Atomic force microscopy study of growth kinetics: Scaling in TiN-TiB2 nanocomposite films on Si(1 0 0)

We used the reactive unbalanced close-field dc-magnetron sputtering growth of TiN-TiB₂ on Si(1 0 0) at room temperature to determine if scaling theory provides insight into the kinetic mechanisms of two-phase nanocomposite thin films. Scaling analyses along with height-difference correlation functions of measured atomic force microscopy (AFM) images have shown that the TiN-TiB₂ nanocomposite films with thickness ranging from 70 to 950 nm exhibit a kinetic surface roughening with the roughness increasing with thickness exponentially. The roughness exponent α and growth exponent β are determined to be ∼0.93 and ∼0.25, respectively. The value of dynamic exponent z, calculated by measurement of the lateral correlation length ξ, is ∼3.70, agreeing well with the ratio of α to β. These results indicate that the surface growth behavior of sputter-deposited TiN-TiB₂ thin films follows the classical Family-Vicseck scaling and can be reasonably described by the noisy Mullins diffusion model, at which surface diffusion serves as the smoothing effect and shot noise as the roughening mechanism.     

Scaling behavior of polished (1 1 0) single-crystal nickel surfaces

The kinetic surface roughening of the polished (1 1 0) plane of a single-crystal nickel is investigated using atomic force microscopy. The polished (1 1 0) surfaces exhibit the scaling behavior characterized by the roughness exponent α=0.83±0.05, the growth exponent β=0.83±0.07 and the skewness=−0.52±0.06, whose values are compared with the theoretical values in statistical growth models in deposition. These characteristics indicate that the scaling behavior of the polished nickel surfaces can be related to a statistical growth model of nonlinear diffusion dynamics in deposition.     

Characterization of electrodeposited nickel film surfaces using atomic force microscopy

Microstructures of nickel surfaces electrodeposited on indium tin oxides coated glasses are investigated using atomic force microscopy. The fractal dimension D and Hurst exponent H of the nickel surface images are determined from a frequency analysis method proposed by Aguilar et al. [J. Microsc. 172 (1993) 233] and from Hurst rescaled range analysis. The two methods are found to give the same value of the fractal dimension D∼2.0. The roughness exponent α and growth exponent β that characterize scaling behaviors of the surface growth in electrodeposition are calculated using the height-difference correlation function and interface width in Fourier space. The exponents of α∼1.0 and β∼0.8 show that the surface growth does not belong to the universality classes theoretically predicted by statistical growth models.     

Thermal and kinetic surface roughening studied by scanning tunneling microscopy and atomic force microscopy

Recent studies of thermal roughening on Si surfaces and kinetic roughening of some growing films, copper and tungsten, by using scanning tunneling microscopy and atomic force microscopy are reviewed. A logarithmic divergence of the surface height fluctuations of Si(111) vicinal surfaces is confirmed, in agreement with the theoretical prediction of rough surface in thermal equilibrium. For the kinetically formed rough surfaces, power law dependences of the interface width on the system size are clearly observed. Furthermore, the tungsten films show a short-range scaling regime and a long-range “smooth” regime. The roughness exponents α are compared with theoretical predictions: for the typical Cu electrode position condition (α=1/2), the exponent appears to be close to that found for local growth models, and for tungsten films (0.7～0.8), it is consistent with recent predictions for growth where surface diffusion is predominant.     

Monte Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang-Landau algorithm

The influence of random site dilution on the critical properties of the two-dimensional Ising model on a square lattice was explored by Monte Carlo simulations with the Wang-Landau sampling. The lattice linear size was L=20-120 and the concentration of diluted sites q=0.1,0.2,0.3. Its pure version displays a second-order phase transition with a vanishing specific heat critical exponent α, thus, the Harris criterion is inconclusive, in that disorder is a relevant or irrelevant perturbation for the critical behaviour of the pure system. The main effort was focused on the specific heat and magnetic susceptibility. We have also looked at the probability distribution of susceptibility, pseudocritical temperatures and specific heat for assessing self-averaging. The study was carried out in appropriate restricted but dominant energy subspaces. By applying the finite-size scaling analysis, the correlation length exponent ν was found to be greater than one, whereas the ratio of the critical exponents (α/ν) is negative and (γ/ν) retains its pure Ising model value supporting weak universality.     

