**2. Heteroepitaxy nucleation and growth modes**

The mechanism of nucleation and initial growth stage of heteroepitaxy dependence on bonding between the layer and substrate across the interface. Since the heteroepitaxy requires the nucleation of a new alloy on a foreign substrate the surface chemistry and physics play important roles in determining the properties of heteroepitaxial growth. In the classical theory, the mechanism of heterogeneous nucleation is determined by the surface and interfacial free energies for the substrate and epitaxial crystal.

Three classical modes of initial growth introduced at first by Ernst Bauer in 1958 can be distinguished: Layer by layer or Frank–Van der Merwe FM two-dimension mode (Frank– Van der Merwe, 1949), Volmer–Weber VW 3D island mode (Volmer–Weber, 1926), and Stranski–Krastanov SK or layer-plus-island mode (Stranski–Krastanov, 1938) as the intermediate case. The layer by layer growth mode arises when dominates the interfacial energy between substrate and epilayer material. In the opposite case, for the weak interfacial energy when the deposit atoms are more strongly bound to each other than they are to the substrate, the island (3D), or VW mode results. In the SK case, 3D island are formed on several monolayers, grown in a layer-by-layer on a crystal substrate. Schematically these growth modes are shown in the Figure 2.1.

Fig. 2.1. Schematic presentation of FM, VW and SK growth modes

GaInAsN cell grown by MBE (Ptak et al 2005), but photovoltages in this material are still low. Recently chemical-beam epitaxy (Nishimura et al., 2007; Yamaguchi et al, 2008; Oshita et al, 2011) has been developed in order to improve the quality of the grown layer, but today it remains a challenge to grow dilute nitride materials with photovoltaic (PV) quality. In this chapter we present some results on thick GaAsN and InGaAsN layers, grown by lowtemperature Liquid-Phase Epitaxy (LPE). In the literature there are only a few works on dilute nitride GaAsN grown by LPE (Dhar et al., 2005; Milanova et al., 2009) and some data

The mechanism of nucleation and initial growth stage of heteroepitaxy dependence on bonding between the layer and substrate across the interface. Since the heteroepitaxy requires the nucleation of a new alloy on a foreign substrate the surface chemistry and physics play important roles in determining the properties of heteroepitaxial growth. In the classical theory, the mechanism of heterogeneous nucleation is determined by the surface

Three classical modes of initial growth introduced at first by Ernst Bauer in 1958 can be distinguished: Layer by layer or Frank–Van der Merwe FM two-dimension mode (Frank– Van der Merwe, 1949), Volmer–Weber VW 3D island mode (Volmer–Weber, 1926), and Stranski–Krastanov SK or layer-plus-island mode (Stranski–Krastanov, 1938) as the intermediate case. The layer by layer growth mode arises when dominates the interfacial energy between substrate and epilayer material. In the opposite case, for the weak interfacial energy when the deposit atoms are more strongly bound to each other than they are to the substrate, the island (3D), or VW mode results. In the SK case, 3D island are formed on

FM

VW

SK

for InGaAsN (Vitanov et al., 2010).

**2. Heteroepitaxy nucleation and growth modes** 

and interfacial free energies for the substrate and epitaxial crystal.

several monolayers, grown in a layer-by-layer on a crystal substrate. Schematically these growth modes are shown in the Figure 2.1.

substrate

substrate

substrate

Fig. 2.1. Schematic presentation of FM, VW and SK growth modes

The growth modes in heteroepitaxy are defined based on thermodynamic models. The sum of the film surface energy and the interface energy must be less than the surface energy of the substrate in order for wetting to occur and then layer by layer growth is expected. The VW growth mode is to be expected for a no wetting epitaxial layer. If γ and γ<sup>0</sup> are the surface free energies of the layer and substrate, respectively, and γi is the interfacial free energy the change in the free energy Δγ associated with covering the substrate with epitaxial layer is:

$$
\Delta \mathbf{y} = \mathbf{y} + \mathbf{y}\_i \mathbf{-} \mathbf{y}\_0 \tag{2.1}
$$

If minimum energy determinates the mode for nucleation and growth, the dominated mechanism will be two-dimensional for Δγ <0 and three-dimensional for Δγ>0. However, even in the case of a wetting epitaxial layer (Δγ <0 ), the existence of mismatch strain can cause islanding after the growth of a few monolayers. This is because the strain energy , increases linearly with the number of strained layers. At some thickness, γ+γi exceeds γ0 and the growth mode transforms from FM to SK resulting in 3D islands on the 2D wetting layer. Whereas it is clear that the VW growth mode is expected for a nonwetting epitaxial layer, the behavior of a wetting deposit is more complex and requires further consideration. Often the interfacial contribution in the limit of zero lattice mismatch and weak chemical interactions between the film and substrate at the interface can be neglected in comparison to the surface free energy (γi ≈ 0). In this case the growth mode is determined entirely by the surface free energies of the film and substrate material.

