Step-edge Barrier Research Articles

Surface-morphology evolution during unstable homoepitaxial growth of GaAs(110)

The time evolution of the surface morphology during growth of GaAs(110) by molecular-beam epitaxy is studied using Nomarski and atomic force microscopy. Depending on the growth temperature and ${\mathrm{As}}_{4}$ overpressure, different types of growth instabilities are observed: large three-dimensional pyramidal features develop under As-deficient growth conditions, whereas step bunching takes place under As-rich conditions. In addition, a crossover from step bunching, attributed to a negative step-edge barrier, to unstable growth typical of a positive step-edge barrier, takes place under As-deficient conditions as the film thickness increases. Under suitable growth conditions, self-organization of the microscopic features during growth leads to the creation of a highly unusual, well-ordered pattern on the surface. We discuss the microscopic origin of the observed instabilities with the help of recent theoretical and experimental results.

Influence of The Electrochemical Environment on Diffusion Processes Near Step and Island Edges: Ag(111) and Ag(100)

AbstractThe electrochemical cell provides a potentially powerful means of altering morphology and islanding phenomena on metallic surfaces. Diffusion and attachment processes on terraces and near step and island edges are known to profoundly affect island sizes, shapes and coarsening kinetics. Using the surface-embedded-atom-model (SEAM) for describing metallic surfaces in the electrolytic environment, we calculate the dependence of the activation energies for the aforementioned diffusion processes on the deposited surface charge for the Ag(111) and Ag(100) surfaces in an electrolytic environment. While all these processes show some degree of dependence on the potential, the step-edge barrier and the edge diffusion processes are the most sensitive. Step-edge barriers increase (to over 1 eV) with large positive potential (0.85 V), while edge diffusion barriers monotonically decrease with positive surface charge on Ag(100) and Ag(111). We assess the effect these diffusion barriers have on island size/shapes and coarsening dynamics and discuss the implications on electrochemical tuning of islanding phenomena.

Step-Edge Barriers on Pt(111): An Atomistic View

The escape of platinum from Pt(111) islands has been examined in the field ion microscope to obtain a direct view of atomic events. No effective barrier to the escape of platinum clusters larger than dimers is found at step edges, but incorporation of individual adatoms is nevertheless more effective at low temperatures. From the temperature dependence of the rate of atom disappearance from Pt(111) islands, the additional step-edge barrier is found as $0.06\ifmmode\pm\else\textpm\fi{}0.01\mathrm{eV}$, quite small compared with the diffusion barrier of 0.26 eV, and in sharp contrast with deductions from growth experiments.

Unstable Growth on Rough Surfaces

We present experimental data for the morphological evolution of InAs buffer layers which are interpreted using continuum equations of motion and kinetic Monte Carlo simulations. Our analysis reveals the presence of an instability even as an initially rough surface smooths during growth. This instability is due to the step-edge barrier and causes a characteristic length to emerge while the surface roughness is decreasing, well before the formation of the mounds. The smoothing is well described by a linear continuum equation identical to that which describes the early stages of spinodal decomposition and has important practical implications for the growth of device buffer layers.

Reliable determination of kinetics parameters of adatoms in thin-film epitaxy

We show that in an interrupted step-flow epitaxy on a vicinal surface, the decay of adatom monomer density on terraces after deposition often has a simple dependence on the monomer diffusion coefficient D, the step-edge sticking probability S, and the extra step-edge energy barrier ${E}_{\mathrm{step}}$ (Schwoebel-Ehrlich barrier). One may reliably determine these kinetics parameters by examining the dependence of the decay rate constant on the average terrace width and the temperature. Such a decay can be monitored by either reflection high-energy electron diffraction or optical reflectance difference techniques.

Roughness evolution of Si(111) by low-energy ion bombardment

We have examined the roughness evolution of the Si(111) surface at T=610 K by 500 eV Ar ion bombardment near normal incidence using scanning tunneling microscopy from submonolayer to multilayer etching of up to 120 bilayers. The observed roughening was inconsistent with diffusion bias roughening, which is the mechanism thought to be dominant in roughening of crystalline surfaces by deposition and etching. The roughness evolution was interpreted in the framework of dynamic scaling, applicable when the step-edge barrier for surface diffusion is low. The roughness and growth exponents measured were in agreement with the numerical simulation of the Kuramoto–Sivashinsky equation with noise in the early time for 2+1 dimensions, which corresponds to the initial stage of dynamic scaling of ion bombardment.

How Sensitive is Epitaxial Growth to Adsorbates?

