Predicting the composition of a sold solution (or alloy) during its growth has been one of the principle themes in the study of crystal growth. Recently, the epitaxial growth of semiconductor compounds, such as ternary alloys of AlGaN and GaAsSb, has also been extensively studied. On the other hand, the interface kinetics during the growth of a solid solution, especially a non-ideal solid solution, has not been fully understood and the theoretical study on the kinetics is still in progress.

    The dependency of the distribution coefficients of a binary ideal solid solution growing from its vapor has been studied by using the Monte Carlo (MC) simulation and the mean field approximation [1, 2]. Our previous studies are then extended to the case of a binary non-ideal (regular) solid solution in the present study. The degree of the non-ideality is expressed by the value of Φ_AB–(Φ_AA+Φ_BB)/2, where Φ_ij is the bonds between i and j atoms.

    The results of MC simulation show that the supersaturation range of lateral growth can be divided into three regions of (a, b, c). When the equilibrium distribution coefficient is smaller than 1, the composition of a solid approaches the equilibrium composition of terrace sites in (a), almost equals to the equilibrium composition of terrace in (b), and increases again in (c), as an increase of supersaturation. The behavior of the chemical composition of a solid can be explained by the relaxation processes on both terraces and terrace-tails, as in the case of ideal solid solution [2].

    The introduction of the non-ideality changes the local atomic arrangements in a solid. These changes are clear in the case where a solid has the composition near A:B~1. Tiny clusters consisting of the ordered arrangement of AB is observed when Φ_AB>(Φ_AA+Φ_BB)/2 and clusters consisting of AA and BB when Φ_AB<(Φ_AA+Φ_BB)/2. The rate of the compositional change of a solid due to an increase of supersaturation is also affected by the non-ideality.

   The mean field approximation model for ideal solid solution is extended for a non-ideal solid solution. The extended model explains the compositional changes in (a) obtained by the present MC simulation.

Reference

[1] K. Matsumoto, T. Irisawa, M. Kitamura, E. Yokoyama, Y. Kumagai, A. Koukitu, J. Crystal Growth 276 (2005) 635.

[2] K. Matumoto, T .Irisawa, M. Kitamura J. Crystal Growth 310 (2008) 646.

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1. Formation processes of stable and metastable phases under Ostwald's step rule: a theoretical study
2. Domain competition in deposition growth