Cracklike surface instabilities in stressed solids

Yang, Wei; Srolovitz, David J.

doi:10.1103/physrevlett.71.1593

Cited by 243 publications

(154 citation statements)

References 11 publications

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“…[1][2][3][4] Many continuum models can be found in the literature on the surface morphological evolution under elastic effects, in which the surfaces are modeled as continuously changed profiles without any discrete structures on them. 2,[5][6][7][8][9][10][11][12][13][14][15][16] The stress in the solid is a destabilizing factor while the surface energy is a stabilizing one, and the planar surface of a stressed solid is unstable for perturbations with wave numbers less than a critical value. [6][7][8][9][10] These models work in the regime above the roughening transition temperature.…”

Section: Introductionmentioning

confidence: 99%

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Zhu

Xiang

2009

Phys. Rev. B

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In heteroepitaxy, the mismatch of lattice constants between the crystal film and the substrate causes misfit strain and stress in the bulk of the film, driving the surface of the film to self-organize into various nanostructures. Below the roughening transition temperature, an epitaxial surface consists of facets and steps and changes its morphology by lateral motion of steps. In this paper, we present a 2 + 1-dimensional continuum model for the long-range elastic interaction on stepped surface of a strained film. The continuum model is derived rigorously from the discrete model for the interaction between steps; thus it incorporates the discrete features of the stepped surfaces. Examples show that our continuum model is much more accurate as an approximation to the discrete model than the traditional continuum approximation. Moreover, in the linear instability of a planar surface, our continuum model gives the transition from step bunching instability to step undulation instability as the distance between adjacent steps increases, which agrees with the experimental observations and the results of discrete models and is missing using the traditional continuum approximation. Numerical simulations of the surface evolution using our model in the nonlinear regime show several different surface morphologies, including the morphology of step bunching which cannot be obtained using the traditional continuum approximation.

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Section: Introductionmentioning

confidence: 99%

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Zhu

Xiang

2009

Phys. Rev. B

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“…The dynamics is ruled here by surface diffusion driven by the interplay between isotropic surface energy and elastic energy [12,13]. When the film is infinitely thick or when the substrate is infinitely rigid, different theoretical [14,15] and numerical [16,17,18,19] approaches revealed finite-time singularities enforced by elastic stress concentration which account for experiments in thick films [8,9] where dislocations can finally develop. However, these models can not describe experiments of thin films in the Stranski-Krastanov type of growth [5,6] where the surface organizes smoothly into islands separated by a wetting layer and evolving with a coarsening dynamics under annealing [6].…”

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confidence: 99%

Nonlinear evolution of a morphological instability in a strained epitaxial film

2007

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A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are derived and solved numerically in two and three dimensions. Above some critical thickness, the surface evolves towards an array of islands separated by a wetting layer. The island chemical potential decreases with its volume, so that the system experiences a non-interrupted coarsening described by power laws with a marked dimension dependence.PACS numbers: 81.15.Aa, 68.35.Ct The dynamics of semiconductor thin films is under active scrutiny due to its importance for both fundamental science and technological applications [1,2]. Indeed, thin film elastic instabilities lead to the self-organization of nanostructures [3] potentially useful e.g. for quantum dots, wires and electronic devices with specific confinement properties [4]. A notorious experimental example is Si/Ge films on a Si substrate which exhibit a variety of structures such as pre-pyramids, pyramids, domes and huts [5,6]. Such epitaxial films experience an elastic stress due to the misfit with the substrate which is relaxed by a morphological instability similar to the Asaro-Tiller-Grinfeld thermodynamical instability in solid-liquid interfaces [7]. This instability was first observed in experiments in helium at low temperature [8] and more generally in various solid interfaces [9,10,11].Although the evolution of epitaxial films involves many complex phenomena regarding surface energy, intermixing and kinetic processes, we focus here on the main effects ruling the dynamics of the morphological instability in strained films. The dynamics is ruled here by surface diffusion driven by the interplay between isotropic surface energy and elastic energy [12,13]. When the film is infinitely thick or when the substrate is infinitely rigid, different theoretical [14,15] and numerical [16,17,18,19] approaches revealed finite-time singularities enforced by elastic stress concentration which account for experiments in thick films [8,9] where dislocations can finally develop. However, these models can not describe experiments of thin films in the Stranski-Krastanov type of growth [5,6] where the surface organizes smoothly into islands separated by a wetting layer and evolving with a coarsening dynamics under annealing [6]. A crucial issue for these systems is the wetting of the substrate by the film [20,21] which is a good candidate for regularizing the dynamics of the instability. Indeed, crack singularities were circumvented near the instability threshold by considering slope dependent wetting effects [22]. However, the interplay between elastic relaxation, surface energy and wetting interactions is still under active study [23,24] and the description of the long term dynamics of the morphological instability in a thin strained film is an open issue. In this Letter, we present a model based on continuum elasticity which we ...

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“…By means of numerical approaches, it is possible to analyse more in general the evolution as in Refs. [112,113], where the formation of cusps separated by deep trenches was also linked to crack propagation. Several other studies are reported in literature (e.g.…”

Section: Non-linear Effectsmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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Cracklike surface instabilities in stressed solids

Cited by 243 publications

References 11 publications

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Nonlinear evolution of a morphological instability in a strained epitaxial film

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

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