Step-edge Barrier Research Articles

Scaling of surface roughness in film deposition with height-dependent step edge barriers.

We perform kinetic Monte Carlo simulations of film growth in simple cubic lattices with solid-on-solid conditions, Ehrlich-Schwoebel (ES) barriers at step edges, and a kinetic barrier related to the hidden off-plane diffusion at multilayer steps. Broad ranges of the diffusion-to-deposition ratio R, detachment probability per lateral neighbor, ε, and monolayer step crossing probability P=exp[-E_{ES}/(k_{B}T)] are studied. Without the ES barrier, four possible scaling regimes are shown as the coverage θ increases: nearly layer-by-layer growth with damped roughness oscillations; kinetic roughening in the Villain-Lai-Das Sarma (VLDS) universality class when the roughness is W∼1 (in lattice units); unstable roughening with mound nucleation and growth, where slopes of logW×logθ plots reach values larger than 0.5; and asymptotic statistical growth with W=θ^{1/2} solely due to the kinetic barrier at multilayer steps. If the ES barrier is present, the layer-by-layer growth crosses over directly to the unstable regime, with no transient VLDS scaling. However, in simulations up to θ=10^{4} (typical of films with a few micrometers), low temperatures (small R,ε, or P) may suppress the two or three initial regimes, while high temperatures and P∼1 produce smooth surfaces at all thicknesses. These crossovers help to explain proposals of nonuniversal exponents in previous works. We define a smooth film thickness θ_{c} where W=1 and show that VLDS scaling at that point indicates negligible ES barriers, while rapidly increasing roughness indicates a small ES barrier (E_{ES}∼k_{B}T). θ_{c} scales as ∼exp(const×P^{2/3}) if the other parameters are kept fixed, which represents a high sensitivity on the ES barrier. The analysis of recent experimental data in the light of our results distinguishes cases where E_{ES}/(k_{B}T) is negligible, ∼1, or ≪1.

Post-Growth Dynamics and Growth Modeling of Organic Semiconductor Thin Films.

The ability to control the properties of organic thin films is crucial for obtaining highly performant thin-film devices. However, thin films may experience post-growth processes, even when the most sophisticated and controlled growth techniques such as organic molecular beam epitaxy (OMBE) are used. Such processes can modify the film structure and morphology and, thus, the film properties ultimately affecting device performances. For this reason, probing the occurrence of post-growth evolution is essential. Equally importantly, the processes responsible for this evolution should be addressed in view of finding a strategy to control and, possibly, leverage them for driving film properties. Here, nickel-tetraphenylporphyrin (NiTPP) thin films grown by OMBE on highly oriented pyrolytic graphite (HOPG) are selected as an exemplary system exhibiting a remarkable post-growth morphology evolution consistent with Ostwald-like ripening. To quantitatively describe the growth, the height-height correlation function (HHCF) analysis of the atomic force microscopy (AFM) images is carried out, clarifying the role of the post-growth evolution as an integral part of the whole growth process. The set of scaling exponents obtained confirms that the growth is mainly driven by diffusion combined with the presence of step-edge barriers, in agreement with the observed ripening phenomenon. Finally, the results together with the overall approach adopted demonstrate the reliability of the HHCF analysis in systems displaying post-growth evolution.

Nonequilibrium Roughness Evolution of Small Molecule Mixed Films Reflecting Equilibrium Phase Behavior

Understanding non-equilibrium phenomena, such as growth, and connecting them to equilibrium phase behavior is a major challenge, in particular for complex multicomponent materials. We use X-ray reflectivity to determine the surface roughness of binary mixtures of several prototypical organic compounds. By analyzing the roughness as a function of composition, we find a systematic behavior depending on the bulk phase behavior in terms of intermixing, co-crystallization or phase separation. Supported by kinetic Monte Carlo simulations, we provide evidence that the growth behavior can be rationalized by a lowered step edge barrier in the mixed films which is induced by reduced in-plane crystallinity.

Interplay of orientational order and roughness in simulated thin film growth of anisotropically interacting particles.

