Numerical and experimental study of critical roof collapse conditions in soft lithography.

One of the major issues during soft lithographic processes is that, if the pressing force on the stamp becomes too high, the stamp may erroneously come into contact with the substrate in zones where contact is not intended. This decreases the patterning accuracy and may lead to badly or nonperforming electronic devices and is therefore undesired. Design rules, available at an early stage in the design phase, are desired to speed-up the development of this technique. Ultimately, these rules should give an indication of the critical pressure that can safely be applied on the stamp thereby avoiding unwanted contact between the stamp and the substrate. To obtain these critical pressures, numerical analyses of the deformation behavior of two characteristic configurations in the microstructured surface pattern of the rubber stamp are performed. The deformation behavior of the rubber is modeled according to a Gaussian and a non-Gaussian approach, leading to a neo-Hookean and Arruda-Boyce constitutive model, respectively. Besides these material nonlinearities, geometrical nonlinearities are taken into account as well. The calculated pressure at which undesired contact takes place (the roof collapse pressure) is compared to experimentally obtained values for two particular types of structures, and the results are in agreement within the error margins of the experiments and those ensuing from the assumptions of the numerical simulations.