Asymmetric fluid-structure dynamics in nanoscale imprint lithography

damping from the etch barrier. The dynamic behavior of such systems can bedescribed byand( zD− zD) + K ( z − z ) f ( z, z, D θ θ D )MD z+ C,[5.1]Z A Z A=( θ −θ) τ ( z,D,θ θD)I D θ+ C θD+ K = ,[5.2]θθ0zwhere the fluid force and torque are functions of position and orientation. Thefluid couples the two, otherwise independent, motions. In the following sections,the set of model parameters are presented with details on the selection of initialconditions for the simulation.5.2 SYSTEM PARAMETERS FOR NUMERICAL SIMULATION5.2.1 Etch Barrier Fluid PropertiesThe capillary pressure is obtained using the surface tension coefficient forthe etch barrier formulation. The surface tension of the various etch barrierformulations, which is composed of free radical generators and cross-linkingagents dissolved in a solution of organic monomer, silylated monomer, anddimethyl siloxane oligomer derivatives, are all nearly identical to withinexperimental error at 28 dynes/cm [Colburn et al 1999]. If the fluid between theplates is water instead of etch barrier, the surface tension is 72 dynes/cm at 20°C.From this, the boundary conditions due to the capillary pressure for the fluidvolume can be computed. The viscosity of the etch barrier layer is the same asthat of water at room temperature and atmospheric pressure, which is about 1 cP(1 × 10 -3 N⋅s/m 2 ). Both the etch barrier and water were considered to have aconstant viscosity and to be incompressible.61