Thermocapillary Patterning of Highly Uniform Microarrays by Resonant Wavelength Excitation

Abstract

For decades, researchers have been exploring pattern-forming instabilities in free surface thin films in the hope of developing alternative lithographic techniques for applications only requiring resolution limits in the submicron range. Previous studies have shown how the pitch and shape of elements in an array can be varied by adjusting the magnitude of surface forces and growth time prior to solidification in situ. Since the formations emerge naturally from an initial flat molten film, the final arrays exhibit ultrasmooth interfaces and are therefore ideally suited to beam-shaping applications such as thin-film micro-optics. Progress in this field has stalled, however, due to the very nature of the formation process. Even when great care is taken to ensure that initial films are defect-free, final arrays still exhibit unacceptable variability in pitch, shape, and height due to ubiquitous sources of noise responsible for instability and growth. In this work, we focus on a thermocapillary instability in slender molten films exposed to a very large thermal gradient. We begin with a discussion and demonstration of why this instability inextricably leads to highly disordered arrays even if initialized by a film with very small amplitude surface roughness. We then demonstrate how spatially periodic modulation of the thermal field, implemented in three different ways, can induce synchronous growth of highly uniform periodic arrays despite noisy initial conditions. Results based on linear and weakly nonlinear stability analysis, Bloch wave analysis, and direct numerical simulation of the interface equation reveal how resonant wavelength excitations occurring between the modulation and instability driving fields are responsible for such rapid and coherent growth. An additional benefit is that the modulation field can be selected to yield an array pitch much smaller than in unmodulated systems.