Schwoebel Barrier Research Articles

STEP-FLOW GROWTH ON SEMICONDUCTOR-LIKE STEPPED SURFACE: A KINETIC MONTE CARLO STUDY

Applying Kinetic Monte Carlo (KMC) technique, we investigated the influence of temperature and step-width on the step-flow growth of a (2D + 1) semiconductor-like uniform-spacing stepped model with inverse Ehrlich–Schwoebel (iES) barrier. The relation between diffusion length (R) and half of step width (L/2) was established to characterize the transition temperature T c for switching between the random deposition growth and step-flow growth on surface. When temperature is lower than T c , the surface growth mode is dominated by random deposition growth. As temperature approaches to T c , the surface growth mode gradually switches to step-flow growth. However, only when the temperature is much higher than T c , the random deposition growth is completely replaced by the step-flow growth. It is found that the step-width effect has a profound influence on surface growth mode in the transition region. The surface morphology undergoes a kinetic step-flow growth to form step-edge aggregation by either increasing temperature or decreasing the step width.

Simulation of multilayer Cu/Pd(100) heteroepitaxial growth by pulse laser deposition

The heteroepitaxial growth of multilayer Cu/Pd(100) thin film via pulse laser deposition (PLD) at room temperature is simulated by using kinetic Monte Carlo (KMC) method with realistic physical parameters. The effects of mass transport between interlayers, edge diffusion of adatoms along the islands and instantaneous deposition are considered in the simulation model. Emphasis is placed on revealing the details of multilayer Cu/Pd(100) thin film growth and estimating the Ehrlich–Schwoebel (ES) barrier. It is shown that the instantaneous deposition in the PLD growth gives rise to the layer-by-layer growth mode, persisting up to about 9 monolayers (ML) of Cu/Pd(100). The ES barriers of 0.08 ± 0.01 eV is estimated by comparing the KMC simulation results with the real scanning tunnelling microscopy (STM) measurements.

Finding polymorphic structures during vicinal surface growth

A hybrid scheme is developed to describe vicinal surface growth during epitaxy on two different time and length scales. For this purpose this algorithm combines two modules based on a continuum and an atomistic approach. The continuum module is realized by a phase-field-model which traces back to the Burton–Cabrera–Frank theory, the atomistic module is based on the anisotropic Ising model which is mapped onto a lattice-gas model. The latter provides thermal density fluctuations resulting in adatom clustering. With increasing temperature the probability for island nucleation on the terraces decreases according to 1-p where p is an Arrhenius-type activation probability which prevents clusters from becoming islands. Within this framework it is possible to find the transition from a rough surface at low temperatures to an evenly stepped surface at high temperatures where slight step meandering is observed. Furthermore two competing mechanisms of step bunching are investigated within this scale bridging algorithm: alternating anisotropic diffusion and different Ehrlich–Schwoebel barriers at the step edges. It is shown that a simulation of step bunching displaying the full variety of phenomena observed in experiments can only be achieved by the consideration of different time and length scales.

Nonlinear evolution of the step meandering instability of a growing crystal surface

The growth of crystal surfaces, under nonequilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus modeled by a free boundary value problem [known as the Burton–Cabrera–Franck model]. In the presence of an asymmetry of the kinetic coefficients (Erlich–Schwoebel barriers), ruling the rates of incorporation of atoms at each step, it has been shown that a train of straight steps is unstable under two-dimensional transverse perturbations. This instability is now known as the Bales–Zangwill instability (meandering instability). We study the nonlinear evolution of the step meandering instability that occurs on a crystalline vicinal surface under growth, in the absence of evaporation, in the limit of a weak asymmetry of atom incorporation at the steps. We derive a nonlinear amplitude equation displaying spatiotemporal coarsening in the limit of weak Erlich–Schwoebel effect. We characterize the self-similar solutions of this equation.

Influence of two different adatom mobilities on the initial heteroepitaxial growth kinetics

