High Concentration Arsenic Diffusion in Crystalline Silicon: An Asymptotic Analysis

For fairly high concentrations, the effective arsenic diffusioncoefficient is known to grow linearly with the concentration.In this paper, we consider the strongly enhanced diffusion ofarsenic by asymptotic methods, and extend the results of a previouspaper (King & Please, 1987) in three ways: we characterizean additional (low-concentration) region; we consider the influenceof the initial data; and we consider the case of constant surfaceconcentration.     

Topological representations of Jahn-Teller distortions

Topological representations (top-reps), which originally were developed to model molecular polyhedral isomerization processes, can be extended to depict the relationships between the polygons and polyhedra involved in Jahn-Teller (JT) distortions. Using this approach, the top-rep of the E ? (b _1g + b _2g) distortion of square planar molecules to rectangle and rhombus isomers becomes a rhombus in which the vertices alternately represent distortions to the rectangle and rhombus isomers. Similarly the top-rep of the E ? e distortion of regular O_h octahedra to elongated D_4h tetragonal bipyramids becomes a triangle in which the vertices represent the three distinct tetragonal bipyramids from a given octahedron and the edge midpoints represent lower symmetry rhombic D_2h intermediates. A regular octahedron can be used as a top-rep for the T ? (e + t ₂) distortions of regular octahedra if the 6 vertices represent distortions to D_4h tetragonal bipyramid isomers, the 8 face midpoints represent distortions to D_3d trigonal antiprism isomers, and the 12 edge midpoints represent lower symmetry rhombic D_2h intermediates. In the case of Jahn-Teller T ? h distortions of regular I_h icosahedra, the corresponding top-rep becomes a regular icosahedron in which the 12 vertices represent distortions to pentagonal D_5d isomers, the 20 face midpoints represent distortions to trigonal D_3d isomers, and the 30 edge midpoints represent D_2h intermediates. A 4-dimensional analogue of the tetrahedron (i.e. the 4-simplex) can be used as a top-rep for the G ? g problem and the H ? g component of the H ? (g + 2h) problem for JT distortions of regular icosahedra. In this case the 5 vertices and the 10 edge midpoints correspond to T_h isomers and D_3d intermediates, respectively.     

高能电子对原子核C12的弹性散射

In this paper, we have calculated the elastic scattering of high energy electrons with nuclei C¹² by phase shift calculation.We take the charge distribution of the nucleus C¹² as following:(1) exponential distribution:ρ(x)=ρ₀θ^-x/a, (2) gaussian distribution:ρ(x)=ρ₀e^(-x2/a2),(3) uniform distribution: ρ(x) ={ρ₀ when 0kR, where a and b are the parameters, and the constant R is the radius of the nucleus C¹². The energy of the electrons is 187 Mev.The result of the calculation shows that the gaussian distribution confirms the experimental result better than the other two kinds of distributions, and gives R=(12)^1/3r₀, where r₀=1.35×10^-13 cm.     

Feedback Control of a Thermal Fluid Using State Estimation

Abstract

In his paper we consider the problem of designing a feedback controller for a thermal fluid. Any practical feedback controller for a fluid flow system must incorporate some type of state estimator. Moreover, regardless of the approach, one must introduce approximations at some point in the analysis. The method presented here uses distributed parameter control theory to guide the design and approximation of practical slate estimators. Wc use finite clement techniques to approximate optimal infinite dimensional controllers based on linear quadratic Gaussian lpar;LQG) and MinMax theory for the Bonssincsq equations. These designs are then compared to full state feedback. We present several numerical experiments and we describe how these techniques can also be applied to sensor placement problems.     

Numerical Differentiation by Finite-Dimensional Regularition

Tikhonov regularization of order one is applied to the differentiationoperation. By minimizing the regularization functional overa finite-dimensional space there results a procedure for numericaldifferentiation. This finite-dimensional regularization resultsin a sparse, symmetric, positive definite matrix problem whencubic splines are chosen as the finite-dimensional space. Theeffects of error in the data on the values of the regularizedderivative can be estimated in terms of the norm of the regularizationoperator. Numerical experiments are presented which illustratethe stability and obtainable accuracy of the method.     

Asymptotic analysis of a combined dissociative and kick-out diffusion mechanism

In this paper a combined dissociative and kick-out model forimpurity diffusion in semiconductors is studied. The mechanismhas been used, for example, as a model for the diffusion ofchromium in gallium arsenide. The authors derive asymptoticsolutions for both one- and two-dimensional surface source (indiffusion)problems and for a one-dimensional outdiffusion problem andillustrate their results by plotting impurity profiles and (forthe two-dimensional problem) contours of constant concentration.By varying the appropriate parameter in the one dimensionalasymptotic solutions, it is possible to describe the transitionfrom profiles characteristic of the kick-out mechanism to thoseof the dissociative mechanism. Aspects of the transition fromdissociative to kick-out behaviour are also obtained for thetwo-dimensional problem.