Schwoebel Barrier Research Articles

Effects of surface anisotropy on the surface morphological response of plasma-facing tungsten

Surface free energy has been hypothesized as the cause behind the experimental evidence (Parish et al., 2014) of a strong correlation between crystallographic orientation and surface morphology changes in helium ion-irradiated tungsten at the early stages of ‘fuzz’ growth in fusion plasma-facing tungsten. Here, this hypothesis is tested through self-consistent dynamical simulation based on an atomistically informed model of surface evolution in plasma-irradiated tungsten. Low-energy helium plasma irradiation of a tungsten surface, even when the ion energy is below the sputtering threshold, generates surface vacancy-adatom pairs in addition to adatoms from the flux of self-interstitial atoms to the surface resulting from the growth of high-pressure helium bubbles. Along with the stress-driven surface morphological instability as the primary driving force, preferential diffusion of these surface adatoms modulated by the associated Ehrlich–Schwoebel (ES) barriers, combined with the surface free energy anisotropy drive the anisotropic surface nanostructure growth. Simulation results for helium irradiation on W(100) show growth of pyramidal surface features, akin to experimental observations. This work confirms the hypothesis on the effect of tungsten surface crystallographic orientation on helium-ion-induced surface morphology changes, where surface mound formation is the outcome of a stress-driven surface morphological instability, while the anisotropic growth of the mounds is controlled by the ES-barrier-modulated anisotropic surface adatom diffusion and faceting of the mounds is controlled by the surface free energy anisotropy.

First-principles study on the effect of alloying elements on the Ehrlich–Schwoebel barriers on Ag(1 1 1)

The Ehrlich–Schwoebel (ES) barriers can significantly affect the growth mode of Ag films. In this paper, the effect of surfactant atoms on the ES potential barriers of Ag(111) is investigated by first-principles calculations. The results show Sc, Ti, Y, Zr, and La could sharply reduce the ES barriers. Furthermore, the energies of the doped systems all decrease during exchanging process except the systems doped by Sc, Ti, Y, and Zr. Therefore, La might be a better surfactant for Ag to reduce the ES barriers and promote the 2D growth.

Impact of Schwoebel Barriers on the Step-Flow Growth of a Multicomponent Crystal

The step-flow and spiral growth of a multicomponent crystal are considered from vapors, taking into account the different possible Schwoebel barriers for each component within the Burton-Cabrera-Frank model. Analytic expressions for the final growth rates of such a multicomponent crystal are determined while considering the kinetic properties of all the individual components and growth conditions. Possible instabilities inherent in the presence of several components are studied, and a stability criterion for the multicomponent case is proposed. It is shown that, in certain cases, nucleation of nanoislands of pure components behind the moving steps can initiate, significantly distorting the growth process. The criterion for the occurrence of such an unstable regime is found.

Surface morphology evolution of N-polar GaN on SiC for HEMT heterostructures grown by plasma-assisted molecular beam epitaxy

The surface morphology evolution of N-polar GaN with growth time was investigated and compared with Ga-polar GaN. N-polar GaN directly grown on SiC substrates was found to have slower 3D-to-2D growth transformation and less coalescence than the Ga-polar counterpart, resulting in rougher surface morphology, whereas the AlN nucleation layer accelerated 3D-to-2D transformation, resulting in smoother surface morphology. N-polar GaN was found to have mound-type surface morphology with clustered atomic steps, unlike the regular screw-type dislocation-mediated step-flow growth observed for Ga-polar GaN. This was explained by the lower diffusion of adatoms on the N-polar surface due to its higher surface energy and higher Ehrlich–Schwoebel barrier. In addition, the increased III/V ratio in N-polar GaN growth was found to reduce the surface roughness from 2.4 nm to 1 nm. Without Si doping, the N-polar GaN high electron mobility transistor (HEMT) heterostructures grown under optimized conditions with smoother surface morphologies exhibited a sheet carrier density of 0.91 × 1013 cm−2 and a mobility of 1220 cm2 (V s)−1. With Si δ-doping, the sheet carrier density was increased to 1.28 × 1013 cm−2 while the mobility was reduced to 1030 cm2 (V s)−1. These results are comparable to the state-of-the-art data of plasma-assisted molecular beam epitaxy-grown N-polar GaN HEMT heterostructures on SiC substrates.

