Modeling and simulation of mechanical effects in two-photon lithography

Mathematical modeling ◼Two approaches were considered during the formulation depending on the material properties of the resin. −Structural model −Rheological model ◼The structural model considered the Surface Tension Force (STF) and Laplace pressure (P) due to the fluid present in between two pillars. −The critical aspect ratio was calculated to be as follows, 𝑨𝑹𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍 =3𝐸𝑑 3𝑃𝐻+8𝛾 sin 𝜃 , ◼The rheological model was formulated based on the assumption that the resin behaves as a non-Newtonian fluid. −It uses the finite volume method with a non-linear viscosity model to capture the flow behaviour of the resin. Modeling and simulation of mechanical effects in two-photon lithography — Alap Mundayoor, Andreas Erdmann, Valeriia Sedova [email protected].de Fraunhofer Institute for Integrated Systems and Device Technology, Erlangen, Germany Rheological simulations Introduction and Motivation ◼Two-photon lithography (TPL) has emerged as a pivotal technique for fabricating highly intricate micro-and nanoscale structures with diverse applications. ◼During the development stage, forces exerted by the solvents significantly affect the structural integrity, quality, and throughput of the fabricated components. ◼Pre-fabrication collapse risk assessment would be of great significance to the experimentalists in the clean room Goal — To develop a first-principles framework predicting mechanical stability limits in TPL fabricated structures. ◼The softer resins tend to show a gradual collapse, mainly due to the external forces acting on the sidewalls. ◼The Bird-Carreau model was chosen to capture the non-linear behaviour. References: 1. Kimiyoshi Deguchi et al.1992 Jpn. J. Appl. Phys. 31 2954. 2. Chini SF, Amirfazli A. Understanding pattern collapse in photolithography process due to capillary forces. Langmuir. 2010 Aug 17;26(16):13707-14. 3. Modelling nanomechanical effects in advanced lithographic materials and processes, S. D'Silva – 2023 (PhD Thesis). 4. Sedova, V., Ogor, F., Rovera, J., Tsilipakos, O., Lemberg, L., Heggarty, K., and Erdmann, A., “Advances in modeling and optimization for twophoton lithography,” in [Computational Optics 2024], Smith, D. G. and Erdmann, A., eds., 13023, 1302309, International Society for Optics and Photonics, SPIE (2024). Finite element simulations Simulations show comparable results to the experimental data (shown above). Model applications ◼Both analytical and FEM models (Figure 1) show that total deformation of pillars increases rapidly with aspect ratio, and structures with lower Young’s modulus are far more prone to collapse at high aspect ratios. ◼Stability map (Figure 2): Visualizes how the critical aspect ratio for collapse depends on both pillar spacing and aspect ratio, clearly separating stable and unstable fabrication regions. Figure 1: Comparison of the analytical and finite element model Figure 2: Stability map based on the critical aspect ratio Conclusion — •Pillar collapse is a highly non-linear process that could depend on a variety of factors apart from the capillary forces considered here. •The analytical model shows agreement with the finite element simulations performed on ANSYS, thereby helping in verification. •The critical aspect ratio can be used as a guidline for experimentalists to mitigate collapse in their structures. www.fabulous3D.eu 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).