Wavelength-multiplexed multi-mode EUV reflection ptychography based on automatic differentiation

Shao et al. Light: Science & Applications (2024)13:196 https://doi.org/10.1038/s41377-024-01558-3 Official journal of the CIOMP 2047-7538 www.nature.com/lsa ARTICLE Open Access Wavelength-multiplexed multi-mode EUV reflection ptychography based on automatic differentiation 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; Yifeng Shao 1,2 ✉ , Sven Weerdenburg 1 , Jacob Seifert2, H. Paul Urbach1, Allard P. Mosk 2 and Wim Coene 1,3 Abstract Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the crossdensity function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool. Introduction As the semiconductor industry advances along the trajectory projected by Moore’s law and approaches the ability to manufacture 3D transistors with features on the order of a few nanometres, conventional metrology solutions are confronted with challenges in addressing the shrinking dimensions when characterising the critical dimensions and the overlay errors of the structures printed on the wafer by lithography1,2. Due to its capability to perform non-invasive inspections of non- Correspondence: Yifeng Shao () 1 Imaging Physics Department, Applied Science Faculty, Delft University of Technology, Lorentzweg 1, Delft 2628 CJ, The Netherlands 2 Nanophotonics, Debye Institute for Nanomaterials Science and Center for Extreme Matter and Emergent Phenomena, Utrecht University, P.O. Box 80000, Utrecht 3508 TA, The Netherlands Full list of author information is available at the end of the article These authors contributed equally: Yifeng Shao, Sven Weerdenburg, Jacob Seifert. isolated and non-periodic patterns, ptychography emerges as a promising candidate for next-generation metrology solutions3–11, offering both amplitude and phase information by means of diffractive imaging with a superior resolution and a larger penetration depth into the materials through the use of extreme ultraviolet (EUV) illumination. As a computational approach, it does not require expensive imaging optics, whose components can be extremely challenging to fabricate for wavelengths in the EUV regime12,13. Instead, it illuminates the sample at overlapping areas during a scan process and reconstructs the image of the sample along with the illumination field from the diffraction patterns measured at the corresponding scanning positions via iterative optimisation14–16. Compared to the enormous synchrotron or freeelectron laser facilities, the compact-sized table-top sources based on high-harmonic generation (HHG) are © The Author(s) 2024 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Shao et al. Light: Science & Applications (2024)13:196 ideal for industrial applications by providing a spatially moderately coherent illumination consisting of spectral harmonics in the EUV regime17–19. Owing to the overlap between the illuminated sample areas at adjacent scanning positions, the dataset offers abundant information with the necessary redundancy for phase retrieval of illumination and sample fields20,21, allowing one to utilise the advantage of the multiple spectral harmonics generated by the HHG source with wavelength-multiplexed reconstruction22–25. In the meantime, one can also tackle the inherent instabilities of the HHG source with ptychography using a modal approach, in which one reconstructs a series of mutually incoherent and independent spatial modes of illumination instead of a single illumination field26–29. Recent progress on HHG sources, especially the significant improvement in brightness and photon flux30,31, enables data acquisition to be completed in a reasonable timeframe and has brought EUV ptychography into the spotlight as a potentially viable technology. However, exploiting information redundancy in the dataset with ptychography leads to a drastic growth in model complexity. To manage the entangled relations between diverse physical processes, automatic differentiation (AD)32 manifests as an ideal tool for building a universal framework for ptychography models33–37 as well as other computational imaging modalities38,39, releasing researchers from the laborious work of manually deriving the formulas and implementing the routines for computing various gradients. In view of metrology applications in the semiconductor industry, it is desired to use a beamline in reflection instead of transmission geometries5,9,10,24,25,40 for wafer samples. Additionally, extending from single wavelength6–8,11 to multiple wavelengths can enhance the measurement throughput and introduce data diversity, allowing accurate characterisation of the structure information. Previous works of wavelength-multiplexed reconstruction with HHG sources, however23,25,41, did not incorporate (...truncated)