Physics-based deep learning network for inverse lithography in two-photon polymerization

Physics-based deep learning network for inverse lithography in two-photon polymerization — Valeriia Sedova1, Yuan Yu1, Thomas Le Deun2, Joёl Rovera2, Jonas Wiedenmann3, Kevin Heggarty2, Andreas Erdmann1 1Fraunhofer Institute for Integrated Systems and Device Technology (IISB), Erlangen, Germany 2IMT Atlantique, Brest, France 3Heidelberg Instruments Mikrotechnik GmbH, Würzburg, Germany EMLC 2025, Dresden, Germany 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Overview 25.11.2025 © Fraunhofer IISBPage 2 Motivation and introduction Forward model development Inverse Lithography Techniques (Optimization) SLM setup Voxel by voxel / DOE implementation Experimental validation Summary 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Motivation and introduction 25.11.2025 © Fraunhofer IISBPage 3 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Two-photon lithography 25.11.2025Page 4 © Fraunhofer IISB 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Limitations of the process 25.11.2025Page 5 Speed of printing Conventional point by point multiphoton lithography (MPL) oHow to make process faster? Parallelization of the process © Fraunhofer IISB Printed Metasurface Parallelized MPL for 3D metasurface writing 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Limitations of the process 25.11.2025Page 6 Proximity effects oIn-plane overlap Modeling is important to overcome the limitations, to scale up the process, to unlock the full potential of metasurface technology and more! oOut-of-plane polymerization (“hot spots”) © Fraunhofer IISB 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Limitations of the process 25.11.2025 © Fraunhofer IISBPage 7 Optimization of the problem (ILT) Target Intensity/power distribution Fabricated structure Missing: the right input Intensity/power distribution Optimization procedure algorithm is needed Target Target ? ? ? 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 How to solve inverse problem? 25.11.2025 © Fraunhofer IISBPage 8 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 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Overview of the models 25.11.2025Page 9 Forward model development 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 JM3 paper: “Advances in modeling and optimization for two-photon lithography” [DOI: 10.1117/1.JMM.24.2.023001] 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Example 25.11.2025 © Fraunhofer IISBPage 16 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Results from the optimization 25.11.2025 © Fraunhofer IISBPage 17 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Results from the optimization 25.11.2025 © Fraunhofer IISBPage 18 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 The outcome of this project 25.11.2025Page 19 Use NNLitho3D for lithographic simulations given the grayscale mask, PSF and physical parameters Optimize the NNLitho3D physical parameters, given mask and structure 3D Predict mask by using UNet Predict mask by optimizing UNet with the help of NNLitho3D 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 © Fraunhofer IISB ITL for voxel by voxel / DOE implementation 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Structure of the optimization framework 25.11.2025 © Fraunhofer IISBPage 21 It is not NN, this is gradient-based optimization using backpropagation — specifically through PyTorch's autograd engine Target pattern (3D desired shape) Sim resist shape vs target Loss calculation (MSE + IoU vs Target) Update Differentiable 3D lithography model Physics-based part Initial power grid Simulated resist shape 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Optimization procedure 25.11.2025 © Fraunhofer IISB Page 22 Tilted view Top view Aim: optimize a dose map (i.e., power at each exposure point) y x Predicted pattern Power map 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Results – 2 lines with 1 um separation 25.11.2025 © Fraunhofer IISBPage 23 1 µm DOE Scanning direction 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Results – 3 lines with no compensation 25.11.2025 © Fraunhofer IISBPage 24 2 µm DOE 1 µm Scanning direction 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Results – 3 lines with compensation 25.11.2025 © Fraunhofer IISBPage 25 2 µm DOE 1 µm Scanning direction 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Generalized compact model 25.11.2025 © Fraunhofer IISBPage 32 Stage 1. Imaging Stage 2. Exposure Stage 3. DarkPhase (reactions in resist) Stage 4. Development Polymer reactions Exposure Initial state development Monomer Radical Active tail Initiator Inactive head oFast, yet sufficiently accurate oInclude reactiondiffusion dynamics oEase of Calibration oRelatively high freedom Dr.Image Gaussian intensity distribution Bulk image Photoinitiator Radical Dill model 𝐶 ∝ 𝑐𝑜𝑛𝑠𝑡. 𝑡  Polymer 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 R + O2 O2 R R R + M Contour customized wafer stack Schematic of two-photon resist model 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 First approach 25.11.2025Page 33 Paper: https://doi.org/10.48550/arXiv.2309.17343 (+) incorporates physics-based principles (-) approximations that are learned through convolutional networks and differentiable models (-) Shrinkage and deformation are modeled as learned nonlinear functions rather than explicit chemical equations Intensity distribution Intensity distribution on top of 2.5D structure Difference 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 First approach 25.11.2025Page 34 Paper: https://doi.org/10.48550/arXiv.2309.17343 (+) incorporates physics-based principles (-) approximations that are learned through convolutional networks and differentiable models (-) Shrinkage and deformation are modeled as learned nonlinear functions rather than explicit chemical equations Target intensity distribution Predicted intensity distribution 40th Mask and Lithography Conference 2025 Dresden, Germany, June 16-18, 2025 Neural network and differentiable 3D lithography model 25.11.2025Page 35 1. Freeze NNlitho3D and set UNet to train mode 2. Provide Resist 3D to UNet (Z axis is Channel axis) 3. Let UNet predict a mask 4. Provide predicted mask and precomputed PSF to NNLitho3D 5. Let NNLitho3D compute a Resist 3D 6. Calculate loss between predicted Resist 3D and target Resist 3D using MSE loss. 7. Backpropagate loss 8. Optimize UNet weights until convergence Not simple MSE but MSE + NNLitho3D This allows to propagate the information about the system back to U-net