Anomalous scaling in epitaxial growth on vicinal surfaces: meandering and mounding instabilities in a linear growth equation with spatiotemporally correlated noise

We have undertaken an extensive analytical and kinetic Monte Carlo study of the (2+1) dimensional discrete growth model on a vicinal surface. A non-local, phenomenological continuum equation describing surface growth in unstable systems with anomalous scaling is presented. The roughness produced by unstable growth is first studied considering various effects in surface diffusion processes (corresponding to temperature, flux, diffusion anisotropy). We found that the thermally activated roughness is well-described by a generalized Lai–Das Sarma–Villain model with non linear growth continuum equation and uncorrelated noise. The corresponding critical exponents are computed analytically for the first time and show a continuous variation in agreement with simulation results of a solid-on-solid model. However, the roughness related to the meandering instability is found, unexpectedly, to be well described by a linear continuum equation with spatiotemporally correlated noise.     

Computer simulations of the Stranski-Krastanov growth of heteroepitaxial films with elastic anisotropy

A three-dimensional finite element method is developed to simulate the surface morphological evolution during the Stranski-Krastanov heteroepitaxial growth. In the formulation, the surface evolves through surface diffusion driven by the gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy and surface energy. Surface condensation rate is assumed to depend on the difference between the surface chemical potential and the chemical potential of the vapor phase. Our simulations reveal that the self-assembly of quantum dots are strongly dependent on the variation of growth rate and elastic anisotropy strength. With appropriate choice of growth rate and elastic anisotropy strength, a relatively more uniform and regular quantum dot array can be obtained.     

Interfacial pattern formation far from equilibrium

Over the past few years diffusion-controlled systems have been shown to share a common set of interfacial morphologies. The singular nature of the microscopic dynamics of surface tension and kinetic growth far from equilibrium are critical to morphology selection, with special importance attributed to the anisotropy of these effects. The morphologies which develop can be organized via a morphology diagram according to the driving force and the effective anisotropy. We focus on the properties of the dense-branching morphology (DBM) which appears for sufficiently weak effective anisotropy, and the nature of morphology transitions between the DBM and dendritic growth stabilized by either surface tension or kinetic effects. The DBM is studied in the Hele-Shaw cell, and its structure analyzed by linear stability analysis. A comparison is made between the power spectrum of the structure and the stability analysis. We then provide a detailed account of the morphology diagram and morphology transitions in an anisotropic Hele-Shaw cell. Theoretically the question of morphology transitions is addressed within the boundary-layer model by computing selected velocities as a function of the undercooling for different values of the surface tension and the kinetic term. We argue that the fastest growing morphology is selected whether it is the DBM, surface tension dendrites, or kinetic dendrites. A comparison is made with our experimental results in electrochemical deposition for the correspondence between growth velocities and morphology transitions.     

薄膜层状外延生长的光学原位实时监测方法

综述了几种用于监控薄膜外延生长的光学原位实时监测方法的进展。其中光反射差法／光反射各向异性谱（ＲＤＳ／ＲＡＳ）和ｐ偏振反射谱（ＰＲＳ），表面光吸收（ＳＰＡ），椭偏仪（ＳＥ）等。在外延过程中已观测到了薄膜层状外延周期振荡。     

Surface modes with biquadratic coupling and uniaxial anisotropy in semi-infinite Heisenberg antiferromagnet