Instead of these three main growth modes additional growth modes and epitaxial growth mechanisms could be distinguished (Scheel, 2003): columnar growth, step flow mode, step bunching, and screw-island growth.

The structural quality of the layer and surface morphology strongly depend on the growth method and the main growth parameters: supersaturation, misorientation of the substrate and the difference of lattice constants between substrate and the epitaxial layer.

In the case of flat substrate, the supersaturation increases until surface nucleation of a new monolayer occurs and its growth cover the substrate, followed by the nucleation of the next monolayer. For compound of limited thermodynamic stability or with volatile constituents like GaAs, GaN, SiC the appearance of the growth mode is largely predetermined by the choice of the growth method due to the inherent high supersaturation in epitaxy from the vapor phase and adjustable low supersaturation in LPE.

The FM growth mode in LPE can only be obtained at quasi-zero misfit as it is established from thermodynamic theory (Van der Merwe, 1979) and demonstrated by atomistic simulations using the Lennard–Jones potential (Grabow and Gilmer, 1988) and also at low supersaturation. At high supersaturation a high thermodynamic driving force leads to a high density of steps moving with large step velocities over the surface and causes step bunching.

The VW mode is typical of VPE. Due to the high supersaturation a large number of surface nuclei arise, which then spread and form three-dimensional islands, that finally coalesce to a compact layer. Continued growth of a layer initiated by the VW mode often shows columnar growth which is a common feature in epitaxy of GaN and diamond. (Hiramatsu *et al*., 1991). The SK mode has been demonstrated by MBE growth of InAs onto GaAs substrate (Nabetani *et al*., 1994).

Dilute Nitride GaAsN and InGaAsN Layers Grown by Low-Temperature Liquid-Phase Epitaxy 73

 Fig. 3.1. Schematic presentation of atom arrangement for two materials with different cubic

*a*ll = *a*<sup>o</sup> ≠ *a*⊥. The out -of-plane lattice constant could be determined from the equation:

In the case of the smaller lattice constant of the growth layer (GaAsN on GaAs for example), *a< a*o the layer will be elastically tensed in two in-plane directions and compressed in the growth directions (the out-of-plane lattice constant will be smaller than substrate lattice constant). Under pseudomorphic growth conditions the cubic lattice doesn't remain cubic:

 *a*<sup>⊥</sup> = *a*[1- *D*(*a*ll/*a* -1)] (3.1)

Beyond a given critical thickness *η*c when a critical misfit strain *ε* is exceeded, a transition from the elastically distorted to the plastically relaxed configuration occurs. In this case both

*f* = (*a* - *a*o)/*a*<sup>o</sup>

 *f*<sup>⊥</sup> = (*a*<sup>⊥</sup> - *a*o)/*a*o = *(1+D-DR)f* (3.2)

*fll* = (*a*ll - *a*o)/*a*o = *Rf*

*R* is a relaxation rate. For pseudomorphic growth *R*=0, and for full strain relaxation *R* =1 If the epilayer is thicker than the critical thickness, there will be sufficient strain energy in the layer to create dislocations to relieve the excess strain. The layer has now returned to its unstrained or equilibrium lattice parameters in both the in-plane and out-of-plane directions and the film to be 100% relaxed. Figure 3.2 shows schematically how a misfit dislocation can

lattice constant: a) before growth; b) for pseudomorphic growth

a b

*a*⊥ - out-of-plane lattice constant of the layer *a*ll - in-plane lattice constant of the layer

relieve strain in the heteroepitaxial structure.

*a* - lattice constant of the unstrained cubic epitaxial layer

*D* = 2*C12*/*C11* , where *C11* and *C12* are elastic constants of the grown layer

mismatch component differ from zero: *a*ll≠ *a*o ≠ *a*⊥. The lattice constant misfit is:

Where:

Observations, analyses and measurements of LPE GaAs on the formation of nuclei and surface terraces show that nuclei grow into well-defined prismatic hillocks bounded by only {100} and {111} planes and they are unique to each substrate orientation, and hillocks tend to coalesce into chains and then into parallel surface terraces (Mattes & Route, 1974). The hillock boundaries may cause local strain fields and variation of the incorporation rates of impurities and dopants, or the local strain may getter or rejects impurities during annealing processes. This inhomogeneity may be suppressed by providing one single step source or by using substrates of well-defined small misorientation. The FM growth mode and such homogeneous layers can only be achieved by LPE or by VPE at very high growth temperatures.

Only at low supersaturation, nearly zero misfit and small misorientation of the substrate the layer by-layer growth mode can be realized and used to produce low dislocation layers for ultimate device performance. Two-dimensional growth is desirable because of the need for multilayered structures with flat interfaces and smooth surfaces. A notable exception is the fabrication of quantum dot devices, which requires three-dimensional or SK growth of the dots. Even here it is desirable for the other layers of the device to grow in a two-dimensional mode. In all cases of heteroepitaxy, it is important to be able to control the nucleation and growth mode.
