Characteristic Fluorescence Correction Research Articles

Bremsstrahlung enhancement in electron probe microanalysis for homogeneous samples using Monte Carlo simulation.

Fluorescence enhancement in samples irradiated in a scanning electron microscope or an electron microprobe should be appropriately assessed in order not to distort quantitative analyses. Several models have been proposed to take into account this effect and current quantification routines are based on them, many of which have been developed under the assumption that bremsstrahlung fluorescence correction is negligible when compared to characteristic enhancement; however, no concluding arguments have been provided in order to support this assumption. As detectors are unable to discriminate primary from secondary characteristic X-rays, Monte Carlo simulation of radiation transport becomes a determinant tool in the study of this fluorescence enhancement. In this work, bremsstrahlung fluorescence enhancement in electron probe microanalysis has been studied by using the interaction forcing routine offered by penelope 2008 as a variance reduction alternative. The developed software allowed us to show that bremsstrahlung and characteristic fluorescence corrections are in fact comparable in the studied cases. As an extra result, the interaction forcing approach appears as a most efficient method, not only in the computation of the continuum enhancement but also for the assessment of the characteristic fluorescence correction.

Separate K-line contributions to fluorescence enhancement in electron probe microanalysis

The behaviour of the fluorescence enhancement correction factor in electron probe microanalysis, as a function of incident electron energy and take-off angle, is assessed for different binary samples in a wide range of compositions. Monte Carlo simulations are employed to validate Reed's correction algorithm [S.J.B. Reed, Characteristic fluorescence corrections in electron-probe microanalysis, Br. J. Appl. Phys. 16 (1965) 913-926], by means of estimating the primary excited radiation volume and the volume corresponding to secondary fluorescence generation. Then, Reed's expression for the fluorescence enhancement has been modified to account for Kα and Kβ line contributions separately. It is clearly shown that in certain cases the assignment of all fluorescent contribution to the Kα lines may be inadequate, particularly when trace element analysis imposes an accurate determination of elemental concentrations.

Quantitative electron microprobe analysis of aluminum, copper, and gold thin films on silicon substrates

The thicknesses of aluminum, copper, and gold thin films on silicon substrates have been measured with an electron probe microanalyzer. k ratio versus thickness calibration curves are obtained by a Monte Carlo simulation of electron scattering. The simulation results based on two energy loss models are compared. One is the continuous slowing down approximation model and another is the hybrid model for the discrete and the continuous energy loss processes. Inner shell ionizations and free electron excitations are selected out for the discrete process in the hybrid model. In both models the Mott cross section and the Gryzinski cross section are used for elastic collisions and ionizations, respectively. The exact film/substrate boundary condition is considered. The characteristic and continuum fluorescence corrections are also included in the simulation. The simulation results agree well with experimental ones measured with a quartz oscillator. Effects of the introduction of the discrete energy loss process and the fluorescence correction are discussed in comparison between simulation and experiment.

Characteristic and continuous fluorescence correction for electron probe microanalysis of thin coatings at oblique incidence

A theoretical approach to characteristic and continuous fluorescence correction for electron probe microanalysis of thin coatings is presented. Calculations are developed for different systems of films on substrates at electron energies in the range 10–60 keV and incidence angles of 0–60°. Comparisons with experimental results are also made. It is shown that these corrections may reach 30% or more when the primary beam energy is increased and decrease significantly when the incidence angle is increased.

An accurate computer correction program for quantitative electron probe microanalysis

The aim of this paper is to present a practical and accurate program of correction based on a new mathematical description of φ(ϱz), which allows a global correction combining atomic number and absorption correction [ZA]. Characteristic and continuum fluorescence corrections are also included to complete the program. Elements of atomic number in the range 4 <Z < 92 and X-ray emission linesKα,Kβ,Lα,Lβ,Mα andMβ are taken into account by the program which is especially designed for difficult cases (light elements, low overvoltages, low accelerating voltages).

Evaluation of the ZAF procedure employed in the NIST/NIH DTSA program

The ZAF matrix correction procedure employed in the Desk Top Spectrum Analyzer program (DTSA) is considerably different from the FRAME matrix correction program from which it was derived. Enough differences exist that an evaluation of the results of quantitative analyses performed with the program needed to be done. The DTSA program is capable of providing all the peak intensities for each element analyzed; therefore, all of the peak fitting and background fitting functions were removed from the FRAME program. Also, since the database incorporated into DTSA contains all of the peak energies and the excitation energies (absorption edge energies) for all x-ray lines, the fitting procedures for computing these energies were removed from the FRAME program.An important change now in the the ZAF procedure is the computation of the atomic number correction. The absorption correction and the characteristic fluorescence correction are unchanged. A continuum fluorescence correction has not yet been included in the program.

A characteristic fluorescence correction factor for use in electron probe microanalysis. II. Evaluation of experimental results and comparisons

A comparison of a recently published secondary characteristic fluorescence correction method especially with the in electron probe microanalysis commonly used Reed procedure is presented along with evaluations of experimental data from literature taking into account the fluorescence correction using the new model. Special attention is directed to the choice of fundamental parameters, such as mass absorption coefficients, fluorescence yields, relative intensities and ionization cross sections, which are found to influence the corresponding results considerably.

Characteristic fluorescence correction for layered samples part I: Closed solution for film-substrate combination

The main difficulty in solving the corresponding integral expressions for characteristic fluorescence of layered samples consists in the choice of an advantageous approximation of the depth distribution function ϕ (z). In accepting a point source, a linear dependence, or a sum of weighted exponential moments to describe primary excitation, a closed mathematical treatment of secondary excitation effects is possible. Part I of this series is restricted to the frequent case of film substrate samples. The contributing factors of fluorescence excitation are calculated assuming a sum of weighted exponential moments for primary depth distribution and using dimensionless variables. The influence of the shape of primary depth distribution is discussed and can be shown to be less than 5% for bulk conditions.

