Electric-current-induced step bunching on Si(111)

Homma, Yoshikazu; Aizawa, Noriyuki

doi:10.1103/physrevb.62.8323

Cited by 65 publications

(62 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, d s = 1.7 − 4.5 nm gives q ef = (0.35 − 0.13)|e| as reported in earlier studies. 10,12,23 This indicates that there is a possibility for highly vicinal surfaces, with small l, to enter into a crossover between attachment-limited and diffusion-limited regimes where the characteristic length d s is comparable to l. It should be mentioned here that it is the d s value as compared to l that determines the regime of sublimation 26 and that Eq. (1) and Eq.…”

Section: B Experimental Results and Discussionmentioning

confidence: 99%

“…Samples were later annealed for time intervals ranging between 15 and 60 minutes at 1270 • C (regime III) with current driven along the miscut in the down-step direction. At this temperature, the Si(111) surface bunches at the high rate of approximately 1 step/second 23 and reaches the phase of antiband formation relatively rapidly, compared to other temperature intervals. Normally, two samples of the same miscut were annealed with the same electric field to confirm consistency of the results.…”

Section: A Experimental Proceduresmentioning

confidence: 99%

See 1 more Smart Citation

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

et al. 2012

View full text Add to dashboard Cite

In this paper, we investigate the antiband instability on vicinal Si(111) surfaces with different angles of misorientation. It is known that prolonged direct current-annealing of Si(111) results in the formation of antibands; i.e., the step bunches with the opposite slope to the primary bunches. We provide a theoretical description of antiband formation via the evolution of the atomic steps' shape. We also derive a criterion for the onset of the antiband instability under the conditions of sublimation controlled by slow adatom surface diffusion. We examine this criterion experimentally by studying the initial stage of the antiband formation at a constant temperature of 1270 • C while systematically varying the applied electromigration field. The experiment strongly supports the validity of the derived theoretical criterion and indicates the importance of accounting for the factor of critical field in the theoretical modeling of step bunching or antiband instabilities. Deduced from the comparison of theory and experiment, the Si surface atoms' effective charge cannot exceed double the elementary charge, set by the lower limit of kinetic characteristic length d s = 0.3 nm. Using d s = 1.7 − 4.5 nm draws values of the effective charge in line with the values reported in earlier studies.

show abstract

Section: B Experimental Results and Discussionmentioning

confidence: 99%

Section: A Experimental Proceduresmentioning

confidence: 99%

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Quite recently it was realised that step bunching is a promising way to study the interactions between the steps 29,30,31,32,33,34 . The physical ground is simple: The steps in the bunch keep a certain distance from each other because the step-step repulsion balances the tendency to further compression of the bunch.…”

Section: Introductionmentioning

confidence: 99%

“…For step bunching induced by surface electromigration, scaling relations of the form (2) have been derived both for non-transparent and transparent steps 26,29,30,34 . Their application to the analysis of experiments 31,32 proceeds in two stages. First, the value of the scaling exponent α or γ is used to determine the kinetic regime and the value of the step interaction exponent n, and subsequently an estimate for the strength of the step-step interaction (in relation to the driving force for step bunching) is extracted from the prefactor of the scaling relation.…”

Section: Introductionmentioning

confidence: 99%

Scaling properties of step bunches induced by sublimation and related mechanisms

et al. 2005

View full text Add to dashboard Cite

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length d d = Ds/K d is larger than the average distance l between the steps on the vicinal surface; here Ds is the surface diffusion coefficient and K d is the step kinetic coefficient. In the opposite limit d d ≪ l the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the form L ∼ H α , lmin ∼ H −γ between the width L, the height H, and the minimum interstep distance lmin of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for the case d d ≫ l. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through comparison with numerical simulations of the discrete step equations, we establish the value γ = 2/(n + 1) for the scaling exponent of lmin in terms of the exponent n of the repulsive step-step interaction, and provide an exact expression for the prefactor in terms of the energetic and kinetic parameters of the system. For the bunch width L we observe significant deviations from the expected scaling with exponent γ = 1 − 1/α, which are attributed to the pronounced asymmetry between the leading and the trailing edges of the bunch, and the fact that bunches move. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.

show abstract

“…The the uniform step train remained stable on heating with a step-up current. This instability has a mysterious temperature dependence, 2,3,4,5,6 with three temperature ranges between 830…”

Section: Introductionmentioning

confidence: 99%

A two-region diffusion model for current-induced instabilities of step patterns on vicinal Si(111) surfaces

Zhao¹,

Weeks²

2005

Surface Science

View full text Add to dashboard Cite

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 MullinsSekerka 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.

show abstract

Electric-current-induced step bunching on Si(111)

Cited by 65 publications

References 29 publications

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

Scaling properties of step bunches induced by sublimation and related mechanisms

A two-region diffusion model for current-induced instabilities of step patterns on vicinal Si(111) surfaces

Contact Info

Product

Resources

About