Advances in Modeling and Optimization for Two-Photon Lithography

Valeriia Sedova, Florie Ogor, Joёl Rovera, Odysseas Tsilipakos, Lisa Lemberg, Kevin Heggarty, Andreas Erdmann — Advances in Modeling and Optimization for Two-Photon Lithography - SPIE Optical Systems Design 2024 - Motivation 25.11.2025 © Fraunhofer IISBPage 2 Example of 2D metasurfaces Source: https://vosdogs.com/harvard-scientists-monitor-points-of-darkness-for-remote-sensing-and-covert-sensingapplications Source: Princeton University Source: FABulous proposal Source: Edinburg Instruments - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 3 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 4 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook - SPIE Optical Systems Design 2024 - Overview of the models 25.11.2025 © Fraunhofer IISBPage 5 Optical model Generation of point spread function (PSF) within resist Resist model Threshold describes polymerization Exposure kinetics Diffusion of a single species Development of the processed photopolymer Exposure kinetics Temperature profile Diffusion and kinetics of multiple species Presence of quencher Development of the processed polymer A full model of polymerization Compact modelThreshold model - SPIE Optical Systems Design 2024 - Threshold model 25.11.2025 © Fraunhofer IISBPage 6 power ~ 1 / threshold - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 7 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook - SPIE Optical Systems Design 2024 - Compact model 25.11.2025 © Fraunhofer IISBPage 8 TPP exposure reaction: 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑇𝑃𝐴 ∝ 𝐼 𝑃𝐴𝐶 = exp (−𝐼∗ 𝐷 ∗ 𝐶) Fickian diffusion: 𝛿[𝑃𝐴𝐶] 𝛿𝑡 = 𝐷∇[𝑃𝐴𝐶] Development Mack model: 𝑅 = 𝑅(𝑎 + 1)(1 − 𝑀) 𝑎 + (1 − 𝑀)+ 𝑅 𝑎 = 𝑁 + 1 𝑁 − 1 (1 − 𝑀) - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 9 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 16 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook - SPIE Optical Systems Design 2024 - Experimental data 25.11.2025 © Fraunhofer IISBPage 17 - SPIE Optical Systems Design 2024 - Calibration results – Threshold model 25.11.2025 © Fraunhofer IISBPage 18 - SPIE Optical Systems Design 2024 - Calibration results – Compact model and Full Model of Polymerization 25.11.2025 © Fraunhofer IISBPage 19 - SPIE Optical Systems Design 2024 - 25.11.2025 © Fraunhofer IISBPage 20 Exposure times that were used in the experiment: •1000 µs •100 µs •10 µs •1 µs Interplay between diffusion kinetics and exposure time - SPIE Optical Systems Design 2024 - Application of model to alternative exposure strategies 25.11.2025 © Fraunhofer IISBPage 21 - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 22 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook - SPIE Optical Systems Design 2024 - First applications of models towards metasurfaces 25.11.2025 © Fraunhofer IISBPage 23 Supercell of an optical metasurface. A: pillars with circular cross-section. B: The design is modified in order to avoid sharp edges. C: Pillars simulated by full polymerization model. Designs A,B: FORTH - SPIE Optical Systems Design 2024 - Double exposure processes 25.11.2025 © Fraunhofer IISBPage 24 - SPIE Optical Systems Design 2024 - Outline 25.11.2025 © Fraunhofer IISBPage 25 Model Description Threshold model Compact model Full model of polymerization Application of the models Impact of parameters on voxel shape Model calibration and verification First applications of models towards metasurfaces Conclusion and outlook