A Mathematical Model Development And Sensitivity Analysis Of Two Photon Polymerization For 3D Micro/nano Fabrication
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Two photon polymerization (2PP) is an effective technique for the fabrication of complex polymeric 3-D micro/nano features using ultrashort pulses from a NIR laser source. The photosensitive material absorbs two photons and initiates the chain polymerization reaction. The interaction of laser pulses with photo responsive resin creates a voxel (volumetric pixel) which defines the resolution of 2PP process. In this work, a mathematical model of the polymerization process that considers the effects of molecular diffusion and polymerization kinetics on the formation of voxel. The increase in temperature upon polymerization and their effect on the polymerization kinetics and molecular diffusion is also considered in the model. The model adheres to the 3D confinement and nonlinear photophysical and photochemical changes that take place in the confined volume. A Design of Experiments methodology is employed to evaluate the sensitivity of the 2PP process on the applied laser power, scanning speed (or exposure time) and photoinitiator concentration. The proposed statistical model is checked for interaction between the process parameters, and multiple comparisons are laid out for evaluating the statistically significant differences. A regression model is developed for the prediction of polymerization resolution based on the experimental data. The developed statistical model is experimentally verified and along with the understanding acquired through the statistical analysis was used for the successful prototyping of various micro/nano structures. Feature sizes of ~1.5 µm in radial direction and ~20 µm in axial direction are fabricated using the existing laser system and 0.4 NA microscope objective. A novel approach for fabricating high aspect ratio in a single laser scan is also presented. Aspect ratios of ~ 100 and higher can be easily achieved with a single laser scan of loosely focused laser pulses. The fabricated structures show good structural integrity, high aspect ratio and fabricated in a single laser scan at moderate laser powers. Also, the deformation and collapse of the polymerized pattern due to cohesive forces and remedial measures are discussed. The presented work demonstrates the ability of low repetition rate laser systems and loosely focused laser pulses for fabrication of high aspect ratio structures in a single laser scan.