Roughness and orientational order in thin films of anisotropic particles are investigated using kinetic Monte Carlo simulations on a cubic lattice. Anisotropic next-neighbor interactions between the lattice particles were chosen to mimic the effects of shape anisotropy in the interactions of disk- or rodlike molecules with van der Waals attractions. Increasing anisotropy leads first to a preferred orientation in the film (which is close to the corresponding equilibrium transition) while the qualitative mode of roughness evolution (known from isotropic systems) does not change. At strong anisotropies, an effective step-edge (Ehrlich-Schwoebel) barrier appears and a nonequilibrium roughening effect is found, accompanied by reordering in the film which can be interpreted as the nucleation and growth of domains of lying-down disks or rods. The information on order and roughness is combined into a diagram of dynamic growth modes.

Influence of gallium surface saturation on GaN nanowire polytype selection during molecular-beam epitaxy

We have examined the influence of Ga surface saturation on gallium nitride (GaN) nanowire (NW) polytype selection during molecular-beam epitaxy. The Ga surface saturation in the absence and presence of nitrogen determines the GaN polytype and morphology (i.e., films vs NW) selection, respectively. We discuss the interplay between surface and step-edge diffusion barriers governing the NW-to-film-transition and the influence of SixNy interlayer formation on zinc blende (ZB) vs wurtzite (WZ) polytype selection of GaN. In addition, distinct exciton emissions associated with ZB and WZ GaN are observed, suggesting a type-I WZ/ZB GaN band-offset. This work provides a crucial step toward the realization of polarization-free, CMOS-compatible GaN-based optoelectronics.

Signature of multilayer growth of 2D layered Bi2Se3 through heteroatom-assisted step-edge barrier reduction

During growth of two-dimensional (2D) materials, abrupt growth of multilayers is practically unavoidable even in the case of well-controlled growth. In epitaxial growth of a quintuple-layered {{rm{Bi}}}_{2}{{rm{Se}}}_{3} film, we observe that the multilayer growth pattern deduced from in situ x-ray diffraction implies nontrivial interlayer diffusion process. Here we find that an intriguing diffusion process occurs at step edges where a slowly downward-diffusing Se adatom having a high step-edge barrier interacts with a Bi adatom pre-existing at step edges. The Se–Bi interaction lowers the high step-edge barrier of Se adatoms. This drastic reduction of the overall step-edge barrier and hence increased interlayer diffusion modifies the overall growth significantly. Thus, a step-edge barrier reduction mechanism assisted by hetero adatom–adatom interaction could be fairly general in multilayer growth of 2D heteroatomic materials.

Slope selection in unstable multilayer growth in 1+1 dimensions: Step flow models with downward funneling.

We study analytically and numerically aspects of the dynamics of slope selection for one-dimensional models describing the motion of line defects, steps, in homoepitaxial crystal growth. The kinetic processes include diffusion of adsorbed atoms (adatoms) on terraces, attachment and detachment of atoms at steps with large yet finite, positive Ehrlich-Schwoebel step-edge barriers, material deposition on the surface from above, and the mechanism of downward funneling (DF) via a phenomenological parameter. In this context, we account for the influence of boundary conditions at extremal steps on the dynamics of slope selection. Furthermore, we consider the effect of repulsive, nearest-neighbor force-dipole step-step interactions. For geometries with straight steps, we carry out numerical simulations of step flow, which demonstrate that slope selection eventually occurs. We apply perturbation theory to characterize time-periodic solutions of step flow for slope-selected profiles. By this method, we show how a simplified step flow theory with constant probabilities for the motion of deposited atoms can serve as an effective model of slope selection in the presence of DF. Our analytical findings compare favorably to step simulations.

Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations

Various properties of Pb(111) nanofilms, prototypical quantum films, have been studied extensively. However, key ab initio-level energy barriers for Pb adatom diffusion on stepped Pb(111) nanofilm surfaces are still not available. Using first-principles density functional theory, we calculate these barriers for films with thicknesses of few monolayers (ML). We find that two-atom exchange is always much more favorable than direct hopping to cross A- or B-type steps. Ehrlich-Schwoebel (ES) barriers for downward transport to a higher-coordination step-edge site depend strongly on the film thickness. For such transport from 2- to 1-ML terraces, or from 4- to 3-ML terraces, there is no an ES barrier, but large ES barriers of more than 100 meV are found from 3- to 2-ML terraces. We also obtain the barriers for diffusion along the step edges and find that these step-edge barriers are significantly larger than terrace diffusion barriers. In addition, we analyze energetics for diffusion on the top flat surface of a nanofilm supported on a vicinal surface, and thus having underlying buried or ghost steps. We quantify the tilted potential energy surface in both ghost A- and B-step regions separating 2- and 3-ML (as well as 3- and 4-ML) terraces. Consequences are discussed for the growth kinetics of supported Pb nanofilms, where the support does not strongly affect electronic states within the film.

