Step bunching, step wandering and faceting: self-organization at Si surfaces

Yagi, Kazuichi; Minoda, Hiroki; Degawa, Masashi

doi:10.1016/s0167-5729(01)00013-9

Cited by 117 publications

(100 citation statements)

References 129 publications

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“…Mechanisms causing step bunching instabilities include strain effects 1,2,7,8 , sublimation under conditions of asymmetric detachment kinetics known as the Ehrlich-Schwoebel (ES) effect 9,10,11 , growth with an inverse ES effect 9,12,13,14 , and surface electromigration 15,16,17,18,19,20,21,22,23,24,25,26,27,28 .…”

Section: Introductionmentioning

confidence: 99%

Scaling properties of step bunches induced by sublimation and related mechanisms

et al. 2005

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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.

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Section: Introductionmentioning

confidence: 99%

Scaling properties of step bunches induced by sublimation and related mechanisms

et al. 2005

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“…A major obstacle to achieving predictive power in such studies, however, is the insufficient control over the complex internal structure of the polycrystalline samples. Hence an important motivation for investigating electromigration-induced effects on simple, well-controlled nanoscale morphologies, such as step patterns on vicinal surfaces [6] and single layer islands [7], is to bridge the gap between the microscopic mechanisms of electromigration and their consequences on technologically relevant length and time scales.Electromigration of islands has been modeled previously using Monte Carlo simulations [8] and continuum theory [9]. The continuum approach to island shape evolution, which treats the island edge as a smooth curve, has been successfully applied to a range of problems including the diffusion [10] and sintering [11] of islands, and the pinch-off of vacancy clusters [12].…”

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confidence: 99%

Complex Shape Evolution of Electromigration-Driven Single-Layer Islands

et al. 2005

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The shape evolution of two-dimensional islands through periphery diffusion biased by an electromigration force is studied numerically using a continuum approach. We show that the introduction of crystal anisotropy in the mobility of edge atoms induces a rich variety of migration modes, which include oscillatory and irregular behavior. A phase diagram in the plane of anisotropy strength and island size is constructed. The oscillatory motion can be understood in terms of stable facets which develop on one side of the island and which the island then slides past. The facet orientations are determined analytically.PACS numbers: 66.30.Qa, The manipulation of nanostructures by macroscopic forces is likely to become a key ingredient in many nanotechnology applications. Understanding the influence of external fields on the shape evolution of nanoscale surface features is therefore of considerable importance. As a first step in this direction we analyze here the effects of an electric current on single-layer islands on a crystalline surface. The islands evolve under surface electromigration, the directed motion of adsorbed atoms due to the slight force transmitted by collisions with the conduction electrons in the sample [1].Electromigration along interfaces and grain boundaries is the most persistent and menacing reliability problem in integrated circuit technology [2,3]. Correspondingly, much work has been devoted to electromigration-induced void formation and breakdown in metallic conductor lines [3], and the capacity for quantitative numerical modeling has been demonstrated at least for simple void geometries [4,5]. A major obstacle to achieving predictive power in such studies, however, is the insufficient control over the complex internal structure of the polycrystalline samples. Hence an important motivation for investigating electromigration-induced effects on simple, well-controlled nanoscale morphologies, such as step patterns on vicinal surfaces [6] and single layer islands [7], is to bridge the gap between the microscopic mechanisms of electromigration and their consequences on technologically relevant length and time scales.Electromigration of islands has been modeled previously using Monte Carlo simulations [8] and continuum theory [9]. The continuum approach to island shape evolution, which treats the island edge as a smooth curve, has been successfully applied to a range of problems including the diffusion [10] and sintering [11] of islands, and the pinch-off of vacancy clusters [12]. Here we focus on the regime of periphery diffusion (PD), where the dominant kinetic process is the migration of atoms along the island boundary. The shape then follows a local evolution law, without coupling to the adatom concentration on the surrounding terrace.We extend the model of [9] by including crystal anisotropy in the adatom mobility. It was observed recently in the context of step flow growth [13] that crystalline anisotropy can change the behavior of step patterns in a qualitative way. In the present case, it lea...

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“…Measurements in silicon have shown that step-bunching can occur on vicinal surfaces, where bands of steps form the appearance of large unstable planes that are actually composed of many small steps with faces parallel to stable planes. 108 Tran discusses the stability of various -69-crystallographic planes of sapphire when these planes are in contact with liquid metals; these planes are not present in the Wulff shape when sapphire is in contact with vapor. 109 The varying size of the hills and valleys in the AFM image of the m-plane sapphire suggests that the facets are coalescing and coarsening, which is expected for these types of facets.…”

Section: Sapphire Interfacial Morphologymentioning

confidence: 99%

Mechanisms of microstructure development at metallic-interlayer/ceramic interfaces during liquid-film-assisted bonding

Sugar¹

2003

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Alumina has been bonded via copper/niobium/copper interlayers, and correlations have been made between various processing conditions (applied load, processing temperature, copper film thickness, surface roughness, etc.) and strength. Four-point bend strengths and micrographs of fracture surfaces have been used to determine the relationship between processing, microstructure, and properties. Transparent sapphire substrates bonded with copper/niobium/copper interlayers were used in model experiments to track the microstructural development of these ceramic/metal interfaces and to identify the important mechanisms that contribute.High interfacial strengths were generally associated with small unbonded regions, extensive breakup of the copper film into isolated particles, ceramic pullout, and regions of niobium/alumina contact where the grain boundary grooves of the alumina are visible on both sides of the fracture surface. Experiments with sapphire substrates showed that asperities in the niobium and grain boundary grooves in the niobium play an important role in the initiation and growth of sapphire/niobium contact. The presence of a liquid film can enhance the kinetics of sapphire/niobium contact and growth by providing a low-temperature high-diffusivity path.-2-The breakup of the copper film was described using two models that were in fairly close agreement. The breakup of the copper film depended on the asperity density in the niobium, niobium grain boundary density, liquid film redistribution, and the breakup of liquid patches via Rayleigh instabilities. The redistribution of the liquid was affected by defect geometry, local film thickness, and local interfacial crystallography.Thermal grooving effects of liquid copper on alumina and niobium were studied using conventional sessile drop experiments. The thermal grooving of one particular grain boundary in alumina when in contact with copper and niobium was studied using a fabricated bicrystal. Both diffusion mechanisms and the dissolution-precipitation reaction of alumina in niobium limited the kinetics of thermal grooving.-iii--iv-

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Step bunching, step wandering and faceting: self-organization at Si surfaces

Cited by 117 publications

References 129 publications

Scaling properties of step bunches induced by sublimation and related mechanisms

Scaling properties of step bunches induced by sublimation and related mechanisms

Complex Shape Evolution of Electromigration-Driven Single-Layer Islands

Mechanisms of microstructure development at metallic-interlayer/ceramic interfaces during liquid-film-assisted bonding

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