Helium crystals under stress: The Grinfeld instability

Torii, R.; Balibar, S.

doi:10.1007/bf00692612

Cited by 80 publications

(44 citation statements)

References 3 publications

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“…For the nonlinear evolution beyond the instability, see [21,22] for analytical work and [23] for phase-field modeling. Concerning experiments, very clean realizations of this instability have been observed in Helium crystals [24] and single crystal polymer films [25].…”

Section: Grinfeld Instability -Classical Way Of Calculation; Effementioning

confidence: 96%

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

2011

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We investigate two destabilization mechanisms for elastic polymer films and put them into a general framework: first, instabilities due to in-plane stress and second due to an externally applied electric field normal to the film's free surface. As shown recently, polymer films are often stressed due to out-of-equilibrium fabrication processes as e.g. spin coating. Via an Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease its energy by undulating its surface by surface diffusion of polymers and thereby relaxing stresses. On the other hand, application of an electric field is widely used experimentally to structure thin films: when the electric Maxwell surface stress overcomes surface tension and elastic restoring forces, the system undulates with a wavelength determined by the film thickness. We develop a theory taking into account both mechanisms simultaneously and discuss their interplay and the effects of the boundary conditions both at the substrate and the free surface.

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Section: Grinfeld Instability -Classical Way Of Calculation; Effementioning

confidence: 96%

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

2011

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“…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].…”

mentioning

confidence: 99%

“…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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“…23 Further studies using piezoelectric transducers confirmed that the corrugations were stress induced. 23 Thin films of InGaAs on GaAs 24 and Si͞Ge, 16,25,26 where lattice mismatch causes stresses of a few GPa, have also exhibited the Grinfeld instability. Crack-like corrugations were observed in a crystallized polymer, and the authors speculated that the stress was due to the preferential orientation of the crystallization.…”

Section: Discussionmentioning

confidence: 92%

Surface microstructure of Zr_41.25Ti_13.75Cu_12.5Ni_10.0Be_22.5, a bulk metallic glass

et al. 1996

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The surface of Zr 41.25 Ti 13.75 Cu 12.5 Ni 10.0 Be 22.5 , a bulk metallic glass prepared by RF induction melting, has been imaged using atomic force microscopy. The untreated surfaces were very smooth; features were no higher than 3 nm over a 10 3 10 mm region, comparable to many polished surfaces. Two types of microstructure were also observed; periodic striations forming either a striped or a checkered structure were present, with wavelengths between 1 and 2 mm, and amplitude of approximately 2 nm; in other cases, "cracked mud"-like patterns were observed. These microstructures could be related to strain-induced surface roughening; preliminary calculations are presented that are consistent with this hypothesis.

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Helium crystals under stress: The Grinfeld instability

Cited by 80 publications

References 3 publications

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

Nonlinear evolution of a morphological instability in a strained epitaxial film

Surface microstructure of Zr_41.25Ti_13.75Cu_12.5Ni_10.0Be_22.5, a bulk metallic glass

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Helium crystals under stress: The Grinfeld instability

Cited by 80 publications

References 3 publications

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

Nonlinear evolution of a morphological instability in a strained epitaxial film

Surface microstructure of Zr41.25Ti13.75Cu12.5Ni10.0Be22.5, a bulk metallic glass

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Product

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Surface microstructure of Zr_41.25Ti_13.75Cu_12.5Ni_10.0Be_22.5, a bulk metallic glass