Asymmetric fluid-structure dynamics in nanoscale imprint lithography

2 2( r − r )3µb dh − 2γp = [2.38]3h dt hThe force is obtained by integrating with respect to r and θF42⎛ − 3µr − ⎞b dh γrb= 2π ⎜⎟3[2.39]⎝ 4hdt h ⎠Equations 2.38 and 2.39 were used to perform numerical simulations of theequation of motion where fluid is modeled with boundary conditions that evolveas the fluid is squeezed out from between the surfaces. This is discussed inChapter 4.2.5 TOPOGRAPHY EFFECTSThe ratio h is an important parameter showing the effects of surfaceσroughness. For h >> 3 , the roughness effects are not important, and theσpressure distribution for corrugated surfaces are qualitatively the same as for flatplate film theory. The roughness effects become important as h → 3σ[Patir andCheng 1978]. The local film thickness is h T= h + δ1+ δ2where h is thenominal film thickness defined as the distance between the mean levels of the twosurfaces. δ 1 and δ 2 are the roughness amplitudes of the two surfaces measuredfrom their mean levels with zero mean and standard deviations σ 1 and σ 2 . Theparameter σ is the composite standard deviation of surface2 2heightsσ = σ 1+ σ .2Assume that the height of the features on the templates is on average 200nm, and that to maximize the density of the circuit elements, the line widths (LW)39