Association

36 3. Experimental details
Figure 3.1.: Surface tensions between substrate
and film. After Lüth (2010). 79
Moreover, the substrate plays a crucial role in epitaxial growth as it initially influences the
arrangement of the atomic species of the growing film. Regarding the substrate, we distinguish
coherent growth (e. g. EuO on YSZ (100)), in which the film will be single crystalline,
from an incoherent growth mode (e. g. EuO on MgO (100)), in which the film may be also
polycrystalline. Depending on a geometrical consideration of surface tensions between the
substrate and the deposited film (Fig. 3.1), different growth modes can be modeled 121 by a
balance of the surface tensions,
γ S = γ S/F + γ F cosϑ, (3.2)
where γ S denotes the tension between substrate and vacuum, γ F between film and vacuum,
and γ S/F between substrate and film. Depending on the angle ϑ between γ S/F and γ F , three
classic modes of thin film growth are distinguished:
1. In the layer-by-layer (Frank-Van der Merwe) growth mode, the adatoms are more strongly
bound to the substrate than to each other. With ϑ = 0, we obtain γ S γ S/F + γ F , which
means that the wetting of adatoms on the substrate is large, because its surface energy
γ S is less than that of the substrate. The layered growth is possible even if there is a
slight lattice mismatch, indicating that a strained-layer epitaxy is feasible.
2. The three-dimensional (3D) island growth (Volmer-Weber) occurs, if adatoms are more
strongly bound to each other than to the substrate, so that they form films consisting of
3D islands. With ϑ>0, we obtain γ S