Evaluation of the sputtering rate variation in SIMS ultra‐shallow depth profiling using multiple short‐period delta layers

We have developed multiple short‐period delta layers as a reference material for SIMS ultra‐shallow depth profiling. Boron nitride delta layers and silicon spacer layers were sputter‐deposited alternately, with a silicon spacer thickness of 1–5 nm. These delta‐doped layers were used to measure the sputtering rate change in the initial stage of oxygen ion bombardment. A significant variation of sputtering rate was observed in the initial 3 nm or less. The sputtering rate in the initial 3 nm was estimated to be about four times larger than the steady‐state value for 1000 eV oxygen ions. Copyright © 2003 John Wiley & Sons, Ltd.     

Ultrashallow depth profiling using SIMS and ion scattering spectroscopy

The accuracy of ultrashallow depth profiling was studied by secondary ion mass spectrometry (SIMS) and high‐resolution Rutherford backscattering spectroscopy (HRBS) to obtain reliable depth profiles of ultrathin gate dielectrics and ultrashallow dopant profiles, and to provide important information for the modeling and process control of advanced complimentary metal‐oxide semiconductor (CMOS) design. An ultrathin Si₃N₄/SiO₂ stacked layer (2.5 nm) and ultrashallow arsenic implantation distributions (3 keV, 1 × 10¹⁵ cm^?2) were used to explore the accuracy of near‐surface depth profiles measured by low‐energy O₂⁺ and Cs⁺ bombardment (0.25 and 0.5 keV) at oblique incidence. The SIMS depth profiles were compared with those by HRBS. Comparison between HRBS and SIMS nitrogen profiles in the stacked layer suggested that SIMS depth profiling with O₂⁺ at low energy (0.25 keV) and an impact angle of 78° provides accurate profiles. For the As⁺‐implanted Si, the HRBS depth profiles clearly showed redistribution in the near‐surface region. In contrast, those by the conventional SIMS measurement using Cs⁺ primary ions at oblique incidence were distorted at depths less than 5 nm. The distortion resulted from a long transient caused by the native oxide. To reduce the transient behavior and to obtain more accurate depth profiles in the near‐surface region, the use of O₂⁺ primary ions was found to be effective, and 0.25 keV O₂⁺ at normal incidence provided a more reliable result than Cs⁺ in the near‐surface region. Copyright © 2007 John Wiley & Sons, Ltd.     

复合载荷下圆底扁球壳非线性稳定性

本文采用半解析方法研究在中心分布载荷及中心集中力联合作用下,圆底扁球壳的非线性稳定性问题.避免了求近似解析解时繁重的人工计算,而p-W_m特征关系仍可由显式表达.     

From the classical to the generalized von Kármán and Marguerre–von Kármán equations

In this work, we describe and analyze two models that were recently proposed for modeling generalized von Kármán plates and generalized Marguerre–von Kármán shallow shells.

First, we briefly review the “classical” von Kármán and Marguerre–von Kármán equations, their physical meaning, and their mathematical justification. We then consider the more general situation where only a portion of the lateral face of a nonlinearly elastic plate or shallow shell is subjected to boundary conditions of von Kármán type, while the remaining portion is free. Using techniques from formal asymptotic analysis, we obtain in each case a two-dimensional boundary value problem that is analogous to, but is more general than, the classical equations.

In particular, it is remarkable that the boundary conditions for the Airy function can still be determined on the entire boundary of the nonlinearly elastic plate or shallow shell solely from the data.

Following recent joint works, we then reduce these more general equations to a single “cubic” operator equation, which generalizes an equation introduced by Berger and Fife, and whose sole unknown is the vertical displacement of the shell. We next adapt an elegant compactness method due to Lions for establishing the existence of a solution to this operator equation.     

浅水中污染物扩散的自适应有限元分析法

介绍浅水中污染物扩散分析中的有限元法.分析包括两个部分:1)流场速度、水面高度的计算;2)根据扩散模型计算污染物浓度场.联合使用了自适应网格技术以期提高解的精度,同时减少计算时间和计算机内存的消耗.通过几个有已知解的实例验证了有限元公式和计算机程序.最后,使用这种联合方法分析泰国Chao Phraya河附近海湾中的污染物扩散.     

Stress concentration around a circular hole in a transversely isotropic spherical shell

Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 99–106, December 2004.     

溃坝问题的间断有限元方法

本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法，给出该方法的精度分析，通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力，并将其推广到求解浅水问题．针对坝底无摩擦，无坡度的理想情形进行讨论，给出方溃坝和圆溃坝问题的数值模拟结果．     

Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods

In this paper, we present a discontinuous Galerkin formulation of the shallow‐water equations. An orthogonal basis is used for the spatial discretization and an explicit Runge–Kutta scheme is used for time discretization. Some results of second‐order anisotropic adaptive calculations are presented for dam breaking problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities like hydraulic jumps. Copyright © 2006 John Wiley & Sons, Ltd.     

The numerical study of roll‐waves in inclined open channels and solitary wave run‐up

In this paper, we introduce a finite‐volume kinetic BGK scheme and its applications to the study of roll and solitary waves. The current scheme is based on the numerical solution of the gas‐kinetic Bhatnagar–Gross–Krook model in the flux evaluation across each cell interface. An intrinsic connection between the BGK model and time‐dependent, non‐linear, non‐homogeneous shallow‐water equations enables us to solve shallow‐water equations automatically with our kinetic scheme. The analytical solution, experimental measurements, and numerical calculations for problems associated with roll‐waves down an inclined open channel and solitary waves incident on a sloped beach are also presented. Copyright © 2005 John Wiley & Sons, Ltd.