Asymmetric fluid-structure dynamics in nanoscale imprint lithography

Chapter 5: Numerical SimulationsA series of numerical simulations to predict the performance of theimprinting systems used in SFIL are discussed in this chapter. A model of themechanical system was developed, which considered two primary modes ofcompliance - axial and torsional. Initial conditions were selected to be similar tothose in the actual SFIL experiments. The actuation was assumed to have anideal feedforward controller. The equations of motion were simulated using afourth order accurate Runge-Kutta scheme with adaptive time marching.Simulation results are presented in this chapter for the case of an inclined surfaceof infinite width with both single and double s-curve position control. Finally, thecase of a parallel, circular plate with a single fluid drop was simulated.5.1 DYNAMIC SYSTEM MODELIn this section the equations governing the dynamic response of theimprinting system are presented. The dynamic equations are developedassuming an imprinting system where the motion is governed by compliance intwo directions: the axial direction along the motion axis of the actuators and arotational direction about an orthogonal axis. The template holding mechanismbased on semi-circle notched flexures discussed in chapter 3 (see Figure 3.4) wasdesigned to be consistent with this assumption and is implemented in the activestage test bed. Equivalently, a single rotational axis can be the orientation axis ofthe template in the multi-imprint stepper where the axis of rotation is an axis thatis a linear combination of the motion provided by the α-β stages. This axis alsopasses through the center of the template surface (see Figure 3.2). Henceforth59