Step wandering due to the structural difference of the upper and the lower terraces

We consider the wandering instability of steps due to a gap in the lifetime of adatoms for evaporation on the upper and the lower terraces. Our study is meant to explain the step wandering observed in the growth of Si(1 1 1) surface near its structural transition temperature. With a linear stability analysis and Monte Carlo simulations, we show that the instability of an isolated step occurs in growth if adatoms on the upper terrace evaporate more easily than those on the lower terrace. For the instability of a vicinal face, additional features are considered as the motion of the phase boundary and the mass flow across it during the phase transformation. It is found that steps and phase boundaries wander in-phase with a rather well-defined periodicity when evaporation is weak. We compare the result with that for a system with a gap in the diffusion coefficient. The simulation results show that the first mechanism is more effective to make the wandering steps in-phase and that the second mechanism induces step wandering in a wider range of parameters.     

In-phase step wandering on vicinal Si(1 1 1) surfaces

The step structure transition between a regular step and a bunched step on vicinal Si(1 1 1) surfaces induced by DC is studied by the kinetic Monte Carlo simulation in a terrace-adatom-step-kink (TASK) model. In the TASK model, effective force due to DC is taken into account explicitly on the mass transport of Si adatoms. In the diffusion-limited regime corresponding to the experimental temperature range II, step bunching is induced by step-up force and in-phase wandering of a regular step is formed by step-down force. The in-phase wandering of a regular step is formed by nucleation growth mode and the amplitude of wandering grows with time in proportion to . The period of in-phase wandering decreases as the effective force increases, consistent with the recent experimental results.     

Regular step formation on concave-shaped surfaces on 6H–SiC(0 0 0 1)

A concave-shaped surface has been prepared in a 6H–SiC(0 0 0 1) substrate by mechanical grinding. As a consequence, the different crystallographic planes building up the 6H–SiC polytype are cut under continuously changing polar angles in all azimuthal directions. Through hydrogen etching, this curved surface breaks up into a whole set of surfaces vicinal to the initial 6H(0 0 0 1) orientation. The local structural reorganisation after hydrogen etching has been studied by scanning electron microscopy (SEM) and atomic force microscopy (AFM). Two types of local bond environments are present at the step edges leading to a strong anisotropy in the surface etching with hydrogen. As a result, the distribution of the terrace width and the step heights varies with the azimuthal angle and reflects the sixfold symmetry of the bulk crystal. For most azimuthal directions, an alternation of large and small terraces, separated by steps of 0.75 nm heights (height of half the 6H polytype, three bilayers) is observed and only for well defined azimuthal directions, equally spaced terraces separated by steps of 1.5 nm height (one unit cell of 6H–SiC, six bilayers) are found. In addition, the polar variations have been studied by taking various line-scans along the concave-shaped surface with AFM. It seems that for polar angles above 3°, step bunching of several SiC steps occurs whereas below 3° the bimodal terrace width distribution is observed.     

Continuum model for low temperature relaxation of crystal steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step-free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.     

Step dynamics in relaxation of sharp corners on crystal surfaces

The dynamic behavior of steps involved in the relaxation of sharp corners in microfabricated structures on crystalline surfaces have been studied. We find that during the early stages of relaxation of slightly tapered trenches on Si(0 0 1), wide (1 1 0) terraces perpendicular to the substrate are formed near the corners of the trench sidewalls. The evolution of a step profile around the corner region, where step density abruptly changes, is analyzed using one-dimensional step models. It is found that, in case that mass transport occurs through surface diffusion, the preexisting steps on the trench sidewall are accumulated in the corner region, and extensive terraces are formed near the corners.     

Methane activation on Ni(1 1 1): Effects of poisons and step defects

We have, theoretically and experimentally, investigated the dissociation of methane on the terraces and steps of a Ni(1 1 1) surface. Using Density Functional Theory (DFT) total energy calculations combined with Ultra High Vacuum (UHV) experiments, we find that the steps exhibit a higher activity than the terraces. We have, furthermore, investigated how carbon and sulfur present on the surface will deactivate the steps, leaving only the terraces active. We find the intrinsic sticking probabilities of methane on the steps and terraces at 500 K to be 2.8 × 10⁻⁷ for the steps and 2.1 × 10⁻⁹ for the terraces, in complete agreement with our calculated difference in activation energy of 17 kJ/mol.     