An examination of scaling behavior in unstable epitaxial mound growth via kinetic Monte Carlo simulations

We investigate the scaling behavior for roughening and coarsening of mounds during unstable epitaxial growth. By using kinetic Monte Carlo (KMC) simulations of two lattice-gas models of crystal surfaces, we find scaling exponents that characterize roughening and coarsening at long times. Our simulation data show that these exponents have a complicated dependence on key model parameters that describe a step edge barrier and downward transport mechanisms. This behavior has not been fully described in previous works. In particular, we find that these scaling exponents vary continuously with parameters controlling the surface current. The kinetic processes of the KMC models that we employ include surface diffusion, edge diffusion, step-edge barriers, and also account for transient kinetics during deposition via downward funneling and transient mobility. Our extensive simulations make evident the salient interplay between step-edge barrier strength and transient kinetic processes.

Coherent X-ray measurement of step-flow propagation during growth on polycrystalline thin film surfaces

The properties of artificially grown thin films are strongly affected by surface processes during growth. Coherent X-rays provide an approach to better understand such processes and fluctuations far from equilibrium. Here we report results for vacuum deposition of C60 on a graphene-coated surface investigated with X-ray Photon Correlation Spectroscopy in surface-sensitive conditions. Step-flow is observed through measurement of the step-edge velocity in the late stages of growth after crystalline mounds have formed. We show that the step-edge velocity is coupled to the terrace length, and that there is a variation in the velocity from larger step spacing at the center of crystalline mounds to closely-spaced, more slowly propagating steps at their edges. The results extend theories of surface growth, since the behavior is consistent with surface evolution driven by processes that include surface diffusion, the motion of step-edges, and attachment at step edges with significant step-edge barriers.

Pentacene Crystal Growth on Silica and Layer-Dependent Step-Edge Barrier from Atomistic Simulations.

Understanding and controlling the growth of organic crystals deposited from the vapor phase is important for fundamental materials science and necessary for applications in pharmaceutical and organic electronics industries. Here, this process is studied for the paradigmatic case of pentacene on silica by means of a specifically tailored computational approach inspired by the experimental vapor deposition process. This scheme is able to reproduce the early stages of the thin-film formation, characterized by a quasi layer-by-layer growth, thus showcasing its potential as a tool complementary to experimental techniques for investigating organic crystals. Crystalline islands of standing molecules are formed at a critical coverage, as a result of a collective reorientation of disordered aggregates of flat-lying molecules. The growth then proceeds by sequential attachment of molecules at the cluster and then terrace edges. Free-energy calculations allowed us to characterize the step-edge barrier for descending the terraces, a fundamental parameter for growth models for which only indirect experimental measurements are available. The barrier is found to be layer-dependent (approximately 1 kcal/mol for the first monolayer on silica, 2 kcal/mol for the second monolayer) and to extend over a distance comparable with the molecular length.

Understanding the grain-growth mechanism of high-performance organic semiconducting diphenyl-dibenzothiopheno[6,5-b:6′,5′-f]thieno[3,2-b]thiophene molecules

We report here our investigation on the grain-growth mechanism of diphenyl-dibenzothiopheno[6,5-b:6′,5′-f]thieno[3,2-b]thiophene (DPh-DBTTT), which was recently published as a high-performance organic semiconductor. Atomic force microscopy revealed that unconventional needle-like structures grew on the surface of DPh-DBTTT thin films, and these structures became more dominant as the film thickness increased and the deposited film's surface temperature decreased. In combination with the crystal structure simulations, the grazing-incidence wide-angle x-ray scattering data indicated that the DPh-DBTTT molecules preferred an edge-on orientation near the interface between the substrate and DPh-DBTTT thin film, while the needle-like structures consisted of a face-on arrangement of the molecules. We suggest that this structural change originates from the large step-edge energy barrier of the DPh-DBTTT molecules. Our findings would be highly valuable to the design of new high-performance organic semiconducting materials and optimization of the conditions of thin-film deposition.

