Asymmetric fluid-structure dynamics in nanoscale imprint lithography

time marching is required to minimize computational time and provide accuratesolutions. This adaptation was done manually by providing the largest stable timestep as input into the simulation. These time steps were determined by bruteforce. Each simulation was broken into several simulation time intervals. Thenthe time step was decreased by a factor of 10 when the simulation showed signsof instability. This was repeated until each run of the simulation was complete.5.3.2 Modeling the Initial Conditions for an ImprintThe equations of motion for the mechanical system represent an initialvalue problem. This ODE system requires a set of known initial conditions.The set of initial conditions was chosen to reflect those existing in the imprintingprocess. A further requirement was that these could be replicated in theexperimental setup.The initial gap between the template and the wafer was assumed to be 2µm. The initial conditions at the left and right boundaries of the flow at x = x αand x = x β are determined by simple volumetric calculations. For a template ofone square inch and a base layer thickness of 200 nm to completely fill the gap,this requires that the volume of fluid dispensed is 0.13 µL (1.3 × 10 -10 m 3 ). Thisminimizes material wastage as well as the force required to squeeze out the fluid.The placement of this fluid volume is assumed to be a line of 2 mm width, whichcompletely wets the template along its length and is along the centerline of thetemplate surface. A 2 µm column of fluid 2.54 cm (1 inch) long and 2mm wideis about 0.1 µL. This fluid volume would thus fill the gap at a base layerthickness of between 100 and 200 nm.68