Island growth in submonolayer deposition with aggregation and fragmentation

Island growth is studied in the case of island aggregation and break-up during submonolayer deposition. It is demonstrated that the island size distributions are of the scaling form and the mean island size has a power-law behaviour corresponding to hyperthermal deposition conditions. The corresponding scaling exponents are analytically derived and compared with the simulations by the revised particle coalescence method developed here. The scaling exponents are found to depend only on the homogeneity exponents of aggregation and fragmentation kernels.Received: 4 September 2003, Published online: 30 January 2004PACS: 68.55.-a Thin film structure and morphology - 68.35.Fx Diffusion; interface formation - 36.40.Sx Diffusion and dynamics of clustersPresent addressM. Rusanen: Institut Français du Pétrole, Groupe de Modélisation Moléculaire, BP 311, 92852 Rueil-Malmaison, France;Present address J. Asikainen: HRS F27, ETH Zentrum, 8092 Zürich, Switzerland     

Off-equilibrium fluctuation-dissipation relation in a spin glass

We report new experimental results obtained on the insulating spin glass CdCr_2-2x In_2x S₄. Our experimental setup allows a quantitative comparison between the thermo-remanent magnetisation and the autocorrelation of spontaneous fluctuations of magnetisation, yielding a complete determination of the fluctuation-dissipation relation. The dynamics can be studied both in the quasi-equilibrium regime, where the fluctuation-dissipation theorem holds, and in the deeply ageing regime. The limit of separation of time-scales, as used in analytical calculations, can be approached by use of a scaling procedure.Received: 2 March 2004, Published online: 9 September 2004PACS: 05.70.Ln Nonequilibrium and irreversible thermodynamics - 75.50.Lk Spin glasses and other random magnets - 07.20.Dt Thermometers - 07.55.Jg Magnetometers for susceptibility, magnetic moment, and magnetization measurementsD. Hérisson: Present address: Department of Engineering Sciences - Division of Solid State Physics, Uppsala University, 751 21 Uppsala, SwedenM. Ocio: deceased 21 December 2003     

Confinement of molecular liquids: Consequences on thermodynamic,static and dynamical properties of benzene and toluene

We relate the dynamical behavior of molecular liquids confined in mesoscopic cylindrical pores to the thermodynamic properties, heat capacity and density and to the static structure by combining different experimental methods (H-NMR, calorimetry, elastic and inelastic neutron scattering, numerical simulations). The crystallization process is greatly reduced or avoided by confinement under standard cooling conditions, instead a glass transition temperature T _g at the 1000s time scale can be observed. The pore averaged local structure of the confined liquid is not noticeably affected when excluded-volume corrections are carefully applied, but follows the density changes reflected by the Bragg peak intensities of the porous matrices. The pore size dependence of T _g is dominated by two factors, surface interaction and finite-size effect. For the smallest pores ( , being the van der Waals radius of a molecule), one observes an increase of T _g and a broadening of the transition region, related to the interaction with the surface that induces a slowing-down of the molecules close to the wall. This is confirmed by neutron scattering experiments and molecular-dynamics simulations at shorter time scales and higher temperatures, which indicate a remaining fraction of frozen molecules. For larger pore sizes, taking the decrease of density under confinement conditions into account, a decrease of T _g is observed. This could be related to finite-size effects onto the putative cooperativity length that is often invoked to explain glass formation. However, no quantitative determination of this length (not to mention its T-dependence) can be extracted, since the interaction with the wall itself introduces an additional length that adds to the complexity of the problem.Received: 1 January 2003, Published online: 30 October 2003PACS: 64.70.Pf Glass transitions - 65.20. + w Thermal properties of liquids: heat capacity, thermal expansion, etc. - 61.12.-q Neutron diffraction and scatteringD. Morineau: Present address: Groupe Matiére Condensée et Matériaux, CNRS-UMR 6626, Bâtiment 11A, Université de Rennes 1, F-35042 Rennes, France.V. Teboul: Present address: Laboratoire des Propriétés Optiques des Matériaux et Applications, CNRS-UMR 6136, Université dAngers, F-49045 Angers, France.Y. Xia: Present address: School of Chemistry, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.     