Scaling behavior and morphology evolution of CH3NH3PbI3 perovskite thin films grown by thermal evaporation

The growth dynamics of CH3NH3PbI3 (MAPbI3) perovskite thin films, deposited by thermal evaporation, has been investigated by atomic force microscope and height–height correlation function analysis. The unstable scaling behavior of initial perovskite films exhibiting the growth of islands, resulting in rougher film formation has been observed. After the formation of continuous film, the roughening has been characterized by analyzing the scaling exponent α ~ 0.70, growth exponent β = 0.79 ± 0.057, 1/z = 0.78 ± 0.038, and 2D fast Fourier transform. Anomalous scaling behavior of the MAPbI3 thin films and the formation of the rapid surface roughening are discovered. It is demonstrated that step-edge barrier induced mound growth may play the dominate role in the growth mechanism of MAPbI3 thin films on Si substrates. Further, the growth behavior of MAPbI3 film on ITO substrates is investigated as a comparison, and it reveals that the growth of MAPbI3 thin films is largely affected by the initial substrates underneath the growing films.

Kinetic Monte Carlo simulations of GaN homoepitaxy on c- and m-plane surfaces.

The surface orientation can have profound effects on the atomic-scale processes of crystal growth and is essential to such technologies as GaN-based light-emitting diodes and high-power electronics. We investigate the dependence of homoepitaxial growth mechanisms on the surface orientation of a hexagonal crystal using kinetic Monte Carlo simulations. To model GaN metal-organic vapor phase epitaxy, in which N species are supplied in excess, only Ga atoms on a hexagonal close-packed (HCP) lattice are considered. The results are thus potentially applicable to any HCP material. Growth behaviors on c-plane (0001) and m-plane (011¯0) surfaces are compared. We present a reciprocal space analysis of the surface morphology, which allows extraction of growth mode boundaries and direct comparison with surface X-ray diffraction experiments. For each orientation, we map the boundaries between 3-dimensional, layer-by-layer, and step flow growth modes as a function of temperature and growth rate. Two models for surface diffusion are used, which produce different effective Ehrlich-Schwoebel step-edge barriers and different adatom diffusion anisotropies on m-plane surfaces. Simulation results in agreement with observed GaN island morphologies and growth mode boundaries are obtained. These indicate that anisotropy of step edge energy, rather than adatom diffusion, is responsible for the elongated islands observed on m-plane surfaces. Island nucleation spacing obeys a power-law dependence on growth rate, with exponents of -0.24 and -0.29 for the m- and c-plane, respectively.

Characterization of step-edge barrier crossing of para-sexiphenyl on the ZnO (101[combining macron]0) surface.

Mass transport processes of conjugated organic molecules (COMs) on inorganic surfaces are essential elements in thin film deposition for hybrid optoelectronic devices. Defects and in particular surface step-edges dictate the molecular nucleation and growth morphology, which itself determine many physical properties of the resulting hybrid interface. Here, we explore the detailed molecular kinetics and transport rates of a single physisorbed para-sexiphenyl (p-6P) molecule crossing a step-edge (a "hetero-Ehrlich-Schwoebel barrier") on the inorganic ZnO (101[combining macron]0) surface by a combination of all-atom molecular dynamics simulations and passage time theory. We determine temperature- and charge-dependent (free) energy landscapes, position-dependent diffusion coefficients, and ultimately the mean first passage time over the step-edges. We find two completely different step-edge crossing mechanisms, the occurrence and rates of which simultaneously depend on both electrostatic and thermal molecule-surface coupling. In weakly coupled systems, the molecule crosses the step relatively quickly (in nanoseconds) by log-roll mechanisms while for strongly coupled systems, it crosses relatively slowly (in microseconds) in a strictly perpendicular fashion. In the latter process, "internal friction" from intramolecular bending and torsional degrees of freedom contribute a significant corrugation to the overall crossing barrier. Furthermore, we show that crossing pathways can also change qualitatively with step-edge height. The great complexity in hetero-barrier crossing of COMs (in contrast to simple atoms) revealed in this study has implications on the interpretation and possible control of nucleation and growth mechanisms at surface defects in hybrid systems.

Surface roughening and scaling behavior of vacuum-deposited SnCl2Pc organic thin films on different substrates

The evolution of surface morphology and scaling behavior of tin (IV) phthalocyanine dichloride (SnCl2Pc) thin films grown on Si(100) and glass substrates have been studied using atomic force microscopy (AFM) and height-height correlation function analysis. X-ray diffraction measurement confirms the crystalline nature of the SnCl2Pc thin film on glass substrate, while no crystallographic ordering is present for the film grown on Si substrate. The growth exponent β is found to be much larger for the film on glass substrate (0.48 ± 0.07) as compared to that on Si substrate (0.21 ± 0.08), which may be due to the high step-edge barrier, so-called Ehrlich-Schwöbel barrier, resulting in the upward dominant growth on glass substrate. From the 2D fast Fourier transform of AFM images and derived scaling exponents, we conclude that the surface evolution follows a mound like growth. These results imply the superiority of glass substrate over the Si substrate for the growth of device quality SnCl2Pc thin film.

