The recent discovery of two-dimensional materials (2DM) has revolutionized solid-state physics andopened up novel potential applications thanks to their ability to confine carriers. Graphene (Gr) and transition metal dichalcogenide (TMDC) are particularly studied as regards their outstanding andpromising electronic, optical but also spintronic properties. Nevertheless, a technological lock for their industrial, notably microelectronic, applications lies in their production by epitaxy with high crystal quality, as exfoliation has intrinsic limitations regarding the size and quality of the 2D crystals. Today’s progress in these materials thence requires further fundamental investigation to understand and control their growth during van der Waals (vdW) epitaxy. It is precisely this blocking point that we target in this thesis by developing a fundamental study in order to elucidate the crucial mechanisms and to predict the optimal growth regimes to produce 2D films with the best crystalline quality. We suggest to investigate the molecular beam epitaxy (MBE) of MoSe2 and WSe2 on Gr deposited on Germanium On Insulator (GeOI) layers. This choice of experimental system is at the same time paradigmatic to reveal generic mechanisms and promising for applications, both with regard to its GeOI pseudo-substrate compatible with microelectronics wafers, and the TMDC films with spintronic applications. This thesis is embedded in an ANR project involving two experimental groups dedicated to the epitaxial growth of the Gr/GeOI system and to the TMDC growth, together with a theoretical group investigating atomic processes via ab initio calculations. The work will be done in close collaboration with all these partners in order to derive a modelization of these experimental systems.

We will derive kinetic Monte-Carlo simulations dedicated to describe the dynamics of epitaxial growth, see Fig. 1 and Ref. [1]. The out-of- equilibrium dynamics will be based on stationary markovian processes related to both deposition, diffusion and attachment/detachment of adatoms. We will consider for this purpose lattice models that renormalize the atomic vibrations defining the characteristic scale of the elementary processes. The transition rates associated with the
escape from a metastable state are dominated by the Boltzmann factor of the binding energy. It will be approximated by two contributions related to the in-plane and out-of-plane neighbors. The elementary processes can be made dependent on different configurations (local height, local configuration, etc) to account for different effects (stoichiometry, wetting, vdW epitaxy, etc) [31]. We will account for different crystalline anisotropies of the substrate and overlayer by considering a fine discretization scheme that allows for the description of the film/substrate alignment and Moiré patterns. We will investigate the influence of the weak vdW interactions and the particularities it introduces for epitaxial growth. Of special interest is their relative strength compared to both the atomic bonding and the thermal energy. They will also be at variance with the long-range elastic interactions that may occur in lattice-mismatched coherent conditions.

[1] Z Ben Jabra, M Abel, F Fabbri, J-N Aqua et al, “Van der Waals Heteroepitaxy of Air-Stable Quasi- Free-Standing Silicene Layers on CVD Epitaxial Graphene/6H-SiC,” ACS Nano 16 (2022) 5920