Experimental Evaluation of Absolute X-RAY Intensities at Low to Moderate Beam Energies

Knowledge of the absolute electron-induced production of the characteristic x-rays for different lines and elements is required for proper evaluation of the characteristic fluorescence correction or for development of “standardless” x-ray quantitative analysis correction procedures. Determination of absolute generated x-ray intensities in thick specimens or even relative generated x-ray intensities for lines of different elements in thick specimens is quite difficult as demonstrated by the lack of agreement of the published attempts to determine absolute generated x-ray intensity yields. The amount of absorption of the generated x-ray intensity in the sample and the amount of x-ray production from secondary fluorescence by other characteristic lines or by the continuum must be calculated. Moreover, the detector efficiency for measuring the different lines must be known. Most investigations of absolute generated x-ray intensities suggest that there is a functional relationship between the generated intensity and the overvoltage (U = Eo/Ec) at which the measurement is made.

The measurement of the fluorescence of Si K x-rays by Au M x-rays

The characteristic fluorescence correction is used in electron probe microanalysis to account for the x-ray intensity excited in element “a” by the x-rays from the characteristic line of another element, “b”, in the sample. Since the excited intensity is not generated by the primary electron beam, it is necessary to apply the fluorescence correction for quantitative elemental analysis. This correction can be significant particularly when element “b” is a major component of the sample and the characteristic line for element “b” is slightly higher in energy than the critical excitation energy for the excited line of element “a”.The fluorescence correction, which is used in the various analytical programs, is described in equation 1.where I'*fa/I'*pa is the ratio of the emitted “a” intensity excited by “b” x-rays to the emitted intensity excited by the primary electron beam. The various parameters in this equation are accurately known for the K x-ray lines, but only very limited information is available for the M x-ray lines.

Fluorescence effects in quantitative microprobe analysis

Characteristic fluorescenceThe theory of characteristic fluorescence corrections was first developed by Castaing. The same approach, with an improved expression for the relative primary x-ray intensities of the exciting and excited elements, was used by Reed, who also introduced some simplifications, which may be summarized as follows (with reference to K-K fluorescence, i.e. K radiation of element ‘B’ exciting K radiation of ‘A’):1.The exciting radiation is assumed to be monochromatic, consisting of the Kα line only (neglecting the Kβ line).2.Various parameters are lumped together in a single tabulated function J(A), which is assumed to be independent of B.3.For calculating the absorption of the emerging fluorescent radiation, the depth distribution of the primary radiation B is represented by a simple exponential.These approximations may no longer be justifiable given the much greater computing power now available. For example, the contribution of the Kβ line can easily be calculated separately.

A general characteristic fluorescence correction for the quantitative electron microbeam analysis of thick specimens, thin films and particles

AbstractA rigorous, general characteristic fluorescence correction for the electron microprobe analysis of samples of given geometry is developed, and specific versions of this equation are presented for the calculation of the fluorescence produced (a) within a homogeneous thin film, (b) in a thin film by x‐ray emission from substrate layers of arbitrary thickness and (c) in a spherical particle. Results of the use of these equations are compared with those obtained using empirical expressions for thin films and show that the empirical expressions are accurate only for films less than 1 μm in thickness. A simplified empirical correction is proposed for particles that is in good agreement with the rigorous correction. The results of calculations using these expressions show that a 2000 Å thick film or a 1 μm diameter particle typically has about 10% of the relative contribution from characteristic fluorescence as occurs in an infinitely thick polished specimen (TPS), a 1 μm thick film has about 30–40% of the contribution in a TPS and a 10 μm diameter particle has more than 50% of the contribution in a TPS. Thus, in particular matrices, certain elements in a 2000 Å thin film or a 1 μm particle can have characteristic fluorescence corrections as high as 5%.

Characteristic x-ray fluorescence correction in thin foil analysis

Characteristic x-ray fluorescence correction in thin foil analysis

A characteristic fluorescence correction for electron-probe microanalysis of thin coatings

An equation is developed for calculating the X-ray fluorescence produced in a coating by characteristic X-rays generated in the substrate material. The correction is applied to experimental microanalysis data obtained for thin coatings deposited on a range of substrate materials and is shown to give satisfactory results. An extension of the method to include multicomponent systems is then described.

Common Sources of Error in Electron Probe Microanalysis

AbstractIn order to reduce the error of quantitative electron probe microanalysis, error sources in the preparation and measurement of specimens and standards must be minimized. These sources of error are described, and literature references for detailed study are given. A critical analysis is made of 150 analytical measurements of binary specimens previously discussed by Poole and Thomas. It is shown that the cases of serious errors reported by these authors are mainly due to poorly characterized or measured specimens and, in. some cases, to the omission of characteristic fluorescence corrections. If these sources of error are eliminated, a much more favorable error distribution can be obtained through relatively simple correction calculations. Further progress in quantitative micro probe analysis is dependent upon measurements under well-controlled conditions and standard materials of experimentally proven microhomogeneity and reliably determined composition.

Characteristic fluorescence corrections in electron-probe microanalysis

A method has been developed for calculating characteristic fluorescence corrections in all cases involving K and L lines, based on the formula derived by Castaing for the case of one K line exciting another K line. A modification to the original formula is proposed, which takes into account more recent work on K line intensities; also some simplifications are suggested which enable corrections to be calculated quickly. Measurements of the relative intensities of K and L lines have been carried out to provide the necessary data for calculating corrections for fluorescence involving K and L lines.