Asymmetric fluid-structure dynamics in nanoscale imprint lithography

the multi-imprint and active stage systems will be referred to as the mechanicalsystem.These equations are developed neglecting lateral motions in the x-ydirections. If the output of each actuation leg is assumed to be identical, then themechanical system can be modeled as a lumped parameter system as seen inFigure 5.1.This system has two degrees of freedom, z and θ. The actuatormotions, z A and z A, are taken as inputs into the mechanical system. The structuralstiffness in the z direction has been modeled as a single composite stiffnessparameter, K Z , with damping coefficient C Z . The template orientation stages arecompliant in torsion with stiffness K θ and damping coefficient C θ . The force, f,and torque, τ, due to the pressure from the etch barrier layer are treated asnonlinear forcing terms in the equations of motions of the system.z, DAz AC ZzC θ,Κ θK ZM, Ipxf, τFigure 5.1 Lumped Parameter ModelThe equations of motions for the mechanical system are derived fromLagrange’s equations. The motion in the vertical and torsional directions ofFigure 5.1 is essentially the classic mass-spring-damper system with active60