The Stability of Lattice Mismatched Thin Films
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ABSTRACT We examine the linear stability of a planar, alloy thin film, exposed to a deposition flux from the vapor. The film surface is subject to stresses generated by compositional inhomogeneity, as well as by film-substrate lattice mismatch. In addition to the misfit induced surface instability shown by numerous previous studies, we find that the deposition flux alone can produce instability and that complex interactions occur when both deposition and surface transport processes are present. Solute expansion stresses result in several novel behaviors. Under certain circumstances, the growing film can be completely stabilized by a tensile misfit and destabilized by the same magnitude of compressive misfit. The predictions of this theory are compared to the results of several experimental studies.
INTRODUCTION Misfit stress is well known to cause changes in the growth mode of thin films. The traditional view is that the misfit stress is relieved by dislocations at the film-substrate interface, which, in turn, leads to the formation of three-dimensional islands [1]. There is now ample theoretical [2-7] and experimental [7-12] evidence that morphological instability can relieve misfit stress substantially in advance of dislocation formation. In the earlier theoretical literature, the stability of a surface perturbation is determined by comparing the stabilizing influence of surface energy to the destabilizing effects of misfit induced elastic strain energy. Since the wave number dependencies of these two effects are different, there exists a critical wave number, a., at which these two energies exactly balance. Smaller wave numbers are unstable, larger ones are stable, and the instability is insensitive to the sign of the misfit c, as a, cxc2. There is an apparent inconsistency between these models, which indicate that misfitting films should be unstable to some range of wave numbers from the onset of growth, and experiments, which generally observe the Stranski-Krastanov growth mode, wherein the planar film grows to some finite thickness before the onset of islanding. This discrepancy has been addressed by a kinetic argument, presented in somewhat different forms by Spencer, Voorhees, and Davis [5] and by Snyder, Mansfield, and Orr [7]. Although the formation of islands is energetically favored, a growing film is kinetically stabilized to their formation until the perturbations grow more rapidly than the film itself. Tersoff and LeGoues [13] and Gao [14] have shown that surface energy anisotropy can also stabilize against the formation of islands, due to the energy needed to form geometrically necessary facets. There is a potentially significant assumption made in earlier theoretical work, which does not hold in the bulk of experiments. Previous models have treated the film as a homogeneous, single component material, whereas many of the experimentally grown films consist of binary, ternary, or higher order alloys. To address this discrepancy, we analyze the stability of binary-alloy thin films, subject to surface
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