Rippling Instability of Supported Polymer Nanolines
Vijaya R. Tirumala, Christopher M. Stafford, Leonidas E. Ocola, Jack F. Douglas, L. Mahadevan
The swelling response of polymer line gratings supported on a rigid substrate has direct implications on their mechanical stability during pattern transfer in nanofabrication. The polymer lines, when swollen in a good solvent, undergo a rippling instability with a well-defined wavelength at the top surface but remain straight and bonded to the substrate at the polymer-substrate interface. These patterns develop due to elastic relaxation of the inhomogeneous compressive strains that arise as a result of the geometric constraints that prevent swelling near the substrate/polymer interface. The ripple wavelength scales linearly with linewidth ( ~ 7w) for gratings that are sufficiently long to overcome finite size effects. The ripple amplitude is independent of grating length but scales with linear swelling degree. These trends were validated for patterned polymer nanolines in the range of (20-250) nm linewidth and a height-to-width aspect-ratio in the range 0.5-5. A simple theory shows that the ripple wavelength and amplitude follow via an analogy to the problem of why the edges of leaves are rippled due to constrained growth.