The energetics of multisheet arrays of two-dimensional islands is studied where the structure of the surface sheet is determined by thermodynamic equilibrium under the constraint of a fixed structure of sheets of buried islands. For the arrangement of islands in a single surface sheet, both a one-dimensional structure of stripes and a two-dimensional structure of square-shaped islands are examined. The buried islands are considered as planar elastic defects characterized by a uniaxially anisotropic double force density, and the surface islands are considered as two-dimensional islands characterized by an isotropic intrinsic surface stress tensor. It is shown that, in cubic crystals with a negative parameter of elastic anisotropy, ϭ(c 11 Ϫc 12 Ϫ2c 44 )/c 44 Ͻ0, the elastic interaction between successive sheets of islands parallel to the ͑001͒ crystallographic plane exhibits an oscillatory decay with the separation between sheets. This oscillatory decay is related to generalized Rayleigh waves in elastically anisotropic crystals. By varying the distance between successive sheets of islands, a transition occurs from vertical correlations between islands where islands of the upper sheet are formed above the buried islands of the lower sheet to anticorrelations between islands where islands of the upper sheet are formed above the spacings in the lower sheet. The separation between successive sheets of islands corresponding to this transition depends drastically on the anisotropy of the double force density of buried islands. Thus an explanation for the recently observed anticorrelations in multisheet arrays of CdSe islands in the ZnSe matrix is obtained.

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.

Perturbation theory is used to compute the angular-intensity correlation function C(q, k|q(?), k(?)) = ?[I(q|k) - ?I(q|k)?][I(q(?)|k(?)) - ?I(q(?)|k(?))]? for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. I(q|k) is the squared modulus of the scattering matrix for the system, and q , q(?) and k , k(?) are the projections on the mean scattering surface of the wave vectors of the scattered and the incident light, respectively. Contributions to C include (a) short-range memory effect and time-reversed memory effect terms, C((1)) ; (b) an additional short-range term of comparable magnitude C((10)) ; (c) a long-range term C((2)) ; (d) an infinite-range term C((3)) ; and (e) a new term C((1.5)) that along with C((2)) displays peaks associated with the excitation of surface polaritons. These new features arise when the factorization approximation is not made in calculating the correlation function C .

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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.