In the heteroepitaxy deposited adatoms in the first layer migrate on a substrate with a heterodiffusion coefficient, while those in all the next layers – with a self-diffusion coefficient. In this paper the effect of two different adatom surface mobilities on the layer heteroepitaxial growth in the presence of an Ehrlich–Schwoebel barrier is studied quantitatively using kinetic model based on rate equations for adatom and 2D island density and coverage in successive layers combined with a feeding zone taking into account interlayer mass transport. It is shown that this effect is essential in the first few monolayers and strongly depends on a ratio hetero-to-self-diffusion coefficient and Ehrlich–Schwoebel barrier. A faster heterodiffusion leads to a more rough initial growth whereas a slower heterodiffusion – to a smoother initial growth. In a transient (homoepitaxial) growth regime from smooth layer-by-layer – to rough growth a slower heterodiffusion retards this transition, while a faster heterodiffusion promotes it, especially at higher Ehrlich–Schwoebel barrier. It is shown that a critical coverage for the next layer nucleation is more appropriate parameter for characterization growth mode transition than a widely used critical island radius because it does not depend on island density and uniquely determines growth mode transition and its dependence on hetero- and self-diffusion coefficients and a critical nucleus size is obtained. The results suggest an opportunity for improving ultrathin (a few monolayers) film surface morphology by manipulating growth mode during deposition by initial (first layer) deposition either at low substrate temperature (low diffusivity) or with high deposition rate and consecutive one either at higher temperature (high diffusivity) or with a lower deposition rate.

A cellular automata algorithm for step dynamics in continuum modeling of epitaxial growth

We adapt a cellular automata algorithm in order to track the steps in a continuum model of epitaxial growth and couple it to adatom diffusion at the terraces. The model is capable to treat the Ehrlich–Schwoebel barrier at steps, which leads to instabilities during epitaxial growth. In order to examine the mound formation a nucleation model beyond the mean field approximation is included in our simulations. We show that the meander instability as well as the onset of mound formation can be treated by this model.

Island coalescence and diffusion along kinked steps on Cu(0 0 1): Evidence for a large kink Ehrlich–Schwoebel barrier

Using temperature-variable scanning tunneling microscopy, we studied the coalescence of vacancy islands on Cu(0 0 1) in ultra-high vacuum. From the temperature dependence of the relaxation of merged vacancy islands to the equilibrium shape we obtain an activation energy of the island coalescence process of 0.76 eV. From that value we deduce an activation energy for the atomic hopping coefficient of E Γ h = 0.89 eV. Comparing our result with previous STM data on step fluctuations with dominant diffusion along straight step segments ( E Γ h = 0.68 eV; [M. Giesen, S. Dieluweit, J. Mol. Catal. A: Chem. 216 (2004) 263]) and step fluctuations with kink crossing ( E Γ h = 0.9 eV; [M. Giesen-Seibert, F. Schmitz, R. Jentjens, H. Ibach, Surf. Sci. 329 (1995) 47]), we conclude that there is a large extra barrier for diffusion of atoms across kinks on Cu(0 0 1) of the order of 0.23 eV. This is the first direct experimental evidence for the existence of a large kink Ehrlich–Schwoebel barrier on Cu(0 0 1).

Fractal-mound growth of pentacene thin films

The growth mechanism of pentacene film formation on SiO2 substrate was investigated with a combination of atomic force microscopy measurements and numerical modeling. In addition to the diffusion-limited aggregation (DLA) that has already been shown to govern the growth of the ordered pentacene thin films, it is shown here for the first time that the Schwoebel barrier effect steps in and disrupts the desired epitaxial growth for the subsequent layers, leading to mound growth. The terraces of the growing mounds have a fractal dimension of 1.6, indicating a lateral DLA shape. This novel growth morphology thus combines horizontal DLA-like growth with vertical mound growth.

Nucleation and growth mechanism of GaAs epitaxial growth

The kinetic Monte Carlo simulations were used to study the nucleation and growth mechanism of GaAs. The Ehrlich–Schwoebel (ES) barrier has an important effect on the growth mechanism. It was shown that the island density mainly depends on the growth temperature: low island density for high temperature, and high island density for low temperature. The islands in the second layer appear at small surface coverage for the high ES barrier or low temperature, while the islands appear at large surface coverage for the low ES barrier or high temperature. In GaAs epitaxial growth the critical size has its original meaning only for the low temperature and the high ES barrier. The single value of the critical size has to be replaced by two sizes in the two different directions because of the anisotropic surface migration.

Influence of epitaxial strain on the terrace and inter-layer diffusions in metal epitaxy

The influence of epitaxial strain on the surface and inter-layer diffusions are investigated using molecular statics and transition state theory with several types of embedded atom method potentials for Ag and Ni. Quantitatively to analyze the competition of the surface and inter-layer diffusions in the instability to the multi-layer growth, Ehrlich–Schwoebel barrier and the attempt frequencies of the surface and inter-layer diffusions by both hopping and exchange mechanisms are considered simultaneously. The attempt frequencies of exchange mechanism are larger by order one than those of hopping mechanism and especially, the difference becomes more severe for the inter-layer diffusion. Considering both the attempt frequency and activation energy barrier shows that the layer-by-layer growth is enhanced by compressive strain for Ag(0 0 1), which is confirmed by the existing linear stability theory and kinetic Monte Carlo simulations.

