An empirical approach to K-shell ionisation cross section by electrons

X-ray production cross sections for Ir and Bi M-subshells induced by electron impact

M-subshell X-ray production cross sections were indirectly measured for Ir and Bi targets irradiated with monoenergetic electron beams. The projectile energy range ran from 2.2 to 28 keV, impinging on Ir and Bi pure bulk targets in a scanning electron microscope. The resulting X-ray emission spectra were acquired with an energy dispersive spectrometer, and processed afterwards by means of a robust parameter optimization procedure developed previously. X-ray production cross sections were finally obtained through an approach involving an analytical prediction for the emission spectra, which relies on the ionization depth distribution function. The values obtained by this approach were compared with empirical and theoretical predictions, appealing to different relaxation data taken from the literature.

Measurement and Calculation of X-Ray Production Efficiencies for Copper, Zirconium, and Tungsten

Electron probe microanalysis (EPMA) is based on physical relations between measured X-ray intensities of characteristic lines and their X-ray production efficiency, which depends on the specimen composition. The quality of the analysis results relies on how realistically the physical relations describe the generation and emission of X-rays. Special experiments are necessary to measure X-ray production efficiencies. A challenge in these experiments is the determination of the detection efficiency of the spectrometer as a function of the photon energy. An energy-dispersive spectrometer was used in this work, for which the efficiency was determined at metrological synchrotron beamlines with an accuracy of ±2%. X-ray production efficiencies for the L series and the Kα series of copper and zirconium and for the M and L series of tungsten were determined at energies up to 30 keV in a scanning electron microscope. These experimental values were compared with calculated X-ray production efficiencies using physical relations and material constants applied in EPMA. The objective of the comparison is the further improvement of EPMA algorithms as well as extending the available database for X-ray production efficiencies. Experimental data for the X-ray production efficiency are also useful for the assessment of spectrum simulation software.

Electron spectroscopy with a diamond detector

An electronic grade single crystal chemical vapour deposition diamond was investigated as a prototype high temperature spectroscopic electron (β^- particle) detector for future space science instruments. The diamond detector was coupled to a custom-built charge-sensitive preamplifier of low noise. A ⁶³Ni radioisotope source (endpoint energy 66 keV) was used to provide a spectrum of β^- particles incident on the detector. The operating temperature of the detector/preamplifier assembly was controlled to allow its performance to be investigated between +100 °C and -20 °C, in 20 °C steps. Monte Carlo modelling was used to: a) calculate the β^- particle spectrum incident on the detector; b) calculate the fraction of β^- particle energy deposited into the detector; and c) predict the β^- particle spectrum accumulated by the instrument. Comparison between the model and experimental data suggested that there was a 4.5 μm thick recombination region at the front of the detector. The spectrometer was demonstrated to be fully operable at temperatures, T, -20 °C ≤ T ≤ 80 °C; the results suggested that some form of polarisation phenomenon occurred in the detector at > 80 °C. This article presents the first report of an energy calibrated (≲ 50 keV) spectroscopic β^- particle diamond detector.

The f-ratio model for quantitative X-ray microanalysis

The f-ratio method is a new quantitative X-ray microanalysis method developed based on a cold field emission scanning electron microscope/energy dispersive spectroscopy system. The f-ratio is calculated with the characteristic X-ray intensities, and the Monte Carlo simulation is employed to build the theoretical relation between the system composition and the f-ratio. In this study, the f-ratio model is formulated with the elemental concentrations and the f-ratio coefficients. The f-ratio models in the binary S-Fe system and the ternary O-Al-Si system were studied, and the beam energy effects were investigated. The quantitative analyses were performed on the standard pyrite (FeS₂) and kyanite (Al₂SiO₅) specimens, and the results show that the f-ratio model is able to achieve a satisfying accuracy.

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

In electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

The f-Ratio Quantification Method for X-ray Microanalysis Applied to Mg-Al-Zn Alloys

The f-ratio quantitative X-ray microanalysis method has been recently developed for binary systems based on a scanning electron microscope/energy dispersive spectroscopy (SEM/EDS) system. This method incorporates traditional EDS experiments and Monte Carlo simulations, and calibration factors are calculated with standard samples to evaluate the differences between them. In this work, the f-ratio method was extended to Mg-Al-Zn multi-element systems using a cold field emission SEM and a tungsten emission SEM. Results show that the stability of the beam current does not influence the f-ratio quantification accuracy. Thus, the f-ratio method is suitable for quantitative X-ray mapping with a long-time acquisition or even an unstable beam current. Comparing with other quantitative techniques including the routine standardless analysis and the standard-based k-ratio method, the f-ratio method is a simple and accurate quantification method.