Effects of surface vacancy-adatom pair formation on PFC tungsten surface morphological response

We report a simulation study of the effect of He-irradiation-induced surface vacancy-adatom pair formation on the surface morphological evolution of plasma-facing component (PFC) tungsten and examine a number of factors that impact such evolution. Our analysis is based on self-consistent dynamical simulations according to an atomistically-informed, continuum-scale surface evolution model that has been developed following a hierarchical multiscale modeling strategy and can access the spatiotemporal scales of relevance to fuzz formation. The model accounts for the flux of surface adatoms generated as a result of the surface vacancy-adatom pair formation effect upon He implantation, which contributes to the anisotropic growth of surface nanostructural features due to the different rates of adatom diffusion along and across step edges of islands on the tungsten surface. We have carried out atomic-scale computations of optimal diffusion pathways along and across island step edges on the W(110) surface and calculated Ehrlich–Schwoebel (ES) barriers in adatom diffusion along and across such step edges. This aspect of surface adatom diffusion contributes to anisotropic surface atomic fluxes, terrace and step diffusive currents, and has been incorporated into our PFC surface evolution model, which predicts the formation of preferentially aligned nanoridge stripe patterns on the PFC surface. We establish that these anisotropic diffusive currents accelerate nanotendril growth on the PFC surface and the onset of surface nanostructure pattern formation. We also explore systematically the dependence of the PFC surface morphological response on the surface temperature and He ion incident flux, characterize in detail the resulting surface topographies and growth kinetics, and compare the predicted surface morphologies with experimental observations. Our simulation predictions for the emerging surface nanostructure patterns under certain plasma exposure conditions are consistent with experimental findings in the literature.

Migration and agglomeration behaviors of Ag nanocrystals in the Ag-doped diamond-like carbon film during its long-time service

Silver-doped diamond-like carbon (Ag-DLC) films are considered as promising materials for the surface modification of mechanical components and biological implants. The long-term stability of Ag-DLC films is essential for their commercial use and requires intensive investigation. In this study, DLC and 10.0 at.% Ag-DLC films were prepared using a hybrid deposition technique, and the existence and evolution of Ag atoms over time were systematically studied. The results show that Ag atoms with a lower Ehrlich–Schwoebel barrier than that of C atoms are more prone to interlaminar diffusion, refining the columnar structure of DLC films and thereby creating a compact structure. In the as-deposited Ag-DLC film, Ag atoms mainly existed as fine nanocrystals with sizes ranging from 3 to 5 nm. Ag elements diffused with time during its long-time service, and fine Ag nanocrystals agglomerated to form large nanocrystals. The calculation results by density functional theory confirmed that the proximity of Ag atoms can lower the system energy, rendering agglomeration thermodynamically stable. Molecular dynamics simulations verified the spontaneous migration and agglomeration behaviors of Ag atoms over time. This study was focused on the evolution of Ag-DLC films over time and would provide guidance for their use in long-term applications.

Frictional shear stress of ZnO nanowires on natural and pyrolytic graphite substrates

The friction behaviour of ZnO nanowires on natural graphite (NG) and highly oriented pyrolytic graphite (HOPG) substrates was tested in ambient conditions by use of optical microscopy based nanomanipulation. Nanowires on the step-free and waviness-free NG substrate exhibit a diameter-independent nominal frictional shear stress of 0.48 MPa, and this provides a benchmark for studying how the surface topography of graphite influences nanowire friction. Nanowires on the HOPG substrate present a significant diameter-dependent frictional shear stress, increasing from 0.25 to 2.78 MPa with the decrease of nanowire diameter from 485 to 142 nm. The waviness of HOPG has a limited effect on the nanowire friction, as a nanowire can fully conform to the substrate. The surface steps on the HOPG can significantly enhance the nanowire friction and lead to a much higher frictional shear stress than that on NG due to mechanical blocking and the presence of a Schwoebel barrier at step edges. The surface steps, however, can also generate small wedge-shaped gaps between a nanowire and substrate, and thus reduce the nanowire friction. With the decrease in nanowire diameter, the capacity for the nanowire to better conform to the substrate reduces the length of the wedge-shaped gaps, leading to the observed increase in nanowire friction. The results have improved our understanding of the unique friction behaviour of nanowires. Such an improved understanding is expected to benefit the design and operation of nanowire-friction-based devices, including bio-inspired fibrillar adhesives, soft grippers, rotary nanomotors, and triboelectric nanogenerators.