Investigation of the critical properties of the three-dimensional weakly diluted potts model

The problem of the type of the phase transition in the three-dimensional weakly diluted Potts model with the number of spin states q= 3 has been investigated by the Monte Carlo method. The temperature dependences of the Binder cumulants, energy, magnetization, specific heat, and susceptibility have been calculated. It is found that the second-order phase transition occurs in a system at the spin concentration p = 0.9. The critical exponents of the magnetization (β), specific heat (α), and susceptibility (γ) and the critical correlation-length exponent v were calculated on the basis of the finite-size scaling theory at p = 0.9.     

The stochastic stabilized Kuramoto-Sivashinsky equation: a model for compact electrodeposition growth

We report on numerical studies of the dynamical behavior of a stochastic version of the stabilized Kuramoto-Shivashinsky equation, in 1 + 1 dimensions, at short times and small length scales. The solution evolves as a rough growing interface, showing a well defined growth exponent β = 0.37±0.04 and a roughness exponent that saturates at a value α = 0.80±0.04. A morphological instability may also develop for certain values of the control parameter and with a well-defined characteristic length. The resulting dynamical scenario and scaling properties compare fairly well with experimental results on slow compact electrodeposition growth.     

Scaling and complex avalanche dynamics in the Abelian sandpile model

We study the two-dimensional Abelian Sandpile Model on a squarelattice of linear size L. We introduce the notion of avalanche’sfine structure and compare the behavior of avalanches and waves oftoppling. We show that according to the degree of complexity inthe fine structure of avalanches, which is a direct consequence ofthe intricate superposition of the boundaries of successive waves,avalanches fall into two different categories. We propose scalingansätz for these avalanche types and verify them numerically.We find that while the first type of avalanches (α) has a simplescaling behavior, the second complex type (β) is characterized by anavalanche-size dependent scaling exponent. In particular, we define an exponent γto characterize the conditional probability distribution functions for these typesof avalanches and show that γ _α = 0.42, while 0.7 ≤ γ _β ≤ 1.0depending on the avalanche size. This distinction provides aframework within which one can understand the lack of aconsistent scaling behavior in this model, and directly addresses thelong-standing puzzle of finite-size scaling in the Abelian sandpile model.     

Controlling energy deposition during the C60 bombardment of silicon: The effect of incident angle geometry

The profile of the energy deposition footprint is controlled during the C₆₀⁺ erosion of Si surfaces by varying the incident energy and/or incident angle geometry. Sputter yield, surface topography, and chemical composition of the eroded surfaces were characterized using atomic force microscopy (AFM) and secondary ion mass spectrometry (SIMS). The experiments show that the 10 keV, 40° incident C₆₀⁺ erosion of Si results in the formation of a C containing, mound-like structure on the solid surface. We find that the occurrence of this C feature can be avoided by increasing the incident energy of the C₆₀⁺ projectile or by increasing the incident angle of the C₆₀⁺ projectile. While both strategies allow for the Si samples to be eroded, the occurrence of topographical roughening limits the usefulness of C₆₀⁺ in ultra-high resolution semiconductor depth profiling. Moreover, we find that the relative effect of changing the incident angle geometry of the C₆₀⁺ projectile on the profile of the energy deposition footprint, and thus the sputter yield, changes according to the kinetic energy of the projectile and the material of the bombarded surface, a behavior that is quite different than what is observed for an atomic counterpart.     

Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence

We study the statistical properties of complex networks constructed from time series of energy dissipation rates in three-dimensional fully developed turbulence using the visibility algorithm. The degree distribution is found to have a power-law tail with the tail exponent α=3.0. The exponential relation between the number of the boxes N_B and the box size l_B based on the edge-covering box-counting method illustrates that the network is not self-similar, which is also confirmed by the hub-hub attraction according to the visibility algorithm. In addition, it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent η=1.163±0.005.     

Critical behavior studies in ferromagnetic (Nd, K)-Mn-O compounds

The critical scaling behavior of K-doped Nd-Mn-O based double-exchange ferromagnetic compounds was studied by measuring isothermal magnetization of Nd_0.84K_0.16MnO₃ and Nd_0.77K_0.23MnO₃ samples. The critical exponents β, γ and δ corresponding to the spontaneous magnetization, initial susceptibility and isothermal magnetization, respectively, were determined by analyzing the magnetization data in terms of the modified Arrott plot method. The critical exponent values of both samples are found to be comparable to values predicted by a mean field model. The role of ferromagnetic clusters on the scaling behavior is discussed. The critical exponent values are found to be consistent with the Widom scaling relation and the universal scaling hypothesis.     

Dynamic scaling behaviors of the restricted-solid-on-solid model on honeycomb and square-octagon lattice substrates

The dynamic scaling behaviors of the restricted-solid-on-solid (RSOS) model on two new types of substrate, which are honeycomb and square-octagon lattice substrates, are studied by means of Kinetic Monte Carlo simulations. The growth exponent β and the roughness exponent α defined, respectively, by the surface width via W ~ t ^β and the saturated width via W _sat ~ L ^α , L being the system size, were obtained by a power-counting analysis. Our simulation results show that the Family-Vicsek scaling is still satisfied. However, the structures of the substrates indeed affect the dynamic behavior of the growth model. The values of the roughness exponents fall between regular and fractal lattices. Deeper analysis show that the coordination number of the substrates play an crucial role.     

Oxygen inducedK-shell ionization of selected elements from sulphur to bromine

K-shell X-ray production cross sections for oxygen ions on thin solid targets of 13 selected elements with atomic numbers between 16 and 35 were measured by a Si(Li) detector at incident ion energies from 7 to 24 MeV. Ionization cross sections are compared with calculations assuming Coulomb-ionization. Best agreement is found with theoretical cross sections that include corrections for binding energy and Coulomb deflection effects. Energy shifts ofK _α andK _β X-rays andK _α /K _β intensity ratios were also measured and are used to deduce information about outer shell ionization.     

Growth dynamics of pulsed laser deposited indium oxide thin films: a substrate dependent study

Indium oxide films are deposited by pulsed laser deposition in the presence of oxygen atmosphere, on different substrates, namely GaAs, Si, quartz, and glass. The structural, morphological, and interface characteristics are studied. Cubic In₂O₃ phase is confirmed by high resolution X-ray diffraction measurements. While the films on Si, glass, and quartz substrates are polycrystalline, the films on GaAs exhibit a preferred orientation along (2 2 2) plane. The structure and crystalline nature of the films are also confirmed by Raman spectroscopy. Furthermore, Raman spectra show the appearance of gallium oxide modes arising due to Ga diffusion from the substrate. The morphology of the films deposited on different substrates is studied by atomic force microscopy and rms roughness values are obtained. A two-dimensional power spectral density analysis has been used to calculate the growth exponent (α). A value of α > 1 (α < 1) for films grown on GaAs/Si (quartz/glass) substrates suggests that the growth on crystalline substrates is governed by the linear diffusion model, whereas the growth on amorphous substrates follows the dynamic scaling behaviour. UV-visible study shows a high optical transmittance of >90% and a band gap value of 3.64 and 3.79 eV for the films deposited on quartz and glass substrates, respectively.     

