Olivier Pierre-Louis

Pressure-Mediated Doping in Graphene

Exfoliated graphene and few layer graphene samples supported on SiO(2) have been studied by Raman spectroscopy at high pressure. For samples immersed on a alcohol mixture, an electron transfer of ∂n/∂P ∼ 8 × 10(12) cm(-2) GPa(-1) is observed for monolayer and bilayer graphene, leading to giant doping values of n ∼ 6 × 10(13) cm(-2) at the maximum pressure of 7 GPa. Three independent and consistent proofs of the doping process are obtained from (i) the evolution of the Raman G-band to 2D-band intensity ratio, (ii) the pressure coefficient of the G-band frequency, and (iii) the 2D band components splitting in the case of the bilayer sample. The charge transfer phenomena is absent for trilayer samples and for samples immersed in argon or nitrogen. We also show that a phase transition from a 2D biaxial strain response, resulting from the substrate drag upon volume reduction, to a 3D hydrostatic compression takes place when going from the bilayer to the trilayer sample. By model calculations we relate this transition to the unbinding of the graphene-SiO(2) system when increasing the number of graphene layers and as function of the surface roughness parameters. We propose that the formation of silanol groups on the SiO(2) substrate allows for a capacitance-induced substrate-mediated charge transfer.

Dynamics of solid thin-film dewetting in the silicon-on-insulator system

Using low-energy electron microscopy movies, we have measured the dewetting dynamics of single-crystal Si(001) thin films on SiO2 substrates. During annealing (T>700 °C), voids open in the Si, exposing the oxide. The voids grow, evolving Si fingers that subsequently break apart into self-organized three-dimensional (3D) Si nanocrystals. A kinetic Monte Carlo model incorporating surface and interfacial free energies reproduces all the salient features of the morphological evolution. The dewetting dynamics is described using an analytic surface-diffusion-based model. We demonstrate quantitatively that Si dewetting from SiO2 is mediated by surface-diffusion driven by surface free-energy minimization.

Electromigration of single-layer clusters

Single-layer atom or vacancy clusters in the presence of electromigration are studied theoretically assuming an isotropic medium. A variety of distinctive behaviors distinguish the response in the three standard limiting cases of periphery diffusion (PD), terrace diffusion, and evaporation-condensation. A general model provides power laws describing the size dependence of the drift velocity in these limits, consistent with established results in the case of PD. The validity of the widely used quasistatic limit is calculated. Atom and vacancy clusters drift in opposite directions in the PD limit but in the same direction otherwise. In absence of PD, linear stability analysis reveals a different type of morphological instability, not leading to island breakdown. For strong electromigration, Monte Carlo simulations show that clusters then destabilize into slits, in contrast to splitting in the PD limit. Electromigration affects the diffusion coefficient of the cluster and morphological fluctuations, the latter diverging at the instability threshold. An intrinsic attachment-detachment bias displays the same scaling signature as PD in the drift velocity.

Non-linear evolution of step meander during growth of a vicinal surface with no desorption

Abstract:Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a multiscale analysis. We give the detailed derivation of the highly nonlinear evolution equation on which a brief account has been given [6]. Decomposing the model into driving and relaxational contributions, we give a profound explanation to the origin of the unusual divergent scaling of step meander (where F is the incoming atom flux). A careful numerical analysis indicates that a cellular structure arises where plateaus form, as opposed to spike-like structures reported erroneously in reference [6]. As a robust feature, the amplitude of these cells scales as t1/2, regardless of the strength of the Ehrlich-Schwoebel effect, or the presence of line diffusion. A simple ansatz allows to describe analytically the asymptotic regime quantitatively. We show also how sub-dominant terms from multiscale analysis account for the loss of up-down symmetry of the cellular structure.

“The Princess and the Pea” at the Nanoscale: Wrinkling and Delamination of Graphene on Nanoparticles

Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, resulting from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum elastic model and have important implications for strain-engineering the electronic properties of graphene.

Implications of random-matrix theory for terrace-width distributions on vicinal surfaces : improved approximations and exact results

Abstract Quantitative measurement of the equilibrium terrace-width distribution of vicinal surfaces enables detailed investigation of step–step interactions. Using results from random-matrix theory, we point out simple analytical expressions that assist in this process, improving considerably over standard techniques and allowing assessment of weak repulsions, heretofore inaccessible except by indirect methods. This approach suggests new properties for experimentalists to measure and, by calibration with exact results, provides insights into controversies about assessing the interaction strength.

Dewetting of a Solid Monolayer

We report on the dewetting of a monolayer on a solid substrate, where mass transport occurs via surface diffusion. For a wide range of parameters, a labyrinthine pattern of bilayer islands is formed. An irreversible regime and a thermodynamic regime are identified. In both regimes, the velocity of a dewetting front, the wavelength of the bilayer island pattern, and the rate of nucleation of dewetted zones are obtained. We also point out the existence of a scaling behavior, which is analyzed by means of a geometrical model.

Terrace-width distributions and step–step repulsions on vicinal surfaces: symmetries, scaling, simplifications, subtleties, and Schrödinger

For more than three decades, measurement of terrace width distributions (TWDs) of vicinal crystal surfaces have been recognized as arguably the best way to determine the dimensionless strength A of the elastic repulsion between steps. For sufficiently strong repulsions, the TWD is expected to be Gaussian, with A varying inversely with the squared variance. However, there has been a controversy over the proportionality constant. From another perspective the TWD can be described as a continuous generalized Wigner distribution (CGWD) essentially no more complicated than a Gaussian but a much better approximation at the few calibration points where exact solutions exist. This paper combines concisely the experimentally most useful results from several earlier papers on this subject and describes some advancements that are in progress regarding numerical tests and in using Schrodinger-equation formalism to give greater understanding of the origin of the CGWD and to give hope of extensions to more general interaction potentials between steps. There are many implications for future experiments.

Continuum Model for Low Temperature Relaxation of Crystal Steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step-free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.

Vicinal silicon surfaces: From step density wave to faceting

This paper investigates faceting mechanisms induced by electromigration in the regime where atomic steps are transparent. For this purpose we study several vicinal orientations by means of in-situ (optical diffraction, electronic microscopy) as well as ex-situ (AFM, microprofilometry) visualization techniques. The data show that faceting proceeds in two stages. The first stage is short and leads to the appearance of a step density wave, with a wavelength roughly independent of the surface orientation. The second stage is much slower, and leads to the formation of a hill-and-valley structure, the period of which depends on the initial surface orientation. A simple continuum model enables us to point out why the wavelength of the step density wave does not depend on the microscale details of the surface. The final wavelength is controlled by the competition between elastic step-step interaction and facet edge energy cost. Finally, the surface stress angular dependence is shown to emerge as a coarsed-grained picture from the step model.