Why Contour Averaging Works for SEM Metrology: Analysis and Validation

As the technology node in semiconductor manufacturing continuously shrinks, the etch-induced etch bias introduced during the etching process cannot be ignored and necessitates correction. The prevailing approach to addressing this issue is model-based etch bias correction. This method involves simulating the etching process by training an etch model that predicts the bias between the After Development Inspection (ADI) contour and the After Etch Inspection (AEI) contour. However, the reliability of the etch data for model training is compromised due to pattern shrinkage during Scanning Electron Microscope (SEM) imaging, which impairs the model’s prediction accuracy. To mitigate these issues, the contour averaging method is frequently employed, although it lacks thorough theoretical explanation and experimental verification. In this study, we validate the effectiveness of contour averaging theoretically and empirically. A relationship is derived between the prediction error of the etch model and the number of averaged contours, showing that contour averaging minimizes measurement errors of etch data. We also demonstrate the improved prediction accuracy of etch model using contour averaging, with both real and generated etch data.