Mechanics of precisely controlled thin film buckling on elastomeric substrate

Stretchable electronics has many important and emerging applications. Sun et al. [Nature Nanotech. 1, 201 (2006)] recently demonstrated stretchable electronics based on precisely controlled buckle geometries in GaAs and Si nanoribbons on elastomeric substrates. A nonlinear buckling model is presented in this letter to study the mechanics of this type of thin film/substrate system. An analytical solution is obtained for the buckling geometry (wavelength and amplitude) and the maximum strain in buckled thin film. This solution agrees very well with the experiments, and shows explicitly how buckling can significantly reduce the thin film strain to achieve the system stretchability.