Calculation of superdiffusion for the Chirikov-Taylor model

It is widely known that the paradigmatic Chirikov-Taylor model presents enhanced diffusion for specific intervals of its stochasticity parameter due to islands of stability, which are elliptic orbits surrounding accelerator mode fixed points. In contrast with normal diffusion, its effect has never been analytically calculated. Here, we introduce a differential form for the Perron-Frobenius evolution operator in which normal diffusion and superdiffusion are treated separately through phases formed by angular wave numbers. The superdiffusion coefficient is then calculated analytically resulting in a Schloemilch series with an exponent beta=3/2 for the divergences. Numerical simulations support our results.     

Cu(111)三维表面岛对表面原子扩散影响的分子动力学研究

采用嵌入原子方法的原子间相互作用势，利用分子动力学方法计算了同质外延生长中不同层数的三维Cu(111)表面岛上表面原子扩散激活能，分析了三维表面岛的层数对表面原子交换扩散和跳跃扩散势垒的影响. 研究结果表明，二维Enrilich-Schwoebel(ES)势垒小于三维ES势垒，且三维ES势垒不随表面岛层数的增加而显著变化. 对于侧向表面为(100)的表面岛，表面原子沿〈011〉方向上的扩散行为，随表面岛层数增加而逐渐变化；在表面岛层数达到3层时，扩散路径上的势垒变化趋于稳定，表面原子扩散以下坡扩散为主. 对于侧面取向为(111)的表面岛，当表面岛层数大于3层后，开始呈现上坡扩散的可能. 关键词： 表面原子 扩散 分子动力学模拟     

Fast dimer diffusion near the island: A computational study

Performing atomic scale simulations, we study the diffusion of small Co clusters on Cu(111) surface in the presence of Co islands. It is revealed that mesoscopic relaxations at the island-substrate interface play an important role during the diffusion events of the clusters. The diffusion barrier of small Co clusters near the islands increases with increasing cluster size. Especially, we find that dimer diffusion near the island with B step is as fast as monomer’s, which might be responsible for the formation of dendritic shaped islands at low temperature.     

The crossover from collective motion to periphery diffusion for two-dimensional adatom-islands on Cu(111)

The diffusion of two-dimensional adatom-islands (up to 100 atoms) on Cu(111) has been studied, using the self-learning kinetic Monte Carlo method (Trushin et?al 2005 Phys. Rev. B 72 115401). A variety of multiple-?and single-atom processes are revealed in the simulations, and the size dependences of the diffusion coefficients and effective diffusion barriers are calculated for each. From the tabulated frequencies of events found in the simulation, we show a crossover from diffusion due to the collective motion of the island to a regime in which the island diffuses through periphery-dominated mass transport. This crossover occurs for island sizes between 13 and 19 atoms. For islands containing 19-100 atoms the scaling exponent is 1.5, which is in good agreement with previous work. The diffusion of islands containing 2-13 atoms can be explained primarily on the basis of a linear increase of the barrier for the collective motion with the size of the island.     

A numerical study on the formation of diffusion flame islands in a turbulent hydrogen jet lifted flame

This paper presents a numerical study on the formation of diffusion flame islands in a hydrogen jet lifted flame. A real size hydrogen jet lifted flame is numerically simulated by the DNS approach over a period of about 0.5 ms. The diameter of hydrogen injector is 2 mm, and the injection velocity is 680 m/s. The lifted flame is composed of a stable leading edge flame, a vigorously turbulent inner rich premixed flame, and a number of outer diffusion flame islands. The relatively long-term observation makes it possible to understand in detail the time-dependent flame behavior in rather large time scales, which are as large as the time scale of the leading edge flame unsteadiness. From the observation, the following three findings are obtained concerning the formation of diffusion flame islands. (1) A thin oxygen diffusion layer is developed along the outer boundary of the lifted flame, where the diffusion flame islands burn in a rather flat shape. (2) When a diffusion flame island comes into contact with the fluctuating inner rich premixed flame, combustion is intensified due to an increase in the hydrogen supply by molecular diffusion. This process also works for the production of the diffusion flame islands in the oxygen diffusion layer. (3) When a large unburned gas volume penetrates into the leading edge flame, the structure of the leading edge flame changes. In this transformation process, a diffusion flame island comes near the leading edge flame. The local deficiency of oxygen plays an important role in this production process.     