Grain size distributions for competitive growth with nucleation

The paper introduces and discusses an idealized competitive growth model with nucleation for the microstructure formation during dense branching phase separation in thin Al/Ge films. Grain size and grain length distributions for the new model are obtained analytically and by simulation. These distributions exhibit a characteristic scaling form similar to cluster size distributions in many other growth models. The cutoff functions in these scaling forms and their influence on the determination of effective exponents are studied in detail. It is found that nucleation introduces a new length scale into the other-wise selfsimilar competitive growth model. This length scale appears only inside the cutoff function and diverges algebraically as the nucleation rate vanishes. We find both analytically and by simulation that the cutoff functions can exhibit stretched exponential behaviour exp(–x ) for large arguments. Our analytical and simulation results for grain size and grain length distributions are in excellent quantitative agreement.     

Phase-field modeling of epitaxial growth: Applications to step trains and island dynamics

In this paper, we present a new phase-field model including combined effects of edge diffusion, the Ehrlich-Schwoebel barrier, deposition and desorption to simulate epitaxial growth. A new free energy function together with a correction to the initial phase variable profile is used to efficiently capture the morphological evolution when a large deposition flux is imposed. A formal matched asymptotic analysis is performed to show the reduction of the phase-field model to the classical sharp interface Burton-Cabrera-Frank model for step flow when the interfacial thickness vanishes. The phase-field model is solved by a semi-implicit finite difference scheme, and adaptive block-structured Cartesian meshes are used to dramatically increase the efficiency of the solver. The numerical scheme is used to investigate the evolution of perturbed circularly shaped small islands. The effect of edge diffusion is investigated together with the Ehrlich-Schwoebel barrier. We also investigate the linear and nonlinear regimes of a step meandering instability. We reproduce the predicted scaling law for the growth of the meander amplitude, which was based on an analysis of a long wavelength regime. New nonlinear behavior is observed when the meander wavelength is comparable to the terrace width. In particular, a previously unobserved regime of coarsening dynamics is found to occur when the meander wavelength is comparable to the terrace width.     

Scaling regimes for second layer nucleation

Nucleation on top of two-dimensional islands with step edge barriers is investigated using scaling arguments. The nucleation rate is expressed in terms of three basic time scales: the time interval between deposition events, the residence time of atoms on the island, and the encounter time required for atoms forming a stable nucleus to meet. Application to the problem of second layer nucleation on growing first layer islands yields a sequence of scaling regimes with different scaling exponents relating the critical island size, at which nucleation takes place, to the diffusion and deposition rates. Second layer nucleation is fluctuation-dominated, in the sense that the typical number of atoms on the island is small compared to , when the first layer island density exponent satisfies . The upper critical nucleus size, above which the conventional mean field theory of second layer nucleation is valid, increases with decreasing dimensionality. In the related case of nucleation on top of multilayer mounds fluctuation-dominated and mean field like regimes coexist for arbitrary values of the critical nucleus size . Received 4 September 2000     

Castaing’s instability in a trapped ultra-cold gas

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to the experiment at JILA [1]. It shows the presence of Castaings instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.Received: 1st October 2002, Published online: 15 July 2003PACS: 03.75.Nt Other Bose-Einstein condensation phenomena - 51.10.+y Kinetic and transport theory of gases - 75.30.Ds Spin wavesO. Prévoté: Present address: Université de Cergy-Pontoise, Département de Physique, 5 mall Gay Lussac, Neuville-sur-Oise, 95031 Cergy-Pontoise, France.     

