Collective buckling of line arrays created by soft lithography

Abstract

The authors analyze the collective buckling of an array of elastic lines with their lower edges built into an elastic substrate of the same material. These lines can interact among themselves through the deformation of the substrate. From the theory of elasticity and elastic structures, an eigenvalue problem is formulated and solved. Calculations show that the lines can buckle collectively into certain ordered patterns, where some of which have been confirmed by experiments. The results are useful for the understanding, design, and application of the nanostructures produced by soft lithography and other embossing techniques.

Prediction of porous dielectric line wiggling phenomenon with metallic hard mask: From simulation to experiment

“…Substrate deformation leads to coupling between lines which results in collective buckling. 6 In our case, the same mechanism can explain the collective lines buckling observed in Figure 3. Figure 4 represents a superposition of the simulation and experimental results previously described for line wiggling for different titanium nitride residual stress as a function of the line dimension.…”

Controllable Wrinkling of Thin Films on Pre-Stretched Elastomers Induced by Gravity

“…In the experiments, collective bulking of nanopillar arrays was explored to promote for nanolithography [Zhang et al, 2006;Lin et al, 2007]. Corresponding numerical analysis showed that the surface pattern of structures was regulated by varying gravitational potential energy of columns [Chen et al, 2008[Chen et al, , 2011Lin et al, 2010;Li et al, 2012].…”