Evaluation of performance of a film-based X-ray tomographic system

The performance of a home-made tomographic system for film-based rotational X-ray tomography is evaluated by comparison of calculated intensity profiles to measured film density profiles within tomograms of aluminium test objects with small implemented defects. The calculated intensity profiles have been obtained using the back-projection and summation method, calculating the linear absorption coefficient by integrating over the entire energy spectrum of the applied microfocus X-ray set. It is shown that the logarithmic response of the X-ray film must be taken into account when relating intensity profiles to film-density units. The resulting calculated film density profiles nicely fits the actually measured profiles, indicating a low total unsharpness. It is concluded that the method is capable of resolving voids down to about 25 µm. However, due to the inherent blurring of the method, image processing techniques must be applied.     

Electron holographic characterization of ultra-shallow junctions in Si for nanoscale MOSFETs

This investigation attempts quantitative characterization of ultra-shallow junctions (USJs) in Si, useful for future generations of nanoscale MOSFETs as predicted by the Semiconductor Industry Association Roadmap. The USJs were fabricated using rapid thermal diffusion (RTD) from a heavily doped n-type surface source onto a heavily doped p-type substrate. The dopant profiles were analyzed using secondary ion mass spectrometry (SIMS), and were further used to calculate the metallurgical junction depth (MJD). One-dimensional (1-D) characterization of the electrical junction depth (EJD) associated with the electrically activated fraction of the incorporated dopants was performed using off-axis electron holography in a transmission electron microscope. 1-D potential profiles were derived from the unwrapped phase of the reconstructed holograms. The EJD was derived from the measured potential distribution across the p-n junction, and quantitative comparison is made with MJD derived from the SIMS profiles. The comparison between calculated electric field and total-charge distributions from the measured potential profiles and the simulated distributions using the SIMS profiles provides a quantitative estimate of the electrical activation of dopants incorporated by the RTD process, within the accuracy limits of this technique, which is discussed herein.     

Slope distribution of a rough surface measured by transmission scattering and polarization

Transmission scattering from medium to air was used to measure the slope distribution of the rough plane surface of a transparent glass hemisphere. A facet model successfully explained the measured results of refraction, scattering, and polarization: Transmission scattering existed for incident angles greater than the critical angle, all measured curves for the normalized scattered intensity versus the facet slope angle for different detection directions overlapped, and the measured polarization of scattering was approximately constant for >99% of the facets. The slope distribution obtained by transmission scattering agrees with those of the surface profiles in the valid range of the profiler and can represent the slope distribution of the rough surface.     

Transmitted scattered light from a thin film with shallow random rough interfaces

The transmitted scattered energy of plane electromagnetic waves from a thin metallic film with shallow rough interfaces bounded by two semi-infinite media is calculated. Both interfaces are modeled as independent stationary random processes with a Gaussian roughness spectrum. Scattering of light is calculated for both TM (p) or TE (s) polarizations for normal and oblique angles of incidence. An integral equation is obtained for the transmitted field based on the Rayleigh method and their solution involves Fourier coefficients, depending on the roughness profiles. We present some results for the case of a single thin metallic film in the attenuated total reflection configuration for s and p polarization around the angle of the excitation of surface-plasma waves θ(sp). The transmitted scattered intensity shows a maximum at the resonant angle θ(sp) in the case of p polarization.     

Intensity control with a free-form lens

A family of free-form lenses for intensity control is designed. The lens can shape an incident collimated beam with a given intensity distribution I1 into a new collimated beam with intensity distribution I2. No symmetry is assumed for the two intensity profiles. The key idea is that the lens design problem can be formulated and solved in terms of an optimization process involving a specific action functional. It is further shown that the free-form lens can be manufactured by a surfacing process using a convex tool.     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

Prediction of interfacial crack path: a direct boundary integral approach and experimental study