The morphology and nucleation kinetics of copper islands during electrodeposition

We describe a study, using in situ transmission electron microscopy, of the shape and nucleation kinetics of three-dimensional islands formed during the electrochemical deposition of copper. By operating an electrochemical cell within an electron microscope, we obtain real-time images of the formation of copper islands on a gold electrode while simultaneously recording electrochemical data such as voltage and current. We first present cyclic voltammetry, where the images show the deposition and stripping processes while the voltammogram demonstrates qualitatively the regimes in which diffusion and surface reaction are the rate limiting steps. We then examine island growth quantitatively under conditions of constant potential. Images recorded during growth at various potentials allow direct visualization of the differences between island shapes in the diffusion limited and kinetically limited growth regimes. Furthermore, a combined analysis of the current transients and the images allows parameters such as the diffusion coefficient, the rate constant and the critical nucleus size to be determined. We discuss these results in the context of electrochemical nucleation and growth models.     

Real-time view of mesoscopic surface diffusion

Photoemission electron microscopy is used to study the thermal decay of Ag islands grown epitaxially on Si(001) surfaces. (2 x 3) Ag reconstructed zones, due to migrating Ag atoms supplied to the surface by the decaying islands, surround each of the islands. The shape of these reconstructed zones depends on the degree of diffusion isotropy in the system. We demonstrate that the imaging of these reconstructed "isocoverage zones" constitutes a unique experimental method for directly observing diffusion fields in epitaxial systems. We describe the dynamics of the thermal decay of the islands and the isozones in the context of a continuum diffusion model.     

MULTIPLE CLUSTER GROWTH OF ULTRA-THIN FILMS WITH ANISOTROPIC EDGE DIFFUSION

The multiple cluster growth of ultra-thin films on a hexagonal substrate with fractal, dendritic and compact morphology has been studied by computer simulation. The influence of the different diffusion processes along island edges on the island shape has been investigated. The results show that the anisotropic corner diffusion induces the dendritic growth, and the anisotropic step diffusion can promote the anisotropic growth and cause the ramified islands growing in three directions. In the case of compact growth, the island shape is mainly determined by the anisotropic corner crossing process. The nonuniform distribution of the multiple cluster formation can be described quantitatively by multifractal. With patterns changing from fractal to compact islands, the width and height of the bell-like or hook-like multifractal spectra increase, while the top f(α) decreases.     

Slope selection of mounds with permeable steps in homoepitaxy

We study the growth of mounds representing stacks of monolayer islands in homoepitaxy assuming terrace-edge-kink mechanism of attachment of atoms to kink sites and allowing a permeability of the single steps. We show that the latter can result in slope selection of the growing mounds at comparatively small values of the Ehrlich-Schwoebel barrier to down-step diffusion. The value of the permeability coefficient at which a slope selection occurs is always very close to the upper limit for complete step permeability. The latter is in agreement with the row-by-row mechanism of step propagation at which the steps are kink-free for most of the time.     

Smoothing of an atomically rough vicinal surface – STM observation and MC simulation

Smoothing of an atomically rough vicinal surface of SrTiO₃ is studied by scanning tunneling microscope (STM) observation and by Monte Carlo (MC) simulation. A complex step pattern that resembles a two-dimensional phase separation pattern is observed on the surface. Analysis of the step pattern during annealing obtained by the STM in comparison with the MC simulation reveals an asymmetry of the relaxation pattern between islands and holes. The asymmetry is attributed to the difference of the mobility of an adatom and an atomic hole, and the asymmetry is enhanced by the step edge diffusion barrier. Values of an effective bond energy and an effective diffusion barrier as well as the surface diffusion coefficient are deduced from the relaxation pattern.     

