The commonly accepted Stranski-Krastanow model, according to which island formation occurs on top of a wetting layer ͑WL͒ of a certain thickness, predicts for the morphological evolution an increasing island aspect ratio with volume. We report on an apparent violation of this thermodynamic understanding of island growth with deposition. In order to investigate the actual onset of three-dimensional islanding and the critical WL thickness in the Ge/Si͑001͒ system, a key issue is controlling the Ge deposition with extremely high resolution ͓0.025 monolayer ͑ML͔͒. Atomic force microscopy and photoluminescence measurements on samples covering the deposition range 1.75-6.1 ML, taken along a Ge deposition gradient on 4 in. Si substrates and at different growth temperatures ͑T g ͒, surprisingly reveal that for T g Ͼ 675°C steeper multifaceted domes apparently nucleate prior to shallow ͕105͖-faceted pyramids, in a narrow commonly overlooked deposition range. The puzzling experimental findings are explained by a quantitative modeling of the total energy with deposition. We accurately matched ab initio calculations of layer and surface energies to finite-element method simulations of the elastic energy in islands, in order to compare the thermodynamic stability of different island shapes with respect to an increasing WL thickness. Close agreement between modeling and experiments is found, pointing out that the sizeable progressive lowering of the surface energy in the first few MLs of the WL reverts the common understanding of the SK growth onset. Strong similarities between islanding in SiGe and III/V systems are highlighted.

Unimodal SiGe islands with dominant f111g facets were grown coherently on pit-patterned Si (001) substrates by molecular beam epitaxy. With increasing Ge deposition, the f111g pyramids evolve from dome-shaped islands, reaching significantly larger volumes than are coherently possible on flat substrates. Finite element calculations and molecular dynamics simulations show that SiGe islands in pits can have less misfit strain with respect to islands of the same shape on flat substrates. The injection of dislocations is thus delayed, allowing for the observed development of coherent islands with a very high aspect ratio. DOI: 10.1103/PhysRevLett.98.176102 PACS numbers: 81.07.ÿb, 68.37.Lp, 68.37.Ps, 71.15.Pd Since the first evidence of coherent SiGe island formation [1,2], self-assembled SiGe islands on Si (001) have been extensively studied due to their compatibility with standard Si technology [3]. It is now well established that the evolution of SiGe islands with deposition results from a competition between the relaxation of misfit strain and the increase of the surface energy. After the initial formation of prepyramids [4] or mounds [5], islands bounded by f105g facets appear. They form square-based pyramids, or rectangular-based hut clusters [1], with a height-to-base aspect ratio (a=r) of 0.1. Further volume increase results in multifaceted dome islands with dominant f15; 3; 23g and f113g facets [6 -8], and an a=r of about 0.2. The increased average steepness of large islands is attributed to more efficient strain relaxation [9,10]. One would expect an island bounded solely by f111g facets to be the natural evolution at large enough volumes, due to a large steepness combined with a close-packed surface. However, at large volumes, strain relaxation by dislocation injection becomes competitive. Hence, under most experimental conditions, domes are followed by dislocated superdomes [11,12], which show an inverted trend in the a=r vs volume. The formation of coherent islands with a higher a=r than domes has only been reported for SiGe alloys of low Ge content [13][14][15]. Still, the barn-shaped islands in Refs. [13,15] have a lower a=r than the ones reported here .In this Letter, we show that a unimodal distribution of coherent SiGe pyramids with dominant f111g facets and a=r 0:37 can be realized on patterned Si (001) substrates by solid source MBE. Such f111g pyramids are the result of a shape transition from domes, accompanied by a substantial increase of the a=r. Molecular dynamics (MD) simulations and elasticity-theory calculations are used to explain the role played by the substrate pattern in altering the strain distribution and favoring coherence at high a=r.Patterned Si(001) substrates with two-dimensionally (2D) periodic pits along two orthogonal h110i directions were obtained by holographic lithography and reactive ion etching [16,17]. To create a well-defined starting surface, a 130 nm thick Si buffer layer was grown with 0:05 nm=s while ramping the temperature from 450 C to 600 C. On sample A only ...

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We compare elastic relaxation and Si-Ge distribution in epitaxial islands grown on both pit-patterned and flat Si(001) substrates. Anomalous x-ray diffraction yields that nucleation in the pits provides a higher relaxation. Using an innovative, model-free fitting procedure based on self-consistent solutions of the elastic problem, we provide compositional and elastic-energy maps. Islands grown on flat substrates exhibit stronger composition gradients and do not show a monotonic decrease of elastic energy with height. Both phenomena are explained using both thermodynamic and kinetic arguments.