Thermodynamic and kinetic instabilities of lattice-matched alloy layers: Compositional and morphological perturbations

Abstract

We study the compositional and morphological instabilities affecting epitaxial alloy layers lattice-matched to their substrate and alloy half spaces under zero net strain. We first calculate analytically the elastically relaxed state of such a system where a composition modulation is coupled to a surface undulation having either the same wavelength or half the wavelength of the composition modulation. The calculations, carried out to second order in undulation amplitude, prove that the coupling energy is nonzero in both cases. Analytical results for undulations of finite amplitude are also obtained. We then use these calculations to study in a unified fashion the thermodynamic and kinetic instabilities of these systems and to determine how compositional and morphological perturbations affect each other. We find that, at variance with the case of lattice-mismatched layers, the critical temperature for thermodynamic compositional instability of nongrowing layers is the same for planar and nonplanar surfaces. For growing layers, we show that the kinetic compositional instability may develop independently of any morphological perturbation. However, whether it is growing or not, a lattice-matched alloy with a finite lateral composition modulation is always unstable against some undulations of its free surface.