Formation Of Step Bunches Research Articles

In situ scanning tunneling microscopy characterization of step bunching on miscut Si(111) surfaces in fluoride solutions

The immersion of Si surfaces in fluoride solutions results in the formation of a hydrogen passivated surface. The resulting surface morphology is dependent on the solution composition and the crystallographic orientation of the surface. Etching of miscut Si(111) in fluoride solutions can lead to the formation of mesa-like features. In this article we show that these features are due to the formation of step bunches during the etching process. The density of these features is dependent on the etch rate, the applied potential, and the fluoride ion concentration of the etching solution.

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pe k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe k can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10 −3 cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.

Decay process of a crater/hillock and step structure transformation

Both the decay process of a crater or a hillock on Si(111) and the step bunching formation accompanying the decay of a periodic array of craters or hillocks on vicinal Si(111) are investigated by using the lattice gas model. We considered two elementary atomic processes, hopping with the Schwoebel effect and evaporation, and carried out the time dependent Monte Carlo simulation. The decay process of a crater or a hillock is caused by the difference of the equilibrium adatom concentrations between at the crater or the hillock edge and at the nearest step edge. The size of a crater or a hillock decreases approximately linearly with time for both kinetics of the diffusion limited and the capture limited. For a periodic array of craters or hillocks on a vicinal surface, the step bunching is formed at the upper side of craters or the lower side of hillocks with the decay of craters or hillocks, in the diffusion-limited kinetics. The evaporation of adatoms accelerates the growth rate of the step bunching and extends the bottom width of craters, reducing the step bunching width.

Quantitative theory of current-induced step bunching on Si(111)

We use a one-dimensional step model to study quantitatively the growth of step bunches on Si(111) surfaces induced by a direct heating current. Parameters in the model are fixed from experimental measurements near 900 $\ifmmode^\circ\else\textdegree\fi{}$C under the assumption that there is local mass transport through surface diffusion and that step motion is limited by the attachment rate of adatoms to step edges. The direct heating current is treated as an external driving force acting on each adatom. Numerical calculations show both qualitative and quantitative agreement with experiment. A force in the step down direction will destabilize the uniform step train towards step bunching. The average size of the step bunches grows with electromigration time $t$ as ${t}^{\ensuremath{\beta}}$, with $\ensuremath{\beta}\ensuremath{\approx}0.5$, in agreement with experiment and with an analytical treatment of the steady states. The model is extended to include the effect of direct hopping of adatoms between different terraces. Monte Carlo simulations of a solid-on-solid model, using physically motivated assumptions about the dynamics of surface diffusion and attachment at step edges, are carried out to study two-dimensional features that are left out of the present step model and to test its validity. These simulations give much better agreement with experiment than previous work. We find a step bending instability when the driving force is along the step edge direction. This instability causes the formation of step bunches and antisteps that is similar to that observed in experiment.

Oblique roughness replication in strained SiGe/Si multilayers

The replication of the interface roughness in SiGe/Si multilayers grown on miscut Si(001) substrates has been studied by means of x-ray reflectivity reciprocal space mapping. The interface profiles were found to be highly correlated and the direction of the maximal replication was inclined with respect to the growth direction. This oblique replication is explained by the influence of the inhomogeneous strain distribution around step bunches. The formation of step bunches is described by a kinetic step-flow model based on the work by Tersoff et al. [Phys. Rev. Lett. 75, 2730 (1995)]. We have generalized this model by taking into account local variations of the in-plane strain. The angle of obliqueness deduced from these calculations agrees very well with the experimental findings.

Two-dimensional dynamical model for step bunching and pattern formation induced by surface reconstruction

Surface reconstruction on sufficiently wide terraces on a vicinal surface can cause the formation of step bunches. We consider this process in the nucleation regime using a two-dimensional (2D) dynamical model that describes both surface reconstruction and the effects of the growth of a reconstructed facet on the motion of neighboring steps. When there is local mass transport, we show that the growth of a reconstructed facet can induce the growth of a similar facet nearby, leading to regular arrangements of flat facets separated by step bunches and to other characteristic 2D step patterns.

Step bunching caused by annealing vicinal GaAs(001) inAsH3and hydrogen ambient in its stationary state

The growth of step bunches on vicinal GaAs(001) annealed in ${\mathrm{AsH}}_{3}{/\mathrm{H}}_{2}$ ambient stops after the step bunches reach a particular size. The surface has reached a stationary state with the ${\mathrm{AsH}}_{3}{/\mathrm{H}}_{2}$ ambient. In this paper, we report how the surface morphology of step bunches in the stationary state depends on the annealing conditions. The fact that step bunching always occurred when vicinal GaAs(001) substrates were annealed in ${\mathrm{AsH}}_{3}{/\mathrm{H}}_{2}$ ambient led us to conclude that ${\mathrm{AsH}}_{3}{/\mathrm{H}}_{2}$ is directly related to its cause. In order to understand the formation mechanism of this step bunching, we develop a microscopic theory that describes step dynamics during annealing. Based on this theory, we propose a formation mechanism that attributes the cause of step bunching to ${\mathrm{AsH}}_{x}$ attached to step edges. We assume that ${\mathrm{AsH}}_{x}$ attached to step edges induces irreversible detachment and incorporation processes for Ga atoms terminating step edges, generating a net upward mass transfer across step edges. This results in the formation of step bunches. By assuming a reasonable coverage of ${\mathrm{AsH}}_{x}$ at step edges the complicated dependence of the size of the stationary step bunches on annealing conditions can be explained.

Interactions between Fluctuating Steps on Vicinal Surfaces: Edge Energy Effects in Reconstruction Induced Faceting

Surface reconstruction can generate effective attractive interactions between steps on vicinal surfaces, leading to the formation of step bunches. Modified repulsive interactions arise from the fluctuations of a step in the asymmetric environment at the edge of the step bunch. These are determined by a mapping to the ground state energy of a quantum particle between two rigid walls in an external field. This yields an edge energy term that controls the dynamics of faceting and causes wider step spacings at the edge of the bunch, in agreement with Monte Carlo simulations.

Spinodal decomposition during step-flow growth

Relatively little is known about the epitaxial growth of alloys that are thermodynamically unstable. An analysis here suggests that spinodal decomposition can take place by formation of step bunches with alternating composition. This provides a possible mechanism for the spontaneous formation of superlattices during molecular beam epitaxy alloy growth. Kinetic effects reduce the degree of decomposition, relative to equilibrium. At sufficiently high growth rates, decomposition is completely suppressed.

Atomic force microscopic study of step bunching and macrostep formation during the growth of L-arginine phosphate monohydrate single crystals

The experimental results of the formation of step bunches and macrosteps on the {100} face of L-arginine phosphate monohydrate crystals grown from aqueous solutions at different supersaturations studied by using atomic force microscopy are described and discussed. It was observed that (1) the step height does not remain constant with increasing time but fluctuates within a particular range of heights, which depends on the region of step bunches, (2) the maximum height and the slope of bunched steps increases with growth time as well as supersaturation used for growth, and that (3) the slope of steps of relatively small heights is usually low with a value of about 8° and does not depend on the region of formation of step bunches, but the slope of steps of large heights is up to 21°. Analysis of the experimental results showed that (1) at a particular value of supersaturation the ratio of the average step height to the average step spacing is a constant, suggesting that growth of the {100} face of L-arginine phosphate monohydrate crystals occurs by direct integration of growth entities to growth steps, and that (2) the formation of step bunches and macrosteps follows the dynamic theory of faceting, advanced by Vlachos et al.

High-temperature scanning tunneling microscopy on vicinal Si(111) and formation of ordered facets

We have measured vicinal surfaces of Si(111) by using high-temperature scanning tunneling microscopy. Above the (7 × 7) (1 × 1) phase transition temperature T c we observe fluctuating monoatomic steps with uniform separation. Below T c the precipitation of 7 × 7 reconstructed terraces necessarily leads to a local reduction of the mean distance between the steps which, depending on the azimuthal orientation, finally gives rise to the formation of step bunches and higher-order facets. In the present work we concentrate on high-temperature observations (920 and 860 K) of (133) and (177) facets, respectively.

Multistep formation and lateral variation in the In composition in InGaAs layers grown by metalorganic vapor phase epitaxy on (001) vicinal GaAs substrates

In this paper, we investigate the substrate misorientation effect on In 0.2Ga 0.8As/GaAs strained quantum wells grown on vicinal GaAs substrates by metalorganic vapor phase epitaxy (MOVPE). Using cross-sectional transmission electron microscopy (TEM), stepbunching in an InGaAs layer is observed. In addition, based on energy-dispersive X-ray (EDX) analysis, we report for the first time lateral variations in the In composition in an InGaAs layer grown on a vicinal substrate. It is found that this variation in In composition and variations in the thickness cause photoluminescence (PL) spectrum broadening. The dependence of PL properties on the growth conditions and on surface misorientation direction is also examined. Experimentals results are explained by discussing the diffusion length of Group III atoms and their tendency to attach to step sites. TEM analysis confirms that the critical layer thickness of an InGaAs layer decreases on a vicinal substrate due to the formation of stepbunches.