Elastic state and thermodynamical properties of inhomogeneous epitaxial layers: Application to immiscible III-V alloys

Abstract

The elastic strain and stress fields and the elastic energy of the system composed of a crystalline epitaxial layer of finite thickness coherently grown on a bulk substrate are calculated, when the intrinsic stress-free lattice parameter of the layer is modulated along directions parallel to the substrate surface. When the modulation has components with spatial periods of the same order as the thickness of the layer, the elastic energy is considerably reduced with respect to the same modulation occurring in a bulk sample. There exists an optimal period of elementary sinusoidal modulation, proportional to the layer thickness. Consequently, for immiscible alloys where changes of composition induce changes of intrinsic lattice parameter, the critical temperature (below which they become thermodynamically unstable with respect to composition modulations) is much higher (and the domain of instability larger) if the material is in the epitaxial layer form than in the bulk form. This extends Cahn’s theory of spinodal decomposition to epitaxial layers. It is also pointed out that if a modulation has started to occur in a growing layer, the elastic deformation induced near the free surface should have important consequences on the subsequent growth of this layer. These results are applied to III-V semiconductors immiscible alloys, such as InxGa1−xAsyP1−y, where such composition modulations are known to exist. New values of the critical temperatures for these alloys are calculated and compared with lower former estimates. The mode of development of these modulations is discussed in light of previous experimental results and these new calculations.