点缺陷对表面生长动力学标度行为的影响

基于含噪声Kuramoto-Sivashinsky方程, 采用动力学重正化群技术, 研究生长表面存在点缺陷或杂质对表面生长动力学标度行为的影响, 得到了相应的粗糙度指数α 和动力学标度指数z. 所得结果表明, 点缺陷的存在使生长表面粗化, 并缩短达到稳定生长的弛豫时间.     

分形基底上受限固-固模型动力学性质的数值模拟研究

为了探讨非完整基底结构对生长表面动力学行为的影响,本文在具有相同分形维数而不同谱维数的谢尔宾斯基箭头和蟹状分形基底上对受限固-固(restricted solid-on-solid,RSOS)模型的生长过程进行了大量的数值模拟研究.通过计算表面宽度和饱和表面极值高度的统计行为对生长表面的动力学行为进行了分析.结果表明,分形基底结构对生长表面的动力学行为具有显著的影响.尽管在两种基底上受限固-固模型的表面宽度均表现出很好的动力学标度行为,仍然满足Family-Vicsek标度规律,但由此计算得到的动力学标度指数并不相同.饱和生长表面的极值高度并不能满足三种常用的极值统计分布,即Weibull,Gumbel和Frechet分布,而是能很好地符合Asym2Sig分布.     

非局域Lai-Das Sarma-Villain方程动力学标度性质的研究

使用动力学重整化群和直接标度分析的方法研究了非局域Lai-Das Sarma-Villain方程的动力学标度性质.动力学重整化群分析表明非局域非线性项的存在能够导致新的固定点和连续变化的动力学标度指数的产生.使用直接标度分析方法则分别得到了在弱耦合和强耦合区内的标度指数值.在弱耦合区域内得到的标度指数与动力学重整化方法得到的标度指数值能很好地吻合. 关键词： 表面生长 动力学重整化群分析 标度分析     

Anomalous roughness in dimer-type surface growth

We point out how geometric features affect the scaling properties of nonequilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning valleys (hilltops) develop spontaneously and the surface facets for all growth (evaporation) biases. More intriguingly, the scaling properties of the rough one dimensional equilibrium surface are anomalous. Its width, W approximately Lalpha, diverges with system size L as alpha = 1 / 3 instead of the conventional universal value alpha = 1 / 2. This originates from a topological nonlocal evenness constraint on the surface configurations.     

Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.     

Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation

We consider the coarsening dynamics of multiscale solutions to a dissipative singularly perturbed partial differential equation which models the evolution of a thermodynamically unstable crystalline surface. The late-time leading-order behavior of solutions is identified, through the asymptotic expansion of a maximal-dissipation principle, with a completely faceted surface governed by an intrinsic dynamical system. The properties of the resulting piecewise-affine dynamic surface predict the scaling law L(Mu) approximately t(1/3), for the growth in time of a characteristic morphological length scale L(Mu). A novel computational geometry tool which directly simulates a million-facet piecewise-affine dynamic surface is also introduced. Our computed data are consistent with the dynamic scaling hypothesis, and we report a variety of associated morphometric scaling functions.     

含时空关联噪声的非局域及各向异性Kardar-Parisi -Zhang方程的直接标度分析

将直接标度分析方法推广应用到含时间空间关联噪声的非局域及各向异性KardarParisiZhang方程的动力学标度分析中,分别得到了方程在强耦合区和弱耦合区的标度指数值.在弱耦合区得到的标度指数能与使用动力学重整化方法得到的结果相吻合 关键词： 表面生长 标度分析 KPZ方程     

随机稀释基底上刻蚀模型动力学标度行为的数值模拟研究

表面界面动力学粗化过程是凝聚态物理领域重要的研究内容,为研究基底不完整性对刻蚀模型动力学 标度行为的影响,本文采用Kinetic Monte Carlo(KMC)方法,分析研究了在随机稀释基底上刻蚀模型(Etching model)生长表面的动力学标度行为.研究发现:尽管随机稀释基底的不完整性会对刻蚀表面的动力学 行为产生显著的影响,导致刻蚀表面粗糙度指数和生长指数有明显的增加, 但其仍基本满足原有的动力学标度规律.此外,本文还对刻蚀表面动力学标度指数的有限尺寸效应进行了 分析讨论.     

Anomalous Scaling of Surface Growth Equations with Spatially and Temporally Correlated Noise

Based on the scaling idea of local slopes by López et al. [Phys. Rev. Lett. 94 (2005) 166103], we investigate anomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang (KPZ), Sun-Guo-Grant (SGG), and Lai-Das Sarma-Villain (LDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.     

On the stability of crystal growth

We investigate properties of solid-on-solid models for crystal growth, involving general microscopic rates of capture of atoms by the crystal surface and of escape of atoms. The rates in this Markov process influence the stability of the growing surface. We prove, for various different ranges of the rate parameters, stability (i.e., ergodicity) and instability (i.e., nullity) of the growth process. Symmetry properties of the process, such as reversibility, dynamic reversibility, and reflection invariance, are proved or disproved under various conditions. We give a measure of surface smoothness that distinguishes between stable and unstable growth.     

Generalised Central Limit Theorems for Growth Rate Distribution of Complex Systems

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.     

Surface structures of equilibrium restricted curvature model on two fractal substrates

With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature(ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension df, but possess different dynamic exponents of random walk zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk zrw. The ERC model growing on the two substrates follows the well-known Family–Vicsek scaling law and satisfies the scaling relations 2α + df≈ z ≈ 2zrw. In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins–Herring equation.     