Effect of step permeability on step instabilities due to alternation of kinetic coefficients on a growing vicinal face

We study the effect of step permeability on step instabilities on a growing vicinal face. When alternation of kinetic coefficients is taken into account, pairing of steps occurs on the vicinal face. Irrespective of the step permeability, the step pairs are stable for a wandering instability. The bunching of step pairs occurs if the steps are impermeable. The bunch size increases with time as t^β with β=1/2, which does not depend on the form of the repulsive interaction potential between steps. The repulsion influences the relation between the step distance in a bunch and the bunch size. When the repulsive potential ζ with the step distance l is given by ζ∼l^-ν, the average step distance in a bunch decreases as with α=1/(ν+1). The exponents, β and α are the same as those in the bunching induced by the Ehrlich-Schowebel effect in growth.     

Monatomic to biatomic step transition during epitaxial growth by step flow

We consider the transition of a two domain vicinal surface composed of alternating terraces having 1 × 2 and 2 × 1 reconstructions and separated by A and B steps to a single domain, 2 × 1 vicinal surface with biatomic steps. The sticking coefficients for the rougher B steps are greater on either side of the step than the corresponding A step sticking coefficients and this is shown to provide the kinetic mechanism for a transition to a single domain surface even when the diffusion coefficients on the two kinds of terraces are markedly different. We also determine the explicit time dependence for the terrace widths, which is of a trancendental form.     

Local Au coverage as driving force for Au induced faceting of vicinal Si(0 0 1): a LEEM and XPEEM study

Adsorption of Au at 850°C on a regular stepped 4° vicinal Si(0 0 1) surface results in a dramatic change of the step morphology: the surface decomposes into areas which are perfectly flat with a (0 0 1) orientation and (1 1 9) facets. Low energy electron microscopy shows the dynamics of the faceting process in real space while X-ray photoemission electron microscopy (XPEEM) allows a spatially resolved determination of the Au coverage at different stages of the faceting process. At a critical Au coverage of ≈1/3 ML (0 0 1) terraces are formed which extend anisotropically along the step edges of the surface. The steps in between the terraces bunch and form step bands in order to conserve the macroscopic miscut of the sample. Driving force for this morphological transformation is a complex (5×3.2) reconstruction formed on the (0 0 1) terraces. XPEEM shows this phase separation also for the Au coverage: on the (0 0 1) terraces the Au coverage is up to 40% higher compared to the step bands. With further increasing Au coverage the width of the Au rich terraces increases while the step bands become steeper. In a second step Au adsorbs on the step bands transforming them into well defined and smooth (1 1 9) facets.     

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.     

UHV-SEM observations of cleaning process and step formation on silicon (111) surfaces by annealing

The cleaning process and step formation by high temperature annealing up to 1250°C on the Si(111) surface are observed by an ultra-high-vacuum scanning electron microscope (UHV-SEM). The clean surface is composed of alternate planes of terraces and step bands with widths of several μm and 1 μm, respectively, in the 〈1?1?2〉 direction. Both planes are inclined by about 10° to each other. The surface steps are not only monolayer steps, but also higher steps comprising several monolayers. Monolayer steps join to form a high step, and 70–80 steps of several monolayers high form a step band by bunching in an average distance of several hundred A toward the 〈1?10〉 direction. The step structure depends on the annealing temperature and on the angle at which the cutting plane is off from the exact 〈111〉 orientation. In several studies of high energy reflection electron microscopy under small grazing angle incidence monolayer steps were observed on the terrace, but no rough structures like the step bands and high steps could be discerned. The step structure observed by the present experiment is compared with those observed by previous workers.     

On the microscopic origin of the kinetic step bunching instability on vicinal Si(0 0 1)

A scanning tunneling microscopy/atomic force microscopy study is presented of a kinetically driven growth instability, which leads to the formation of ripples during Si homoepitaxy on slightly vicinal Si(0 0 1) surfaces miscut in [1 1 0] direction. The instability is identified as step bunching, that occurs under step-flow growth conditions and vanishes both during low-temperature island growth and at high temperatures. We demonstrate, that the growth instability with the same characteristics is observed in two dimensional kinetic Monte Carlo simulation with included Si(0 0 1)-like diffusion anisotropy. The instability is mainly caused by the interplay between diffusion anisotropy and the attachment/detachment kinetics at the different step types on Si(0 0 1) surface. This new instability mechanism does not require any additional step edge barriers to diffusion of adatoms. In addition, the evolution of ripple height and periodicity was analyzed experimentally as a function of layer thickness. A lateral “ripple-zipper” mechanism is proposed for the coarsening of the ripples.     

Local electromigration model for crystal surfaces

The dynamics of crystal surfaces in the presence of electromigration is analyzed. From a phase field model with a migration force which depends on the local geometry, a step model with additional contributions is derived in the kinetic boundary conditions. These contributions trigger various surface instabilities, such as step meandering, bunching, and pairing on vicinal surfaces. Experiments are discussed.     

