geometry, and more. Our results indicated that in case of overexposure, an anisotropic distortion of the CH geometry is present, where gamma-axis is the major axis, with larger impact on the pattern surface as compared to the X-axis. This result has been also confirmed later through defect inspection, where we found that 94% of bridging defects detected occurred along the gamma-axis, while only 6% of bridging occurred along the X-axis. In conclusion, our results indicated that the proposed analysis technique is highly effective for the analysis and interpretation of massive metrology datasets, and that the dimensionality increase of the dataset has a negligible impact on this technique's performance.