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Explore the comprehensive history and cutting-edge developments in extreme ultraviolet (EUV) lithography through this technical lecture delivered by industry experts Tony Yen and Ronald Goossens from ASML. Trace the evolution of next-generation lithography technologies from their origins in the late 1970s and early 1980s, when optical lithography faced perceived resolution limits of 0.5 µm, through EUV's lengthy thirty-year development journey that began in the mid-1980s. Discover how optical lithography's unexpected advances, particularly 193-nm immersion lithography, provided crucial time for EUV technology to mature before entering high-volume semiconductor production in 2019 at the 7-nm logic node. Learn about the latest lithographic results from 0.55 numerical aperture (NA) exposure systems that became available in 2024, and understand how high-NA EUVL enables continued scaling of logic and DRAM devices while potentially supporting future device architectures. Examine the fundamental resolution principles governing EUV lithography through the k₁λ/NA expression, comparing current EUV k₁ factors of 0.4 with optical immersion lithography's production-proven k₁ values below 0.3. Gain insights into ASML's EUV technology roadmap and explore strategies for further resolution enhancement, including discussions on achieving lower k₁ factors and the potential need for even higher numerical apertures in future lithography systems.