Deformation of elastomeric pyramid pen arrays in cantilever-free scanning probe lithography

Cantilever-free scanning probe lithography (SPL) employs soft elastomeric pen arrays to deliver material or energy to a surface to achieve a high-resolution, high-throughput, and low-cost nanopatterning. In particular, microscale elastomeric pyramid pen arrays are often adopted as the cantilever-free architecture owing to their distinct structural and mechanical properties. To better understand the mechanical behavior of the elastomeric pyramid pen array during the lithographic printing process, we numerically investigate the compression of an elastomeric pyramid array in a nonadhesive and frictionless contact with a rigid substrate. Simple scaling laws of the width of the contact surface with respect to the compression displacement and force are found and compared with previous models and experiments. By changing the interpyramid distance or the thickness of the base of the pyramid array, increasing deviations from the established scaling laws are observed and explained. Furthermore, we demonstrate that the unique morphology of a compressed pyramid primarily determines the unusual shape of the features fabricated by a specific cantilever-free SPL technique.