Continuum modeling of heteroepitaxial growth on silicon: elastic relaxation, surface-energy minimization, misfit dislocations and intermixing.

Integration of different materials, such as GaAs or Ge, on Si via heteroepitaxy is nowadays a key step involved in the fabrication of a multitude of devices, some already in the market. However, full control over the different, sometimes competing phenomena taking place during deposition [1] has yet to be reached. Simulations can be precious in limiting the growth-parameter space to be sampled in actual experiments when searching for the desired system quality and morphology. In this work we present a continuum approach able to tackle heteroepitaxy while matching typical experimental sizes and time scales. A convenient and general description of surface-energy anisotropy is introduced [2] and several illustrative applications to semiconductors are described, exploiting both Phase-Field and sharp-interface approaches. Successful comparison with experiments is demonstrated for qualitatively different systems. We also discuss how to simultaneously tackle elastic and plastic relaxation. In particular, we show how the stress field associated with an assigned distribution of misfit dislocations can be computed on the fly, its contribution to the surface chemical potential deeply influencing the growth mode and/or the morphology of the growing front. [1] F. Montalenti, D. Scopece, and Leo Miglio, Comptes Rendus Physique 14 (7), 542-552 (2013). [2] M. Salvalaglio , R. Backofen , R. Bergamaschini , F. Montalenti , and Axel Voigt, Cryst. Growth Des. (2015); (DOI:10.1021/acs.cgd.5b00165)