We consider the growth of facets associated with coherently strained semiconductor islands. Surprisingly, the island growth rate is found to rapidly self-limit, which has important consequences for island size distributions. A new explanation for the elongation of strained faceted islands is proposed as a natural consequence of facet growth kinetics. [S0031-9007(98)06262-0] PACS numbers: 68.55. -a, 81.15. -z Mechanisms of facet formation and growth are longstanding issues in surface physics and materials science [1]. In particular, faceting governs many key processes in crystal growth and etching [2]. More recently, it has been discovered that facets also play a central role in the growth of coherently strained semiconductor islands [3][4][5][6][7]. Here the situation is particularly intriguing from the growth physics perspective because of the spatial variation in strain across the surface of the faceted island. Despite the fact that coherently strained semiconductor islands are presently receiving considerable attention as a means of fabricating quantum dot devices [8], insight into the facet growth mechanisms has remained limited.In this Letter we identify two surprising consequences of strained facet growth which dramatically influence island growth kinetics. First, we demonstrate that the island growth rate decreases rapidly with increasing island size. This implicates an important role of faceting as a means of inducing self-limiting growth and narrowing island size distributions, even in low misfit systems. Second, a shape instability of strained islands arises as a natural consequence of facet growth which provides a new explanation for the origin of elongated hut cluster shapes observed in strained layer epitaxy [3].Consider the generic model of facet growth illustrated in Figs. 1(a) and 1(b). A pyramidal island of half base length s is bounded by four facets inclined at an angle u to the surface. The three-dimensional island grows via the nucleation of two-dimensional islands of height a on the facet surfaces [ Fig. 1(b)]. Such an embryo is shown originating from the bottom left hand corner of the facet in Fig. 1(a) which, as discussed later, is an energetically favorable nucleation site. We assume that the embryo shape is dominated by surface energy considerations such that the step energy g b is a minimum for a direction in the facet plane, inclined at an angle w to the base of the island. This is a good approximation as long as gradients in the surface elastic energy density are small compared with the anisotropy in step energy. Details of the critical nucleus shape will, however, not influence the important qualitative features of the model.We model the growth of strained facets as a direct transformation between the planar strained film and the embryo, which is strictly valid in the limit of zero supersaturation (i.e., annealing of the planar film in the absence of deposition). However, the analysis will also apply to deposition if the supersaturation is very small, which is true for many situat...

We identify a new mechanism of stress driven surface morphological evolution in strained semiconductor films. Surface roughness forms by a cooperative mechanism involving the sequential nucleation of islands and pits, which is distinct from the conventional view of ripple formation as an Asaro-Tiller-Grinfeld (ATG) instability. This mechanism is operative both during annealing and growth and competes with the ATG instability as a kinetic pathway to ripple formation. [S0031-9007(96)00853-8] PACS numbers: 68.35.MdThe morphological stability of stressed solids is a subject of considerable scientific and technological importance. It is directly relevant to several key issues in materials science ranging from stress corrosion cracking through to phase transformations and strained layer epitaxy. Since the pioneering work of Asaro and Tiller [1] and Grinfeld (ATG) [2], it is generally argued that above a critical wavelength l c the planar surface of a stressed solid is unstable to the formation of undulations [3][4][5]. This is because the energy reduction associated with elastic relaxation of the undulations exceeds the increase in surface energy. In the case of thin-film deposition, it is therefore envisioned that an initially planar film surface will gradually roughen in the growth direction over extended regions with a characteristic lateral wavelength. The observation of continuous surface ripple patterns on strained semiconductor layers over large areas would appear to give direct confirmation of this view [6,7]. Indeed, the patterns observed in cross section often closely resemble the sinusoidal roughness profiles used as a basis for the instability theory [8,9].In this Letter we reveal an entirely new mechanism of surface ripple formation, which is linked to the activated nature of island and pit formation. The ripple forms by a cooperative mechanism involving the sequential nucleation of islands and pits. This is very different from the gradual strain induced roughening mechanism normally envisioned [3-9] and has important implications for our fundamental understanding of the 2D to 3D transition of strained systems.To determine the mechanism of surface ripple formation we have studied the stress induced 2D to 3D transition in the technologically important Si x Ge 12x system. Our method involves a novel two stage process in which a thin (5 nm) planar Si 0.5 Ge 0.5 alloy layer is first grown at relatively low temperatures to ensure a nominally planar surface. The ripple morphology is then formed by a gentle postdeposition anneal at around 590 ± C for 5 min. This approach emulates equilibrium surface conditions, at least locally, as closely as possible. A map of the surface evolution during growth was obtained from atomic force microscopy (AFM) measurements of the ripple geometry at different temperature regions of one sample wafer.To capture the mechanism of surface ripple formation, use was made of the natural temperature gradient across the sample [10]. At the center of the wafer, corresponding to a temperature...

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