Correlation of self-organized surface nanostructures and anisotropic electron transport in nonpolar ZnO (10−10) homoepitaxy

Self-organized surface nanostructures were formed during laser molecular beam epitaxy of nonpolar ZnO (10−10). The growth mechanism of the nanostructures was related to a Schwoebel barrier effect generated during ZnO homoepitaxy. Small islands elongated along the [001] direction were generated on two-dimensional (2D) growing surfaces above the critical thickness. With increasing film thickness, the anisotropic islands developed homogeneous nanostripe arrays with stripe lengths above 5μm and connected by some branches. Highly anisotropic surface morphology markedly influenced electron transport of ZnO films and Mg0.12Zn0.88O∕ZnO multiquantum wells (MQWs) with conductivity parallel to the nanostripe arrays by more than one order of magnitude larger than that observed perpendicular to the nanostripe arrays. We propose that the origin of anisotropic conductivity of ZnO films resulted mainly from anisotropically distributed scattering centers of electrons related to grain boundaries between nanostripe arrays. Furthermore, the surface nanostructures consisting of nanostripe arrays gave rise to the anisotropic surface roughness at the heterointerface between Mg0.12Zn0.88O and ZnO layers and contributed to the anisotropy of 2D electron transport of the MQWs at low temperatures.

Diffusion of adatom in the selective epitaxial growth of Si(100): A molecular dynamics study

Tight-binding molecular dynamics simulation is performed for a Si adatom on the surface containing the {311} facet and the Si(100) surface to reproduce and explain the behavior of the {311} facet in the selective epitaxial growth of Si(100). In the simulation the adatom is observed to diffuse from the {311} facet to the Si(100) surface along the pathway of a trough between the dimer rows on Si(100) surface. By the tight-binding total energy calculation, it is also clarified that adatoms easily diffuse to the Si(100) surface because, after the adatom surmounts the first energy barrier to diffuse to the step edge near the {311} facet, there is no additional Schwoebel barrier and the other energy barriers gradually decrease to the top of the dimer row of Si(100). The pathway of the trough between dimer rows on the Si(100) surface is found to be energetically more favorable than the direct pathway to the dimer row from the tight-binding total energy calculation. Our tight-binding molecular dynamics simulation elucidates the mechanism responsible for the behavior of the {311} facet in the selective epitaxial growth of Si(100).

Simulation of multilayer homoepitaxial growth on Cu (100) surface

The processes of multilayer thin Cu films grown on Cu (100) surfaces at elevated temperature (250–400 K) are simulated by mean of kinetic Monte Carlo (KMC) method, where the realistic growth model and physical parameters are used. The effects of small island (dimer and trimer) diffusion, edge diffusion along the islands, exchange of the adatom with an atom in the existing island, as well as mass transport between interlayers are included in the simulation model. Emphasis is placed on revealing the influence of the Ehrlich–Schwoebel (ES) barrier on growth mode and morphology during multilayer thin film growth. We present numerical evidence that the ES barrier does exist for the Cu/Cu(100) system and an ES barrier EB>0.125 eV is estimated from a comparison of the KMC simulation with the realistic experimental images. The transitions of growth modes with growth conditions and the influence of exchange barrier on growth mode are also investigated.

Growth modes and self-organization in the epitaxy of ferromagnetic SrRuO3 on SrTiO3(001)

Abstract We report on the self-organized formation of one-dimensional finger-like structures and the subsequent surface smoothing that occurs in the epitaxial growth of ferromagnetic and conductive SrRuO3 films on SrTiO3(001) substrates. We show that at an early stage of growth there are three-dimensional (3D) islands nucleated along the substrate steps, and we detail their coalescence to form fingers and later the coalescence of fingers to form planar surfaces. The influence of the Erlich–Schwoebel barrier on the morphology evolution is demonstrated. We discuss on the driving forces promoting 3D growth at the early stages.

Effects of the Ehrlich–Schwoebel potential barrier on the Wolf–Villain model simulations for thin film growth

Wolf–Villain (WV) model is a simple model used to study ideal molecular beam epitaxy (MBE) growth by using computer simulations. In this model, an adatom diffuses instantaneously within a finite diffusion length to maximize its coordination number. We study statistical properties of thin films grown by this model. The morphology of the WV model is found to be kinetically rough with a downhill particle diffusion current. In real MBE growth, however, there are additional factors such as the existence of a potential barrier that is known as the Ehrlich–Schwoebel (ES) barrier. The ES barrier is an additional barrier for an adatom that diffuses over a step edge from the upper to a lower terrace which is known to induce an uphill particle current. We found that with the addition of the ES barrier, the WV–ES model morphology is rough with mound formation on the surface when the barrier is strong enough. To confirm these results, the correlation function is also studied. We find no oscillation in the correlation function in the WV model. For the WV–ES model, the correlation function oscillates. These results confirm that a strong enough ES barrier can cause mound formation on the WV surface in our study.

