Controlled Self-Organization of Atom Vacancies in Monatomic Gallium Layers

Abstract

Ga adsorption on the Si(112) surface results in the formation of pseudomorphic Ga atom chains. Compressive strain in these atom chains is relieved via creation of adatom vacancies and their selforganization into meandering vacancy lines. The average spacing between these line defects can be controlled, within limits, by adjusting the chemical potential of the Ga adatoms. We derive a lattice model that quantitatively connects density functional theory (DFT) calculations for perfectly ordered structures with the fluctuating disorder seen in experiment and the experimental control parameter . This hybrid approach of lattice modeling and DFT can be applied to other examples of line defects in heteroepitaxy. DOI: 10.1103/PhysRevLett.99.116102 PACS numbers: 68.35.ÿp, 05.65.+b, 68.37.Ef, 81.16.Dn Many physical, chemical, and biological phenomena are manifestations of self-organization of matter, such as crystal growth, protein folding, or formation of galaxy clusters. Well-known examples of self-organization in advanced materials systems include the formation of magic metal clusters, pyramid quantum dots, quantum dot superlattices in heterostructures [1], and the ordering of atom vacancies into line defects or vacancy line superstructures [2 -4]. For application purposes, it would be essential to control the size, uniformity, and spacing of such nano-objects. This goes against the odds of thermodynamic fluctuations that are especially profound in low-dimensional systems, and the stochastic nature of nucleation and growth.Here, we show that the average spacing between VLs in a monatomic Ga layer on Si(112) can be controlled and varied continuously, within limits, via the chemical potential of the adsorbate species, . Ga vacancies self-organize into a n 1 VL superstructure [ Fig. 1(a)-1(c)], similar to the formation of the well-known n 2 superstructures for Ge on Si(100) [2 -4]. Entropic fluctuations compete with this ordering process, however, resulting in meandering VLs where the average line spacing is fixed by the chemical potential. The meandering amplitude is limited by elastic repulsions between VLs. Such a two-dimensional (2D) interacting vacancy line system has been modeled as a 1D random walker trapped in a harmonic potential representing the collective mean field of all the other VLs [4]. For systems such as Ge on Si(100), this 1D model seems to capture the observed meandering quite well, allowing for a straightforward determination of the kink energy and line repulsion from statistical analysis of fluctuations in Scanning Tunneling Microscopy (STM) images.Step fluctuations on vicinal crystal surfaces have been analyzed in similar fashion, using continuum modeling [5].An interesting question is how the constraints imposed by the discreteness of a lattice modifies the elastic interactions that are driving the self-organization of vacancies, particularly for short VL spacings. Discrete VL spacings conceivably lead to significant vacancy-vacancy correlations that cannot be captured by the usual mean field or ...

Advances and applications in the FIREBALLab initio tight‐binding molecular‐dynamics formalism

“…The combination of MD capabilities of FIREBALL and the accurate simulation of STM images (based on the local-orbital Hamiltonian provided by FIREBALL) has proven very useful to unravel the atomic geometry for the quasi-one dimensional surface reconstruction of Ga on Si(112) [138,139]. Recent progress in scanning probe instrumentation tends to combination of both AFM and STM into one tool, where the tunneling current and force is recorded simultaneously.…”

Crystalline Structure and Vacancy Ordering across a Surface Phase Transition in Sn/Cu(001)

“…Critical phenomena at surfaces often present specific features, like surface critical exponents , or critical temperatures different from the bulk . Phase transitions with surface specific properties include structural transformations of the top atomic layers of a crystal (surface reconstruction), surface melting, enrichment of one component at the surface of a solid binary alloy (surface segregation), sophisticated phenomena related to self-organization, like the ordering of atom vacancies into line defects or vacancy line superstructures, − specific kinetics for Under Potential Deposition conditions, and structural transformations of organic ultrathin films or metallic layers . Other examples include magnetically ordered systems, with a surface Curie temperature different from the bulk, Mott or Wigner–Mott transition, or collective states, including superconductivity, , and charge density waves (CDWs). − In last years, CDW phase transitions have been reported for different metals on the (100) faces of noble metals, notably Cu(100), including In, Tl, Sn, Bi, , and Pb .…”

Influence of interface reconstruction on the formation and superconductive properties of metastable Pb-Ga alloy films

“…16 Film thicknesses were fixed at about 8 ML. 17 We employed established procedures for calibrating the deposition rate of Pb 18 and that of Ga. 16,19 The √ 3-Pb interface was prepared by depositing 1/3 ML of Pb onto Si(111)-(7×7) at 250 • C, following the procedures by Ganz et al 20 The √ 3-Ga phase was prepared by depositing approximately 1.5 ML of Ga onto clean Si(111)-(7×7) at room temperature. The substrate was subsequently heated at 650 • C to evaporate the excess Ga until the ( √ 3 × √ 3) low energy electron diffraction pattern was fully developed with 1/3 ML of Ga remaining on the surface.…”