Impact of the pulse contrast ratio on molybdenum Kα generation by ultrahigh intensity femtosecond laser solid interaction

We present an extended experimental study of the absolute yield of Kα x-ray source (17.48 keV) produced by interaction of an ultrahigh intensity femtosecond laser with solid Mo target for temporal contrast ratios in the range of 1.7 × 107-3.3 × 109 and on three decades of intensity 1016-1019  W/cm². We demonstrate that for intensity I ≥ 2 × 1018  W/cm² Kα x-ray emission is independent of the value of contrast ratio. In addition, no saturation of the Kα photon number is measured and a value of ~2 × 1010 photons/sr/s is obtained at 10 Hz and I ~1019  W/cm². Furthermore, Kα energy conversion efficiency reaches the same high plateau equal to ~2 × 10-4 at I = 1019  W/cm² for all the studied contrast ratios. This original result suggests that relativistic J × B heating becomes dominant in these operating conditions which is supposed to be insensitive to the electron density gradient scale length L/λ. Finally, an additional experimental study performed by changing the angle of incidence of the laser beam onto the solid target highlights a clear signature of the interplay between collisionless absorption mechanisms depending on the contrast ratio and intensity.

Determination of the Effective Detector Area of an Energy-Dispersive X-Ray Spectrometer at the Scanning Electron Microscope Using Experimental and Theoretical X-Ray Emission Yields

A method is proposed to determine the effective detector area for energy-dispersive X-ray spectrometers (EDS). Nowadays, detectors are available for a wide range of nominal areas ranging from 10 up to 150 mm2. However, it remains in most cases unknown whether this nominal area coincides with the "net active sensor area" that should be given according to the related standard ISO 15632, or with any other area of the detector device. Moreover, the specific geometry of EDS installation may further reduce a given detector area. The proposed method can be applied to most scanning electron microscope/EDS configurations. The basic idea consists in a comparison of the measured count rate with the count rate resulting from known X-ray yields of copper, titanium, or silicon. The method was successfully tested on three detectors with known effective area and applied further to seven spectrometers from different manufacturers. In most cases the method gave an effective area smaller than the area given in the detector description.

Self-consistent method for quantifying indium content from X-ray spectra of thick compound semiconductor specimens in a transmission electron microscope

Based on Monte Carlo simulations of X-ray generation by fast electrons we calculate curves of effective sensitivity factors for analytical transmission electron microscopy based energy-dispersive X-ray spectroscopy including absorption and fluorescence effects, as a function of Ga K/L ratio for different indium and gallium containing compound semiconductors. For the case of InGaN alloy thin films we show that experimental spectra can thus be quantified without the need to measure specimen thickness or density, yielding self-consistent values for quantification with Ga K and Ga L lines. The effect of uncertainties in the detector efficiency are also shown to be reduced.

Quantum-trajectory Monte Carlo method for study of electron–crystal interaction in STEM

A quantum trajectory Monte Carlo method is developed to simulate electron scattering and secondary electron cascade process in crystalline specimen.

Interfacial energy-dispersive spectroscopy profile X-ray resolution measurements in variable pressure SEM

A procedure has been developed to follow degradation of energy-dispersive spectroscopy (EDS) X-ray lateral resolution in a variable pressure scanning electron microscope. This procedure is based on evaluation of the EDS profile shape change for different experimental conditions. Some parameters affecting the X-ray resolution in high-vacuum mode have been taken into account. Good agreement between the simulated and experimental EDS profiles shows the reliability of the proposed procedure. A significant improvement in measurement of the EDS profile interfacial distance (DINT) has been achieved.