Structural evolution of AlN nano-structures: Nanotips and nanorods

Aluminum nitride (AlN) nanostructures were prepared using thermal chemical vapour deposition process. At growth temperatures of 950 °C, AlN nanotips with apex diameters of 10 nm, base diameters of ∼100 nm, and length of ∼2000 nm were obtained. Whereas when the growth temperature was 1200 °C, we obtained shorter and thicker AlN nanorods. Compelling microscopic evidences were obtained to show that stacked AlN platelets of diminishing size formed the building blocks for the nanotips. A reducing Ehrlich–Schwoebel barrier introduced into a diffusion mediated growth model explains the formation of AlN nanorods at increasing growth temperatures.

Submonolayer growth of Fe on aGaAs(100)−2×6reconstructed surface

We present the results of in situ STM measurements of the submonolayer growth of Fe on the Ga-rich and As-terminated $(2\ifmmode\times\else\texttimes\fi{}6)$ reconstruction of the GaAs(100) surface. In the beginning of the nucleation regime (0.1 ML), the surface reconstruction influences the nucleation sites, so that almost round islands are observed solely on the top of the As rows. In the growth regime from 0.3 to 0.6 ML the islands become elliptically elongated along the [011] direction due to faster diffusion of Fe atoms along the As rows. Throughout our study, Fe atom loss is observed, becoming more pronounced from 0.6 ML onwards, due to the penetration of Fe into the substrate. This penetration leads to a trapping mechanism, which not only changes the diffusion properties of Fe clusters but also supplies extra energy to adatoms atop the Fe islands to surmount the Schwoebel barrier, resulting in a two-dimensional island nucleation from 0.3 ML onwards. A structural nucleation model is presented which provides insight into the interface structure and intermixing in the submonolayer regime.

Influence of Schwoebel barrier and diffusion anisotropy on step density oscillation amplitude during epitaxial growth

Speeding up of step density oscillations (SDO) damping on singular surface with Schwoebel barriers was demonstrated by Monte Carlo simulation. Estimation of Schwoebel barrier necessary for complete absence of SDO was carried out. Increase of atomic surface anisotropy was shown to be responsible for slowing down SDO damping and oscillations phase shift for anisotropy similar to anisotropy on (0 0 1) reconstructed surfaces.

The influence of substrate anisotropy on laser-focused atom deposition studied by two-dimensional Monte Carlo simulation

We study the role of the surface diffusion anisotropy in the fabrication of nanostructures by laser-focused (“cold”) atom lithography, and on the stability of nanostructures using two-dimensional kinetic Monte Carlo simulations. The simulations were performed using one- and two-directional standing-wave fields (using two different wave profiles) and two different diffusion models (limited and total diffusion model) on anisotropic surfaces, such as (110) surfaces of face-centered-cubic crystals, or reconstructed surfaces such as Si(100). The simulations were made with and without Schwoebel barriers. Our diffusion-deposition models reproduce qualitatively experimental results.

Modelling of layer epitaxial growth: surface morphology and growth mode transitions

Recently we have proposed a simple kinetic model for layer epitaxial growth, which combines a rate equation approach and a concept of a feeding zone. With this model it has distinctively been shown on how with decreasing adatom surface diffusivity and/or increasing the Ehrlich–Schwoebel (ES) barrier height the growth mode crosses over from a smooth layer-by-layer (LL) growth to a rough 3D growth, and a “phase diagram” of the growth mode in the parameter space has been constructed. This paper reports on a systematic study the effect of a critical nucleus size, the growing island collision behaviour (impingement/coalescence) and the existence (in the case of heteroepitaxy) of two different adatom surface mobilities (heterodiffusion in the first layer and self-diffusion in all the next ones) on the epitaxial growth. It is shown that the increase of a critical nucleus size expands a rough growth region, whereas the island collision behaviour weakly affects on the growth mode transition but significantly influences on the nucleation kinetics. The effect of two adatom mobilities is essential at initial stages and dramatically depends on the relation between them: a slower heterodiffusion results in a smoother initial growth and thus retards the transition to a rough growth, whereas a faster heterodiffusion promotes it especially at a higher ES barrier.