Physical Society Colloquium

Modulated Interface Lithography (MIL): The Nanoworld Beyond Bénard Instability

Sandra Troian

Caltech

Experiments by several groups during the past decade have demonstrated that molten nanofilms whose free surface is exposed to large thermal gradients undergo spontaneous formation of nanopillar arrays with a pitch on the order of 1-10 microns. These 3D microarrays can adopt various in-plane symmetry ranging from lamellar to hexagonal depending on initial and boundary conditions. Once the thermal gradient is removed, the structures rapidly solidify in place resulting in nanostructures with extraordinarily smooth surfaces, particularly advantageous for optical and photonic applications including microarrays or optical resonators. Control over this process requires identification of the physical mechanism responsible for this phenomenon. There are currently three prevailing explanations based on linear stability analysis: (i) electrostatic attraction between the molten film and proximate substrate due to induced surface image charge (Chou et al. 2002), (ii) interface radiation pressure from coherent reflections of acoustic phonons (Schäffer et al. 2003), and (iii) film fluctuation enhancement by thermocapillary forces (Troian et al. 2009 - 2011). In this talk, we first describe the process by which fluid elongations are triggered by a long-wavelength thermocapillary instability (“nano-Bénard flow”) which cannot be suppressed by capillary forces. Linear stability and Lyapunov analysis of the governing interface equation shows there is no critical number for onset of instability and no steady state if the film is not mass limited i.e. nanopillars grow continuously toward the proximate cooler target. We then compare these predictions with ongoing experiments in our laboratory which appear to confirm the thermocapillary mechanism. We conclude with recent studies of resonant wavelength phenomena which can be used to induce a degree of uniformity in array formations. In total, these results point the way toward 3D lithography based on modulation of surface forces.