Alexandre Danescu

The Asaro–Tiller–Grinfeld instability revisited

Abstract Deposition of a thin film on a solid substrate in the presence of a misfit leads to a growth instability that favors three-dimensional (3D) morphology of the free surface. The amount of the misfit and the conditions of the film deposition (molecular beam epitaxy) lead to an elastic problem, where surface energy has the same order of magnitude as the bulk energy. The instability occurs at a critical thickness of the film. The value of the critical thickness is shown to be given by the competition between the bulk and surface effects. We investigate (via a Fourier method) the Asaro–Tiller–Grinfeld instability for cubic materials and in the presence of an arbitrary misfit. We solve the problem in the general case and we specialize our results to recover values which are in good agreement with experimental data in the case of a In 1− x Ga x As alloy. We consider in a 3D framework sinusoidal perturbations of the free boundary at arbitrary orientations with respect to crystallographic axes. Thus, we are able to minimize the sum of the bulk and surface energies with respect to the orientation and therefore to predict qualitative aspects of the surface morphology.

Spherical curves design for micro-origami using intrinsic stress relaxation

Selective etching of pre-stressed multi-layered structures releases intrinsic stresses creating flexible microscopic shapes (rolls, spirals, tubes, etc.). A question of major interest is how to control design, composition, and etching process in order to obtain a prescribed macroscopic object? We report here the basic steps for (i) the mechanics of the fine curvature control, (ii) the object design and etching process, and we illustrate our approach by the design and fabrication of a three-dimensional device, two face-to-face spiral caps at optical wavelength scale.

Interface accommodation mechanism for weakly interacting epitaxial systems

We report here an interface accommodation mechanism observed by using in situ grazing incidence X-ray diffraction in the very early stages of Ge epitaxial growth on SrTiO3. This mechanism leads to interface-localized misfit accommodation and involves two regimes: very early dislocation emergence followed by a damped collective oscillatory lattice parameter evolution. We show that this behavior is compatible with the simplest nonlinear Frenkel-Kontorova model assuming the weak elastic-chain/substrate interaction.

Vertical correlations in superlattices using the Grinfeld method

Abstract In this paper, we analyse the energetics of a multilayered structures like, for instance, B/A/B/A substrate . It is well-known that a coherent pre-strained B layer on an A substrate will generally results in a corrugation of the free-surface of the B layer. This behavior is the result of stress relaxation in the B-layer and the phenomenon is known as the Asaro-Tiller-Grinfeld instability. We extend the methods used for a two-layer structure to a multilayered structure and the main application is the vertical correlation in superlattices. We analyse the energetics of a corrugated B layer which is grown on a A/B/A substrate , where the A layers are flat but the intermediate B layer is already corrugated. We show that the self-organization of the second B layer, due to elastic interactions in the bulk, depends on the corrugation of the first B layer and the generic best situation is that of a top-on-top (also called correlated layers) vertical alignment. We also prove that the interaction energy between two successive B layers attains a maximum at a critical thickness of the intermediate A layer. This interaction energy has the same order of magnitude as the elastic energy release due to free-surface corrugation at each upper surface of a B layer.

Fabrication of self-rolling geodesic objects and photonic crystal tubes

This paper presents a stress engineering method that allows the design and fabrication of the analogs of single-wall nanotubes in the class of photonic crystals. The macroscopic shape of the final object is obtained through the stress relaxation of a pre-stressed multilayer planar design. We illustrate the extent of the proposed method by various single-layer and multilayer photonic crystals tubes and micron-scale objects with 5-fold symmetry.

Multiphase mean curvature flows with high mobility contrasts: A phase-field approach, with applications to nanowires

Abstract The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface evolution laws depend also on interface mobility coefficients. Having in mind some applications where highly contrasted or even degenerate mobilities are involved, for which classical phase field models are inapplicable, we propose a new effective phase field approach to approximate multiphase mean curvature flows with mobilities. The key aspect of our model is to incorporate the mobilities not in the phase field energy (which is conventionally the case) but in the metric which determines the gradient flow. We show the consistency of such an approach by a formal analysis of the sharp interface limit. We also propose an efficient numerical scheme which allows us to illustrate the advantages of the model on various examples, as the wetting of droplets on solid surfaces or the simulation of nanowires growth generated by the so-called vapor–liquid–solid method.

A metric-based approach to multiphase mean curvature flows with mobilities

Abstract We summarize in this note a few theoretical and numerical results described with more details in the forthcoming paper [5] devoted to a new phase field model for approximating mean curvature flows. Our work is motivated by the simulation of multiphase mean curvature flows with possibly inhomogeneous surface tensions and mobility coefficients. The key aspect of our model is to incorporate the mobilities not in the phase field energy (which is conventionally the case) but in the metric which determines the gradient flow. We show the consistency of such approach by a formal analysis of the sharp interface limit. We also propose an efficient numerical scheme which allows us to illustrate the advantages of the model on various examples, as the wetting of droplets on solid surfaces or the simulation of nanowires growth generated by the so-called vapor-liquid-solid method.

Self-assembly 'micro-origami' photon cages as hollow micro-resonators

Selective etching of pre-stressed multi-layered structures releases intrinsic stresses creating flexible macroscopic shapes (rolls, spirals, tubes…). Combining mechanical and photonic concepts, we develop an experimental approach by controlling material composition, mask design and etching process in order to obtain prescribed macroscopic 3D hollow optical micro-cavities. New photonic microstructures are proposed for an efficient light trapping in low index media. Cylindrical hollow cavities formed by bending a photonic crystal membrane are designed. Using numerical simulations, strong confinement of photons is demonstrated for very open resonators. The resulting strong light matter interaction can be exploited in optical devices comprising an active material embedded in a low index matrix like polymer or even gaz.

Strain‐Structure Relationship at Meso‐scale for 2D Granular Materials

In an attempt to study the influence of the heterogeneities of a granular sample on its macroscopic behavior, we introduce a meso‐scale in the multi‐scale approach using a partition of a granular sample into sub‐domains surrounded by branch vectors. We investigate the relation between strain and structure at meso‐scale and propose a model able to predict this strain‐structure relationship.

Generalized Stefan Models

In this paper we discuss models able to account for discontinuities of the temperature field across a immaterial interface. Our theory is based on a scalar interfacial field and cover two previously proposed theories of Pried and Shen [6] and Dascalu and Danescu [4]. We briefly present an application to the problem of solidification of an under-cooled liquid.