Elemental composition and thickness determination of thin films by electron probe microanalysis

Electron probe microanalysis (EPMA) applies to solid samples of homogenous (bulk) chemical composition and can usually not be applied to structures which are inhomogeneous in the micrometer range such as thin film systems down to a few nm. However, in combination with the established thin film software Stratagem, the thickness as well as the elemental composition of thin films on a substrate can be determined. This has been recently successfully demonstrated for Fe‐Ni on Si and Si‐Ge on Al2O3 thin film systems. For both systems five samples of different elemental composition and a reference were produced and characterised by inductively coupled plasma mass spectrometry (ICP‐MS), Rutherford backscattering (RBS), and transmission electron microscopy (TEM) as reference values. Last year, a new and open‐source thin film evaluation programme called BadgerFilm has been released. It can also be used to determine thin film composition and thickness from intensity ratios of the unknown sample and standards (k‐ratios). In this contribution, we re‐evaluated the data acquired for the Fe‐Ni and Si‐Ge systems using the BadgerFilm software package and compared the obtained elemental compositions and thickness values with the results of the Stratagem software and the reference methods. The conclusion is that the BadgerFilm software shows good agreement with the elemental composition and thickness calculated by Stratagem (mostly <2% for both composition and thickness) and with the reference values for two representative thin film systems (<1%–2% for composition and <10%–20% for thickness).

can also be used to determine thin film composition and thickness from intensity ratios of the unknown sample and standards (k-ratios). In this contribution, we reevaluated the data acquired for the Fe-Ni and Si-Ge systems using the BadgerFilm software package and compared the obtained elemental compositions and thickness values with the results of the Stratagem software and the reference methods. The conclusion is that the BadgerFilm software shows good agreement with the elemental composition and thickness calculated by Stratagem (mostly <2% for both composition and thickness) and with the reference values for two representative thin film systems (<1%-2% for composition and <10%-20% for thickness).

| INTRODUCTION
There are several published studies that prove the capability of electron probe microanalysis (EPMA), in both variants WDS (wavelength-dispersive X-ray spectroscopy) and EDS (energydispersive X-ray spectroscopy) detection modes, to determine accurately the elemental composition and thickness of thin films 1-5 by employing the thin film analysis software package Stratagem. 6 The Stratagem quantification algorithm was developed by Pouchou and Pichoir, who initially made significant progress on building models for the standards based and standardless analysis of homogeneous bulk specimens. 7,8 These models imply the description of the number of ionizations for different depths in the sample, which is called the ϕ (ρz) ionization depth distribution curve. Normally, for the calculation of the elemental composition of an unknown sample, the so-called kratios (or k-values) need to be determined, which are a common parameter for standard-based analysis. It is defined as the peak intensity ratio of a certain line l of a certain element i after background subtraction between the unknown sample and a standard sample, normalized to live time and beam current: For a pure element standard 0 ≤ k ≤ 1. When the k-ratios are used, uncertainties in the atomic data such as the fluorescence yield of a certain X-ray line and experimental uncertainties such as the detector efficiency cancel out. Also, other over-or underestimated corrections which are applied to both, unknown and standard samples, reduce the errors and make the calculated results more reliable.
Pouchou and Pichoir also extended the models and developed methods to analyse thin films on substrates. In this case, different ϕ (ρz) curves need to be calculated for each film and the substrate. In addition, characteristic and bremsstrahlung fluorescence produced in one of the layers can significantly influence the X-ray excitation process in other layer(s), and these effects need to be taken into account.
Using these models, it is possible to determine the film mass thicknesses (ρz, in μg/cm 2 , or mass deposition) as well as the film(s) and substrate elemental compositions. 9 By assuming a density of the film, the thickness can be extracted. It was demonstrated that the unconventional way of introducing the film thickness (an easily measurable parameter) into the software results in the overall film density. 10 Particularly for porous films, this parameter is of particular relevance, 11 because if related to an assumed skeletal density of the material walls within the film, it will lead to the film porosity. The latter holds true under the assumption that the ϕ (ρz) model does not significantly deviates for this type of geometry (the model assumes 'solid' films), that is, the size of the pores is small enough.
In Stratagem, the k-ratios need to be provided. To improve the accuracy of the calculation of the chemical composition and thickness of the thin layer(s), k-ratios at different accelerating voltages shall be used. The reason for this is that at low acceleration voltages, where the electrons have a small penetration depth, the interaction volume is close to the surface and mainly interacts in the films. With higher acceleration voltages the interaction volume expands further into the sample and, therefore, further into the substrate. The k-ratios of elements only present in the film normally decrease with the accelerating voltage while the k-ratios of the elements in the substrate increase.
Once having calculated the k-ratios from the measurements of the unknown and standard samples, the Stratagem algorithm starts fitting the provided k-ratios for different acceleration voltages simultaneously by calculating theoretical k-ratios using the ϕ (ρz) models.
Several thin film material systems have been published as being successfully analysed with Stratagem with respect to the determination of their elemental composition and thickness. [1][2][3][4][5] Recently, Moy  Further studies and refinements of the algorithm for thin film systems and application examples were also published recently by Moy and Fournelle. 13 The data that need to be provided for the calculation of such thin film systems are the k-ratios of the constituent elements for one or more accelerating voltages.
In this contribution, we re-evaluated the data acquired for the Fe- Hence, for the analysis of the Al 2 O 3 substrate, only the Al Kα line has been evaluated in the analysis and the oxygen has been co-quantified by setting it stoichiometrically to Al.
As already described in the Introduction, the same k-ratios as measured and reported in Hodoroaba et al. 14   behaviour of the k-ratios fits for these two thin film systems as illustrated in Figure 1 is representative for all the other samples of different relative compositions.

| RESULTS AND DISCUSSION
Once having the k-ratios fitted as in Figure 1 for all the samples, the elemental composition and thickness of all the thin films of the two film system sets could be calculated by the BadgerFilm software. F I G U R E 3 Film thickness for the series of (A) Fe-Ni and (B) Si-Ge films as calculated by Stratagem (in red), by BadgerFilm (in blue), from the same measured k-ratios, and as measured by TEM. In the upper panels the relative deviation of the calculated thicknesses to the reference values measured by TEM are shown.