A continuum description of the energetics and evolution of stepped surfaces in strained nanostructures

As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by the discrete nature of the material, namely, crystallographic surface steps. It is shown that the formation energy of surface steps depends on the sign of extensional strain of the crystal surface, and this behavior plays a crucial role in surface evolution. The nature of this dependence implies that there is no energetic barrier to nucleation of islands on the growth surface during deposition, and that island faces tend toward natural orientations which have no counterpart in unstrained materials. This behavior is expressed in terms of a small number of parameters that can be estimated through atomistic analysis of stepped surfaces. The continuum framework developed is then applied to study the time evolution of surface shape of an epitaxial film being deposited onto a substrate. The kinetic equation for mass transport is enforced in a weak form by means of a variational formulation [...].Comment: 25 pages, 7 figs, KEYWORDS=surface diffusion, surface energy, morphology evolution, semiconductor material, stability and bifurcatio

Determining the energetics of vicinal perovskite oxide surfaces

The energetics of vicinal SrTiO$_3$(001) and DyScO$_3$(110), prototypical perovskite vicinal surfaces, has been studied using topographic atomic force microscopy imaging. The kink formation and strain relaxation energies are extracted from a statistical analysis of the step meandering. Both perovskite surfaces have very similar kink formation energies and exhibit a similar triangular step undulation. Our experiments suggest that the energetics of perovskite oxide surfaces is mainly governed by the local oxygen coordination.Comment: 16 pages, 4 figure

Probing the Structure and Energetics of Dislocation Cores in SiGe Alloys through Monte Carlo Simulations

We present a methodology for the investigation of dislocation energetics in segregated alloys based on Monte Carlo simulations which equilibrate the topology and composition of the dislocation core and its surroundings. An environment-dependent partitioning of the system total energy into atomic contributions allows us to link the atomistic picture to continuum elasticity theory. The method is applied to extract core energies and radii of 60 degrees glide dislocations in segregated SiGe alloys which are inaccessible by other methods.Comment: 5 pages, to be published in Physical Review Letter

Surface energetics and structure of the Ge wetting layer on Si(100)

Ge deposited on Si(100) initially forms heteroepitaxial layers, which grow to a critical thickness of ~3 MLs before the appearance of three-dimensional strain relieving structures. Experimental observations reveal that the surface structure of this Ge wetting layer is a dimer vacancy line (DVL) superstructure of the unstrained Ge(100) dimer reconstruction. In the following, the results of first-principles calculations of the thickness dependence of the wetting layer surface excess energy for the c(4×2) and 4×6 DVL surface reconstructions are reported. These results predict a wetting layer critical thickness of ~3 MLs, which is largely unaffected by the presence of dimer vacancy lines. The 4×6 DVL reconstruction is found to be thermodynamically stable with respect to the c(4×2) structure for wetting layers at least 2 ML thick. A strong correlation between the fraction of total surface induced deformation present in the substrate and the thickness dependence of wetting layer surface energy is also shown

Silicon and III-V compound nanotubes: structural and electronic properties

Unusual physical properties of single-wall carbon nanotubes have started a search for similar tubular structures of other elements. In this paper, we present a theoretical analysis of single-wall nanotubes of silicon and group III-V compounds. Starting from precursor graphene-like structures we investigated the stability, energetics and electronic structure of zigzag and armchair tubes using first-principles pseudopotential plane wave method and finite temperature ab-initio molecular dynamics calculations. We showed that (n,0) zigzag and (n,n) armchair nanotubes of silicon having n > 6 are stable but those with n < 6 can be stabilized by internal or external adsorption of transition metal elements. Some of these tubes have magnetic ground state leading to spintronic properties. We also examined the stability of nanotubes under radial and axial deformation. Owing to the weakness of radial restoring force, stable Si nanotubes are radially soft. Undeformed zigzag nanotubes are found to be metallic for 6 < n < 11 due to curvature effect; but a gap starts to open for n > 12. Furthermore, we identified stable tubular structures formed by stacking of Si polygons. We found AlP, GaAs, and GaN (8,0) single-wall nanotubes stable and semiconducting. Our results are compared with those of single-wall carbon nanotubes.Comment: 11 pages, 10 figure

How metal films de-wet substrates - identifying the kinetic pathways and energetic driving forces

We study how single-crystal chromium films of uniform thickness on W(110) substrates are converted to arrays of three-dimensional (3D) Cr islands during annealing. We use low-energy electron microscopy (LEEM) to directly observe a kinetic pathway that produces trenches that expose the wetting layer. Adjacent film steps move simultaneously uphill and downhill relative to the staircase of atomic steps on the substrate. This step motion thickens the film regions where steps advance. Where film steps retract, the film thins, eventually exposing the stable wetting layer. Since our analysis shows that thick Cr films have a lattice constant close to bulk Cr, we propose that surface and interface stress provide a possible driving force for the observed morphological instability. Atomistic simulations and analytic elastic models show that surface and interface stress can cause a dependence of film energy on thickness that leads to an instability to simultaneous thinning and thickening. We observe that de-wetting is also initiated at bunches of substrate steps in two other systems, Ag/W(110) and Ag/Ru(0001). We additionally describe how Cr films are converted into patterns of unidirectional stripes as the trenches that expose the wetting layer lengthen along the W[001] direction. Finally, we observe how 3D Cr islands form directly during film growth at elevated temperature. The Cr mesas (wedges) form as Cr film steps advance down the staircase of substrate steps, another example of the critical role that substrate steps play in 3D island formation

First-principles studies of kinetics in epitaxial growth of III-V semiconductors

We demonstrate how first-principles calculations using density-functional theory (DFT) can be applied to gain insight into the molecular processes that rule the physics of materials processing. Specifically, we study the molecular beam epitaxy (MBE) of arsenic compound semiconductors. For homoepitaxy of GaAs on GaAs(001), a growth model is presented that builds on results of DFT calculations for molecular processes on the beta2-reconstructed GaAs(001) surface, including adsorption, desorption, surface diffusion and nucleation. Kinetic Monte Carlo simulations on the basis of the calculated energetics enable us to model MBE growth of GaAs from beams of Ga and As_2 in atomistic detail. The simulations show that island nucleation is controlled by the reaction of As_2 molecules with Ga adatoms on the surface. The analysis reveals that the scaling laws of standard nucleation theory for the island density as a function of growth temperature are not applicable to GaAs epitaxy. We also discuss heteroepitaxy of InAs on GaAs(001), and report first-principles DFT calculations for In diffusion on the strained GaAs substrate. In particular we address the effect of heteroepitaxial strain on the growth kinetics of coherently strained InAs islands. The strain field around an island is found to cause a slowing-down of material transport from the substrate towards the island and thus helps to achieve more homogeneous island sizes.Comment: 12 pages, 7 figures, REVTeX, Final version to appear in Appl. Phys. A (2002). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm