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.     

时间分数阶Edwards-Wilkinson方程的标度行为研究

分别采用数值模拟和标度分析方法对1+1维时间分数阶Edwards-Wilkinson方程的标度行为进行研究.利用Caputo分数阶导数数值解求得的生长指数与采用直接标度分析方法得到的结果一致.     

1+1维Wolf-Villain模型奇异标度行为的数值模拟

采用Kinetic Monte Carlo(KMC)方法对描述分子束外延生长(MBE)的1+1维Wolf-Villain模型进行大尺寸和长生长时间的数值模拟研究,以消除渡越行为的影响.计算得到整体和局域标度指数.结果显示,在所模拟的空间和时间尺度范围内,1+1维Wolf-Villain模型仍呈现出固有奇异标度行为.这一结论与López等人最近的理论分析结果不一致.     

Element-free Galerkin (EFG) method for analysis of the time-fractional partial differential equations

The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin (EFG) method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α (0<α ≤1). The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.     

Analytical Approach for Nonlinear Partial Differential Equations of Fractional Order

The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial diffusion of biological populations. The homotopy-perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian's decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian's decomposition method. Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions. The basis ideas presented in the paper can be further applied to solve other similar fractional partial differential equations.     

含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程,并能对其进行统一的研究.研究发现, KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律;而MBE 方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合     

Phonon localization in Ge nanoislands and its manifestation in Raman spectra

Multilayer structures with germanium nanoislands that are formed on the silicon (111) surface upon submonolayer deposition by molecular-beam epitaxy have been investigated using Raman spectroscopy. To interpret the experimental Raman spectra, numerical calculations of the spectra have been performed for nanoislands containing from several to several hundred germanium atoms. The calculations demonstrate that the in-plane sizes of nanoislands (with sizes less than 2–3 nm) substantially affect the frequencies of phonons localized in these nanoislands. The experimental Raman spectra confirm the occurrence of the quantum size effect.     

Comparison of organic thin films deposited by supersonic molecular-beam epitaxy and organic molecular-beam epitaxy: The case of titanyl phthalocyanine

Recently, supersonic molecular-beam epitaxy (SuMBE) was invented as an alternative method for the deposition of organic material, using higher kinetic energies for deposition than conventional organic molecular-beam epitaxy (OMBE). Using titanyl phthalocyanine (TiOPc) as a model substance, we show that the SuMBE deposition results in increased crystal quality of the deposited material. This is induced by the high kinetic energy of the molecular-beam in SuMBE, which leads to increased molecular mobility on the surface, resulting in larger crystal sizes and higher crystal quality. Alternatively, similar films as made by OMBE can be deposited by SuMBE at lower substrate temperatures. This temperature reduction may be of interest for the deposition of stacked organic devices on underlying heat sensitive layers, as they are quite common in organic electronic devices.     

Stability study and time resolution measurement of straw tube detectors

Pramana - This article provides numerical simulations of the time-fractional coupled Korteweg–de Vries and Klein–Gordon equations via the local meshless collocation method (LMCM)...     

Time-fractional extensions of the Liouville and Zwanzig equations

This paper presents extensions to the classical stochastic Liouville equation of motion that contain the Riemann-Liouville and Caputo time-fractional derivatives. At first, the dynamic equations with the time-fractional derivatives are formally obtained from the classical Liouville equation. A feature of these new equations is that they have the same common formal solution as the classical Liouville equation and therefore may be used for study of the Hamiltonian system dynamics. Two cases of the time-dependent and time-independent Hamiltonian are considered separately. Then, the time-fractional Liouville equations are deduced from the short- and long-time asymptotic expansions of the obtained dynamic equations. The physical meaning of the resulting equations is discussed. The statements of the Cauchy-type problems for the derived time-fractional Liouville equations are given, and the formal solutions of these problems are presented. At last, the projection operator formalism is employed to derive the time-fractional extensions of the Zwanzig kinetic equations and the corresponding formal statistical operators from the time-fractional Liouville equations.     

Investigation of the peculiarities of Ge island growth on Si (100) under MBE conditions

The results of investigating the features of Ge-island formation on Si (100) under conditions of molecular-beam epitaxy is presented. Nanosized structures at heteroboundaries (islets and quantum dots) are attracting great interest due to new useful properties and broad prospects of their application.     

Kinetic model for a step edge in epitaxial growth

A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the density of kinks and "edge adatoms" along the step edge. Equilibrium and kinetic steady states, corresponding to zero and nonzero deposition flux, respectively, are derived for a periodic sequence of step edges. The theoretical results are compared to results from kinetic Monte Carlo (KMC) simulations of a simple solid-on-solid model, and excellent agreement is obtained. This theory provides a starting point for modeling the growth of two-dimensional islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.     

