A. D. Romig

Principles of analytical electron microscopy

This text discusses the fundamentals which lay a foundation for todays state-of-the-art microscopy. All currently important areas in analytical electron microscopy--including electron optics, electron beam/specimen interactions, image formation, x-ray microanalysis, energy-loss spectroscopy, electron diffraction and specimen effects--have been given thorough attention.

CALCULATIONS OF MOTT SCATTERING CROSS SECTION

Calculations of Mott elastic scattering cross section of electrons for most elements of the periodic table up to element number 94 in the energy range 20 eV–20 keV have been performed. The Dirac equation transformed to a first‐order differential equation was solved numerically. The influence of the choice of atomic potential on the scattering factor was studied in comparison to a simple muffin‐tin approximation of the atomic potential in solids. The application of calculated cross sections to a conventional Monte Carlo model for electron scattering using modified Bethe equation is described and results concerning the electron backscattering for different atomic potentials are compared.

Definition of the spatial resolution of X-ray microanalysis in thin foils

Abstract The spatial resolution of X-ray microanalysis in thin foils is defined in terms of the incident electron beam diameter and the average beam broadening. The beam diameter is defined as the full width tenth maximum of a Gaussian intensity distribution. The spatial resolution is calculated by a convolution of the beam diameter and the average beam broadening. This definiyion of the spatial resolution can be related simply to experimental measurements of composition profiles across interphase interfaces. Monte Carlo calculations using a high-speed parallel supercomputer show good agreement with this definition of the spatial resolution and calculations based on this definition. The agreement is good over a range of specimen thicknesses and atomic number, but is poor when excessive beam tailing distorts the assumed Gaussian electron intensity distributions. Beam tailing occurs in low-Z materials because of fast secondary electrons and in high-Z materials because of plural scattering.

Studies of interfacial segregation in the analytical electron microscope: A brief review

Abstract The analytical electron microscope (AEM) can be used to obtain quantitative elemental analysis with a spatial resolution of 1μm with accompanying composition changes of

Interdiffusion in the Ta-W system

Interdiffusion in the Ta‐W system, a continuous body‐centered‐cubic solid solution, has been investigated in the temperature range 1300–2100 °C with single‐phase diffusion couples prepared by chemical vapor deposition. Fine inclusions, presumably oxides or carbides, decorated the couple interfaces and served as Kirkendall markers. The diffusion annealing times ranged from 16 h to 220 days. The resulting concentration profiles were measured with the electron microprobe and analytical electron microscope. The chemical diffusion coefficient was determined by the classical Boltzmann–Matano technique. The intrinsic diffusivities were determined by the technique of Darken. In the composition range 20–80 at. % W, the activation energy Q for chemical diffusion was constant at 130.5±1.5 kcal/mole. The activation energies for the intrinsic diffusion coefficients at the composition of the Kirkendall marker plane, approximately 70 at. % W, were Q(Ta)=132.3±0.5 kcal/mole and Q(W)=122.0±0.5 kcal/mole.

Effect of Cu at Al grain boundaries on electromigration behavior in Al thin films

The distribution of copper in aluminum thin films is examined with respect to how the copper can influence electromigration behavior. Al-Cu thin films annealed in the single phase region, to just below the solvustemperature, have 0-phase Al2Cu precipitates at the aluminum grain boundaries. The grain boundaries between precipitates are depleted in copper. Al-Cu thin films heat treated at lower temperatures, within thetwo phase region, also have 0-phase precipitates at the grain boundaries but the aluminum grain boundariescontinuously become enriched in copper, perhaps due to the formation of a thin coating of 0-phase at the grain boundary. Here, it is proposed that electromigration behavior of aluminum is improved by addingcopper because the 0-phase precipitates may hinder aluminum diffusion along the grain boundaries. It was also found that resistivity of Al-Cu thin films decrease during accelerated electromigration testing prior to failure. Pure Al films did not exhibit this behavior. The decrease in resistivity is attributed to theredistribution of copper from the aluminum grain matrix to the 0-phase precipitates growing at the grain boundaries thereby reducing the number of defects in the microstructure.

Quantitative X-Ray Analysis: Theory and Practice

An overview of the basic principles and techniques used to determine chemical composition, on the micrometer scale, with the SEM and EPMA was presented in Chapter 8. We outlined the approach to quantitation, the need for matrix corrections, and the physical origins of the matrix effects. The x-ray production process and the use of φ(ρz) curves to describe x-ray production were introduced. Finally, we discussed the three major matrix effects, atomic number (Z), absorption (A), and fluorescence (F) and showed, on a conceptual basis, how they are calculated. This chapter presents the more detailed theory and equations which can be used to determine the three major matrix corrections for quantitative analysis of flat polished specimens. The two commonly used correction schemes, the ZAF and φ (ρz) methods, will be described separately although the two schemes are, in many ways, closely related.

Parallel simulation of electron-solid interactions: A rapid aid for electron microscope data interpretation

Abstract Monte Carlo electron trajectory simulations have been adapted to run on a parallel supercomputer. The increased speed achieved by parallelization of the Monte Carlo code results in the ability to model small probability events easily. The techniques for parallelization of the algorithm are presented here along with examples of applications. The applications include the calculation of the X-ray spatial resolution in thin films, backscattered electron imaging of voids in Al metallizations and X-ray production in thin-film specimens.

A time dependent regular solution model for the thermal evaporation of an Al‐Mg alloy

A series of Al‐6.27 at. % Mg alloys were thermally evaporated in a vacuum at 1910 K. The length of time during which the alloy was molten and was evaporating was varied from very short times to a length of time sufficient for complete evaporation of the alloy. The thickness and average composition of the deposited films were determined with thin‐film x‐ray microanalysis in the analytical electron microscope. A solution/flux model was developed to simulate the evaporation process. The model treated the liquid Al‐Mg alloy as a regular solution using experimentally determined Raoultian activity coefficients. The evaporative flux was calculated according to the expression of Langmuir. The solution and flux equations were numerically integrated with respect to time to accommodate changes in mass and liquid alloy composition as the molten alloy evaporated. The agreement between the model and the experimental data (evaporation rate, rate of composition change in the molten alloy, film thickening rate, and averag...

Qualitative X-Ray Analysis

The first stage in the analysis of an unknown is the identification of the elements present, i.e., the qualitative analysis. Qualitative x-ray analysis is often regarded as straightforward, meriting little attention. The reader will find far more references to quantitative analysis than to qualitative analysis, which has been relatively neglected in the literature, with a few exceptions (e.g., Fiori and Newbury, 1978). It is clear that the accuracy of the final quantitative analysis is meaningless if the elemental constituents of a sample have been misidentified. As a general observation, the major constituents of a sample can usually be identified with a high degree of confidence, but when minor or trace level elements are considered, errors can arise unless careful attention is paid to the problems of spectral interferences, artifacts, and the multiplicity of spectral lines observed for each element. Because of the differences in approach to qualitative EDS and WDS analysis, these techniques will be treated separately.