Machine Learning Topography Prediction and Optimization in Maskless Grayscale Laser Lithography

Abstract:

A machine learning (ML) framework was developed for the prediction of surface topography obtained with maskless grayscale laser lithography based on the spatial distribution of the applied laser energy dose, or virtual photomask. Artificial neural networks (ANNs) were employed, with the virtual photomask and its radial averages selected as input variables and the surface elevation selected as the output variable. Training of ANNs was carried out with data acquired from the production of models comprising a wide range of representative geometries. Hyperparameter optimization was performed by assessing the accuracy of trained ANNs, with the final configuration comprising a single hidden layer with 15 neurons and a Sigmoid activation function. The trained ANN was then employed within an iterative optimization algorithm to determine the best virtual photomask for the production of new objects by updating the virtual photomask based on the predicted error, thus automatically compensating for proximity effects and sharp dose transitions. The developed approach achieved a reduction in average build error from 2.8 µm to 1.3-1.5 µm compared to standard experimental approaches in a single build, improving not only accuracy but also greatly reducing time requirements for optimization of the process.

• Periodical: Key Engineering Materials (Volume 1047)
• Pages: 11-20
• Online since: April 2026
• Authors: Adrian H.A. Lutey*, David Kuhness, Seyyedhossein Mckee, Marco Negozio, Markus Postl, Barbara Stadlober
• Keywords: Artificial Neural Network, Machine Learning, Maskless Grayscale Laser Lithography, Process Optimization

References

[1] A. Grushina, Direct-write grayscale lithography, Advanced Optical Technologies 8 (2019) 163–169.

DOI: 10.1515/aot-2019-0024

[2] J. Dunkel, F. Wippermann, A. Brückner, A. Bräuer, A. Tünnermann, Laser lithographic approach to micro-optical freeform elements with extremely large sag heights, Opt. Express 20 (2012) 4763.

DOI: 10.1364/OE.20.004763

[3] R. He, S. Wang, G. Andrews, W. Shi, Y. Liu, Generation of Customizable Micro-wavy Pattern through Grayscale Direct Image Lithography, Sci Rep 6 (2016) 21621.

DOI: 10.1038/srep21621

[4] J. Loomis, D. Ratnayake, C. McKenna, K.M. Walsh, Grayscale lithography—automated mask generation for complex three-dimensional topography, J. Micro/Nanolith. MEMS MOEMS 15 (2016) 013511.

DOI: 10.1117/1.JMM.15.1.013511

[5] Z. Zhu, S. Wei, R. Liu, Z. Hong, Z. Zheng, Z. Fan, D. Ma, Freeform surface design for high-efficient LED low-beam headlamp lens, Optics Communications 477 (2020) 126269.

DOI: 10.1016/j.optcom.2020.126269

[6] J. Du, F. Gao, Y. Zhang, Y. Guo, C. Du, Z. Cui, Modified proximity function for OPC in laser direct writing, in: C.J. Progler (Ed.), Santa Clara, CA, 2000: p.1047.

DOI: 10.1117/12.388940

[7] J. Erjawetz, D. Collé, G. Ekindorf, P. Heyl, D. Ritter, A. Reddy, H. Schift, Bend the curve – Shape optimization in laser grayscale direct write lithography using a single figure of merit, Micro and Nano Engineering 15 (2022) 100137.

DOI: 10.1016/j.mne.2022.100137

[8] T. Onanuga, M. Rumler, A. Erdmann, Simulation flow and model verification for laser direct-write lithography, J. Micro/Nanolith. MEMS MOEMS 16 (2017) 1.

DOI: 10.1117/1.JMM.16.3.033511

[9] D. Weichert, P. Link, A. Stoll, S. Rüping, S. Ihlenfeldt, S. Wrobel, A review of machine learning for the optimization of production processes, Int J Adv Manuf Technol 104 (2019) 1889–1902.

DOI: 10.1007/s00170-019-03988-5

[10] W. "Grace" Guo, Q. Tian, S. Guo, Y. Guo, A physics-driven deep learning model for process-porosity causal relationship and porosity prediction with interpretability in laser metal deposition, CIRP Annals 69 (2020) 205–208.

DOI: 10.1016/j.cirp.2020.04.049

[11] P. Kareem, Y. Shin, Synthesis of Lithography Test Patterns Using Machine Learning Model, IEEE Trans. Semicond. Manufact. 34 (2021) 49–57.

DOI: 10.1109/TSM.2021.3052302

[12] X. Sun, S. Yin, H. Jiang, W. Zhang, M. Gao, J. Du, C. Du, U-Net convolutional neural network-based modification method for precise fabrication of three-dimensional microstructures using laser direct writing lithography, Opt. Express 29 (2021) 6236.

DOI: 10.1364/OE.416871

[13] P. Minetola, F. Calignano, M. Galati, Comparing geometric tolerance capabilities of additive manufacturing systems for polymers, Additive Manufacturing 32 (2020) 101103.

DOI: 10.1016/j.addma.2020.101103

[14] F.H. Dill, W.P. Hornberger, P.S. Hauge, J.M. Shaw, Characterization of positive photoresist, IEEE Trans. Electron Devices 22 (1975) 445–452.

DOI: 10.1109/T-ED.1975.18159

[15] M.D. Smith, J.D. Byers, C.A. Mack, The lithographic impact of resist model parameters, in: J.L. Sturtevant (Ed.), Santa Clara, CA, 2004: p.322.

DOI: 10.1117/12.537581

[16] N. Xie, D. Jones, G. Lopez, Comprehensive modeling of the lithographic errors in laser direct write, Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena 37 (2019) 061603.

DOI: 10.1116/1.5122660