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In this letter, we demonstrate a relation between the boundary curvature$\kappa$ and the wrinkle wavelength $\lambda$ of a thin suspended film underboundary confinement. Experiments are done with nanocrystalline diamond filmsof thickness $t \approx 184$~nm grown on glass substrates. By removing portionsof the substrate after growth, suspended films with circular boundaries ofradius $R$ ranging from approximately 30 to 811 $\mu$m are made. Due toresidual stresses, the portions of film attached to the substrate are ofcompressive prestrain $\epsilon_0 \approx 11 \times 10^{-4}$ and the suspendedportions of film are azimuthally wrinkled at their boundary. We find that$\lambda$ monotonically decreases with $\kappa$ and present a model predictingthat $\lambda \propto t^{1/2}(\epsilon_0 + \Delta R \kappa)^{-1/4}$, where$\Delta R$ denotes a penetration depth over which strain relaxes at a boundary.This relation is in agreement with our experiments and may be adapted to othersystems such as plant leaves. Also, we establish a novel method for measuringresidual compressive strain in thin films.

Boundary Curvature Effect on the Wrinkling of Thin Suspended Films