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Register a new userA Two-Region Diffusion Model for Current-Induced Instabilities of Step Patterns on Vicinal Si(111) Surfaces
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We study current-induced step bunching and wandering instabilities with subsequent pattern formations on vicinal surfaces. A novel two-region diffusion model is developed, where we assume that there are different diffusion rates on terraces and in a small region around a step, generally arising from local differences in surface reconstruction. We determine the steady state solutions for a uniform train of straight steps, from which step bunching and in-phase wandering instabilities are deduced. The physically suggestive parameters of the two-region model are then mapped to the effective parameters in the usual sharp step models. Interestingly, a negative kinetic coefficient results when the diffusion in the step region is faster than on terraces. A consistent physical picture of current-induced instabilities on Si(111) is suggested based on the results of linear stability analysis. In this picture the step wandering instability is driven by step edge diffusion and is not of the Mullins-Sekerka type. Step bunching and wandering patterns at longer times are determined numerically by solving a set of coupled equations relating the velocity of a step to local properties of the step and its neighbors. We use a geometric representation of the step to derive a nonlinear evolution equation describing step wandering, which can explain experimental results where the peaks of the wandering steps align with the direction of the driving field.
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We introduce a simple two region model where the diffusion constant in a small region around each step on a vicinal surface can differ from that found on the terraces. Steady state results for this model provide a physically suggestive mapping onto kinetic coefficients in the conventional sharp-step model, with a negative coefficient arising from faster diffusion in the step region. A linear stability analysis of the resulting sharp-step model provides a unified and simple interpretation of many experimental results for current-induced step bunching and wandering instabilities on both Si(111) and Si(001) surfaces.
For more than three decades, measurement of terrace width distributions (TWDs) of vicinal crystal surfaces have been recognized as arguably the best way to determine the dimensionless strength $tilde{A}$ of the elastic repulsion between steps. For sufficiently strong repulsions, the TWD is expected to be Gaussian, with $tilde{A}$ varying inversely with the squared variance. However, there has been a controversy over the proportionality constant. From another perspective the TWD can be described as a continuous generalized Wigner distribution (CGWD) essentially no more complicated than a Gaussian but a much better approximation at the few calibration points where exact solutions exist. This paper combines concisely the experimentally most useful results from several earlier papers on this subject and describes some advancements that are in progress regarding numerical tests and in using Schrodinger-equation formalism to give greater understanding of the origin of the CGWD and to give hope of extensions to more general interaction potentials between steps. There are many implications for future experiments.
The formation of a Ag stabilized regular step lattice on vicinal Si(111) miscut towards [11-2] is reported. The step bunching characteristic of the clean surface is prevented by a single-domain Si(111)-(3x1)-Ag reconstruction. The nanostructured surface is used as a template for growing one-dimensional arrays of 1 nm sized Ag quantum dots with a preferential spacing of 1.5 nm along the rows.
Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the diffusion of adatoms on terraces with boundary conditions at sharp steps, as first studied by Burton, Cabrera and Frank (BCF). Recent electromigration experiments on vicinal Si surfaces suggest the need for more general boundary conditions in a BCF approach. We study a discrete 1D hopping model that takes into account asymmetry in the hopping rates in the region around a step and the finite probability of incorporation into the solid at the step site. By expanding the continuous concentration field in a Taylor series evaluated at discrete sites near the step, we relate the kinetic coefficients and permeability rate in general sharp step models to the physically suggestive parameters of the hopping models. In particular we find that both the kinetic coefficients and permeability rate can be negative when diffusion is faster near the step than on terraces. These ideas are used to provide an understanding of recent electromigration experiment on Si(001) surfaces where step bunching is induced by an electric field directed at various angles to the steps.
We examine the structure and the evolution of Ge islands epitaxially grown on vicinal Si(111) surfaces by scanning tunneling microscopy. Contrary to what is observed on the singular surface, three-dimensional Ge nanoislands form directly through the elastic relaxation of step-edge protrusions during the unstable step-flow growth. As the substrate misorientation is increased, the islands undergo a shape transformation which is driven by surface energy minimization and controlled by the miscut angle. Using finite element simulations, we show that the dynamics of islanding observed in the experiment results from the anisotropy of the strain relaxation.
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