Generic dynamic scaling in kinetic roughening

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation functions, which leads to the different anomalous forms of scaling recently observed in growth models. We derive all the existing forms of anomalous dynamic scaling from a new generic scaling ansatz. The different scaling forms are subclasses of this generic scaling ansatz associated with bounds on the roughness exponent values. The existence of a new class of anomalous dynamic scaling is predicted and compared with simulations.     

生长初期Ta膜的表面动态演化行为

用磁控溅射方法在单晶Si衬底上沉积膜厚为15—250nm的Ta膜.基于原子力显微镜获得的薄膜表面形貌，用动力学标度理论量化表征薄膜表面动态演化行为.结果表明：当膜厚d<50nm时，薄膜生长指数β≈0.17，而d>50nm后β≈0.45；随着d增加，粗糙度指数α由0.24逐渐增加到0.69，且在d>50nm后趋于稳定.Ta膜的表面动态演化行为揭示了其由小岛聚合结构向连续膜演化的生长过程.与自阴影等非局域效应引起的非稳定行为不同的是，当d<50nm时，薄膜表面动态演化的非稳定行为来源于生长初期的小岛聚合，表面小岛沿膜面切向的生长优于沿法向的生长.随着d继续增加，薄膜以连续膜形式生长，表面动态演化趋于稳定.     

分形基底上刻蚀模型动力学标度行为的 数值模拟研究

为探讨分形基底结构对生长表面标度行为的影响, 本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为. 研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为, 并且满足Family-Vicsek标度规律. 虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同, 但模拟得到的标度指数却不同, 并且粗糙度指数 α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2. 由此可以看出, 标度指数不仅与基底的分形维数有关, 而且和分形基底的具体结构有关.     

薄膜生长中的表面动力学(Ⅱ)

本文较全面地从理论上研究了薄膜生长过程中原子在表面上的各种动力学表现，涉及的内容包括亚单层生长时，原子在表面上的扩散，粘接，成核，以及已经形成的原子岛之间的相互作用，兼并，失稳，退化等一系列过程。在第一部分(即0—6章，刊登在《物理学进展》23卷1期上)介绍了薄膜生长动力学的基础之后，从第7章开始我们侧重研究一个在向同性和各向异性表面都普遍成立的原子岛尺寸大小及密度分布的标度定律；建立了一套研究在各向同性和各向异性表面上二维原子岛退化过程的广义动力学标度理论。基于对层间质量扩散通道的研究，本文提出了两种不同的原子下跃机制，既任意跃迁机制和选择跃迁机制，并做了进一步的实验验证。利用这一新的层间质量扩散机制，我们成功地解释了实验上观测到的三维原子岛的退化规律。更加有趣的是，本文讨论了应力对岛的形状和各种动力学规律的影响。在最后我们还提出了一个利用凝聚能转化来控制二维原子岛生长的方法，其目的是希望能够找到一种人为有效地在表面上制备低维量子结构的方法。     

Rapid roughening in thin film growth of an organic semiconductor (diindenoperylene)

The scaling exponents alpha, beta, and 1/z in thin films of the organic molecule diindenoperylene deposited on SiO2 under UHV conditions are determined. Atomic-force microscopy, x-ray reflectivity, and diffuse x-ray scattering were employed. The surface width displays power law scaling over more than 2 orders of magnitude in film thickness. We obtained alpha = 0.684+/-0.06, beta = 0.748+/-0.05, and 1/zeta = 0.92+/-0.20. The derived exponents point to an unusually rapid growth of vertical roughness and lateral correlations. We suggest that they could be related to lateral inhomogeneities arising from the formation of grain boundaries between tilt domains in the early stages of growth.     

Dynamic scaling and optical properties of Zn（S,O, OH） thin film grown by chemical bath deposition

The scaling behavior and optical properties of Zn(S, O and OH) thin films deposited on soda-lime glass substrates by chemical bath deposition method were studied by combined roughness measurements, scanning electron microscopy and optical properties measurement. From the scaling behaviour, the value of growth scaling exponent β , 0.38±0.06, was determined. This value indicated that the Zn(S, O, OH) film growth in the heterogeneous process was influenced by the surface diffusion and shadowing effect. Results of the optical properties measurements disclosed that the transmittance of the film was in the region of 70%-88% and the optical properties of the film grown for 40 min were better than those grown under other conditions. The energy band gap of the film deposited with 40 min was around 3.63 eV.     

Kinetic growth mechanisms of sputter-deposited Au films on mica: from nanoclusters to nanostructured microclusters

Au nanostructured film was deposited on mica by room temperature RF sputtering. The growth mechanism of the film was studied analyzing the evolution of the film morphology as a function of its thickness by the atomic force microscopy. In the early stages of a growth the film evolution proceeds by the nucleation and growth of nanoclusters. After a critical thickness the growth of microclusters formed by the joining of nanoclusters in preferential nucleation sites, onto a quasicontinuous film, is observed. We quantified the evolution of the mean nanoclusters height and surface density and of the film roughness. This data were analyzed by the dynamic scaling theory of growing interfaces obtaining the scaling and roughness exponents z and β whose values suggest a conservative growth process. We also quantified the growth of the microclusters showing that it is consistent with a coalescence/impingement dynamic. About the formation of the microclusters, furthermore, we speculate that their origin is strongly correlated to the features of the sputtering technique in connection with the deposition on a high-diffusivity substrate.     

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of (1+1)-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy (LMBE) and the nonlinear Lai--Das Sarma--Villain (LDV) equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.