This paper presents the development of a higher-order direct boundary integral-displacement discontinuity method for crack propagation in layered elastic materials. The method is based on the dual boundary integral equations of linear elasticity which are solved by means of a quadratic boundary element formulation. The analytical solution for a point force within a bonded half-plane region is used to derive the kernel functions of the boundary integral equations. Square-root displacement-discontinuity elements are used to model the crack tips, and stress intensity factors may be computed using the numerically predicted values of the displacement discontinuity components at the midpoints of these crack-tip elements. An algorithm based on the maximum tensile-stress criterion is then developed and incorporated into the boundary element model to predict the paths of cracks propagating in layered elastic materials.In the experimental part of this study, crack profiles for straight-through-cracked, compact-tension specimens of the anodically bonded silicon/Pyrex glass system are measured by profilometry. The plane strain prediction of the crack-propagation path is compared with the experimentally measured crack profiles. Consistent with the prediction, the interfacial crack is observed to kink away from the strong, anodically-bonded interface and propagate into the more compliant glass layer. The predicted initial kink angle of 26° agrees very well with the average measured value of 28°. The measured path of the crack is also in very good agreement with the predicted path over about the first 120 microns of crack growth with increasing deviation observed beyond that.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Role of tissue structure in photon migration through breast tissues

Photon migration has been investigated experimentally in vitro on human breast tissues, bovine liver, tissue phantoms, and theoretically by Monte Carlo simulations and diffusion theory. The spatial intensity profiles have been measured at the output surface of a sample illuminated by a collimated beam. Experimental results have then been compared with simulations that assume the sample to be homogeneous. Measurements on phantoms, i.e., fat emulsion and microspheres suspension, and on liver are in good agreement with theory. On the other hand, the width of the intensity profiles measured on breast tissues (adipose and fibrous) are systematically larger than those measured on phantoms or calculated by simulations. The structure of these samples, not considered in simulations and not present in phantoms, explains these differences.     

Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate

In this paper we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The heat conduction and the plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm recently developed by the authors is applied to handle the problem of having negative mode I stress intensity factors. The Finite Element Method was additionally used to model the crack problem and to compute the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the material nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings.     

Intensity profiles along the RHEED streaks for various thin film surface morphologies

Intensity distribution profiles of reflection high energy electron diffraction (RHEED) along the (00) and (01) reciprocal rods are calculated as a function of the grain width, the height difference between neighbouring grains (intergrain roughness), and the surface roughness of the individual grain (intragrain roughness). The calculations include the refraction and the absorption of electron beams and the shadowing effect by the neighbouring grains. The calculations show that the major intensity moves from the three-dimensional (3D) Bragg diffraction to the specular beam as the grain width increases and that a remarkable change in the intensity profiles occurs when the grain width becomes comparable with the decay length of the electron beam in the film. Not only the growth of 3D Bragg peaks but also shifts of the peak positions, induced by the increase of the intra- and intergrain roughness, are simulated. The calculated spectra are compared with the experimental intensity profiles along the streaks measured together with a RHEED intensity oscillation during a homoepitaxy of Ag films.     

Cross-wind profiling based on the scattered wave scintillation in a telescope focus

The problem of wind profile reconstruction from scintillation of an optical wave scattered off a rough surface in a telescope focus plane is considered. Both the expression for the spatiotemporal correlation function and the algorithm of cross-wind velocity and direction profiles reconstruction based on the spatiotemporal spectrum of intensity of an optical wave scattered by a diffuse target in a turbulent atmosphere are presented. Computer simulations performed under conditions of weak optical turbulence show wind profiles reconstruction by the developed algorithm.     

Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach

A new computational method based on the equivalent domain integral (EDI) is developed for mode I fracture analysis of orthotropic functionally graded materials (FGMs) subjected to thermal stresses. By using the constitutive relations of plane orthotropic thermoelasticity, generalized definition of the J-integral is converted to an equivalent domain integral to calculate the thermal stress intensity factor. In the formulation of the EDI approach, all the required thermomechanical properties are assumed to have continuous spatial variations through the functionally graded medium. Developed methodology is integrated into a fracture mechanics research finite element code FRAC2D using graded finite elements that possess cubic interpolation. Steady-state and transient temperature distribution profiles in orthotropic FGMs are computed using the finite elements based heat transfer analysis software HEAT2D. EDI method is validated and domain independence is demonstrated by comparing the numerical results obtained using EDI to those calculated by an enriched finite element method and to those available in the literature. Single and periodic edge crack problems in orthotropic FGMs are examined in order to study the influences of principal thermal expansion coefficient and thermal conductivity components, relative crack length and crack periodicity on the thermal stress intensity factors. Numerical results show that among the three principal thermal expansion coefficient components, the in-plane component perpendicular to the crack axis has the most significant influence on the mode I stress intensity factor. Gradation profile of the thermal expansion coefficient parallel to the crack axis is shown to have no effect on the outcome of the fracture analysis.     