The secondary X-ray fluorescence and absorption near the interface of multi-material: case of EDS microanalysis

A simple model is proposed to take into account secondary X-ray fluorescence and absorption effects near the interface. This model is based on the investigation of the shape change of the first derivative equation that can fit the sigmoidal EDS profile obtained when a high vacuum electron beam passes through the interface of two adjacent materials. The contribution of the photoelectric absorption of primary X-rays (characteristic and Bremsstrahlung) and the secondary fluorescence on the degradation of the X-ray spatial resolution can be easily quantified. The close agreement between the simulated (Monte Carlo simulation using the Casino software) and the experimental data serves to assess the reliability of this developed model.

Experimental and Monte Carlo simulated spectra of a liquid-metal-jet x-ray source

A prototype x-ray system based on a liquid-metal-jet anode was evaluated within the framework of the LABSYNC project. The generated spectrum was measured using a CZT-based spectrometer and was compared with spectra simulated by three Monte Carlo codes: MCNPX, PENELOPE and EGS5. Notable differences in the simulated spectra were found. These are mainly attributable to differences in the models adopted for the electron-impact ionization cross section. The simulation that more closely reproduces the experimentally measured spectrum was provided by PENELOPE.

Analysis of biologically-derived small particles--searching for geometry correction factors using Monte Carlo simulation

A Monte Carlo simulation was used to determine geometry correction factors that increase accuracy of quantitative X-ray microanalysis of laterally semithick biological materials. A model composed of cellulose with homogeneously distributed biological elements and lateral dimensions between 0.5-25 μm was chosen. The specimen was exposed to 5, 10, and 15 keV electrons, the net intensities of characteristic X-rays registered for the elements, and presented as a function of the lateral dimensions of the model. This showed the double decay exponential function fitted the distribution of X-ray intensities in relation to the model size. The applicability of the function as a correction method was successfully tested for 30 specimens with varying composition and dimensions. The value of relative error decreased from ±60% to ±5% when the correction was applied. Moreover, the minimal lateral size of the material was defined, below which the correction is not required. The simulation also revealed that the difference of the weighted sum of Z²/A between the unknown and the standard could reach 25% without significant influence on the quantitative results. The correction method could be helpful for accurate assessment of elemental composition in biological or organic matrices, when their lateral dimensions are smaller than the distribution range.

Proton induced quasi-monochromatic x-ray beams for soft x-ray spectroscopy studies and selective x-ray fluorescence analysis

We present the analytical features and performance of an x-ray spectroscopy end station of moderate energy resolution operating with proton-induced quasi-monochromatic x-ray beams. The apparatus was designed, installed and operated at the 5.5 MV Tandem VdG Accelerator Laboratory of the Institute of Nuclear Physics, N.C.S.R. "Demokritos," Athens. The setup includes a two-level ultrahigh vacuum chamber that hosts in the lower level up to six primary targets in a rotatable holder; there, the irradiation of pure element materials-used as primary targets-with few-MeV high current (~μA) proton beams produces intense quasi-monochromatic x-ray beams of selectable energy. In the chamber's upper level, a six-position rotatable sample holder hosts the targets considered for x-ray spectroscopy studies. The proton-induced x-ray beam, after proper collimation, is guided to the sample position whereas various filters can be also inserted along the beam's path to eliminate the backscattered protons or/and to absorb selectively components of the x-ray beam. The apparatus incorporates an ultrathin window Si(Li) spectrometer (FWHM 136 eV at 5.89 keV) coupled with low-noise electronics capable of efficiently detecting photons down to carbon Kα. Exemplary soft x-ray spectroscopy studies and results of selective x-ray fluorescence analysis are presented.

What remains to be done to allow quantitative X-ray microanalysis performed with EDS to become a true characterization technique?

