Asymmetric fluid-structure dynamics in nanoscale imprint lithography

the composite stiffness was calibrated using the results from one experimentaldata set (known as the calibration set). The calibrated composite stiffness wasused to perform simulations that were then correlated to an independent set ofexperimental results (known as the correlation set). From the simulation results,it is inferred that the actual composite stiffness was less than previouslyestimated. A comparison of the correlation set and the simulation supports thehypothesis. The data show similar trends and are reasonably close. However,there are still discrepancies, especially at large times, which may be due toparticles and other unknown parameters that have not been calibrated. Theseissues require further investigation. The following details the process used incalibrating the composite stiffness parameter.A calibration simulation was performed taking initial conditions thatapproximate the conditions for a specific set of measured data. With the fiberoptic spectrometer probes spaced 0.7 inches apart, the measured gap thickness foreach probe was 4780 nm and 2360 nm and the probe locations are assumed to besymmetric about the center of rotation of the template holding mechanism. Thisleads to an average height of 3570 nm with θ ~ 1.36 × 10 -4 radians and totalactuation of 5 µm. These initial conditions were used to perform a simulation ofthe squeeze film dynamics of the active stage system.The composite axial stiffness and damping were systematically decreaseduntil the agreement between the film thickness from the experiments and thesimulations were within five percent. The axial stiffness was 1.5 × 10 6 N/m andthe damping constant was 75 N⋅s/m. The remaining system parameters in thenumerical simulation were taken from table 5.2. Figure 6.4 shows the data setused in the calibration of the composite stiffness. The simulated film thicknessand the experimentally obtained film thickness values are within two percent.85