Continuum modeling of vertical heterostructures: elastic properties and morphological evolution

The development of cutting-edge opto- and micro-electronic devices requires novel fabrication techniques, able to deliver high-quality materials, monolithically integrable into Si-based technology. Theoretical models and simulations supporting the experimental activities are highly needed to fully understand the growth physics at the nano- and micro-scale and tailor semiconductor heterostructures for technological applications. In this work, the modeling of the plasticity onset and of the morphological evolution for Ge/Si vertical heterostructures is introduced, fostered by the peculiar features of such systems with respect to the standard heteroepitaxy. Indeed, the aim of this thesis is to understand the main properties of systems with large height-to-base aspect-ratios, in order to offer new solutions for the realization of heterostructures with unprecedented material quality. Continuum models are selected to describe length scales ranging from a few nanometers to microns, and time scales of minutes (or even more). By means of the linear elasticity theory equations, solved by Finite Element Method (FEM) simulations, the competition between elastic and plastic relaxation in vertical Ge/Si systems is investigated. The critical parameters for the insertion of dislocations are determined for a single-layer structure, made of a SiGe layer on a Si pillar, and then generalized to multilayer configurations. Moreover, the possibility to achieve coherent structures at any size is demonstrated, provided that a proper grading of the Ge content during the growth is considered. A recipe for the calculation of such a grading of the Ge content is also introduced. Several comparisons with experiments show the generality of the proposed investigation for heterostructures at the nanoscale, and the versatility of the developed method. Moreover, thanks to dedicated experiments stimulated by the theoretical predictions, dislocation-free structures are proven to be feasible also at the micrometer scale. The three-dimensional evolution in time of vertical microcrystals is investigated by means of a phase-field model and FEM simulations. In particular, the annealing of Ge on Si microcrystals is modeled by considering the surface diffusion driven by the tendency toward the minimization of the surface energy. This allows the evolution induced by annealing of single structures to be described. Moreover, the coalescence mechanism for crystal arrays, resulting in the formation of a suspended film, is predicted. Such an evolution is confirmed by dedicated experiments and leads to the fabrication of a promising system for the high-quality heterogeneous integration of semiconductors. The coalescence occurring for closely spaced crystals during high-temperature growth is also assessed. The original extensions of the PF model, required by the theoretical investigations of the morphological evolution, are illustrated in the details. Particular attention is devoted to the description of anisotropic surface energies responsible for crystal faceting in thermodynamic regimes. Moreover, further extensions of the method, dealing with an accurate description of the growth processes, are reported.