Epidemic spreading with nonlinear infectivity in weighted scale-free networks

In this paper, we investigate the epidemic spreading for the SIR model in weighted scale-free networks with the nonlinear infectivity and weighted transmission rate. Concretely, we introduce the infectivity exponent α and the weight exponent β into the epidemic system, then examine the impact of α and β on the epidemic spreading. We show that one can adjust the values of α and β to rebuild a nonzero finite epidemic threshold. Furthermore, we also find the infectivity exponent α has a stronger effect not only on the epidemic threshold, but also on the epidemic prevalence. In addition, it is also interesting to see that the absence of the epidemic threshold appears not very dejected, since the prevalence grows much more slowly as the transmission rate λ increases.     

Etch front roughening in wrinkly metal

Scaling behavior of wrinkle evolution due to chemical etching of Au on stretchable substrate is studied by atomic force microscopy. The surfaces were etched with a small drop of KI solution. Scaling exponent α decreased with the etch time, from 0.93 to 0.62. For dynamic exponent β up to 30 min we find it to be 0.16 ± 0.05. Within the same time frame, the wavelength increases as ∼t^0.23+−0.05 but drops at 45 min as ∼t^{−1.22+−0.42} and saturates. At this stage, we observe percolation island type features along with some wrinkles. The measured value of α at this stage is 0.62 ± 0.02; consistent with the percolation model. The wavelength coarsening at this stage suggests the existence of chemically driven spinodal decomposition. Our obtained value of α and β is consistent with the value of z obtained from correlation length which is given by ξ = t^1/z. We find z = 4.87 ± 0.50. Our experiment suggests wrinkle formation in thin films on viscoelastic surface occurs in three stages.     

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.     

Growth dynamics of ZnPc and TiOPc thin films: Effect of crystallinity on anomalous scaling behavior

The surface morphology evolution and scaling behavior of zinc phthalocyanine (ZnPc) and titanyl phthalocyanine (TiOPc) thin films have been studied using atomic force microscopy, X-ray diffraction and height difference correlation function analysis. In contrast to the large growth exponent (β) values and anomalous scaling behavior previously reported for other crystalline molecular thin films, significantly small β and anomaly values were observed for amorphous TiOPc thin films. The relatively small anomaly value of ZnPc thin films, though larger than that of TiOPc thin films, is also rationalized by the lack of crystallographic ordering at the initial stage of growth.     

Atomic configurations during Si incorporation on GaAs(001) in As atmosphere evidenced by reflectance difference spectroscopy

The structural ordering of surface atoms during Si deposition on singular and vicinal GaAs(001) surfaces has been studied by reflectance difference (RD) spectroscopy using the difference function between the Si-covered and the bare surface. In dependence on the Si coverage the difference spectra correspond to RD spectra of the bare Si(001)-(1×2) or of the As-terminated Si(001):As(2×1) surface. This finding and the behaviour of RD transients recorded at 3.8 eV photon energy allows to define a (3×2)α phase with Si dimers in the top layer and Ga dimers in the third layer, and a (3×2)β phase with As-dimer rows on top of Si in the second layer.     

Effects of evolving surface morphology on yield during focused ion beam milling of carbon

We investigate evolving surface morphology during focused ion beam bombardment of C and determine its effects on sputter yield over a large range of ion dose (10¹⁷-10¹⁹ ions/cm²) and incidence angles (Θ = 0-80°). Carbon bombarded by 20 keV Ga⁺ either retains a smooth sputtered surface or develops one of two rough surface morphologies (sinusoidal ripples or steps/terraces) depending on the angle of ion incidence. For conditions that lead to smooth sputter-eroded surfaces there is no change in yield with ion dose after erosion of the solid commences. However, for all conditions that lead to surface roughening we observe coarsening of morphology with increased ion dose and a concomitant decrease in yield. A decrease in yield occurs as surface ripples increase wavelength and, for large Θ, as step/terrace morphologies evolve. The yield also decreases with dose as rippled surfaces transition to have steps and terraces at Θ = 75°. Similar trends of decreasing yield are found for H₂O-assisted focused ion beam milling. The effects of changing surface morphology on yield are explained by the varying incidence angles exposed to the high-energy beam.