Particle-resolved dynamics during multilayer growth ofC60

Using large-scale kinetic Monte Carlo (KMC) simulations, we investigate the nonequilibrium surface growth of the fullerene ${\text{C}}_{60}$. Recently we have presented a self-consistent set of energy barriers that describes the nucleation and multilayer growth of ${\text{C}}_{60}$ for different temperatures and adsorption rates in quantitative agreement with experiments [Bommel et al., Nat. Commun. 5, 5388 (2014)]. We found that ${\text{C}}_{60}$ displays lateral diffusion resembling colloidal systems, however it has to overcome an atomlike energetic step-edge barrier for interlayer diffusion. Here we focus on the particle-resolved dynamics, and the interplay between surface morphology and particle dynamics during growth. Comparing ${\text{C}}_{60}$ growth with an atomlike system, we find significant differences in the evolution of the surface morphology, as well as the single-particle dynamics on the growing material landscape. By correlating the mean-squared displacement of particles with their current neighborhood, we can identify the influence of the different time scales that compete during growth and can pinpoint the differences between the two systems.

Scaling behavior of ZnPc thin films grown on CuI interlayers

The growth behavior and consequent surface morphology evolution of zinc phthalocyanine (ZnPc) thin films deposited on a CuI interlayer were studied using atomic force microscopy and height difference correlation function (HDCF) analysis. The planar phthalocyanine thin films grown on non-interacting substrates have previously been reported to show anomalous scaling behavior such as large growth exponents, s, sometimes larger than 0.5, and small anomaly values, ρ, typically smaller than 0.6. In contrast, ZnPc thin films on a CuI interlayer (CuI/ ZnPc) in this work showed conventional scaling behavior with a s value of 0.26 ± 0.05 and a ρ value of 0.91. The HDCF analyses and x-ray diffraction results indicate that the expected interdigitated electron donor-acceptor interface was hardly formed for the CuI/ZnPc thin film system due to the lack of surface-parallel crystallites with high step edge barriers.

Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies.

Semiconductor quantum dots and wires are important building blocks for future electronic and optoelectronic devices. The common way of producing semiconductor nanostructures is by molecular beam epitaxy (MBE). In this additive growth process atoms are deposited onto crystalline surfaces and self-assemble into 3D structures. Here we present a subtractive process, in which surface vacancies are created by ion impacts. On terraces of crystalline surfaces their nucleation forms depressions which coarsen and finally lead to a self-organized 3D morphology. It is shown that this kind of spontaneous pattern formation is inherent to the ion induced erosion process on crystalline surfaces and is analogous to 3D growth by MBE. However, novel facets are found due to slightly different energetics and kinetics of ad-atoms and surface vacancies, especially at Ehrlich-Schwoebel step-edge barriers. Depending on the crystal orientation, three-fold, four-fold, six-fold symmetry, as well as extremely regular periodic nanogrooves can be produced on different orientations of group IV (Si, Ge) and III-V (GaAs, InAs) semiconductors.

Growth, structure and morphology of epitaxial Fe(0 0 1) films on GaAs(0 0 1)c(4 × 4)

We studied epitaxy, growth, structure and morphology of thin Fe(0 0 1) films on the As-rich GaAs(0 0 1)-c(4 × 4) surface, deposited by molecular beam epitaxy at growth temperatures between room temperature and 250° C. Electron and x-ray diffraction (XRD) techniques evidence epitaxial growth with Fe(0 0 1)[1 0 0] ∥ GaAs(0 0 1)[1 0 0]. The residual strain derived from the XRD results is consistent with recent stress measurements. Cross-sectional transmission electron microscopy reveals an abrupt interface for room-temperature films and the formation of a ∼10 nm thick crystalline Fe–Ga–As intermediate layer at 250° C. The dependence of the surface morphology on growth temperature and annealing evidences a kinetic roughening of the Fe surface at growth temperatures of 100–200° C due to the presence of step-edge barriers.