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

We study the compositional and morphological instabilities affecting expita xial alloy layers lattice-matched to their substrate and alloy half spaces under zero net strain. We fu-st calculate analytically the elastically rela xed state of such a system where a composition modulation is coupled to a s urface undulation having either the same wavelength or half the wavelength of the composition modulation. The calculations, carried out to second orde r in undulation amplitude, prove that the coupling energy is nonzero in bot h cases. Analytical results for undulations of finite amplitude are also ob tained. We then use these calculations to study in a unified fashion the th ermodynamic and kinetic instabilities of these systems and to determine how compositional and morphological perturbations affect each other. We find t hat, at variance with the case of lattice-mismatched layers, the critical t emperature 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 an y morphological perturbation. However, whether it is growing or not, a latt ice-matched alloy with a finite lateral composition modulation is always un stable against some undulations of its fi ee surface.