CO coverages as low as ${10}^{\ensuremath{-}3}$ monolayers---which may result from background partial pressures in the low ${10}^{\ensuremath{-}11}$ mbar range---are found to affect island shapes, island densities, step-edge barriers for adatoms and film roughness during homoepitaxial growth on Pt(111). The effects are traced to preferential adsorption of CO molecules on low coordinated Pt atoms.

Simple model for anisotropic step growth

We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and Monte Carlo simulations, we study the morphology of growing steps in detail. In particular, under typical molecular beam epitaxy conditions the step morphology is linearly unstable in the model and develops fingers separated by deep cracks. The vertical roughness of the step grows linearly in time, while horizontally the fingers coarsen proportional to ${t}^{0.33}$. We develop scaling arguments to study the saturation of the ledge morphology for a finite width and length of the terrace.

Beyond Intensity Oscillations

The decay in the oscillatory amplitude of diffraction intensity from an epitaxial growth front is due to the buildup of a multilevel step structure. This can occur as a result of kinetic limitations when the substrate temperature is sufficiently low or the deposition rate is very high so that thermal equilibrium cannot be ochieved during growth. Another mechanism that can lead to a multilevel growth front is the existence of a step edge barrier at the steps so that deposited atoms cannot diffuse "downward" at the step edge which leads to a mound like structure. In this paper we describe the characteristics of the diffraction intensity angular profile from the initial layer-by-layer structure to the final multilevel structure. A particular emphasis will be placed on the characteristics of the reciprocal space structure when the amplitude of the intensity oscillation decays to zero.

Prefactor and Step Edge Barrier Determination for Initerlayer Diffusion in Homoepitaxial Systems: Ag/Ag(111)

Interlayer diffusion is controlled by the probability that an atom will hop from a higher to a lower level. This probability depends on the additional step edge barrier ΔEs which an atom experiences at a step because of the lower coordination as it moves over the barrier, and possibly on the different prefactors νs, νt for an atom at the step versus one at a terrace position. It is important to develop experimental methods that separate out the two contributions. We have reanalyzed the STM-based method,1 which measures the fraction of islands with second layer occupation at different deposition temperatures, to show how the two contributions can be identified. In addition, we have developed a diffraction-based method that measures the step density of nucleated islands as they compete for atom capture with the steps at the perimeter of the terraces. RHEED experiments on Ag/Ag(111) result in ΔEs=0.15±0.03 eV and νs/νt=2.3×102±0.2, in good agreement with the results, ΔEs=0.13±0.03 eV and νs/νt=103±0.3, deduced from the data of Ref. 1.

New Nonlinear Evolution Equation for Steps during Molecular Beam Epitaxy on Vicinal Surfaces

A nonlinear evolution equation for a vicinal surface growing in the step flow mode is derived in the limit of weak desorption. This limit turns out to be singular, and nonlinearities of arbitrary order need to be taken into account. The meandering instability caused by step edge barriers leads to a step morphology with a fixed meander wavelength, cusp singularities, and a step width increasing as $\sqrt{t}$ without bound. Full lattice gas simulations confirm this picture, and the observed step morphology is derived analytically from the evolution equation.

A kinetic Monte Carlo study of the growth of Si on Si(100) at varying angles of incident deposition

Two- and three-dimensional kinetic Monte Carlo simulations were used to model the deposition of a hyperthermal molecular beam at varying angles of incidence. The simulations incorporate realistic deposition and diffusional moves, and feature many-layer growth for large systems containing up to 80 000 atoms. Kinetic Monte Carlo simulations for the three-dimensional model mimic the deposition and growth of Si on a Si(100) substrate at close to experimental length- and timescales. At high angles of incidence for the beam, the formation of porous columnar structures seen in the two-dimensional simulations evolve into flakes in the three-dimensional model. The growth angles of the columns and flakes follow the same general trends as previous ballistic deposition and molecular dynamics simulations, but existing theories do not adequately represent the simulation data. In the two-dimensional model, the effect of an additional step-edge reflection barrier increases the porosity of the deposited films at conditions for which columnar growth would be observed in the absence of the additional barrier. Raising the substrate temperature increases the widths of the columns and flakes perpendicular to the path of the beam. Increased substrate temperature also affects the depth to which grown films remain defect-free before columnar growth begins.