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

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 t ^1/2, 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. Received 4 May 2000 and Received in final form 8 September 2000     

Finding polymorphic structures during vicinal surface growth

A hybrid scheme is developed to describe vicinal surface growth during epitaxy on two different time and length scales. For this purpose this algorithm combines two modules based on a continuum and an atomistic approach. The continuum module is realized by a phase-field-model which traces back to the Burton–Cabrera–Frank theory, the atomistic module is based on the anisotropic Ising model which is mapped onto a lattice-gas model. The latter provides thermal density fluctuations resulting in adatom clustering. With increasing temperature the probability for island nucleation on the terraces decreases according to 1-p where p is an Arrhenius-type activation probability which prevents clusters from becoming islands. Within this framework it is possible to find the transition from a rough surface at low temperatures to an evenly stepped surface at high temperatures where slight step meandering is observed. Furthermore two competing mechanisms of step bunching are investigated within this scale bridging algorithm: alternating anisotropic diffusion and different Ehrlich–Schwoebel barriers at the step edges. It is shown that a simulation of step bunching displaying the full variety of phenomena observed in experiments can only be achieved by the consideration of different time and length scales.     

Far-infrared probe of size dispersion and population fluctuations in doped self-assembled quantum dots

We investigate the FIR magneto-optical transitions in doped self-assembled InAs quantum dots with an average filling ranging from 0.6 to 6 electrons per dot. Significant changes in the magnetic field dispersion, the line-width and the amplitude of the transitions are observed as the doping level is varied, in agreement with our theoretical calculations. We show that our technique is an effective tool to obtain informations regarding the dot size homogeneity and the electron filling uniformity.Received: 22 July 2003, Published online: 2 October 2003PACS: 73.21.La Quantum dots - 78.20.Ls Magnetooptical effects - 78.30.Fs III-V and II-VI semiconductors - 78.67.Hc Quantum dotsE. Deleporte: Present address: Laboratoire de Photonique Quantique et Moleculaire, École Normale Superieure de Cachan, 94235 Cachan Cedex, FranceJ.M. Gérard: Present address: CEA-Grenoble DRFMC/SP2M/PSC, Laboratoire de Physique des semiconducteurs, 38054 Grenoble, France     

Self-patterned Si surfaces as templates for Ge islands ordering

We propose a two-step process, which is based on substrate nano-patterning by means of growth instabilities in a first step and self-assembling of Ge dots on the top of surface instabilities in a second step. We used the instabilities that develop during the growth of Si(Ge) layers on both nominal and vicinal Si (1 1 1) or (0 0 1) surfaces. Depending on the growth conditions (Ge concentration, growth temperature, thickness), various growth instability regimes were observed: pure kinetic regime, kinetically activated strain-induced regime and pure strain-driven regime. In the case of Si/Si growth, kinetic instabilities developed at different growth temperatures depending on the surface orientation. The critical exponents describing evolution with time have been determined: amplitude At^β and wavelength Lt^α. Experimental results show that each instability regime appears for a given growth temperature range that critically depends on the concentration of Ge. Evolution with time also depends on the Ge concentration. But in all cases, we evidence discrepancies between the experimental critical exponents and those predicted by classical modelling. We also give some examples of Ge dots self-organization on substrates nano-patterned (periodically undulated) by means of the different growth instabilities described above. In all cases, we observe Ge dots ordering along the substrate undulations due to step and/or strain effects. On kinetic instabilities (Si/Si(0 0 1) vicinal), Ge islands preferentially nucleate on step bunches. On SiGe(0 0 1) template layers, Ge dots nucleate on top of the SiGe undulations. In that case, strain gradients improved island ordering. The best ordering was achieved using SiGe(0 0 1) 10° off misoriented template layers as a result of almost perfect anisotropic morphology.     

