Modeling of two-photon lithography including oxygen diffusion using a generalized compact model

Introduction Modeling the realistic two-photon polymerization (TPP) Model description Model calibration Calibration using a multi-objective genetic optimizer from Dr.LiTHO. Figure 1: Four simulation stages of the generalized compact model. Figure 3: Voxel dimensions from simulation and experimental measurementsbplotted against average power at four exposure times at 1 μs, 10 μs, 100 μs, and 1000 μs. Conclusion: Model performance — Maintains computational efficiency and improves alignment with experimental data across all exposure times. Incorporates additional chemical and physical mechanisms. Helps to predict outcomes under different setups. 1Sedova, V., Ogor, F., Rovera, J., Tsilipakos, O., Lemberg, L., Heggarty, K., and Erdmann, A., “Advances in modeling and optimization for two-photon lithography,” in [Computational Optics 2024], Smith, D. G. and Erdmann, A., eds., 13023, 1302309, International Society for Optics and Photonics, SPIE (2024). Goal — Extend the functionality and improve the performance of the compact model1. Yuan Yua, Valeriia Sedovaa, Christian Schwemmera, Jonas Wiedenmannb, Andreas Erdmanna [email protected].de aFraunhofer-Institut für Integrierte Systeme und Bauelementetechnologie IISB, Erlangen, Germany bHeidelberg Instruments Mikrotechnik GmbH (HIMT), Würzburg, Germany Modeling of two-photon lithography including oxygen diffusion using a generalized compact model — Time-dependent Dill model Approximation impact of oxygen depletion in exposed areas The Dill model for TPP: The effective dose 𝐷: Time-dependent 𝐶: Under identical conditions, 𝐶, varies with exposure times as: 𝜕[𝐼𝑛𝑖𝑡𝑖𝑎𝑡𝑜𝑟] 𝜕𝑡 = 𝐶  𝐼 [𝐼𝑛𝑖𝑡𝑖𝑎𝑡𝑜𝑟] (1) 𝐷 = 𝐶  𝑡  𝐼 𝑅𝑡(2) 𝐶 = 𝐷  𝐴𝑟𝑒𝑎 (𝑅𝑡)  𝐼   𝑡   𝑃   (3) 𝐶, = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡 (4) Reactions in photoresist Quench reactive intermediates through oxygen, which inhibits reactions. Diffuse oxygen between two quenching reactions to capture its impact. Termination via chain coupling, quenching, and self-trapping. Propagation through diffusion to mimic chain growth. Polymerization based on concentrations of reactive sites and monomers. Figure 2: Simulated cross-sectional profiles of oxygen, radical (R), and the resulting polymer distribution within the photoresist. All axes are in micrometers (μm). O2 R Polymer initial state 1st quench diffusion 2nd quench propagation polymerization Dr.Image Gaussian intensity distribution Bulk image Photoinitiator Radical Dill model 𝐶 = c𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡  Mack model DArT Fast marching algorithm Local development rate Quenching Diffusion Quenching Termination Propagation Polymerization Smoluchowski theory Gaussian convolution ℱ{ℱ(𝐺)  ℱ(𝑓)} 𝑑[𝐴𝐵] 𝑑𝑡 = 𝑘 𝐴 [𝐵] R + O2 O2 R + O2 R R R+M Contour Polymer customized wafer stack Stage 1: Imaging Stage 2: Exposure Stage 3: Dark Phase Stage 4: Development www.fabulous3D.e u This project has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement nº 101091644. UK participants in Horizon Europe Project FABulous are supported by UKRI grant nº 10062385 (MODUS). Calibration results —