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

Lattice-mismatched heteroepitaxial growth is nowadays a key step involved in the fabrication of a multitude of devices. 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 morphology. In this work we present a continuum approach able to tackle heteroepitaxy while matching typical experimental sizes and time scales. Starting from a suitable free-energy functional describing both elastic and surface energy , evolution is described based on a surface-diffusion model including an external flux. A convenient and general description of surface-energy anisotropy (allowing us to simulate faceting also in the “strong anisotropy” regime) 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 our attempt 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. It must be noted that for miscible systems, such as Ge/Si, the above set of phenomena is not yet sufficient to yield a realistic description of the growth process. At high growth temperatures, indeed, entropy of mixing can lead to significant surface exchanges between deposited and surface atoms. Tackling intermixing is possible, but it requires for a considerable extension of the formalism [3,4]. [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, Faceting of equilibrium and metastable nanostructures: a Phase-Field model of surface diffusion tackling realistic shapes, accepted for publication on Cryst. Growth Des. (2015); (DOI:10.1021/acs.cgd.5b00165) [3] R. Bergamaschini, J. Tersoff, Y. Tu, J. J. Zhang, G. Bauer, and F. Montalenti. Phys. Rev. Lett. 109, 156101 (2012) [4] R. Backofen, R. Bergamaschini, and A. Voigt. Philosophical Magazine 94, 2162 (2014).