薄膜外延生长的计算机模拟

以Cu膜为例，用Monte-Carlo算法模拟了薄膜生长的随机过程，并提出了更加完善的模型.在合理选择原子间相互作用计算方法的基础上，考虑了原子的吸附、在生长表面的迁移及迁移所引起的近邻原子连带效应、从生长表面的脱附等过程.模拟计算了薄膜的早期成核情况以及表面粗糙度和相对密度.结果表明，随着衬底温度的升高或入射率的降低，沉积在衬底上的原子逐步由离散型分布向聚集状态过渡形成一些岛核，并且逐步由二维岛核向三维岛核过渡.在一定的原子入射率下，存在三个优化温度，成核率最高时的最大成核温度Tn、薄膜的表面粗糙度最低 关键词： Monte-Carlo算法 计算机模拟 薄膜生长     

Growth mechanisms for wire-like epitaxial gold silicide islands on Si(1 1 0) surfaces

Epitaxial islands grown on various substrates are usually strained because of differences in lattice constants of the materials of the island and the substrate. Shape transition in the growth of strained islands has been proposed as a mechanism for strain relief and a way to form self-organized quantum wires. Shape transition usually leads to an elongated island growth. However, an elongated island growth may also be due to an anisotropic diffusion of material, the anisotropy being imposed by the symmetry of the substrate surface. In the present example, growth of gold silicide wire-like nanostructures on a Si(1 1 0) surface has been investigated by photoemission electron microscopy (PEEM). Growth of elongated unidirectional gold silicide islands, with an aspect ratio as large as 12:1, has been observed by PEEM following gold deposition on the Si substrate and subsequent annealing at the Au-Si eutectic temperature. Distribution of the width and the length of the gold silicide islands as a function of island area shows a feature similar to that for the shape transition. However, detailed investigations reveal that the elongated growth of gold silicide islands is rather mainly due to anisotropic diffusion of gold due to the twofold symmetry of the (1 1 0) surface of the Si substrate.     

Formation of copper islands on a native SiO2 surface at elevated temperatures

A combination of in situ X-ray photoelectron spectroscopy analysis and ex situ scanning electron- and atomic force microscopy has been used to study the formation of copper islands upon Cu deposition at elevated temperatures as a basis for the guided growth of copper islands. Two different temperature regions have been found: (I) up to 250 °C only close packed islands are formed due to low diffusion length of copper atoms on the surface. The SiO₂ film acts as a barrier protecting the silicon substrate from diffusion of Cu atoms from oxide surface. (II) The deposition at temperatures above 300 °C leads to the formation of separate islands which are (primarily at higher temperatures) crystalline. At these temperatures, copper atoms diffuse through the SiO₂ layer. However, they are not entirely dissolved in the bulk but a fraction of them forms a Cu rich layer in the vicinity of SiO₂/Si interface. The high copper concentration in this layer lowers the concentration gradient between the surface and the substrate and, consequently, inhibits the diffusion of Cu atoms into the substrate. Hence, the Cu islands remain on the surface even at temperatures as high as 450 °C.     

Strain-driven morphology of Si1-xGex islands grown on Si(100)

A study has been carried out on the morphology and structure of three-dimensional (3D) SiGe islands grown by molecular beam epitaxy (MBE) on Si(100) substrates. Samples of Si1-xGex alloys have been prepared to investigate the effects either of the alloy composition or of the growth temperature. Atomic force microscopy (AFM) evidenced the growth of 3D islands and transmission electron microscopy (TEM) demonstrated wetting layer growth on Si(100), independently on the deposition conditions. Energy dispersive spectroscopy (EDS) micro-analyses carried out on cross-sections of large Si1-xGex islands with defects allowed a measurement of the Ge distribution in the islands. To the best of our knowledge, these have been the first experimental evidences of a composition change inside SiGe islands. The interpretation of the experimental results has been done in terms of strain-enhanced diffusion mechanisms both of the growing species (Si and Ge) and of small islands.     