Kinetic step bunching instability during surface growth

We study the step bunching kinetic instability in a growing crystal surface characterized by anisotropic diffusion. The instability is due to the interplay between the elastic interactions and the alternation of step parameters. This instability is predicted to occur on a vicinal semiconductor surface Si(001) or Ge(001) during epitaxial growth. The maximal growth rate of the step bunching increases like F4, where F is the deposition flux. Our results are complemented with numerical simulations which reveal a coarsening behavior in the long time evolution for the nonlinear step dynamics.     

Step bunching to step-meandering transition induced by electromigration on Si(1 1 1) vicinal surface

The step configuration of a vicinal Si surface is studied under electromigration and a gradient of temperature. An abrupt transition (ΔT = 4 °C) from step-meandering to step bunching is found at 1225 °C for a step-down direct-current direction. This transition starts by random fluctuations which then extend on the whole surface. The transition is studied in the framework of a linear stability analysis of the usual Burton-Cabrera-Frank model by comparing the amplification factors of step-meandering and step bunching instabilities. Both compete at a given temperature, but since the amplification factors behave differently with temperature, bunching abruptly supersedes meandering above a critical temperature.     

Vicinal and on-axis surfaces of 6H-SiC(0001) thin films observed by scanning tunneling microscopy

Surfaces of 6H-SiC(0001) homoepitaxial layers deposited on vicinal (3.5° off (0001) towards [11 0]) and on-axis 6H---SiC wafers by chemical vapour deposition have been investigated using ultra-high vacuum scanning tunneling microscopy. Undulating step configurations were observed on both the on-axis and the vicinal surfaces. The former surface possessed wider terraces than the latter. Step heights on both surfaces were 0.25 nm corresponding to single bilayers containing one Si and one C layer. After annealing at T>1100°C for 3–5 min in UHV, selected terraces contained honeycomb-like regions caused by the transformation to a graphitic surface as a result of Si sublimation. A model of the observed step configuration has been proposed based on the observation of the [ 110] or [1 10] orientations of the steps and energetic considerations. Additional deposition of very thin (2 nm) SiC films on the above samples by gas source molecular beam epitaxy was performed to observe the evolution of the surface structure. Step bunching and growth of 6H---SiC layers and formation of 3C---SiC islands were observed on the vicinal and the on-axis surfaces, respectively, and controlled by the diffusion lengths of the adatoms.     

Study of CO diffusion on stepped Pt(1 1 1) surface by scanning tunneling microscopy

We have used a time-dependent tunneling current mode based on scanning tunneling microscopy/spectroscopy (STM/STS) to study the tracer diffusion of CO molecules along steps and on terraces of Pt(1 1 1). The results show that the hopping rate of CO molecules along steps is about 10 times faster than that on terraces in the measured temperature range. The diffusion activation energies are 5.1 kcal/mol and 3.8 kcal/mol on terraces and along steps, respectively. The lower activation energy and faster hopping rate for CO molecules diffusing along steps provide evidence that steps provide fast diffusion channels for CO molecules on stepped Pt(1 1 1) surfaces.     

Oxygen adsorption on stepped Pd(100) surfaces

We use scanning tunneling microscopy (STM) and high-resolution core-level spectroscopy (XPS) measurements to study the initial oxidation of vicinal Pd(100) surfaces exhibiting close-packed (111) steps. The XPS data analysis is supported by detailed surface-core level shift calculations based on density-functional theory. Both STM images and the XPS spectra are found to be perfectly consistent with a characteristic zigzag O decoration of the Pd steps predicted by a preceding cluster-expansion based theoretical study [Y. Zhang and K. Reuter, Chem. Phys. Lett. 465, 303 (2008)]. Continued oxygen uptake leads to the additional stabilization of a p(2 × 2)-O overlayer on the Pd(100) terraces, and ultimately to step bunching with the resulting large Pd(100) terraces covered by the PdO(101) surface oxide.     

A titanium-rich (111) surface of SrTiO3 single crystals by thermal annealing

A very smooth (111) titanium-rich surface was obtained by annealing SrTiO₃ single crystals in UHV. The surface structure was investigated with SEM, STM and LEED and was found to consist of terraces, interrupted by multi-unit-cell high steps, obviously a result of step bunching. The surface unit cell, is enlarged as a result of our particular preparation procedure. Received: 18 December 1996/Accepted: 18 December 1996     

Features of hydrogen adsorption on a Ni(997) surface

The change of the initial sticking coefficient for a Maxwellian beam of hydrogen on Ni(997) has been determined as a function of beam temperature and angle of incidence. At low temperatures adsorption is governed by the steps, at high temperatures adsorption on the terraces is more dominant. Adsorption on the terraces is probably an activated process whereas adsorption on the step sites is non-activated. There seems to be little diffusion of undissociated H₂ between steps and terraces.