Step barrier effects during early stages of the kinetic roughening of fcc(111) surfaces

The influence of the additional Ehrlich–Schwoebel step barrier and temperature on the early stages of kinetic roughening and mound formation of fcc(111) surfaces is studied by means of kinetic Monte Carlo simulations. Increasing the Ehrlich–Schwoebel barrier, the growth mode develops from nearly layer-by-layer growth to statistical (Poisson) growth mode with the formation of wedding-cake-like shaped mounds. The evolution of the growth morphology is characterized by scaling laws with effective critical exponents. On the one hand, coarsening for growth without step barrier follows exponents neff=0.35 and βeff=0.20 for the characteristic lateral distance (coarsening exponent) and the rms roughness, respectively. On the other hand, coarsening is strongly suppressed for large step barriers (neff=0.05, βeff=0.52, Poisson growth) in agreement with different experimental results, e.g., for the formation of mounds during the homoepitaxy of Ag(111) and Pt(111). The lateral roughness on short distances is governed by the low roughness exponent α=0.58 for all growth conditions independently of the growth mode.

Revisiting step instabilities on crystal surfaces. Part II: General theory

The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on stability of different mechanisms and their interplay: elastic step-step interactions, the Schwoebel barrier, and the chemical coupling of the diffusion fields on adjacent terraces. In this second part, we present a stability analysis of the general problem without recourse to the quasistatic approximation. This analysis reveals the existence of a supplementary mechanism, which we label the “dynamics effect” as it follows from accounting for all the convective and transient terms in the governing equations. This effect can be stabilizing or destabilizing depending on the ratio of step attachment/detachment kinetics to terrace diffusion kinetics. Further, we find that this dynamics effect remains significant in the slow deposition/evaporation regime, thereby invalidating the classical postulate underlying the quasistatic approximation. Finally, revisiting experiments of crystal growth on Si(111)-7 × 7 and GaAs(001), our analysis provides an alternative explanation of the observed step bunching, one that does not require the mechanisms previously invoked in the literature.

Correlating surface stoichiometry and termination in SrTiO3 films grown by hybrid molecular beam epitaxy

Hybrid oxide molecular beam epitaxy (hMBE), a thin-film deposition technique in which transition metal cations are delivered using a metal-organic precursor, has emerged as the state-of-the-art approach to the synthesis of electronic-grade complex oxide films with a stoichiometric growth window. However, numerous questions remain regarding the chemical mechanisms of the growth process and the surface properties of the resulting films. To examine these properties, thin film SrTiO3 (STO) was prepared by hMBE using a titanium tetraisopropoxide (TTIP) precursor for Ti delivery and an elemental Sr source on annealed STO and Nb-doped STO substrates with varying TTIP:Sr flux ratios to examine the conditions for the reported stoichiometric growth window. The films were transferred in vacuo to an x-ray photoelectron spectroscopy system to study the surface elemental composition. Samples were examined using x-ray diffraction to compare our surface sensitive results with previously reported measurements of the bulk of the films in the literature. Ex situ studies by atomic force microscopy, scanning tunneling microscopy, and low-energy electron microscopy confirmed the presence of surface reconstructions and an Ehrlich–Schwoebel barrier consistent with A-site SrO termination. We find that a surface exhibiting a mixture of SrO and TiO2 termination or a full SrO termination is necessary to obtain stoichiometric adsorption-controlled growth. These results indicate that surface Sr is necessary to maintain the chemical equilibrium for stoichiometric growth during the hMBE process, which is important for the design of future interfacial systems using this technique.

Effects of adatom mobility and Ehrlich–Schwoebel barrier on heteroepitaxial growth of scandium nitride (ScN) thin films