Massenspektrometrische untersuchungen der kondensation von dünnen schichten auf fremden unterlagen: II. Wachstums- und desorptionskinetik von Ag auf W

The growth and desorption kinetics of silver films on clean polycrystalline tungsten were investigated with a mass-spectrometric technique. The growth of the crystal phase started in the third monolayer by nucleation. This process occurred initially with increasing supersaturation until steady-state growth conditions were established. The evaporation coefficient β for the room-temperature films was unity. For the high-temperature films β was found to be lower than 1. The light and scanning micrographs showed that the silver films consist of isolated islands with strong epitaxial orientation to the substrate. The thermal desorption spectra confirmed qualitatively the island structure of the deposit. The kinetics data were explaned by the formation of diffusion zones around the growing cluster.     

Real time observation of GeSi/Si(001) island shrinkage due to surface alloying during Si capping

The Si capping of Ge/Si(001) islands was observed by in situ time-resolved transmission electron microscopy. During the initial stages of the Si deposition, islands were observed not only to flatten but also to shrink in volume. This unexpected shrinkage is explained by taking into account the intermixing of the deposited Si with the wetting layer and a consequently induced diffusion of Ge from the islands into the wetting layer. A model of the capping process which takes into account Ge diffusion is presented which is in good agreement with the experimental data.     

Quantum size effect on the diffusion barriers and growth morphology of Pb/Si(111)

An intriguing growth morphology of Pb islands on a Si(111) surface is observed in our STM experiments: the growth of a Pb layer on Pb islands with unstable heights starts from the periphery and moves towards the center, while the nucleation of the next layer on stable Pb islands starts away from the periphery. Using first-principles total energy calculations, we have studied the diffusion barriers of Pb adatoms on a freestanding Pb(111) film as a function of film thickness. The diffusion barriers are found to be very low (<60 meV), and a bi-layer oscillation due to the quantum size effect (QSE) is observed, with a lower barrier on the odd-layered, relatively unstable Pb films. The diffusion barrier difference between the odd- and even-layered film is as large as 40 meV. The observed unusual growth can be attributed to this big difference in the diffusion barriers due to QSE.     

Coalescence in an insular film in the presence of sources I. Decaying sources

The effects of decaying sources have been examined with regard to the time dependence of the critical and mean dimensions of islands of spherical-segment or cylindrical forms for various modes of diffusion transport; the same has been done for the number per unit area and the supersaturation. The size distribution of the islands has also been determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 122–128, November, 1978.We are indebted to V. M. Ievlev for numerous discussions and to A. I. Prokof'ev for assistance with the numerical integration.     

Atomic processes in vacancy island motion on Ag(111)

We present results of molecular dynamics simulations of the motion of monatomic-deep vacancy islands on Ag(111), using interaction potentials from the embedded atom method. The individual processes appearing in a large set of runs, at three different temperatures, are identified. From the statistics thus collected, we find that the predominant mechanism underlying the diffusion of vacancy islands on Ag(111) is the diffusion of atoms along the periphery of the vacancy islands.     

FORMATIONS OF FRACTAL ISLANDS AGGREGATED WITH DISCS IN GAUSSIAN DISTRIBUTION ON NONLATTICE SUBSTRATES

The growth mechanism of fractal islands on a two-dimensional nonlattice substrate with periodic boundary conditions has been investigated by using Monte Carlo technique. Results show that the fractal dimension d_f of the final ramified islands is almost independent of the diffusion step length, mobility and rigid rotation of the islands. The characteristics of the size distribution of the discs in an island do not change the dimension d_f of the island. However, we find that d_f increases linearly with the surface coverage ρ of the system and its slope decreases with the increase of the mean diameter of the discs.