Growth Mechanisms

4 Film Preparation by Pulsed Laser Deposition

4.1.3 Deposition Parameters

Suitable deposition parameters for the fabrication of sesquioxide films with the PLD setup employed in this work were already determined by [Kuz06]. Some of these parameters were further investigated and optimized for improved film quality.

The substrate temperature has a critical impact on the crystallinity of the deposited films, since it determines the mobility of the atoms on the film surface. Its influence was investigated in [Kuz06] for a set of 500 nm thick Sc₂O₃ films deposited on α-Al₂O₃ at different substrate temperaturesT up to 700^◦C. Since an increase of the film crystallinity with increasing temperature was shown by X-ray diffraction measurements, substrate temperatures of at least 700^◦C were chosen for film growth.

As described in [Die92], the vaporization rate for pulsed laser deposition above the abla-tion threshold typically increases sublinearly with increasing pulse fluence. Since higher fluences often lead to a higher density of parasitic particulates, working at pulse fluences slightly above the ablation threshold of the target material is beneficial. An ablation threshold slightly below 1.5 J/cm² was estimated in [Kuz06] for Sc₂O₃. It has also been shown in [Kei97] that a power density of 7.5×10⁷W/cm² was sufficient for ablation of Y₂O₃ from a sintered powder target with an excimer laser at 248 nm. Assuming a ho-mogeneous temporal energy distribution during the 20 ns long laser pulse, this value also corresponds to an ablation threshold of approximately 1.5 J/cm². Hence in this work, film fabrication was performed with laser fluences of about 1.5 to 2.5 J/cm². A range is given for the laser fluence, as it was changing over time with the beam quality of the excimer laser, the adjustment of the focussing optics and the transmission of the entrance-port window. In order to obtain such laser fluences on the target, the excimer laser was usually operated at a pulse energy of 800 mJ, of which merely about 10 to 20 % was transmitted into the vaccuum chamber and focussed onto a target area of approximately 0.06 cm². The influence of the oxygen pressure pO₂ on the film properties was also investigated in [Kuz06]. Sc₂O₃ films with almost identical properties and a good crystallinity were deposited on α-Al₂O₃ for partial oxygen pressures ranging from 10⁻³mbar to 10⁻²mbar.

Thus, most of the films were fabricated using oxygen pressures in this range.

4.2 Growth Mechanisms

Figure 4.2: Film growth modes: (a) Frank-Van der Merwe, (b) Volmer-Weber, (c) Stranski-Krastanov and (d) step flow

Film growth can be categorized in different growth modes (see Fig. 4.2), depending on the relation between the free energies of the film surface (γ_f), the substrate surface (γ_s), and the interface between film and substrate (γ_i). The relation between these energies during nucleation is given by Young’s equation [Kai02]:

γ_s =γ_i+γ_fcosϕ (4.1)

Here,ϕis the wetting angle of a liquid nucleus on the substrate. If the interaction between substrate and film atoms is greater than the one between adjacent film atoms (γ_s> γ_f+γ_i), layer-by-layer growth takes place, which is also known as Frank-van der Merwe growth or two-dimensional (2D) growth (Fig. 4.2a). In this case, the growth of one monolayer is finished before nucleation of the next monolayer takes place. The opposite case is called island growth, Volmer-Weber growth or three-dimensional (3D) growth (Fig. 4.2b). Since the interaction between film atoms is greater than between adjacent film and substrate atoms (γ_s < γ_f+γ_i), separate three-dimensional islands are formed. A hybrid form of the two cases described above is the Stranski-Krastanov growth mode (Fig. 4.2c), which is characterized by a change of growth mode from layer-by-layer to island growth. Stranski-Krastanov growth is usually caused by a lattice mismatch between substrate and film, which results in two dimensional strain and an increase of the elastic energy with the layer thickness. If the film exceeds a critical thickness, misfit dislocations will be introduced to relieve the mismatch strain and the growth mode changes.

4 Film Preparation by Pulsed Laser Deposition

4.2.2 Lattice Matching

One aim of this work has been the fabrication of monocrystalline films by epitaxial growth.

Epitaxy denotes an ordered film growth on a crystalline substrate. It is characterized by a crystallographic correlation, forcing the film to grow with the orientation given by the substrate. If substrate and film materials are identical the process is called homoepitaxy, otherwise heteroepitaxy. Since a refractive index difference between film and substrate is required for waveguiding, this work focuses on heteroepitaxial growth.

In order to realize epitaxial growth, a high degree of lattice matching between film and substrate is required. Ideal lattice matching is given if film and substrate possess the same crystal structure and lattice constant. Lattice matching in a less strict definition is also possible for materials with different crystal structures but similar lattice planes. In this case, the lattice spacings a_0,f and a_0,s of the film and substrate plane, respectively, have to be integer multiples:

n a_0,f =m a_0,s n, m∈N^∗, n= 1∨m= 1 (4.2) Epitaxial growth is not only possible with perfect lattice matching, but also, to a certain degree, with a lattice mismatch f, as defined by the following equation:

f = n a_0,f−m a_0,s

n a_0,f (4.3)

As long as the lattice mismatch does not exceed a critical value, which is dependent on the film thickness and the material properties, the lattice spacings of the film can fit those of the substrate by inducing elastic deformations [Fra49]. Such a growth process is termed pseudomorph.

4.2.3 Growth Kinetics

During PLD, the growing film is usually not in thermodynamic equilibrium. The vapor possesses a high supersaturation, leading to a large nucleation rate. If the surface diffusion is not sufficient, the deposited material cannot rearrange itself to minimize the surface energy. Thus, the thermodynamic model described in section 4.2.1 cannot be applied and kinetic effects have to be considered. Although homoepitaxial growth is assumed in the following considerations, most of them can be applied to heteroepitaxial systems with perfect lattice matching as well.

Both the intralayer and interlayer mass transport have to be considered to understand the possible 2D growth modes on a surface with atomically flat terraces. Intralayer and interlayer mass transport denote the diffusion of atoms on a terrace and the diffusion to lower terraces, respectively. An important kinetic parameter describing the intralayer mass transport is the diffusion lengthl_D. It determines the average distance an atom can travel on a flat surface before being trapped.

4.2 Growth Mechanisms If l_D is larger than the average terrace width, the adatoms possess a sufficiently high mobility to reach the terrace edges and expand them. This behavior, leading to propa-gating steps, is illustrated in Fig. 4.2d and is called step flow growth. In case of a slower intralayer mass transport, nucleation on the terraces will take place. At first, new nuclei will be formed, but then, with increasing density, it becomes more and more likely for atoms to attach to existing nuclei, thus forming islands.

In this case, the growth mode strongly depends on the interlayer mass transport, as a steady interlayer mass transport will allow the atoms which are deposited on top of an existing island to diffuse to the lower layer. In the ideal case, termed layer-by-layer growth, each layer is completed before nucleation on the next one takes place. The other extreme is multilayer growth due to second-layer nucleation; as the interlayer mass transport is very limited, nucleation will take place on top of islands before they have merged to form a complete layer. In reality, a growth mode in between those two extreme cases will occur.

4 Film Preparation by Pulsed Laser Deposition