We address the role and the influence of both biquadratic exchange and uniaxial anisotropy in the study of bulk and surface magnetic excitations for a two-sublattices semi-infinite Heisenberg antiferromagnet. The calculations apply to combined effect and are based on a matching technique within the framework of both non-interacting spin-wave theory and random phase approximation. Emphasis has been laid upon the advantage of handling bulk and surface spin precessional fields, characterized by their symmetry in particular. Analytic expressions for the bulk and surface equations of motion are also derived which enables us to analyze qualitatively the nature of the modes by observing the response of the energy branches to the variation of both biquadratic exchange and single-ion anisotropy field as well as exchange parameters occurring on the surface. Two numerical applications of the theoretical formalism developed in this work are described. First concerns the situation when the free surface model is assumed. The second application considers the existence of surface perturbations and treats the effects of the presence of biquadratic exchange term on the bulk and surface spin-wave spectra showing two kinds of surface propagating modes which depend on the presence or not of the uniaxial anisotropy contribution and also on the variations of the bulk-surface exchange parameters. A significant conclusion which this work reached relates to the checking of the results obtained in the literature by using our own theoretical formalism. We show that this formalism is very well adapted to calculations of localized bulk and surface spin-wave modes associated with the simultaneous presence of biquadratic exchange and uniaxial anisotropy. Also, the results obtained for the bulk spin fluctuations field as well as for the magnetic surface waves, are found to be in qualitative agreement with those obtained in the literature. The analytic formulation presented in this work provides an accurate and practical scheme for calculating the surface spin dynamics under the influence of surface exchange parameters, biquadratic coupling and uniaxial anisotropy terms.     

On the microscopic origin of the kinetic step bunching instability on vicinal Si(0 0 1)

A scanning tunneling microscopy/atomic force microscopy study is presented of a kinetically driven growth instability, which leads to the formation of ripples during Si homoepitaxy on slightly vicinal Si(0 0 1) surfaces miscut in [1 1 0] direction. The instability is identified as step bunching, that occurs under step-flow growth conditions and vanishes both during low-temperature island growth and at high temperatures. We demonstrate, that the growth instability with the same characteristics is observed in two dimensional kinetic Monte Carlo simulation with included Si(0 0 1)-like diffusion anisotropy. The instability is mainly caused by the interplay between diffusion anisotropy and the attachment/detachment kinetics at the different step types on Si(0 0 1) surface. This new instability mechanism does not require any additional step edge barriers to diffusion of adatoms. In addition, the evolution of ripple height and periodicity was analyzed experimentally as a function of layer thickness. A lateral “ripple-zipper” mechanism is proposed for the coarsening of the ripples.     

Morphological anisotropy during migration enhanced epitaxy of GaAs(0 0 1)

The GaAs(0 0 1) surface morphology and structure during growth by migration enhanced epitaxy (MEE) has been studied by reflection high energy electron diffraction and scanning tunneling microscopy. Changes induced by varying the incident As/Ga flux ratio, growth temperature and the total amount of material deposited in each cycle have been studied and the results compared with GaAs(0 0 1) growth by conventional molecular beam epitaxy (MBE). Comparison of the surface morphology at the end of the Ga and As cycles indicates no clear evidence for any enhancement in the Ga adatom diffusion length during the Ga cycle. However, the morphological anisotropy of the growth front does change significantly and it is proposed that this changing anisotropy during MEE enables Ga adatom diffusion along both azimuths. The surface anisotropy during MEE growth is found to increase with the Ga/As ratio. Although there is a clear correlation between composition and morphology, we have also found that highly ordered and flat surfaces are not necessarily an indication of stoichiometric material. We also attempt to clarify a recent controversy on the structure of the c(4 × 4) reconstruction by studying the surface structure at the end of the As cycle as a function of the As/Ga ratio.     

Anisotropic surface tension and the liquid drop model

The liquid drop model assumes that the surface tension of all nuclei is isotropic. The consequences of relaxing this assumption are studied. First a macroscopic theory of anisotropic surface tension is presented. Then with a particular choice for the functional form of the surface tension tensor, this theory is applied to a charged liquid drop. A small anisotropy in the surface tension can significantly distort a highly charged drop and lower its fission barrier.     

Self-organized formation of shell-like InAs/GaAs quantum dot ensembles

Formation of a multimodal quantum dot (QD) ensemble by strained layer epitaxy of InAs on GaAs near the critical value for the onset of the 2D-3D transition is studied. Reflection anisotropy spectroscopy is employed to confirm that a smooth surface is maintained during strained layer growth prior to QD formation. Instantaneous capping after deposition leads to InAs quantum wells with some thickness flucuations. Multimodal QD InAs ensembles form after an at least short growth interruption prior to cap layer deposition. The QDs consist of pure InAs with heights varying in steps of complete InAs monolayers. Related exciton energies indicate a simultaneous increase of both height and lateral extension, i.e. a shell-like increase of sizes. The formation of the multimodal QD ensemble is described by a kinetic approach. A growth scenario is presented where QDs having initially shorter base length stop vertical growth at a smaller height, accounting for the experimentally observed shell-like sub-ensemble structure.     

