The composition modulation effect in GaInPAs solid solutions as a manifestation of energy resonance after material's spinodal decomposition

Abstract

The Cahn(cid:21)Hilliard model concepts are extended to describe the spinodal decomposition of Ga x In 1 − x P y As 1 − y solid solutions grown on the InP substrate. The energy of elastic deformation of the thin layer of a solid solution was calculated on the assumption of its coherent conjugation with the massive InP substrate. The excess energy of component mixing in the solid phase was modeled in accordance with the simple solution model, when the simultaneous substitution of components in the metal and metalloid sub lattices of the sphalerite structure is incorporated. The system of di(cid:27)erential equations describing vari-ations of the composition of a semiconductor solid solution after its spinodal decomposition was solved numerically under various thermodynamic conditions. The temperature-concentration intervals in which the oscillations of the supersaturated metastable state of the solid phase may take place were found by analyzing the phase portrait of the resulting system of di(cid:27)erential equations. We obtained the thermodynamic synthesis conditions ensuring the appearance of the microoscillations of the solid solution composition. It was shown that the development of intensive oscillations (composition modulation e(cid:27)ect in material) is caused by the mutual transition of all excess thermodynamic energy of mixing of an unstable solid phase into the energy of elastic stresses of the coherently conjugated layers of decaying material (energy resonance). The shape of the component concentration pro(cid:28)les in the obtained oscillatory process di(cid:27)ers si-gni(cid:28)cantly from the shape corresponding to harmonic oscillations. One reason for this is the complex dependence of the model’s parameters of the distribution on the material’s composition. Another reason is that the solutions found are in close proximity to the resonance, which is characterized by a signi(cid:28)cant increase in the oscillation amplitude and, as a consequence, the manifestation of nonlinear properties of the system. The results obtained clearly illustrate the formation of concentration domains during the spinodal decomposition of the multicomponent semiconductor solid phase. The results of the parameter calculation for the oscillatory process were compared with the data on the modulation composition e(cid:27)ect, which is experimentally observed during the production of elastically strained Ga x In 1 − x P y As 1 − y heterostructures. The interval of thermodynamic parameters of the growing system which ensures the development of the composition modulation e(cid:27)ect in Ga x In 1 − x P y As 1 − y solid solutions was considered in detail.