Shape Evolution During Growth

Chen et al. [89] reported that during the two-dimensional (2D) to three-dimensional (3D) transition in a Ge05Si05/ Si(001) QD system, the lateral width and inclination angle of the islands evolve continuously until the island is bounded by stable {501} facets. This phenomenon was later confirmed by Vailionis et al. [177] who investigated the 2D to 3D transition during the growth of Ge on Si(001) using STM and found "prepyramids" before the formation of {501}-faceted pyramids. The prepyramids have rounded bases and are bounded by steps oriented approximately along (110). The aspect ratio of the prepyramids varies from 0.03 to 0.05, increasing with increasing island size. When the base width of a prepyramid reaches 16-20 nm, the prepyra-mid transforms into {501}-faceted pyramids. At the point of the transformation from prepyramids to pyramids, the island volume remains approximately constant and Ge atoms in the islands rearrange so that the island width decreases while the island height increases. As the growth continues, pyramids all finally transform into domes.

Both experimental and theoretical investigations have shown that QD shapes change during the growth of the QD [88, 98, 177]. However, different experiments show different evolution processes. For example, by growing Ge QDs on Si (001) in an ultra high vacuum, chemical-vapor deposition system at temperatures of 550 °C and 700 ° C, Thanh [178] reported two different evolutions of island shapes:

(1) from a metastable square-base truncated pyramid formed by {501} facets and a {100} facet on the top, to a dome with {111} facets, and

(2) from the same metastable shape to a dome with {311} facets.

From the study of the growth of Ge08Si02/Si (001), which proceeds in a similar way to the growth of Ge/Si (001) but with the length scales expanded by the reduced strain, Floro et al. [90, 179] showed that the {501} facets are extremely stable over a range of deposition thicknesses. Beyond a certain thickness, the islands with {501} facets transform to domes with steep {h11} facets. As the film thickens, dome formation continues, and the dome facets approach {311}. All of the above experimental observations show one point in common: the contact angle between the sidewalls of the islands and the substrate increases with increasing island size. This is consistent with theoretical considerations [162, 175, 180]. For example, Spencer and Tersoff [162] calculated the equilibrium morphology of a coherent epitaxial strained layer grown under the S-K mode, in an isotropic two-dimensional continuum model. Assuming an unfaceted surface and assuming that mass transport caused by surface gradients in the chemical potential occurs only by surface diffusion, and based on the fact that the equilibrium morphology has a constant chemical potential along the free surface, they concluded that very small islands have a fixed asymptotic width and a vanishingly small aspect ratio. With increasing volume, the island initially grows in the vertical direction which makes the small island have an arbitrarily small aspect ratio. At a larger volume both the island width and aspect ratio continue to increase. The contact angle between the island side-wall and the substrate increases continuously with size and a sufficiently large island approaches a ball shape sitting on top of the wetting layer. On the basis that stable shapes have minimum energy and considering the fully faceted islands, Daruka et al. [180] studied in a two-dimensional model, the equilibrium shape and the shape evolution in the growth of strained islands. They predicted that the first-order shape transition (discontinuous shape change) is a very general phenomenon in island growth. They found that at the smallest volumes there is no island at all; all the material remains in the planar wetting layer. Above a lower transition, the island is stable and consists of shallow side facets. At a critical island volume, the shallow side facets are substituted by steep side facets so that the overall aspect ratio increases discontinuously.

Goldfarb, Briggs et al. [181-183] considered growth in the Ge/Si system at temperatures of 620 °C and 690 °C, using in-situ STM observations. At the lower temperature, they reported the formation of huts, while at the higher temperature, strain was initially relieved by hut pits with their apex down. They developed a model of hut growth, with the early stages being limited by surface diffusion. The later stages of growth have the smaller huts dissolving, as in Ostwald ripening, but with the released material reagglomerat-ing rather than contributing to the coarsening of the larger huts. At higher temperatures, the role of true Ostwald ripening increases. This model explained the skewed and bimodal distributions seen in their STM experiments.

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