The impact of secondary fluorescence on the material compositions measured by X-ray analysis for layered semiconductor thin films is assessed using simulations performed by the DTSA-II and CalcZAF software tools. Three technologically important examples are investigated: AlxGa1−xN layers on either GaN or AlN substrates, InxAl1−xN on GaN, and Si-doped (SnxGa1−x)2O3 on Si. Trends in the differences caused by secondary fluorescence are explained in terms of the propensity of different elements to reabsorb either characteristic or bremsstrahlung X-rays and then to re-emit the characteristic X-rays used to determine composition of the layer under investigation. Under typical beam conditions (7–12 keV), the quantification of dopants/trace elements is found to be susceptible to secondary fluorescence and care must be taken to prevent erroneous results. The overall impact on major constituents is shown to be very small with a change of approximately 0.07 molar cation percent for Al0.3Ga0.7N/AlN layers and a maximum change of 0.08 at% in the Si content of (SnxGa1−x)2O3/Si layers. This provides confidence that previously reported wavelength-dispersive X-ray compositions are not compromised by secondary fluorescence.

One of the limiting factors for the analysis of minor elements in multiphase materials by electron probe microanalysis is the effect of secondary fluorescence (SF), which is not accounted for by matrix corrections. Although the apparent concentration due to SF can be calculated numerically or measured experimentally, detailed investigations of this effect for fine-grained materials are scarce. In this work, we use the Monte Carlo simulation program PENEPMA to examine and correct the effect of SF affecting micron-sized mineral inclusions hosted by other minerals. A concentration profile across an olivine [(Mg,Fe)2SiO4] inclusion in chromite (Fe2+Cr2O4) is measured and used to assess the reliability of calculations, where different boundary geometries are examined. Three application examples are presented, which include the determination of Cr in olivine and serpentine [Mg3Si2O5(OH)4] inclusions hosted by chromite and of Fe in quartz (SiO2) inclusions hosted by almandine garnet (Fe3Al2Si3O12). Our results show that neglecting SF leads to concentrations that are overestimated by ~0.1–0.8 wt%, depending on inclusion size. In addition, assuming a straight boundary yields to an underestimation of SF effects by a factor of ~2–4. Because its long-range nature, SF severely compromises trace element analyses even for phases as large as 1 mm in size.

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.

Secondary fluorescence effects are important sources of characteristic X-ray emissions, especially for materials with complicated geometries. Currently, three approaches are used to calculate fluorescence X-ray intensities. One is using Monte Carlo simulations, which are accurate but have drawbacks such as long computation times. The second one is to use analytical models, which are computationally efficient, but limited to specific geometries. The last approach is a hybrid model, which combines Monte Carlo simulations and analytical calculations. In this article, a program is developed by combining Monte Carlo simulations for X-ray depth distributions and an analytical model to calculate the secondary fluorescence. The X-ray depth distribution curves of both the characteristic and bremsstrahlung X-rays obtained from Monte Carlo program MC X-ray allow us to quickly calculate the total fluorescence X-ray intensities. The fluorescence correction program can be applied to both bulk and multilayer materials. Examples for both cases are shown. Simulated results of our program are compared with both experimental data from the literature and simulation data from PENEPMA and DTSA-II. The practical application of the hybrid model is presented by comparing with the complete Monte Carlo program.

Secondary fluorescence (SF), typically a minor error in routine electron probe microanalysis (EPMA), may not be negligible when performing high precision trace element analyses in multiphase samples. Other factors, notably wavelength dispersive spectrometer defocusing, may introduce analytical artifacts. To explore these issues, we measured EPMA transects across two material couples chosen for their high fluorescence yield. We measured transects away from the fluorescent phase, and at various orientations with respect to the spectrometer focal line. Compared to calculations using both the Monte Carlo simulation code PENEPMA and the semi-analytical model FANAL, both codes estimate the magnitude of SF, but accurate correction requires knowledge of the position of the spectrometer with respect to the couple interface. Positioned over the fluorescent phase or otherwise results in a factor of 1.2–1.8 of apparent change in SF yield. SF and spectrometer defocusing may introduce systematic errors into trace element analyses, both may be adequately accounted for by modeling. Of the two, however, SF is the dominant error, resulting in 0.1 wt% Zn apparently present in Al at 100 μm away from the Zn boundary in an Al/Zn couple. Of this, around 200 ppm Zn can be attributed to spectrometer defocusing.

Secondary fluorescence, the final term in the familiar matrix correction triumvirate Z·A·F, is the most challenging for Monte Carlo models to simulate. In fact, only two implementations of Monte Carlo models commonly used to simulate electron probe X-ray spectra can calculate secondary fluorescence—PENEPMA and NIST DTSA-IIa (DTSA-II is discussed herein). These two models share many physical models but there are some important differences in the way each implements X-ray emission including secondary fluorescence. PENEPMA is based on PENELOPE, a general purpose software package for simulation of both relativistic and subrelativistic electron/positron interactions with matter. On the other hand, NIST DTSA-II was designed exclusively for simulation of X-ray spectra generated by subrelativistic electrons. NIST DTSA-II uses variance reduction techniques unsuited to general purpose code. These optimizations help NIST DTSA-II to be orders of magnitude more computationally efficient while retaining detector position sensitivity. Simulations execute in minutes rather than hours and can model differences that result from detector position. Both PENEPMA and NIST DTSA-II are capable of handling complex sample geometries and we will demonstrate that both are of similar accuracy when modeling experimental secondary fluorescence data from the literature.