Scandium nitride (ScN) is an emerging rock salt indirect bandgap semiconductor and has attracted significant interest in recent years for thermoelectric energy conversion, as a substrate for defect-free GaN growth, as a semiconducting component in single-crystalline metal/semiconductor superlattices for thermionic energy conversion, as well as for Al1−xScxN-based bulk and surface acoustic devices for 5G technologies. Most ScN film growth traditionally utilizes physical vapor deposition techniques such as magnetron sputtering and molecular beam epitaxy, which results in stoichiometric films but with varying crystal quality, orientations, microstructures, and physical properties. As epitaxial single-crystalline ScN films with smooth surfaces are essential for device applications, it is important to understand the ScN growth modes and parameters that impact and control their microstructure. In this Letter, we demonstrate that large adatom mobility is essential to overcome the Ehrlich–Schwoebel (E–S) and grain boundary migration barriers and achieve defect (voids, dislocations, stacking faults, etc.)-free single-crystalline ScN films. Using the substrate temperature to tune adatom mobility, we show that nominally single-crystalline ScN films are achieved when the homologous temperature is higher than ∼0.3. For homologous temperatures ranging from 0.23 to 0.30, ScN films are found to exhibit significant structural voids in between pyramidal growth regions with multiple in-plane orientations resulting from additional lateral growth off the facets of the pyramids and broken epitaxy after ∼80 nm of growth. The in-depth discussion of the growth modes of ScN presented here explains its varying electrical and optical properties and will help achieve high-quality ScN for device applications.

Formation of Double Steps on Si (100): Effect of Permeability of the A-Steps

A model of the elementary step motion on a two-domain (100) silicon surface during crystallization from a molecular beam is proposed. The model takes into account the possibility of an adatom transition to an adjacent terrace before incorporation into a kink at the A-step edge (the effect of the A-step permeability). It is shown that the permeability of the A-step contributes to the faster pairing of the A- and B-steps and, consequently, transition to a single-domain surface. For the fast pairing of the steps, it is sufficient only the presence of an inverse Ehrlich–Schwoebel barrier for the attachment of adatoms to the A-step from the B-type terrace. A conventional barrier (for the attachment from the A-type terrace) may be absent, which is consistent with the results of quantum chemical calculations.

Ar+-sputtered Ge (001) surface nanostructuring at target temperature above the recrystallization threshold

Nanoscale pattern formation on Ge (001) surface by 500 eV Ar+ bombardment has been studied for a wide range of ion incidence angles at a temperature of 300° C. In the angular regime 0° to 65°, a fourfold symmetric topography forms which shows a remarkable transition into highly regular one-dimensional asymmetric pattern at grazing incidences, known as perpendicular mode ripples. The four-fold symmetric patterns are found to retain their symmetry under the concurrent substrate rotation during sputtering, while the ripples show degeneration into hole structure with a weak fourfold symmetric pattern. The dynamics of the observed patterns has also been investigated in a wide range of ion fluence from 1 × 1017 to 1 × 10 20 ions cm−2. The square topographies are found to be determined by Ehrlich–Schwoebel barrier induced diffusion bias driven growth process, whereas, the ripple formation implies the role of incidence ion beam direction.

Stability of Vicinal Surfaces: Beyond the Quasistatic Approximation.

We revisit the step bunching instability without recourse to the quasistatic approximation and show that the stability diagrams are significantly altered, even in the low-deposition regime where it was thought sufficient. In particular, steps are unstable against bunching for attachment-detachment limited growth. By accounting for the dynamics and chemical effects, we can explain the onset of step bunching in Si(111)-(7×7) and GaAs(001) without resort to the inverse Schwoebel barrier or step-edge diffusion. Further, the size-scaling analysis of step-bunch growth, as induced by these two combined effects, agrees with the bunching regime observed at 750 °C in Si(111)-(7×7).

Formation of nearly defect-free nanoripples by sputtering of GaAs (001) surface at high temperature

The evolution of GaAs (001) surface morphology by normal incidence 1 keV Ar+ ion sputtering at high temperature has been investigated for different temperature and ion fluence. An anisotropic surface modulation is observed above the substrate recrystallization temperature ∼300 °C. With increase of sputtering time, they evolve into highly ordered and almost defect-free ripple-like structure consisting of alternate arrays of elongated terraces and nano-grooves with ridges along the <11¯0> direction. Such surface instability is attributed to the effect of anisotropic surface diffusion of vacancies in the presence of Ehrlich–Schwoebel barrier. The amplitude and wavelength of the ripple show a power law increase with sputtering time and finally saturate at longer time irradiation.