Submonolayer island formation and the onset of multilayer growth during Ag/Ag(100) homoepitaxy

Results from a scanning tunneling microscopy study are presented for the initial stages of Ag/Ag(100) homoepitaxy, and behavior is analyzed via Monte Carlo simulations of an appropriate lattice-gas model. Submonolayer nucleation and growth of two-dimensional islands is examined for substrate temperatures, T, between 295 and 370 K. The variation with flux of the mean island density, N av, reveals that island formation is effectively irreversible at 295 K, and leads to an estimate of 0.38 eV for the terrace diffusion barrier (using an attempt frequency of 10 13/s). The variation of N av with T reveals a transition to reversible island formation at around 320 K. This transition temperature (and the T-dependence of N av) are used to extract an effective value of 0.3 eV for the bond energy of an adsorbed dimer, assuming nearest-neighbor pairwise-additive interactions between adsorbed atoms. We indicate how the actual dimer bond energy could differ, e.g. in the presence of biased diffusion of separated adatom pairs which enhances their recombination, and thus increases effective dimer stability. The onset of multilayer growth, and specifically the formation of second-layer islands, is examined at 295 K to assess the degree of interlayer transport. Comparison with simulations yields an estimate of 30 meV for the effective value of an additional step-edge barrier (using an attempt frequency of 10 13/s). Using this result, subsequent multilayer kinetic roughening is predicted, consistent with experimental observations.

Unstable growth and coarsening in molecular-beam epitaxy

The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assumed that the origin of the initial instability of a planar surface is the Ehrlich–Schwoebel step-edge barrier for adatom diffusion. Two mechanisms of coarsening are identified: (i) surface diffusion driven by an uneven distribution of bonding energies, and (ii) mound coalescence driven by random deposition. Semiquantitative estimates of the coarsening time are given in each case. When the surface slope saturates, an asymptotic dynamical exponent z=4 is obtained.

O-induced modification of growth of thin Cu films on Ru(0001)

The film growth of Cu on clean and O-precovered Ru(0001) substrates at temperatures between 300 and 450 K is studied by means of scanning tunneling microscopy. On clean Ru(0001), the Cu films grow in a multilayer mode. For an O precoverage, $({\ensuremath{\theta}}_{\mathrm{O}})l0.1$ monolayer (ML), O remains trapped at the Cu/Ru interface and the Cu film grows similarly as on clean Ru(0001). Precovering the Ru(0001) substrate with more than 0.1 ML of O strongly modifies the film morphology. The excess O migrates to the surface of the growing film and acts as a surfactant. Domains of an O/Cu structure are formed, the lateral extension of which linearly increases with ${\ensuremath{\theta}}_{\mathrm{O}}.$ For $0.4l{\ensuremath{\theta}}_{\mathrm{O}}l~0.5\mathrm{}\mathrm{ML},$ the O/Cu structure covers the film surface completely. For $0.2l~{\ensuremath{\theta}}_{\mathrm{O}}l~0.5\mathrm{}\mathrm{ML},$ a perfect layer-by-layer growth with a relatively high nucleation density is forced at temperatures around 400 K. Decreasing the temperature and/or ${\ensuremath{\theta}}_{\mathrm{O}}$ yields multilayer growth. For $0.4l{\ensuremath{\theta}}_{\mathrm{O}}l~0.5\mathrm{}\mathrm{ML},$ temperatures above 430 K, and substrate terrace widths below 100 nm, step-flow growth is observed. Two different types of O/Cu surfactant structures ($A$- and $B$-type) are identified. The $A$-type structure is established for $0.1l{\ensuremath{\theta}}_{\mathrm{O}}l~0.4\mathrm{}\mathrm{ML},$ and displays some ordering on a local scale (distorted hexagonal lattice). It causes heterogeneous nucleation at surface sites formed by a misfit-induced moir\'e-like relaxation of the Cu film. Its surfactant effect can be described by the concept of two mobilities, which is based on a low adatom mobility during nucleation, and a high adatom mobility on top of small islands. This implies an increase of the attempt rate of Cu adatoms for step descent, enhancing interlayer diffusion. The $B$-type structure is established for $0.4l{\ensuremath{\theta}}_{\mathrm{O}}l~0.5\mathrm{}\mathrm{ML},$ and contains a more irregular arrangement of O atoms. We assume that it behaves like a continuous O/Cu layer, on top of which the adatoms migrate. Its surfactant effect is attributed to a large diffusion barrier and a small additional step-edge barrier prevailing on top of the O/Cu layer. The latter also implies increased interlayer diffusion. The relationship of our results to previously observed work-function oscillations in the O-modified Cu film growth on Ru(0001) is discussed.

