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The effect of systematic errors on the hybridization of optical critical dimension measurements



Mark Alexander Henn, Richard M. Silver, Nien F. Zhang, Hui Zhou, Bryan M. Barnes


In hybrid metrology two or more measurements of the same measurand are combined to provide a more reliable result that ideally incorporates the individual strengths of each of the measurement methods. While these multiple measurements may come from dissimilar metrology methods such as optical critical dimension (OCD) measurements and scanning electron microscopy (SEM), we will investigate the hybridization of similar OCD methods, featuring a focus-resolved simulation study of systematic errors performed at orthogonal polarizations. Specifically errors due to line edge and line width roughness (LEWR) are known to contribute a systematic bias and its inherent correlated errors. In order to investigate the sensitivity of the measurement to LEWR we follow a modeling approach proposed by Kato et al. who studied the effect of LEWR on extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Similar to their findings, we have observed that LEWR leads to a systematic bias in the data. Since the critical dimensions (CDs) are determined by fitting the respective model data to the measurement data by minimizing the difference measure or chi square function, a proper description of the systematic bias is crucial to obtaining reliable results and to successful hybridization. In scatterometry, an analytical expression for the influence of LEWR on the measured orders can be derived, and accounting for this effect leads to a modification of the model function that not only depends on the critical dimensions but also on the magnitude of the roughness. For finite arrayed structures however, such an analytical expression cannot be derived. We demonstrate how to account for the systematic bias and that, if certain conditions are met, a significant improvement of the reliability of hybrid metrology both for combining dissimilar and similar measurement tools can be achieved.
Proceedings Title
SPIE Modeling Aspects in Optical Metrology V
Conference Dates
June 23-25, 2015
Conference Location


hybrid metrology, electromagnetic simulation, sensitivity and uncertainty evaluation


, M. , Silver, R. , Zhang, N. , Zhou, H. and Barnes, B. (2015), The effect of systematic errors on the hybridization of optical critical dimension measurements, SPIE Modeling Aspects in Optical Metrology V, Munich, -1, [online], (Accessed March 3, 2024)
Created June 21, 2015, Updated November 10, 2018