Diffusion versus sticking anisotropy: Anisotropic growth of organic molecular films

The molecular/crystal orientation and morphology of active molecular structures is a key determinant for the function of nanoscaled organic devices, yet little is known regarding the processes that govern thin film growth. Here, we show that either sticking or diffusion anisotropy can control the growth depending on preparation conditions. This is illustrated by an investigation into the growth of sexiphenyl (6P) on the anisotropic TiO₂(1 1 0)-(1 × 1) single crystal surface. The great differences in crystallite orientation and morphology observed are explained by the domination of the growth kinetics by either sticking or diffusion anisotropy depending on growth temperature.     

Spin-wave theory for the dynamics induced by direct currents in magnetic multilayers

A spin-wave theory is presented for the magnetization dynamics in a ferromagnetic film that is traversed by spin-polarized carriers at high direct-current densities. It is shown that nonlinear effects due to four-magnon interactions arising from dipolar and surface anisotropy energies limit the growth of the driven spin wave and produce shifts in the microwave frequency oscillations. The theory explains quantitatively recent experimental results in nanometric point contacts onto magnetic multilayers showing downward frequency shifts (redshifts) with increasing current, if the external field is on the film plane, and upward shifts (blueshifts), if the field is perpendicular to the film.     

Acoustic waves generated by a laser point pulse in a transversely isotropic cylinder

A three-dimensional (3D) model is presented to predict the acoustic waves generated by a laser point pulse in a transversely isotropic cylinder. The Fourier series expansion and the two-dimensional Fourier transform are introduced to calculate the 3D transient response under either the ablation or the thermoelastic generation. The presented physical model and the numerical inverse scheme are applied to a fiber reinforced composite cylinder with a strong anisotropy. Experimental radial displacements of the cylinder surface are detected by the laser ultrasonic technique and analyzed by the ray trajectories for both generation regimes. Corresponding theoretical displacements are obtained numerically and compared to the experimental signals. Good agreement is found between theoretical and experimental results. The focusing effects that anisotropy gives rise to are observed in both theory and experiment under either regime.     

Model Studies of Rayleigh Instabilities via Microdesigned Interfaces

The energetic and kinetic properties of surfaces play a critical role in defining the microstructural changes that occur during sintering and high-temperature use of ceramics. Characterization of surface diffusion in ceramics is particularly difficult, and significant variations in reported values of surface diffusivities arise even in well-studied systems. Effects of impurities, surface energy anisotropy, and the onset of surface attachment limited kinetics (SALK) are believed to contribute to this variability. An overview of the use of Rayleigh instabilities as a means of characterizing surface diffusivities is presented. The development of models of morphological evolution that account for effects of surface energy anisotropy is reviewed, and the potential interplay between impurities and surface energy anisotropy is addressed. The status of experimental studies of Rayleigh instabilities in sapphire utilizing lithographically introduced pore channels of controlled geometry and crystallography is summarized. Results of model studies indicate that impurities can significantly influence both the spatial and temporal characteristics of Rayleigh instabilities; this is attributed at least in part to impurity effects on the surface energy anisotropy. Related model experiments indicate that the onset of SALK may also contribute significantly to apparent variations in surface diffusion coefficients.     

Noise field anisotropy of surface sources in a coastal region with arbitrary bottom relief and sound velocity profile

The noise field anisotropy of surface sources in a coastal region with an arbitrary three-dimensional bottom relief and an arbitrary sound velocity profile is investigated. The results of computations performed by a computer code in two stages are presented. The first stage consists in the computation of horizontal rays, i.e., the projections of the real rays multiply reflected from the bottom and sea surface onto the horizontal plane. The second stage summarizes the contributions of the noise sources lying within the surface elements that are cut out on the sea surface by a narrow ray tube launched from the point of observation in a given direction. The computations show that, in the coastal region, the noise field is essentially anisotropic, and this anisotropy occurs not only in the vertical plane, which is characteristic of the deep ocean, but in the horizontal plane as well.     

