In this expression e is the first-order dipole-moment expansion coefFicient, V, is the volume of a primitive unit cell, and M+ and M are the masses of the positive and negative ions, respectively. The frequency of the incident light is denoted by co, and cv & is the frequency of the transverse optical modes of infinite wavelength. Explicit expressions for the renormalized frequency Qi(ro) and the damping constant ri(&e) were obtained to second order in the cubic and quartic anharmonic force constants in I. It was shown there as well that the COefriCient (4rre'/V, ) (M++M )/M+M Can be identified with (ese")o~s',where es and e"arethe static and Tela 8, 1064Tela 8, (1966 [English transl. : Soviet Phys. -Solid State 8, 850 (1966)j.This paper will be referred to as I, and all references to equations from this paper will be prefixed by I.

The elastic energy associated with alloy composition modulation in the epitaxial film of a III-V semiconductor alloy on the [001]-substrate is calculated in the analytic form. Composition modulation both in the directions parallel to the substrate surface and in the growth direction are taken into account. It is shown that the minimum of the elastic energy corresponds to the modulation along the [100]- (and/or [010]-) direction, the period of the modulation d being small compared to the film thickness h (d≪h). The ‘‘soft mode’’ of composition modulation is exponentially localized near the free surface, the localization length l being l=d/2π. The elastic energy caused by this modulation is less by the factor 1/2c11/(c11+c12) than the elastic energy corresponding to spinodal decomposition in the bulk sample. This factor is ≊1/3 for III-V alloys. Critical temperatures of spinodal decomposition Tc are calculated for a number of epitaxial ternary III-V alloys. The diffusion which occurs only in the very thin subsurface layer (nearly monolayer) is shown to provide exponential amplification of the composition modulation amplitude δc(0)∼exp(Δh/l) at early stages of the subsequent layer-by-layer growth.

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A kinetic theory of the instability of homogeneous alloy growth with respect to fluctuations of alloy composition is developed. The growth mechanism studied is the step-flow growth of an alloy from the vapor on a surface vicinal to the ͑001͒ surface of a cubic substrate. The epitaxial growth implies that the adsorbed atoms migrate on the surface during the growth of each monolayer, and that their motion is ''frozen'' after the completion of the monolayer. ''Frozen'' fluctuations of alloy composition in all completed monolayers create, via a composition-dependent lattice parameter, an elastic strain that influences the migration of adatoms of the growing monolayer. The migration consists of diffusion-and strain-induced drift in an effective potential. For temperatures lower than a certain critical temperature T c , strain-induced drift dominates diffusion and results in the kinetic instability of the homogeneous alloy growth. In an approximation linear in the fluctuation amplitude, the instability means the exponential increase of the fluctuation amplitude with the thickness of the epitaxial film. It is shown that the critical temperature of the kinetic instability T c increases with the increase of elastic effects. The wave vector k c of the most unstable mode of composition fluctuations is determined by the interplay of the anisotropic elastic interaction and the anisotropic diffusion of the adatoms on a stepped vicinal surface. The direction of the wave vector k c differs from the lowest-stiffness direction of the crystal. Regions in k space of both stable and unstable modes are found by model calculations.

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