Advanced Modeling of Two-Photon Lithography

Valeriia Sedova, Yuan Yu, Alap Mundayoor Fraunhofer Institute for Integrated Systems and Device Technology (IISB), Erlangen, Germany OPTICS MEET-UP 2025, Jena, Germany Advanced Modeling of Two-Photon Lithography — OPTICS MEET-UP, Jena, Germany, September 25, 2025 Motivation and introduction 25.11.2025 © Fraunhofer IISBPage 2 Two-photon lithography https://www.upnano.com/castle-on-a-pencil-tip/ https://heidelberg-instruments.com/visit-us-at-laser-world-of-photonics-2022/ OPTICS MEET-UP, Jena, Germany, September 25, 2025 Motivation and introduction 25.11.2025 © Fraunhofer IISBPage 3 Two-photon absorption Maria Goeppert Mayer (1906-1972) PhD thesis: “Über elementarakte mit zwei quantensprüngen,” (1931) https://bliqphotonics.com/what-is-two-photon-microscopy/. 𝐼∝ 𝐼 𝐼∝ 𝐼  1 photon excitation 2 photon excitation OPTICS MEET-UP, Jena, Germany, September 25, 2025 Limitations of the process 25.11.2025 © Fraunhofer IISBPage 4 Speed of printing Conventional point by point multiphoton lithography (MPL) oHow to make process faster? Parallelization of the process https://youtu.be/a2V699sbHEk?feature=shared OPTICS MEET-UP, Jena, Germany, September 25, 2025 Limitations of the process 25.11.2025Page 5 Proximity effects oIn-plane overlap oOut-of-plane polymerization (“hot spots”) © Fraunhofer IISB Modeling is important to overcome the limitations, to scale up the process, to unlock the full potential of metasurface technology and more! OPTICS MEET-UP, Jena, Germany, September 25, 2025 Modeling the two-photon lithography 25.11.2025Page 6 Forward models Optical model Generation of point spread function (PSF) within resist Resist model Threshold describes polymerization Exposure kinetics Diffusion and kinetics of multiple species Presence of quencher Development of the processed polymer Exposure kinetics Temperature profile Diffusion and kinetics of multiple species Presence of quencher Development of the processed polymer A full model of polymerization Generalized compact model*Threshold model OPTICS MEET-UP, Jena, Germany, September 25, 2025 Generalized compact model 25.11.2025 © Fraunhofer IISBPage 7 Modeling the realistic two-photon lithography (TPL): start from the “voxel” Optical elements Stage Gaussian intensity distribution 1 Bulk image 2 Oxygen Radical Polymerization degree 4Dark phase: initial state →quenching →diffusion →quenching → termination →propagation →polymerization 𝐶, = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡  Photoinitiator Radical 3 𝜕[𝑃𝐼] 𝜕𝑡 = 𝐶  𝐼 [𝑃𝐼] PI: Photoinitiator CDill: Photosensitivity Adapted Dill model: Approximation of oxygen depletion: Photoinitiation: 5Development: DArT Voxel Mack model Fast marching method OPTICS MEET-UP, Jena, Germany, September 25, 2025 Stage Generalized compact model 25.11.2025 © Fraunhofer IISBPage 8 Application: line writing Laser power = constant Scan speed = constant Infinite oxygen supply Polymerization degree DArT Oxygen Radical (isolated) Radical (total) OPTICS MEET-UP, Jena, Germany, September 25, 2025 How to solve inverse problem? 25.11.2025 © Fraunhofer IISBPage 9 1. Build the Forward Model: 2. Solve the Optimization Problem Use gradient-based methods (e.g., backpropagation) Employ a generator model to reconstruct the solution … Polymer Quenching Diffusion Quenching Termination Propagation Polymerization R + O2 R + O2 O2 R R R + M Mack model Resist Exposur e OPTICS MEET-UP, Jena, Germany, September 25, 2025 25.11.2025 © Fraunhofer IISBPage 16 •Resins behave as a non-Newtonian fluid •Non-linear viscosity (𝜂) model, 𝜂 → 𝑓(𝛾󰇗) where 𝛾󰇗 is the strain rate/rate of deformation of the fluid. •The domain is divided into “finite volumes” where the Navier Stokes equations are solved for each time step of the simulation. Methodology: Rheological model OPTICS MEET-UP, Jena, Germany, September 25, 2025 25.11.2025 © Fraunhofer IISBPage 17 Finite element simulations: [Young’s modulus 0.85 GPa, Thermal condition 110 °C] Numerical setup: Mesh count: ~200k cells, number of cores: 16, simulation time: ~3.5 hrs Model Validation Results Mostafa Kotkat Fraunhofer Institute for Integrated Systems and Device Technology (IISB), Erlangen, Germany OPTICS MEET-UP 2025, Jena, Germany Color Centers in SiC for Quantum Optics — OPTICS MEET-UP, Jena, Germany, September 25, 2025 Color Centers (CC) 25.11.2025 © Fraunhofer IISBSeite 19 Fei Fred Wang, 2016 Stefania Castelletto, 2022 Diamond is not suitable for large scale production OPTICS MEET-UP, Jena, Germany, September 25, 2025 Collection Optics 25.11.2025 © Fraunhofer IISBPage 20 𝑑  Θ Θ 𝑛 ≈ 2.57 𝑛 = 1 NA = 0.9 Maximum collection efficiency is less than 5% Marina Radulaski, 2017 Fraunhofer IISB OPTICS MEET-UP, Jena, Germany, September 25, 2025 Comparison between collectors 25.11.2025 © Fraunhofer IISBPage 21 3 um 2 um 3 um 2 um 2 um 2 um 𝑑 𝑑  Collection efficiency NA = 0.9 OPTICS MEET-UP, Jena, Germany, September 25, 2025 Summary 25.11.2025 © Fraunhofer IISBPage 22 •Color Centers: Nature’s Optical Fingerprints •SiC: A Promising Host for Next-Gen Applications •Think of CCs as Tiny Dipole Emitters •Efficiency Hinges on Depth & Structure •Smart Design: Balancing Physics, Fabrication & Testing Thank you for your attention! Backup slides OPTICS MEET-UP, Jena, Germany, September 25, 2025 Neural network and differentiable 3D lithography model 25.11.2025 © Fraunhofer IISBPage 25 Differentiable 3D lithography model U-Net Desired 3D structure Predicted dose distribution Predicted 3D structure Loss is defined by the desired and predicted resist pattern Data-driven part Physics-based part