Jean-Noël Aqua

Density profiles in a classical Coulomb fluid near a dielectric wall. I. Mean-field scheme

The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant ∈w are studied from the first Born–Green–Yvon (BGY) equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when ∈w>1, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the density profiles vary very fast in the vicinity of the wall when ∈w≠1. The formal solution of the associated inhomogeneous Debye–Hückel equations will be given in Paper II, together with a systematic fugacity expansion which allows to retrieve the results obtained from the truncated BGY hierarchy. In the present paper the exact density profiles are calculated analytically up to first order in the coupling parameter. The expressions show the interplay between three effects: the geometric repulsion from the impenetrable wall; the electrostatic effective attraction (∈w>1) or repulsion (∈w<1) due to its dielectric response; and the Coulomb interaction between each charge and the potential drop created by the electric layer which appears as soon as the system is not symmetric. We exhibit how the charge density profile evolves between a structure with two oppositely-charged layers and a three-layer organization when ∈w varies. (The case of two ideally conducting walls will be displayed elsewhere).

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. II. Weak-Coupling Systematic Expansions

In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different at short or large distances from the wall. This variation is involved in the inhomogeneous Debye–Hückel equation obeyed by the screened pair potential. Then the main difficulty lies in the determination of the latter potential at every distance. We solve this problem by devising a systematic expansion with respect to the ratio of the fundamental length scales involved in the two coulombic effects at stake. (The application of this method to a plasma confined between two ideally conducting plates and to a quantum plasma will be presented elsewhere). As a result we derive the exact analytical perturbative expressions for the density profiles up to first order in the coupling between charges. The mean-field approach displayed in Paper I is then justified.

Density profiles in a quantum Coulomb fluid near a hard wall

Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any regularization. In the framework of the grand-canonical ensemble, we use an equivalence with a classical system of loops with random shapes, based on the Feynman–Kac path-integral representation of the quantum Gibbs factor. After systematic resummations of Coulomb divergences in the Mayer fugacity expansions of loop densities, there appears a screened potential φ. It obeys an inhomogeneous Debye–Hückel equation with an effective screening length which depends on the distance from the wall. The formal solution for φ can be expanded in powers of the ratios of the de Broglie thermal wavelengths λαs of each species α and the limit of the screening length far away from the wall. In a regime of low degeneracy and weak coupling, exact analytical density profiles are calculated at first order in two independent parameters. Because of the vanishing of wave-functions close to the wall, density profiles vanish gaussianly fast in the vicinity of the wall over distances λαs, with an essential singularity in Planck constant ħ. When species have different masses, this effect is equivalent to the appearance of a quantum surface charge localized on the wall and proportional to ħ at leading order. Then, density profiles, as well as the electrostatic potential drop created by the charge-density profile, also involve a term linear in ħ and which decays exponentially fast over the classical Debye screening length ξD. The corresponding contribution to the global surface charge exactly compensates the charge in the very vicinity of the surface, so that the net electric field vanishes in the bulk, as it should.

Classical and quantum algebraic screening in a Coulomb plasma near a wall: A solvable model

The static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/y3, though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y3 tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled.

Tailoring Strain and Morphology of Core–Shell SiGe Nanowires by Low-Temperature Ge Condensation

Selective oxidation of the silicon element of silicon germanium (SiGe) alloys during thermal oxidation is a very important and technologically relevant mechanism used to fabricate a variety of microelectronic devices. We develop here a simple integrative approach involving vapor-liquid-solid (VLS) growth followed by selective oxidation steps to the construction of core-shell nanowires and higher-level ordered systems with scalable configurations. We examine the selective oxidation/condensation process under nonequilibrium conditions that gives rise to spontaneous formation of core-shell structures by germanium condensation. We contrast this strategy that uses reaction-diffusion-segregation mechanisms to produce coherently strained structures with highly configurable geometry and abrupt interfaces with growth-based processes which lead to low strained systems with nonuniform composition, three-dimensional morphology, and broad core-shell interface. We specially focus on SiGe core-shell nanowires and demonstrate that they can have up to 70% Ge-rich shell and 2% homogeneous strain with core diameter as small as 14 nm. Key elements of the building process associated with this approach are identified with regard to existing theoretical models. Moreover, starting from results of ab initio calculations, we discuss the electronic structure of these novel nanostructures as well as their wide potential for advanced device applications.

Shape and coarsening dynamics of strained islands.

We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semiconductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elastocapillary effect. We first describe both analytically and numerically the formation of an equilibrium island using a two-dimensional continuous model. We have found that these equilibrium island-like solutions have a maximum height h_{0} and they sit on top of a flat wetting layer with a thickness h_{w}. We then consider two islands, and we report that they undergo a noninterrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasistatic dynamics, where the mass transfers are proportional to the chemical potential difference of the islands. It is associated with a time scale t_{c} that is a function of the distance d between the islands and leads to the shrinkage of the smallest island. Once its height becomes smaller than a minimal equilibrium height h_{0}^{*}, its mass spreads over the entire system. Our results pave the way for a future analysis of coarsening of an assembly of islands.

New strategies for producing defect free SiGe strained nanolayers

Strain engineering is seen as a cost-effective way to improve the properties of electronic devices. However, this technique is limited by the development of the Asarro Tiller Grinfeld growth instability and nucleation of dislocations. Two strain engineering processes have been developed, fabrication of stretchable nanomembranes by deposition of SiGe on a sacrificial compliant substrate and use of lateral stressors to strain SiGe on Silicon On Insulator. Here, we investigate the influence of substrate softness and pre-strain on growth instability and nucleation of dislocations. We show that while a soft pseudo-substrate could significantly enhance the growth rate of the instability in specific conditions, no effet is seen for SiGe heteroepitaxy, because of the normalized thickness of the layers. Such results were obtained for substrates up to 10 times softer than bulk silicon. The theoretical predictions are supported by experimental results obtained first on moderately soft Silicon On Insulator and second on highly soft porous silicon. On the contrary, the use of a tensily pre-strained substrate is far more efficient to inhibit both the development of the instability and the nucleation of misfit dislocations. Such inhibitions are nicely observed during the heteroepitaxy of SiGe on pre-strained porous silicon.