Mechanical micro- and nano-patterning processes rely on engineering the interactions between a stamp and a substrate to accommodate surface roughness and particle defects while retaining the geometric integrity of printed features. We introduce a set of algorithms for rapidly simulating the stamp–substrate contact, and we use them to show that advantageous behavior can occur when the stamp consists of a finite-thickness layer bonded to a layer with different elastic properties. The simulations use two-dimensional load-response functions describing in discrete space the response of a stamp surface's shape to a localized unit load. These load-response functions incorporate the contributions both of local, indentation-like displacements and of plate-like bending of finite-thickness stamp layers. The algorithms solve iteratively for contact pressure distributions that, when spatially convolved with the load response, yield deformations consistent with the properties of the stamp and the substrate. We investigate three determinants of stamp performance: conformation to sinusoidal substrate topographies, distortion of material around stamp protrusions, and conformation to isolated spherical dust particles trapped between the stamp and the substrate. All simulation results are encapsulated in dimensionless models that can be applied to the efficient selection of stamp geometries, materials, and loading conditions. A particularly striking finding is that a stamp with a finite-thickness compliant coating bonded to a more rigid support can conform more closely to a trapped particle under a given load than a homogeneous stamp with the properties of the coating. This finding could be used to minimize the impact of particle defects on patterning processes.
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