Dynamic scaling, island size distribution, and morphology in the aggregation regime of submonolayer pentacene films

Scaling behavior of the island size distribution through a universal scaling function f(u) is demonstrated for submonolayer pentacene islands in the aggregation regime (0.1相似文献   

Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001)

We study the onset and development of ledge instabilities during growth of vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the formation of periodic patterns at [110] close packed step edges on surfaces vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The corresponding wavelength and its temperature dependence are studied in detail. Simulations suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by dimer nucleation at the step edge. Our results are in agreement with recent continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal surfaces.     

Stability-instability transitions in silicon crystal growth

In order for a crystal to grow, source atoms must be incorporated into the underlying lattice. Typically, this process occurs on the surface in one of two modes: either through island nucleation or through step flow. However, a third, morphologically unstable growth mode has been predicted. Monitoring the surface of ultraflat substrates with an in situ scanning electron microscope, we prove that for the (111) face of silicon there is a transition from stable step flow to morphological instability and then to island nucleation.     

First-principles studies of kinetics in epitaxial growth of III–V semiconductors

We demonstrate how first-principles calculations using density-functional theory (DFT) can be applied to gain insight into the molecular processes that rule the physics of materials processing. Specifically, we study the molecular beam epitaxy (MBE) of arsenic compound semiconductors. For homoepitaxy of GaAs on GaAs (001), a growth model is presented that builds on results of DFT calculations for molecular processes on the β2-reconstructed GaAs (001) surface, including adsorption, desorption, surface diffusion, and nucleation. Kinetic Monte Carlo simulations on the basis of the calculated energetics enable us to model MBE growth of GaAs from beams of Ga and As₂ in atomistic detail. The simulations show that island nucleation is controlled by the reaction of As₂ molecules with Ga adatoms on the surface. The analysis reveals that the scaling laws of standard nucleation theory for the island density as a function of growth temperature are not applicable to GaAs epitaxy. We also discuss heteroepitaxy of InAs on GaAs (001), and report first-principles DFT calculations for In diffusion on the strained GaAs substrate. In particular, we address the effect of heteroepitaxial strain on the growth kinetics of coherently strained InAs islands. The strain field around an island is found to cause a slowing down of material transport from the substrate towards the island, and thus helps to achieve more homogeneous island sizes. Received: 2 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Modelling of kink nucleation and propagation along steps of finite length

A discrete model for kink nucleation and propagation along steps of finite length is developed. The step velocities were calculated as a function of the step length, the first order rate constants, k_s and k_K, for kink nucleation and propagation respectively, and a kink interaction parameter. The two limiting kinetic regimes of short and long steps as well as the intermediate transitional regime were considered. For very short steps, S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, the velocity varied directly with the number of sites S. Steps which met the criterion S² ? $\text{k}{}_{\mathrm{<mtext>K</mtext>}}\text{k}{}_{\mathrm{<mtext>s</mtext>}}$, were shown to have velocities on the order (2k_Kk_s)^{$\text{1}\text{2}$}, independent of step length. Step velocities were constant over large ranges of the kink interaction parameter. The steps were shown to be “sharp” for zero or attractive kink interaction, but with sufficiently large kink repulsion very diffuse steps could be formed. The density of kinks and numbers of kinks nucleated along an atom row were also calculated.     

Role of patterning in islands nucleation on semiconductor surfaces

Quantum dots (QDs) grown on semiconductors surfaces are actually the main researchers' interest for applications in the forthcoming nanotechnology era. New frontiers in nanodevice technology rely on the precise positioning of the nucleation site and on controlling the shape and size of the dots. In this article we will review some recent studies regarding the control of the nucleation process on semiconductor surfaces. A few approaches to form ordered patterns on surfaces are described: natural patterning induced by surface instabilities (as step bunching or step meandering), in situ substrate patterning by Scanning Tunneling Microscopy (STM), high resolution patterning by Focused Ion Beam (FIB). Growth of epitaxial layers of semiconductors (Ge/Si(100) and InAs/GaAs(100)) on patterned surfaces has been studied by STM or Atomic Force Microscopy (AFM) unveiling the way in which the first atoms start to aggregate and identifying their exact nucleation site. Control of the dot size to match the patterning typical wavelength has been achieved by using surfactants on misoriented substrates. STM images acquired in real time allows one to identify the mechanism of Ge cluster formation on patterned Si(100), and to follow the island transition from pre-pyramid to pyramid. Nucleation of ordered Ge dots on SiO₂ substrates has been obtained thanks to FIB tight patterning, achieving island densities of 3.5×10¹⁰/cm². To cite this article: N. Motta et al., C. R. Physique 7 (2006).     

