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Into the Future with Metrology - The Challenges of Digitalization

Scatterometry as an example for inverse problems

Our modern society is significantly influenced by the performance and miniaturization of microchips. Over the last decades, the complexity of integrated circuits has regularly doubled in relation to component costs (Moore's Law). Metrology in semiconductor manufacturing technology has also played a part in this development. 

Already today, structure sizes of less than 10 nm are achieved, which places very special demands on their measurement of the structures, e.g. for quality control. Optical scattering methods, such as scatterometry, offer a fast, indirect and precise measuring method for determining the geometric properties of nanostructured surfaces.  The surface is illuminated with light and the reflected radiation intensity is measured. From the intensity pattern, the original nanostructure can be reconstructed by solving an inverse problem. To solve the inverse problem, it is necessary to simulate the measurement process as accurately as possible, which corresponds to a virtual experiment.

Current state

In close cooperation of the departments 8.4, 7.1 and 4.2, the evaluation methods in optical metrology have been continuously improved in recent years, which is reflected in a large number of joint publications and various projects. 

Currently, a nanometer sized line structure has been investigated in which an irregularity of the line spacing, the so-called "pitchwalk", occurs. For this structure, the sensitivity of different influencing variables on the virtual measurement results was investigated in a virtual experiment in order to gain statements for the optimization of future measurement setups. PTB cooperates in this field with the Weierstaß Institute for Applied Analysis and Stochastics, the Technical University of Berlin and JCMwave GmbH. 

Aims and outlook

The virtual experiment in scatterometry uses idealizations, approximations and simplifications compared to the real experiment. The goal is to estimate deviations from the real experiment by using suitable error models. As a result it should be achieved that more realistic uncertainties can be specified for the virtual experiment in scatterometry. 


  1. N. Farchmin, M. Hammerschmidt, P.-I. Schneider, M. Wurm, B. Bodermann, M. Bär and S. Heidenreich, Efficient Bayesian inversion for shape reconstruction of lithography masks, J. Micro/Nanolithography, MEMS and MOEMS, 19(2), 024001 (2020). Opens external link in new windowhttps://doi.org/10.1117/1.JMM.19.2.024001

  2. M. Casfor Zapata, N. Farchmin, M. Pflüger, K. Nikolaev, V. Soltwisch, S. Heidenreich, C. Laubis, M. Kolbe and F. Scholze. SPIE Advanced Lithography 113251D (2020). Opens external link in new windowhttps://doi.org/10.1117/12.2552037 

  3. S. Heidenreich, H. Gross and M. Bär, Bayesian approach to determine critical dimensions from scatterometric measurements. Metrologia 55(6) (2018). Opens external link in new windowhttps://doi.org/10.1088/1681-7575/aae41c