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Abstract Two-photon lithography (TPL) is an attractive technique for nanoscale additive manufacturing of functional three-dimensional (3D) structures due to its ability to print subdiffraction features with light. Despite its advantages, it has not been widely adopted due to its slow point-by-point writing mechanism. Projection TPL (P-TPL) is a high-throughput variant that overcomes this limitation by enabling the printing of entire two-dimensional (2D) layers at once. However, printing the desired 3D structures is challenging due to the lack of fast and accurate process models. Here, we present a fast and accurate physics-based model of P-TPL to predict the printed geometry and the degree of curing. Our model implements a finite difference method (FDM) enabled by operator splitting to solve the reaction–diffusion rate equations that govern photopolymerization. When compared with finite element simulations, our model is at least a hundred times faster and its predictions lie within 5% of the predictions of the finite element simulations. This rapid modeling capability enabled performing high-fidelity simulations of printing of arbitrarily complex 3D structures for the first time. We demonstrate how these 3D simulations can predict those aspects of the 3D printing behavior that cannot be captured by simulating the printing of individual 2D layers. Thus, our models provide a resource-efficient and knowledge-based predictive capability that can significantly reduce the need for guesswork-based iterations during process planning and optimization. 

Two-photon lithography (TPL) is a laser-based additive manufacturing technique that enables the printing of arbitrarily complex cm-scale polymeric 3D structures with sub-micron features. Although various approaches have been investigated to enable the printing of fine features in TPL, it is still challenging to achieve rapid sub-100 nm 3D printing. A key limitation is that the physical phenomena that govern the theoretical and practical limits of the minimum feature size are not well known. Here, we investigate these limits in the projection TPL (P-PTL) process, which is a high-throughput variant of TPL, wherein entire 2D layers are printed at once. We quantify the effects of the projected feature size, optical power, exposure time, and photoinitiator concentration on the printed feature size through finite element modeling of photopolymerization. Simulations are performed rapidly over a vast parameter set exceeding 10,000 combinations through a dynamic programming scheme, which is implemented on high-performance computing resources. We demonstrate that there is no physics-based limit to the minimum feature sizes achievable with a precise and well-calibrated P-TPL system, despite the discrete nature of illumination. However, the practically achievable minimum feature size is limited by the increased sensitivity of the degree of polymer conversion to the processing parameters in the sub-100 nm regime. The insights generated here can serve as a roadmap towards fast, precise, and predictable sub-100 nm 3D printing. 

Abstract Two-photon lithography (TPL) is a direct laser writing process that enables the fabrication of cm-scale complex three-dimensional polymeric structures with submicrometer resolution. In contrast to the slow and serial writing scheme of conventional TPL, projection TPL (P-TPL) enables rapid printing of entire layers at once. However, process prediction remains a significant challenge in P-TPL due to the lack of computationally efficient models. In this work, we present machine learning-based surrogate models to predict the outcomes of P-TPL to >98% of the accuracy of a physics-based reaction-diffusion finite element simulation. A classification neural network was trained using data generated from the physics-based simulations. This enabled us to achieve computationally efficient and accurate prediction of whether a set of printing conditions will result in precise and controllable polymerization and the desired printing versus no printing or runaway polymerization. We interrogate this surrogate model to investigate the parameter regimes that are promising for successful printing. We predict combinations of photoresist reaction rate constants that are necessary to print for a given set of processing conditions, thereby generating a set of printability maps. The surrogate models reduced the computational time that is required to generate these maps from more than 10 months to less than a second. Thus, these models can enable rapid and informed selection of photoresists and printing parameters during process control and optimization.