Observation of free surface-induced bending upon nanopatterning of ultrathin strained silicon layer

We provide evidence of nanopatterning-induced bending of an ultrathin tensile strained silicon layer directly on oxide. This strained layer is achieved through the epitaxial growth of silicon on a Si(0.84)Ge(0.16) virtual substrate and subsequent transfer onto a SiO(2)-capped silicon substrate by combining hydrophilic wafer bonding and the ion-cut process. Using high resolution transmission electron microscopy, we found that the upper face of the strained silicon nanostructures fabricated from the obtained heterostructure using electron beam lithography and dry reactive ion etching displays a concave shape. This bending results from the free-surface-induced strain relaxation, which implies lattice out-of-plane expansion near the edges and concomitant contraction at the center. For a ～ 110 nm × 400 nm × 20 nm nanostructure, the bending is associated with an angle of 1.5° between the Formula: see text] vertical atomic planes at the edges of the ～ 110 nm side. No bending is, however, observed at the strained Si/SiO(2) interface. This phenomenon cannot be explained by the classical Stoney's formula or related formulations developed for nanoscale thin films. Here we employed a continuum mechanical approach to describe these observations using three-dimensional numerical calculations of relaxation-induced lattice displacements.