Propagation of a general multi-Gaussian beam in turbulent atmosphere in a slant path

The propagation of a multi-Gaussian beam in turbulent atmosphere in a slant path is studied. The analytical expression for the average intensity of a general multi-Gaussian beam is derived. As special cases the average intensities of a two- and a four-Gaussian beam are investigated and numerically calculated. The investigation reveals that at lower altitude and with large sigma the intensity distribution at the receiver plane can have a shape (multiple peaks) similar to that at the source plane. But with increase in altitude or decrease in sigma, the multiple peaks gradually disappear and evolve into the profile of a fundamental Gaussian beam. From the comparisons between the different propagations we can see that the beam spreading due to wavelength and initial waist width in a slant path is much slower than that in a horizontal path.     

A SiC bicrystal junction on the (0 0 0 1) plane

A SiC bicrystal junction in which two crystals superpose with a common (0001) plane has been investigated by optical microscopy and X-ray precession camera techniques. The behaviour of such a junction is discussed from the viewpoint of sintering and grain boundaries in SiC using a crystallographic concept of compound tessellation. Six examples of bicrystals are considered with respect to the observed and calculated superposing rotation angles and the densities of the superpositions.     

Asymmetrical prism for beam shaping of laser diode stacks

A beam-shaping scheme for a laser diode stack to obtain a flattop output intensity profile is proposed. The shaping element consists of an asymmetrical glass prism. The large divergence-angle compression in the direction perpendicular to the junction plane and the small divergence-angle expansion in the parallel direction are performed simultaneously by a single shaping element. The transformation characteristics are presented, and the optimization performance is investigated based on the ray-tracing method. Analysis shows that a flattop intensity profile can be obtained. This beam-shaping system can be fabricated easily and has a large alignment tolerance.     

Dynamic stress intensity factors due to scattering of harmonic waves by a crack in an infinite medium

An analytical method for calculating dynamic stress intensity factors in the mixed mode (combination of opening and sliding modes) using complex functions theory is presented. The crack is in infinite medium and subjected to the plane harmonic waves. The basis of the method is grounded on solving the two‐dimensional wave equations in the frequency domain and complex plane using mapping technique. In this domain, solution of the resulting partial differential equations is found in the series of the Hankel functions with unknown coefficients. Applying the boundary conditions of the crack, these coefficients are calculated. After solving the wave equations, the stress and displacement fields, also the J‐integrals are obtained. Finally using the J‐integrals, dynamic stress intensity factors are calculated. Numerical results including the values of dynamic stress intensity factors for a crack in an infinite medium subjected to the dilatation and shear harmonic waves are presented.     

Crack-tip constraint and j-controllings stable growth of crack in plane stress case

The finite element analyses are performed to model quasi-static crack growth under mode I plane stress in a compact tension specimen and a centre-cracked plain. It is found that the triaxial constraint and stress-field defined by HRR solution in crack-tip regions for a stationary crack have been better met by those presented in the propagating crack-tip for two different thin specimens, namely, J-dominance is continuously valid. The J-resistance curves measured experimentally from the two specimen geometries coincide with each other and agree well with those calculated by FEM simulations.     

Line-spring model for surface cracks in a reissner plate

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.     

Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating

Comparative studies have been made on the holographic plane grating and the ruled varied-line-spacing (VLS) plane grating designed for two kinds of objective Monk-Gillieson type high-resolution grazing incidence monochromator, I and II. The ray-traced performance of monochromator types I and II on a synchrotron radiation beam line was evaluated in terms of resolving power and spectral purity by the introduction of new concepts of effective Gaussian line and purity profiles. The resolving power defined on the basis of the effective Gaussian profile is consistent with the spectral purity of the beam emerging from the exit slit and is more realistic as compared with those defined in the conventional manner, especially when spectral images have asymmetric profiles. It is concluded that holographic plane gratings recorded with a spherical and an aspheric wave front are capable of providing high resolution with high spectral purity and are fully interchangeable with the corresponding ruled VLS plane gratings. This interchangeability provides more flexibility for users in choosing a proper grating for a high-resolution grazing incidence monochromator of the Monk-Gillieson type.