Mueller Matrix Ellipsometric Approach on the Imaging of Sub-Wavelength Nanostructures

authored by: Tim Käseberg, Jana Grundmann, Thomas Siefke, Petr Klapetek, Miroslav Valtr, Stefanie Kroker, Bernd Bodermann
Abstract: Conventional spectroscopic ellipsometry is a powerful tool in optical metrology. However, when it comes to the characterization of non-periodic nanostructures or structured fields that are much smaller than the illumination spot size, it is not well suited as it integrates the results over the whole illuminated area. Instead, imaging ellipsometry can be applied. Especially imaging Mueller matrix ellipsometry is highly useful in nanostructure characterization and defect inspection, as it is capable to measure the complete Mueller matrix for each pixel in a microscope image of the sample. It has been shown that these so-called Mueller matrix images can help to distinguish geometrical features of nanostructures in the sub-wavelength regime due to visible differences in off-diagonal matrix elements. To further investigate the sensitivity of imaging Mueller matrix ellipsometry for sub-wavelength sized features, we designed and fabricated a sample containing geometrical nanostructures with lateral dimensions ranging from 50 to 5,000 nm. The structures consist of square and circular shapes with varying sizes and corner rounding. For the characterization of their Mueller matrix images, we constructed an in-house Mueller matrix microscope capable of measuring the full Mueller matrix for each pixel of a CCD camera, using an imaging system and a dual-rotating compensator configuration for the ellipsometric system. The samples are illuminated at 455 nm wavelength and the measurements can be performed in both transmission and reflection. Using this setup, we systematically examine the sensitivity of Mueller matrix images to small features of the designed nanostructures. Within this contribution, the results are compared with traceable atomic force microscopy measurements and the suitability of this measurement technique in optical nanometrology is discussed. AFM measurements confirm that the fabricated samples closely match their design and are suitable for nanometrological test measurements. Mueller matrix images of the structures show close resemblance to numerical simulations and significant influence of sub-wavelength features to off-diagonal matrix elements.
External Organisation(s): National Metrology Institute of Germany (PTB)
Friedrich Schiller University Jena
Czech Metrology Institute (CMI)
Brno University of Technology
Technische Universität Braunschweig
Type: Article
Journal: Frontiers in Physics
Volume: 9
Publication date: 21.01.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Biophysics, Materials Science (miscellaneous), Mathematical Physics, Physics and Astronomy(all), Physical and Theoretical Chemistry
Electronic version(s): https://doi.org/10.3389/fphy.2021.814559 (Access: Open)

BibTeX

@article{52887a659d7c41e49cd6b253336f2cd3,
title = "Mueller Matrix Ellipsometric Approach on the Imaging of Sub-Wavelength Nanostructures",
abstract = "Conventional spectroscopic ellipsometry is a powerful tool in optical metrology. However, when it comes to the characterization of non-periodic nanostructures or structured fields that are much smaller than the illumination spot size, it is not well suited as it integrates the results over the whole illuminated area. Instead, imaging ellipsometry can be applied. Especially imaging Mueller matrix ellipsometry is highly useful in nanostructure characterization and defect inspection, as it is capable to measure the complete Mueller matrix for each pixel in a microscope image of the sample. It has been shown that these so-called Mueller matrix images can help to distinguish geometrical features of nanostructures in the sub-wavelength regime due to visible differences in off-diagonal matrix elements. To further investigate the sensitivity of imaging Mueller matrix ellipsometry for sub-wavelength sized features, we designed and fabricated a sample containing geometrical nanostructures with lateral dimensions ranging from 50 to 5,000 nm. The structures consist of square and circular shapes with varying sizes and corner rounding. For the characterization of their Mueller matrix images, we constructed an in-house Mueller matrix microscope capable of measuring the full Mueller matrix for each pixel of a CCD camera, using an imaging system and a dual-rotating compensator configuration for the ellipsometric system. The samples are illuminated at 455 nm wavelength and the measurements can be performed in both transmission and reflection. Using this setup, we systematically examine the sensitivity of Mueller matrix images to small features of the designed nanostructures. Within this contribution, the results are compared with traceable atomic force microscopy measurements and the suitability of this measurement technique in optical nanometrology is discussed. AFM measurements confirm that the fabricated samples closely match their design and are suitable for nanometrological test measurements. Mueller matrix images of the structures show close resemblance to numerical simulations and significant influence of sub-wavelength features to off-diagonal matrix elements.",
keywords = "ellipsometry, imaging ellipsometry, metrology, mueller ellipsometry, mueller matrix ellipsometry, nanometrology, nanostructures",
author = "Tim K{\"a}seberg and Jana Grundmann and Thomas Siefke and Petr Klapetek and Miroslav Valtr and Stefanie Kroker and Bernd Bodermann",
note = "Funding information: This work is funded through the project 17FUN01 “BeCOMe” within the Programme EMPIR. The EMPIR initiative is cofounded by the European Union{\textquoteright}s Horizon 2020 research and innovation program and the EMPIR Participating Countries. This project (20FUN02 “POLight”) has received funding from the EMPIR programme co-financed by the Participating States and from the European Union{\textquoteright}s Horizon 2020 research and innovation programme. SK also acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy—EXC-2123 QuantumFrontiers—390 837 967.",
year = "2022",
month = jan,
day = "21",
doi = "10.3389/fphy.2021.814559",
language = "English",
volume = "9",
journal = "Frontiers in Physics",
issn = "2296-424X",
publisher = "Frontiers Media S.A.",
}