This article reviews different methods used to perform quantitative X-ray microanalysis in the electron microscope and also demonstrates the urgency of measuring the fundamental parameters of X-ray generation for the development of accurate standardless quantitative methods. Using ratios of characteristic lines acquired on the same X-ray spectrum, it is shown that the Cliff and Lorimer K A-B factor can be used in a general correction method that is appropriate for all types of specimens and electron microscopes, providing that appropriate corrections are made for X-ray absorption, fluorescence, and indirect generation. Since the fundamental parameters appear in the K A-B factor, only the ratio of the ionization cross sections needs to be known, not their absolute values. In this regard, the measurement of ratios of the K A-B factor (or intensities at different beam energies of the same material with no change of beam spreading in the material) permits the validation for the best models to compute the ratio of ionization cross sections. It is shown, using this method, that the nonrelativistic Bethe equation, to compute ionization cross section, is very close to the equation of E. Casnati et al. (J Phys B 15, 155-167, 1982) and also to the equations proposed by D. Bote and F. Salvat (Phys Rev A 77, 042701, 2008) for the computation of the ratio of ionization cross sections. The method is extended to show that it could be used to determine the values of the Coster-Kronig transitions factors, an important fundamental parameter for the generation of L and M lines that is mostly known with poor accuracy. The detector efficiency can be measured with specimens where their intensities were measured with an energy dispersive spectrometer detector, the efficiency of which has been measured in an X-ray synchrotron (M. Alvisi et al., Microsc Microanal 12, 406-415, 2006). The spatial resolution should always be computed when performing quantitative X-ray microanalysis and the equations of R. Gauvin (Microsc Microanal 13(5), 354-357, 2007) for bulk materials and the one presented in this article for thin films should be used. The effects of X-rays generated by fast secondary electrons and by Auger electrons are reviewed, and their effect can be detrimental for the spatial resolution of materials involving low-energy X-ray lines, in certain specific conditions. Finally, quantitative X-ray microanalysis of heterogeneous materials is briefly reviewed.

Development of a new quantitative X-ray microanalysis method for electron microscopy

Quantitative X-ray microanalysis of thick samples is usually performed by measuring the characteristic X-ray intensities of each element in a sample and in corresponding standards. The ratio of the measured intensities from the unknown material to that from the standard is related to the concentration using the ZAF or ϕ(ρz) equations. Under optimal conditions, accuracies approaching 1% are possible. However, all the experimental conditions must remain the same during the sample and standard measurements. This is not possible with cold field emission scanning electron microscopes (FE-SEMs) where beam current can fluctuate around 5% in its stable regime. Very little work has been done on variable beam current conditions (Griffin, B.J. & Nockolds, C.E., Scanning 13, 307-312, 1991), and none relating to cold FE-SEM applications. To address this issue, a new method was developed using a single spectral measurement. It is similar in approach to the Cliff-Lorimer method developed for the analytical transmission electron microscope. However, corrections are made for X rays generated from thick specimens using the ratio of the characteristic X-ray intensities of two elements in the same material. The proposed method utilizes the ratio of the intensity of a characteristic X-ray normalized by the sum of X-ray intensities of all the elements measured for the sample, which should also reduce the amplitude of error propagation. Uncertainties in the physical parameters of X-ray generation are corrected using a calibration factor that must be previously acquired or calculated. As an example, when this method was applied to the calculation of the composition of Au-Cu National Institute of Standards and Technology standards measured with a cold field emission source SEM, relative accuracies better than 5% were obtained.

Spectrum simulation in DTSA-II

Spectrum simulation is a useful practical and pedagogical tool. Particularly with complex samples or trace constituents, a simulation can help to understand the limits of the technique and the instrument parameters for the optimal measurement. DTSA-II, software for electron probe microanalysis, provides both easy to use and flexible tools for simulating common and less common sample geometries and materials. Analytical models based on (rhoz) curves provide quick simulations of simple samples. Monte Carlo models based on electron and X-ray transport provide more sophisticated models of arbitrarily complex samples. DTSA-II provides a broad range of simulation tools in a framework with many different interchangeable physical models. In addition, DTSA-II provides tools for visualizing, comparing, manipulating, and quantifying simulated and measured spectra.

Investigation of range-energy relationships for low-energy electron beams in silicon and gallium nitride

The electron beam technique of the Scanning Electron Microscopy (SEM) has been widely used for the characterization of bipolar devices and photodiode materials. The resolution of an electron beam technique is affected by the interaction of the beam and the specimen. The size of this interaction volume, commonly termed the generation volume, is usually characterized by what is called the electron penetration range and is measured from the surface. Since there is currently no consensus on the expressions to use in the calculation of the electron range, this paper provides an analysis of the three most commonly used semiempirical expressions. They are the Gruen range, the universal curve of Everhart and Hoff, and the maximum range of Kanaya and Okayama. This analysis is done using data from the statistical method of Monte Carlo simulations. It was found that the Everhart and Hoff universal curve performs better at low beam energies than the equation of Kanaya and Okayama. However, the validity of all the three expressions is questionable below 5 keV. In order to overcome this, fitted expressions based on the extrapolated range are provided for beam energies below 5 keV in the case of Si and GaN materials. The accuracy of these expressions is affected by the physical parameters used in the Monte Carlo simulations.

