Energy-based thermal reflow simulation for 3D polymer shape prediction using Surface Evolver

An intensive, energy-based analysis of the thermal reflow of thermoplastic polymer structures is presented. Poly (methyl methacrylate) (PMMA) was patterned by grayscale electron beam lithography. The obtained rectangular, micron-scale structures were transformed into lens-like structures by thermal reflow near the glass transition temperature of the original PMMA. Representative parameters obtained from these reflow experiments were used to model the reflow process by using a new, energy-based, finite element, soapfilm method using the free software Surface Evolver. The time-, temperature- and molecular-weight-dependent geometry evolution of the PMMA structures could be described by an apparent contact-angle-evolution time constant and a shape-evolution time constant. The developed model allows the prediction of intermediate geometries during the reflow process occurring between the initial and the final energy optimal geometry. The proposed model is independent from the explicit knowledge of material-specific parameters such as viscosity or glass transition temperature. Extensive experimental data for PMMA reflow is provided. Simulation examples are given for a contact-angle-dominated reflow which demonstrate a good agreement between model and experiment.