Kinetic Instability of Semiconductor Alloy Growth
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291 Mat. Res. Soc. Symp. Proc. Vol. 583 © 2000 Materials Research Society
(T ; 6000 C) are of the order D zt10-19 - 10-16 cm 2s-l [5]. These diffusion coefficients are too small to develop a composition-modulated structure during the growth time, and another kinetic mechanism than the bulk migration of atoms is needed for the structure formation. Such a mechanism should involve surface migration of atoms where surface diffusion coefficients are of the order of D 10-6 - 10-5 cm 2s-1 [5]. These diffusion coefficients are sufficiently high to develop composition-modulated structures in the process of crystal growth. Guyer and Voorhees [6] examined the linear kinetic instability of the alloy growth above the thermal roughening temperature. They considered the coupling of compositional and morphological instabilities and took into account the average lattice mismatch between the growing alloy film and the substrate. They showed that the stress generated by compositional inhomogeneities, can be either stabilizing or destabilizing, depending on the sign of the mismatch. However, they used the approximation of an isotropic elastic medium. This approximation did not allow them to detect effects connected with the existence of elastically soft directions. In the present paper, we focus on a linear stability analysis of the alloy epitaxial growth, where we take into account both the bulk elastic anisotropy of zinc-blend semiconductors and the surface anisotropy of (001) surface. THEORY We study the instability which may occur in an open system in the process of the growth of a binary alloy A,-cB,, and our treatment is applicable also to the growth of a ternary semiconductor alloy A,-,BcC. The focus is given on the instability of the alloy growth with respect to fluctuations of composition 6c. The theory linear in 6c is developed, and the criterion is found that the amplitude of composition fluctuation increases with the epitaxial film thickness. This means that the growth of a homogeneous alloy is unstable, and the growth may result in an alloy with a spatial modulation of composition. We consider the growth of an alloy from the vapor. We study the epitaxial film on a substrate where the monolayers from the 1st to the Mth are completed, and the (M+ l)st monolayer is the growing one. Growth on atomically smooth surfaces proceeds via the surface migration of adatoms and via their incorporation into the growing monolayer. In the process of the growth of each Lth monolayer (1 < L < M), there appears the fluctuation of alloy composition Sc(r; L), where r = (x, y) is the two-dimensional position vector. Since we neglect the migration of atoms in the bulk, the fluctuations of composition are "frozen" after the given monolayer is covered by subsequent monolayers. First, "frozen" fluctuations of composition in the top completed Mth monolayer, 5c(r; M), affect the migration of adatoms in the next, growing, (M+l)st monolayer via a short-range potential U"rh'B) (r; M+1) acting on adatoms A and B. Second, "frozen" fluctuations in all co
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