Exchange processes in interlayer diffusion – kinks, corners and the growth mode

Interlayer diffusion, i.e. mass transport between different terraces, is known to be an essential process for obtaining layer-by-layer growth, avoiding formation of three-dimensional (3D) islands when growing thin films. We present experimental results for the growth of cobalt on Pt (111), which demonstrate the importance of kinks and corners for interlayer diffusion. We show that Co grows two-dimensionally as long as strain caused by the Pt-Co interface keeps the step edges rough, with a high kink density, and then transforms to 3D growth with straight steps. The results for growth with adsorbed carbon monoxide show that CO acts as a surfactant, causing two-dimensional growth unless heterogeneous nucleation occurs. Again, this process is related to roughening of the steps, being a new mechanism for the action of a surfactant. A scanning tunneling microscopy study at the atomic scale confirms the fact that step descent happens only at kinks and (concave) corners, and in conjunction with simulations allows us to identify some of the relevant atomic-exchange processes. We finally argue that the dependence of the growth mode on the step morphology, together with straightening of the steps by step–step interaction, can lead to an instability of the growth mode. Received: 27 March 2000 / Accepted: 4 September 2000 / Published online: 7 March 2001     

Adatom diffusion on vicinal surfaces with permeable steps

We study the behavior of single atoms on an infinite vicinal surface assuming certain degree of step permeability. Assuming complete lack of re-evaporation and ruling out nucleation the atoms will inevitably join kink sites at the steps but will do many attempts before that. Increasing the probability for step permeability or the kink spacing lead to increase of the number of steps crossed before incorporation of the atoms into kink sites. The asymmetry of the attachment-detachment kinetics (Ehrlich-Schwoebel effect) suppresses the step permeability and completely eliminates it in the extreme case of the infinite Ehrlich-Schwoebel barrier. A negligibly small drift of the adatoms in a direction perpendicular to the steps leads to a significant asymmetry of the distribution of the permeability events, the atoms thus visiting more distant steps in the direction of the drift. The curves are fitted with an exponential function containing a constant which can be considered as a length scale of the effect of the drift. Some conclusions concerning the stability of the vicinals are drawn.      

Fragment charge correlations and spinodal decomposition in finite nuclear systems

Enhanced production of events with almost equal-sized fragments is experimentally revealed by charge correlations in the multifragmentation of a finite nuclear system selected in ¹²⁹Xe central collisions on ^nat Sn. The evolution of their weight with the incident energy: 32, 39, 45, 50 AMeV, is measured. Dynamical stochastic mean-field simulations performed at 32 AMeV, in which spinodal instabilities are responsible for multifragmentation, exhibit a similar enhancement of this kind of events. The above experimental observation evidences the spinodal decomposition of hot finite nuclear matter as the origin of multifragmentation in the Fermi energy regime.Received: 22 November 2002, Revised: 22 April 2003, Published online: 30 September 2003PACS: 25.70.Pq Multifragment emission and correlations - 24.60.Ky Fluctuation phenomenaG. Tabacaru: Present address: Cyclotron Institute, Texas A&M University, College station, Texas 77845, USA.N. Le Neindre: Permanent address: Institut de Physique Nucléaire, IN2P3-CNRS, F-91406 Orsay cedex, France.