A Cluster-Based Method for Quantitative Characterization and Uncertainty Evaluation of Areal Step Height in Structured Surface Metrology

Quantitative characterization and uncertainty evaluation of areal step height are of increasing importance for semiconductor manufacturing. However, step characterizations often confront problems of repeatability and reproducibility due to fitting of upper and lower planes. To solve this problem, we propose a cluster-based method for step height characterization and uncertainty evaluation. By data reconstruction and
$K$
-means clustering, our method converts characterizing steps into approximating Euclidean distances, without necessity to fit planes. Moreover, it can evaluate uncertainties simultaneously with parameterization. The proposed method is first validated with synthetic data. Then, two experiments, respectively, on nominal 5
$\mu \text{m}$
and 90 nm standard artifacts are carried out. The characterization results highly conform to the calibrated values, with 0.0986% and 1.22% differences, respectively. Comparing to the latest ISO method, the cluster-based method presents better performance on repeatability and reproducibility. The experimental results demonstrate that the method works well for measurement either with or without outliers.