Shape relaxation of epitaxial mesa for finite-size strain-engineering

Silicon-Germanium (Si$_{1-x}$Ge$_x$) layers are commonly used as stressors in the gate of MOSFET devices. They are expected to introduce a beneficial stress in the drift and channel regions to enhance the electron mobility. When reducing the gate lateral size, one of the major issues is the stress relaxation which results in a significant decrease in the electron mobility. We report a new morphological evolution of a strained epitaxial SiGe nanolayer on a silicon gate (mesa) driven by strain inhomogeneity due to finite-size effects. Unlike the self-induced instability of strained films, this evolution arises here due to the elastic inhomogeneity originating from the free frontiers. We analyze the growth dynamics within the thermodynamic surface diffusion framework accounting for elasticity and capillarity, the former being solved in two dimensions thanks to the Airy formalism. The resulting dynamical equation is solved with a decomposition on eigenmodes, and reveals different developments depending upon the mesa geometric parameters. Mass transfer occurs towards the relaxed areas and creates a beading at the nanolayers free surface with either a W or V shape as a function of time and geometry. The evolution is then controlled by the proportions of the structure as well as its scale.