Surface morphology and a dynamic scaling analysis in epitaxial growth: A kinetic Monte Carlo study

We use Kinetic Monte-Carlo (KMC) simulations based on the solid-on-solid model to see the evolution of the surface morphology for different materials. We have performed a qualitative and quantitative study of the homo-epitaxial growth for (Cu, Co, Ge, and GaAs) over a large range of temperature, varying between 300 K and 700 K. Based on the growth morphology, we found two sets of materials. This classification is also confirmed by the analysis of their dynamic scaling properties (measurements of the critical exponents derived from the height–height correlation functions). Our results were compared to the available experimental and theoretical results and seem advantageous for the understanding of the growth dynamics. Different atomistic mechanisms may intervene in favoring adatoms attachment to surface steps. Here we have focused on the effect of the Ehrlich–Schwoebel barrier. However, we discussed how the magnitude of this barrier affects the scaling exponents as well as the surface morphology.

Stepped morphology on vicinal 3C- and 4H-SiC (0001) faces: A kinetic Monte Carlo study

Stepped morphologies on vicinal 3C- and 4H-SiC (0001) surfaces with the miscut toward [11¯00] or [112¯0] directions have been studied with a three-dimensional kinetic Monte Carlo model. In the model, a three-dimensional lattice mesh was established based on the crystal lattice of 3C-and 4H-SiC to fix the positions of atoms and interatomic bonding. Periodic boundary conditions were applied in the lateral direction while helicoidal boundary conditions were used in the direction of crystal growth. Events, such as adatoms attachment, detachment and interlayer transport at the step edges, and adatoms adsorption and diffusion on the terraces were considered in the model. Effects of Ehrlich–Schwoebel barriers at downward step edges and incorporation barriers at upwards step edges were also considered. Moreover, the atoms of silicon and carbon were treated as the minimal diffusing species independently to achieve more elaborate information for the behavior of atoms in the crystal surface. The simulation results showed that multiple-height steps were formed on the vicinal 4H-SiC (0001) surfaces, whereas single bilayer-height stepped morphologies were observed on the vicinal 3C-SiC (0001) surfaces. Furthermore, zigzag shaped edges were observed for both of 3C- and 4H-SiC (0001) surfaces with the miscut toward [112¯0] direction. At last, the formation mechanism of the stepped morphology was also analyzed.

Vacancy-controlled friction on 2D materials: Roughness, flexibility, and chemical reactions

It was recently reported that the presence of vacancy could dramatically increase nanoscale friction of graphene, while its underlying mechanism remains unknown [1]. In this study, molecular dynamics simulation is carried out to examine the possible mechanisms that could contribute to friction enhancement on chemically modified and/or vacancy-contained graphene. It is found that the change in out-of-plane flexibility due to vacancies has only a limited influence on friction. In contrast, the Schwoebel barrier, the chemical reactivity of dangling bonds at the atomic step edges, as well as the roughening induced by functional groups can contribute more to nanoscale friction of graphene. This study provides a friction-mechanism map that correlates frictional behavior to various atomic scale mechanisms, which is useful for understanding the nanoscale friction of defected graphene.

Three-Dimensional ES Barrier Promotes the Steps Formation

Physical vapor deposition (PVD) has been an important method to synthesize metallic nanorods during the past two decades. Based on the main physical process of crystal growth, this letter made a growth model of metallic nanorods with kinetic lattice Monte Carlo (KLMC) method and studied the effects of three-dimensional (3D) Ehrlich–Schwoebel (ES) barrier during the metallic nanorods growth. According to the simulation results, a large 3D ES barrier affects the surface morphology apparently. With analyze the simulation results, 3D ES barrier promotes the step formation and increases the step height greatly, and it is the main factor of metallic nanorods formation.

Qualitative analysis of growth mechanism of polycrystalline InAs thin films grown by molecular beam epitaxy

The mechanism of surfaces/interfaces and precise control of growth morphology is a key parameter for any specific device application. Herein, we report on a qualitative growth study of molecular beam epitaxy-grown polycrystalline InAs thin films on a lattice-mismatched Si(1 0 0) substrate using atomic force microscopy. The height-height correlation function (HHCF) and power spectral density function (PSDF) were employed to analyze the surface structures. Clear oscillatory behavior in the HHCF for sufficiently larger lateral distances suggests a mound-like morphology, which was confirmed by the existence of a characteristic frequency peak in the PSDF. The growth mechanism is described qualitatively by the Schwoebel barrier (roughening) effect coupled with the Mullins diffusion model (smoothing effect).