On the production of X-rays by low energy ion beams

Although electron beams with energies of a few keV can excite fluorescent X-ray production from solids, ion beams of comparable energy cannot do so. The reason for this situation is that it is the velocity of the incident particle, rather than its energy, which determines whether an ionization event can be generated.

Win X-ray: a new Monte Carlo program that computes X-ray spectra obtained with a scanning electron microscope

A new Monte Carlo program, Win X-ray, is presented that predicts X-ray spectra measured with an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM) operating between 10 and 40 keV. All the underlying equations of the Monte Carlo simulation model are included. By simulating X-ray spectra, it is possible to establish the optimum conditions to perform a specific analysis as well as establish detection limits or explore possible peak overlaps. Examples of simulations are also presented to demonstrate the utility of this new program. Although this article concentrates on the simulation of spectra obtained from what are considered conventional thick samples routinely explored by conventional microanalysis techniques, its real power will be in future refinements to address the analysis of sample classifications that include rough surfaces, fine structures, thin films, and inclined surfaces because many of these can be best characterized by Monte Carlo methods. The first step, however, is to develop, refine, and validate a viable Monte Carlo program for simulating spectra from conventional samples.

The quantitative analysis of thin specimens: a review of progress from the Cliff-Lorimer to the new zeta-factor methods

A new quantitative thin-film X-ray analysis procedure termed the zeta-factor method is proposed. This new zeta-factor method overcomes the two major limitations of the conventional Cliff-Lorimer method for quantification: (1) use of pure-element rather than multielement, thin-specimen standards and (2) built-in X-ray absorption correction with simultaneous thickness determination. Combined with a universal, standard, thin specimen, a series of zeta-factors covering a significant fraction of the periodic table can be estimated. This zeta-factor estimation can also provide information about both the detector efficiency and the microscope-detector interface system. Light-element analysis can also be performed more easily because of the built-in absorption correction. Additionally, the new zeta-factor method has several advantages over the Cliff-Lorimer ratio method because information on the specimen thickness at the individual analysis points is produced simultaneously with compositions, thus permitting concurrent determination of the spatial resolution and the analytical sensitivity. In this work, details of the zeta-factor method and how it improves on the Cliff-Lorimer approach are demonstrated, along with several applications.

X-ray microanalysis of a coated nonconductive specimen: Monte Carlo simulation

The microanalysis of nonconductive specimen in a scanning electron microscope is limited by charging effects. Using a charge density model for the electric field buildup in a nonconductive specimen irradiated by electrons, a Monte Carlo simulation method has been applied to alumina (Al2O3). The results show a change in the depth distribution for characteristic and bremsstrahlung X-ray, phi(pz) curves, and psi(pz) curves (with absorption) for both elements' K alpha lines. The influence of the electric field on the measured X-ray intensity is shown. The dependency of this influence by the three parameters, electron energy, X-ray energy, and charge density, is clarified.

Measurement of X-ray emission efficiency for K-lines

Results for the X-ray emission efficiency (counts per C per sr) of K-lines for selected elements (C, Al, Si, Ti, Cu, Ge) and for the first time also for compounds and alloys (SiC, GaP, AlCu, TiAlC) are presented. An energy dispersive X-ray spectrometer (EDS) of known detection efficiency (counts per photon) has been used to record the spectra at a takeoff angle of 25 degrees determined by the geometry of the secondary electron microscope's specimen chamber. Overall uncertainty in measurement could be reduced to 5 to 10% in dependence on the line intensity and energy. Measured emission efficiencies have been compared with calculated efficiencies based on models applied in standardless analysis. The widespread XPP and PROZA models give somewhat too low emission efficiencies. The best agreement between measured and calculated efficiencies could be achieved by replacing in the modular PROZA96 model the original expression for the ionization cross section by the formula given by Casnati et al. (1982) A discrepancy remains for carbon, probably due to the high overvoltage ratio.