Experimental Measurement of Anisotropy in Crystal-Melt Interfacial Energy

Experimental methods for the determination of anisotropy in crystal-melt interfacial energy are explored. Equilibrium shape measurements of liquid droplets entrained in single-phase solid are utilized and results are reported for an Al-Cu and an Al-Si alloy. The grain boundary groove method for determination of interfacial energy anisotropy is also examined. A complete coupled-groove solution is presented for a general tilt-boundary groove. The effects of various physical parameters, including interface energy anisotropy, on the groove shape are discussed.     

Optimized growth of compensated ferrimagnetic insulator Gd_3Fe_5O_(12) with a perpendicular magnetic anisotropy

Compensated ferrimagnetic insulators are particularly interesting for enabling functional spintronic,optical,and microwave devices.Among many different garnets,Gd_3 Fe_5 O_(12)(GdIG) is a representative compensated ferrimagnetic insulator.In this paper,we will study the evolution of the surface morphology,the magnetic properties,and the magnetization compensation through changing the following parameters:the annealing temperature,the growth temperature,the annealing duration,and the choice of different single crystalline garnet substrates.Our objective is to find the optimized growth condition of the GdIG films,for the purpose of achieving a strong perpendicular magnetic anisotropy(PMA) and a flat surface,together with a small effective damping parameter.Through our experiments,we have found that the surface roughness approaching 0.15 nm can be obtained by choosing the growth temperature around 700℃,together with an enhanced PMA.We have also found the modulation of magnetic anisotropy by choosing different single crystalline garnet substrates which change the tensile strain to the compressive strain.A measure of the effective magnetic damping parameter(α_(eff)=0.04 ± 0.01) through a spin pumping experiment in a GdIG/Pt bilayer is also made.Through optimizing the growth dynamics of GdIG films,our results could be useful for synthesizing garnet films with a PMA,which could be beneficial for the future development of ferrimagnetic spintronics.     

薄膜中异常晶粒生长理论及能量各向异性分析

针对柱状晶薄膜，建立了异常晶粒生长理论模型.指出薄膜中的晶粒生长，除像传统的整体材料中的晶粒生长一样考虑晶界能外，还应当考虑表面能、界面能和应变能.对能量的各向异性进行了回顾性分析.从表面能的最小化考虑，面心立方和体心立方薄膜的择优取向或织构应分别为（111）和（110）；而从应变能的最小化考虑，面心立方和体心立方薄膜的择优取向或织构应分别为（110）和（100）. 关键词： 薄膜 异常晶粒生长 模型 织构     

Spectroscopic studies of electron surface states on liquid helium

Field-ion microscopy has been previously used [1–4] to determine the surface energy anisotropy of tungsten and iridium. Drechsler and Nicholas [5] have used field emission patterns of equilibrium shapes of emitters to determine the surface energy anisotropies for a number of fcc and bcc metals including α-iron. The purpose of the present paper is to report some observations by field-ion microscopy on the vacuum faceting of α-iron and the surface energy anisotropy at about half the absolute melting point. Qualitative results on the effect of hydrogen on the surface energy anisotropy are also presented.     

Reflectance anisotropy spectroscopy of metal nanoclusters formed on semiconductor surface

Optical anisotropy of indium nanoclusters formed on the (001) surface of indium arsenide was found by differential reflectance anisotropy spectroscopy. The fact of such an observation for nanocluster arrays unambiguously evidences the presence of their macroscopic anisotropy which could not be disclosed by conventional diagnostics techniques. The scale of the observed plasmonic anisotropy signal exceeds by two orders of magnitude the scale of anisotropy signals from valence-bond structures formed on a semiconductor surface. A resonant feature observed in reflectance anisotropy spectra is interpreted in the model of coupled dipole plasmons belonging to ellipsoidal nanoparticles. Estimation based on the experimental spectra shows that within the sample surface the lengths of ellipsoid semiaxes differ from each other by a few percent.