Coarsening scenarios in unstable crystal growth

Crystal surfaces may undergo thermodynamical as well kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern formation and coarsening dynamics. We are finally able to attack the problem analytically and get rigorous results. Three dynamical scenarios are possible: perpetual coarsening, interrupted coarsening, and no coarsening. In the perpetual coarsening scenario, mound size increases in time as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise n=1/4.Comment: Changes in the final part. Accepted for publication in Phys. Rev. Let

Re-entrant Layer-by-Layer Etching of GaAs(001)

We report the first observation of re-entrant layer-by-layer etching based on {\it in situ\/} reflection high-energy electron-diffraction measurements. With AsBr$_3$ used to etch GaAs(001), sustained specular-beam intensity oscillations are seen at high substrate temperatures, a decaying intensity with no oscillations at intermediate temperatures, but oscillations reappearing at still lower temperatures. Simulations of an atomistic model for the etching kinetics reproduce the temperature ranges of these three regimes and support an interpretation of the origin of this phenomenon as the site-selectivity of the etching process combined with activation barriers to interlayer adatom migration.Comment: 11 pages, REVTeX 3.0. Physical Review Letters, in press

Kinetic modelling of epitaxial film growth with up- and downward step barriers

The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We generalize this concept in a solid-on-solid growth model, in which a barrier dependent on the particle coordination (number of lateral bonds) exists whenever the particle performs an interlayer diffusion. The rules do not distinguish explicitly if the particle is executing a descending or an ascending interlayer diffusion. We show that the usual model, with a step barrier in descending steps, produces spurious, columnar, and highly unstable morphologies if the growth temperature is varied in a usual range of mound formation experiments. Our model generates well-behaved mounded morphologies for the same ES barriers that produce anomalous morphologies in the standard model. Moreover, mounds are also obtained when the step barrier has an equal value for all particles independently if they are free or bonded. Kinetic roughening is observed at long times, when the surface roughness w and the characteristic length $\xi$ scale as $w ~ t^\beta$ and $\xi ~ t^\zeta$ where $\beta \approx 0.31$ and $\zeta \approx 0.22$, independently of the growth temperature.Comment: 15 pages, 7 figure

Strong anisotropy in surface kinetic roughening: analysis and experiments

We report an experimental assessment of surface kinetic roughening properties that are anisotropic in space. Working for two specific instances of silicon surfaces irradiated by ion-beam sputtering under diverse conditions (with and without concurrent metallic impurity codeposition), we verify the predictions and consistency of a recently proposed scaling Ansatz for surface observables like the two-dimensional (2D) height Power Spectral Density (PSD). In contrast with other formulations, this Ansatz is naturally tailored to the study of two-dimensional surfaces, and allows to readily explore the implications of anisotropic scaling for other observables, such as real-space correlation functions and PSD functions for 1D profiles of the surface. Our results confirm that there are indeed actual experimental systems whose kinetic roughening is strongly anisotropic, as consistently described by this scaling analysis. In the light of our work, some types of experimental measurements are seen to be more affected by issues like finite space resolution effects, etc. that may hinder a clear-cut assessment of strongly anisotropic scaling in the present and other practical contexts

Modelling of epitaxial film growth with a Ehrlich-Schwoebel barrier dependent on the step height

The formation of mounded surfaces in epitaxial growth is attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growth using a ES barrier explicitly dependent on the step height. Our model has an intrinsic topological step barrier even in the absence of an explicit ES barrier. We show that mounded morphologies can be obtained even for a small barrier while a self-affine growth, consistent with the Villain-Lai-Das Sarma equation, is observed in absence of an explicit step barrier. The mounded surfaces are described by a super-roughness dynamical scaling characterized by locally smooth (faceted) surfaces and a global roughness exponent $\alpha>1$. The thin film limit is featured by surfaces with self-assembled three-dimensional structures having an aspect ratio (height/width) that may increase or decrease with temperature depending on the strength of step barrier.Comment: To appear in J. Phys. Cond. Matter; 3 movies as supplementary materia

Selecting a single orientation for millimeter sized graphene sheets

We have used Low Energy Electron Microscopy (LEEM) and Photo Emission Electron Microscopy (PEEM) to study and improve the quality of graphene films grown on Ir(111) using chemical vapor deposition (CVD). CVD at elevated temperature already yields graphene sheets that are uniform and of monatomic thickness. Besides domains that are aligned with respect to the substrate, other rotational variants grow. Cyclic growth exploiting the faster growth and etch rates of the rotational variants, yields films that are 99 % composed of aligned domains. Precovering the substrate with a high density of graphene nuclei prior to CVD yields pure films of aligned domains extending over millimeters. Such films can be used to prepare cluster-graphene hybrid materials for catalysis or nanomagnetism and can potentially be combined with lift-off techniques to yield high-quality, graphene based electronic devices

Phenomenology of iron-assisted ion beam pattern formation on Si(001)

Pattern formation on Si(001) through 2 keV Kr+ ion beam erosion of Si(001) at an incident angle of # = 30° and in the presence of sputter codeposition or co-evaporation of Fe is investigated by using in situ scanning tunneling microscopy, ex situ atomic force microscopy and electron microscopy. The phenomenology of pattern formation is presented, and experiments are conducted to rule out or determine the processes of relevance in ion beam pattern formation on Si(001) with impurities. Special attention is given to the determination of morphological phase boundaries and their origin. Height fluctuations, local flux variations, induced chemical inhomogeneities, silicide formation and ensuing composition-dependent sputtering are found to be of relevance for pattern formation

Phenomenology of iron-assisted ion beam pattern formation on Si(001)

Pattern formation on Si(001) through 2 keV Kr+ ion beam erosion of Si(001) at an incident angle of # = 30° and in the presence of sputter codeposition or co-evaporation of Fe is investigated by using in situ scanning tunneling microscopy, ex situ atomic force microscopy and electron microscopy. The phenomenology of pattern formation is presented, and experiments are conducted to rule out or determine the processes of relevance in ion beam pattern formation on Si(001) with impurities. Special attention is given to the determination of morphological phase boundaries and their origin. Height fluctuations, local flux variations, induced chemical inhomogeneities, silicide formation and ensuing composition-dependent sputtering are found to be of relevance for pattern formation

Wave function mapping in graphene quantum dots with soft confinement

Using low-temperature scanning tunneling spectroscopy, we map the local density of states (LDOS) of graphene quantum dots supported on Ir(111). Due to a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphene-like. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moir{\'e} potential and a 10% penetration of an Ir surface resonanceComment: 7 pages, 11 figures, DFT calculations directly showing the origin of soft confinment, correct identification of the state penetrating from Ir(111) into graphen