Diffusion Dynamics during the Nucleation and Growth of Ge=Si Nanostructures on Si(111) F. Ratto, 1, * ,† A. Locatelli, 2 S. Fontana, 2 S. Kharrazi, 3 S. Ashtaputre, 3 S. K. Kulkarni, 3 S. Heun, 4 and F. Rosei 1, * ,‡ 1 INRS Energie, Mate ´riaux et Te ´le ´communications, Universite ´ du Que ´bec, 1650 Boulevard Lionel Boulet, J3X 1S2 Varennes (QC), Canada 2 Sincrotrone Trieste SCpA, SS 14 Km 163.5, 34012 Basovizza, Italy 3 DST Unit on Nanoscience, Physics Department, University of Pune, Pune 411007, India 4 Laboratorio Nazionale TASC-INFM-CNR, Area Science Park, SS 14 Km 163.5, 34012 Basovizza, Italy (Received 17 November 2005; published 8 March 2006) We report a low energy electron microscopy study of the relation between self-organized Ge=Si111 nanostructures and their local environment. By comparison with Monte Carlo simulations, three- dimensional islands are shown to display a substantial tendency towards self-ordering. This tendency may result from the diffusive nature of the nucleation processes. The size of individual nanostructures does not significantly correlate with the distance between neighboring islands. Thus energetic factors are thought to govern the competition among coexisting nanostructures to capture the deposited mass. DOI: 10.1103/PhysRevLett.96.096103 PACS numbers: 68.55.Ac, 68.37.Nq, 68.60.Dv, 81.07.Ta The self-organization of three-dimensional (3D) nano- structures as a result of semiconductor heteroepitaxy is an important phenomenon in crystal growth [1,2]. In this context Ge nanostructures on Si(111) represent a model system, with a view to applications in micro- and optoe- lectronics. The growth of germanium on low index silicon surfaces is known to follow the Stranski-Krastanov (SK) mode [3]; i.e., 3D islands nucleate due to a roughening transition from a critically thick wetting layer (WL). Ge nanostructures embedded within a Si matrix are expected to behave as artificial atoms, or quantum dots. The posi- tioning and relative dimensions of self-organized 3D is- lands identify critical issues both for a fundamental under- standing and for future device engineering. In this Letter, we pursue the following questions: (i) Do self-organized 3D nuclei display a tendency towards self-ordering? (ii) What factors govern the relative growth of individual nanostructures; i.e., what is the competition among differ- ent nuclei to gather the mass deposited on the surface? Both issues can be described in terms of kinetic pro- cesses based on diffusion, nucleation, and capture [4]. The development of a 3D island arises from the growth of a stable nucleus. The latter generally results from a collision process involving a number of diffusing adatoms greater than a critical threshold [5]. The occurrence probability of such a collision event is proportional to the local density of adatoms. Upon formation, the critical nucleus starts cap- turing the diffusing atoms in its neighborhood, thus giving rise to a local decrease in the adatoms’s density. Within this adatom-depleted region the probability of nucleating a second island is correspondingly reduced [6]. On an iso- tropic surface, the consequences of this phenomenon may be naively pictured as an isotropic repulsion among nuclei. This could result in a tendency towards a local compact ordering of the islands. Self-ordering would be merely kinetically driven, i.e., would not follow from any mini- mization of the system potentials. On the other hand, energetic factors would lead to a similar configuration [7]. Order may be induced by either a preexisting stress pattern in the WL [8] or elastic interactions among nuclei [9]. A hexagonal array would follow from the symmetry of the Si(111) surface and the isotropic character of island- island interactions. Despite this, most experimental reports depict a random scattering of self-organized nuclei [10]. The growth of the islands as well might be governed by diffusive phenomena [11]. In this context deposited atoms would tend towards and be captured by — on average — the closest nuclei. The process could then be described by the Mulheran capture zone model [12,13], projecting a corre- lation between the growth rate of every island and the area of the relevant cell in the Voronoi tessellation [14]. Thus the competition among neighboring nuclei for gathering the mass supplied to the surface would follow local laws. On the other hand, a growth process not consistent with the Mulheran model could be related to energetic factors. These might either prompt deposited atoms to preferen- tially reach islands for reasons else than their geometric proximity, or the 3D islands to unevenly exchange mass afterwards [15]. Under these circumstances some nuclei would reach a thermodynamically steadier structure than others and develop thereafter at a different pace [16]. Here we test these concepts by comparing the output of model descriptions with our experimental results. Our experiments were performed by depositing 10 monolayers (ML) Ge from a molecular beam source on clean Si(111) surfaces kept at different temperatures T, in an ultrahigh vacuum environment (base pressure 10 10 mbar). The surface morphology was imaged in situ by low energy electron microscopy (LEEM) with a lateral resolution of 10 nm [17]. By acquiring LEEM movies during the growth process, Ge=Si111 islands have been dynamically observed to grow with undetectable lateral movement (see movie file in EPAPS material [18]). Thus we can approximate their centers of mass with the relevant nucleation sites. This in turn allows us to infer experimentally the nuclei layout. To PRL 96, 096103 (2006) PHYSICAL REVIEW LETTERS week ending 10 MARCH 2006 0031-9007= 06=96(9)=096103(4)$23.00 096103-1  2006 The American Physical Society