Surface diffusion mechanism for step bunching

The influence of local atomic interactions on step bunching and step debunching of vicinal fcc(111) surfaces inclined in the [2\ifmmode\bar\else\textasciimacron\fi{}11] direction is modeled by kinetic Monte Carlo simulations under annealing conditions. Different local interactions give rise to characteristic step bunch configurations. By using transition probabilities describing local atomic interactions where both the initial and the final number of atomic bonds are involved in the surface diffusion process, and in addition strongly enhanced surface diffusion along the close-packed 〈011\ifmmode\bar\else\textasciimacron\fi{}〉 step edges, a quasiequilibrium configuration consisting of large (100) and (111) terraces evolves. On the other hand, for a system with strongly enhanced surface diffusion along the 〈011\ifmmode\bar\else\textasciimacron\fi{}〉 step edges, but for all other directions local isotropic diffusion where only the initial number of atomic bonds before a hop is considered, a quasiequilibrium surface configuration is formed with a step bunch consisting of alternating (021) and (012) facets surrounded by large (111) terraces. Strongly enhanced surface diffusion along 〈011\ifmmode\bar\else\textasciimacron\fi{}〉 step edges is also shown to be necessary for the stability of step bunches for the investigated system. Finally, we show that the step bunching can be completely quenched for compact steps, by means of an increased step-edge barrier for mass transport across the 〈011\ifmmode\bar\else\textasciimacron\fi{}〉 step edges. This shows that step bunching cannot occur without mass transport between adjacent terraces.

Step-edge barriers: truths and kinetic consequences

Observations of individual atoms on metal surfaces have shown that the diffusion potential at descending steps is not the simple repulsive barrier usually assumed in crystal growth. Instead, atoms may be held in asymmetric traps at step edges, and there are significant distortions of the potential near ascending steps. That the presence of step-edge traps instead of repulsive barriers can have a crucial effect on atomic kinetics is demonstrated by analyzing three processes important in crystal growth: the lifetime of atoms before incorporating into a cluster, dissociation of atoms from lattice steps, and incorporation on vicinal surfaces.

On the onset of InAs islanding on InP: influence of surface steps

We investigate the transition from two- to three-dimensional growth of thin InAs films on InP by chemical beam epitaxy. This transition is shown to strongly depend on growth temperature and on the misorientation-or the presence of surface steps — on the InP surface where the InAs film is deposited. Low temperature photoluminescence measurements on InP-InAs-InP quantum well structures and atomic force microscopy analysis of InAs-InP structures indicate different islanding behaviors for substrates with different misorientations, the onset of islanding process occurring earlier for misoriented than for nominal substrates. The shape and distribution of the islands indicate the existence of a step edge barrier altering the diffusion dynamics on the surface. Low growth temperature is shown to delay islanding for a fixed deposition time and also limit island formation to certain regions of the sample where smooth corrugations (slope ∼1°) are observed.

Effect of kinks and concerted diffusion mechanisms on mass transport and growth on stepped metal surfaces

We study the effect of kinks and concerted atomic mechanisms on diffusion processes relevant to metal-on-metal homoepitaxy on fcc metal surfaces vicinal to the fcc (100) direction. First, we carry out extensive finite-temperature molecular dynamics simulations based on the effective medium theory to search for diffusion mechanisms that dominate the mass transport perpendicular and parallel to step edges. Then, the energetics of these processes are studied by ground state calculations. Our results show that kinks play an important role for diffusion both across and along step edges. In particular, the combined effect of kinks and concerted exchange is found to be able to remove locally the step edge barrier for mass transport across the step. The relative importance of some of the processes depends on the local tilt of the interface. We report results for copper, silver, and nickel, and discuss the generic features of energetics of diffusion processes in effective medium theory and other semi-empirical many-atom models. We also consider the implications of our results on surface growth and for models of surface growth under molecular beam epitaxy conditions.

Kinetic model for molecular beam epitaxial growth on a singular surface

We present a new kinetic model for molecular beam epitaxial growth on a singular surface which combines the modified rate equations approach with a concept of a feeding zone. The model involves irreversible nucleation, growth and coalescence of 2D islands in each layer and consists of an infinite set of coupled differential equations for adatom and 2D island densities and coverage in successive growing layers. It is shown that in the complete condensation regime and in the absence of step edge barriers, the homoepitaxial growth mode is fully determined by a single dimensionless parameter which is proportional to the ratio of the surface diffusion coefficient and the deposition flux. With decreasing this parameter, the growth mechanism crosses over from smooth 2D layer-by-layer growth to rough multilayer growth and eventually to very rough Poisson random deposition growth with time-divergent rms roughness. The extension of the model to the case of the heteroepitaxy by introducing different coefficients in the first and the next layers is presented as well.