New approximate solution for time-fractional coupled KdV equations by generalised differential transform method

In this paper,the generalised two-dimensional differential transform method (DTM) of solving the time-fractional coupled KdV equations is proposed.The fractional derivative is described in the Caputo sense.The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial.An illustrative example shows that the generalised two-dimensional DTM is effective for the coupled equations.     

Development of the Design of Super-Multiperiod Structures Grown by Molecular-Beam Epitaxy and Emitting in the Terahertz Range

Journal of Experimental and Theoretical Physics - A design of terahertz (THz) radiation source has been developed based on an AlGaAs/GaAs superlattice grown by molecular-beam epitaxy. The gain and...     

Heteroepitaxy of erbium-doped silicon layers on sapphire substrates

The possibility of using sublimation molecular-beam epitaxy as an efficient method for growing erbium-doped silicon layers on sapphire substrates for optoelectronic applications is analyzed. The advantage of this method is that the erbium-doped silicon layers can be grown at relatively low temperatures. The use of sublimation molecular-beam epitaxy makes it possible to grow silicon layers of good crystal quality. It is demonstrated that the growth temperature affects not only the structure of silicon-on-sapphire layers but also the crystallographic orientation of these layers. The electrical and luminescence properties of the erbium-doped silicon layers are discussed. It is revealed that structures of this type exhibit intense erbium photoluminescence at a wavelength of 1.54 μm.     

Structure and peculiarities of the (8 × n)-type Si(001) surface prepared in a molecular-beam epitaxy chamber: A scanning tunneling microscopy study

A clean Si(001) surface thermally purified in an ultrahigh vacuum molecular-beam epitaxy chamber has been investigated by means of scanning tunneling microscopy. The morphological peculiarities of the Si(001) surface have been explored in detail. The classification of the surface structure elements has been carried out, the dimensions of the elements have been measured, and the relative heights of the surface relief have been determined. A reconstruction of the Si(001) surface prepared in the molecular-beam epitaxy chamber has been found to be (8 × n). A model of the Si(001)-(8 × n) surface structure is proposed. The text was submitted by the authors in English.     

Effect of growth conditions on photoluminescence of erbium-doped silicon layers grown using sublimation molecular-beam epitaxy

Erbium-doped epitaxial silicon layers were grown using two different growth techniques, namely, commonly used molecular-beam epitaxy (MBE) and solid-phase epitaxy (SPE). It is shown that an erbium-doped silicon epitaxial layer deposited through SPE on a cold substrate and subsequently annealed displays amore intense photoluminescence at a wavelength of 1.54 μm than do MBE-grown layers. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 102–104. Original Russian Text Copyright ? 2004 by Shengurov, Svetlov, Chalkov, Andreev, Krasil’nik, Kryzhkov.     

Exchange interaction in InAs nanocrystal quantum dots

The near band-gap level structure in high-quality colloidal InAs nanocrystal quantum dots within the very strong confinement regime is investigated. Size-selective photoluminescence excitation and fluorescence line narrowing measurements reveal a size-dependent splitting between the absorbing and the emitting states. The splitting is assigned to the confinement-enhanced electron–hole exchange interaction. The size dependence of the splitting significantly deviates from the idealized 1/r³scaling law for the exchange splitting. A model incorporating a finite barrier which allows for wavefunction leakage is introduced. The model reproduces the observed 1/r²dependence of the splitting and good agreement with the experimental data is obtained. The smaller barriers for embedded InAs dots grown by molecular-beam epitaxy, are predicted to result in smaller exchange splitting as compared with colloidal dots with a similar number of atoms.     

Bright and singular soliton solutions of the conformable time-fractional Klein–Gordon equations with different nonlinearities

Finding the exact solutions of nonlinear fractional differential equations has gained considerable attention, during the past two decades. In this paper, the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities are studied. Several exact soliton solutions, including the bright (non-topological) and singular soliton solutions are formally extracted by making use of the ansatz method. Results demonstrate that the method can efficiently handle the time-fractional Klein–Gordon equations with different nonlinearities.     

Photoluminescence of Si/Ge nanostructures grown by molecular-beam epitaxy at low temperatures

Multilayer Si/Ge nanostructures grown by molecular-beam epitaxy at low temperatures (250–300°C) of germanium deposition are studied using photoluminescence and atomic-force microscopy (AFM). It is assumed that, upon low-temperature epitaxy, the wetting layer is formed through the intergrowth of two-dimensional (2D) and three-dimensional (3D) nanoislands.