"Soft Si": effective stiffness of supported crystalline nanomembranes

We investigate the effective mechanical response of a layered system consisting of a thin crystalline sheet (nanomembrane) on a bulk substrate, with a high elastic mismatch (in the range of 5 to 9 orders of magnitude) between the stiff sheet and the compliant substrate. Using finite-element mechanics models and indentation experiments ranging from micro to nano, we show that the mismatch between the sheet and substrate elastic moduli, the length scale of deformation, and the sheet thickness all play a significant role in defining the effective stiffness of the layered system. For a wide range of indenter sizes, the mechanical response of the composite system is indistinguishable from that of the compliant substrate. In particular, at large indenter sizes, the mechanical response of the layered system is dominated by that of the compliant substrate. For decreasing indenter sizes, the effective stiffness of the layered structure reaches a finite value different from either the one expected for the compliant substrate or for a bulk crystal of the same material as the stiff top membrane.