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Experimental determination of the oxygen K-shell fluorescence yield using thin SiO2 and Al2O3 foils
Spectrochimica Acta Part B 124 (2016) 94–98
Contents lists available at ScienceDirect
Spectrochimica Acta Part B journal homepage: www.elsevier.com/locate/sab
Experimental determination of the oxygen K-shell fluorescence yield using thin SiO2 and Al2O3 foils P. Hönicke ⁎, M. Kolbe, M. Krumrey, R. Unterumsberger, B. Beckhoff Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany
a r t i c l e
i n f o
Article history: Received 25 July 2016 Received in revised form 23 August 2016 Accepted 24 August 2016 Available online 28 August 2016 Keywords: Atomic fundamental parameters X-ray fluorescence spectroscopy Fluorescence yield X-ray reflectometry Quantitative analysis
a b s t r a c t In this work, the K-shell fluorescence yield for oxygen ωO,K−shell is determined experimentally, employing the radiometrically calibrated X-ray fluorescence instrumentation of the Physikalisch-Technische Bundesanstalt (PTB), Germany's National Metrology Institute. Four free-standing thin foils with two different thicknesses of both SiO2 and Al2O3 were used in order to derive an experimental value for this atomic fundamental parameter. Multiple excitation photon energies were applied to record fluorescence spectra of all four samples. The resulting value (ωO,K−shell = 0.00688 ± 0.00036) is almost 20 % higher than the commonly used value from the Krause tables [M. Krause, Atomic Radiative and Radiationless Yields for K and L shells, J. Phys. Chem. Ref. Data 8(2), 307–327 (1979)]. In addition, the achieved total uncertainty budget for the new experimental value is reduced significantly in comparison to available literature data. For validation purposes, thin SiO2 layers on Si samples were used. Here, the layer thicknesses derived from X-ray reflectometry are well in line with our X-ray fluorescence quantification results based on the new experimental value for the O K-shell fluorescence yield. © 2016 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
The ongoing development of thin film materials for applications in different fields of research and production often require an accurate and reliable analysis. If a non-destructive quantitative characterization of the elemental composition is needed, often only fundamental parameter-based – or even reference-free X-ray fluorescence (XRF) spectroscopy is available as an analytical method due to the extremely low availability of reference materials or calibration samples with sufficient similarity to the analytical problem in terms of the matrix elemental and spatial composition. This is particularly the case for nanoscaled material systems, where the variety of element combinations and analytical questions increases steadily and at a much faster pace than that at which reference materials can currently be developed. However, the achievable accuracy of the quantitative results is often limited by the uncertainty of the fundamental parameters involved. Especially for low-Z elements, they are large and often only estimated. This drastically limits the feasibility of fundamental parameter based quantification for light elements such as oxygen. As particularly oxides are very much present in many fields of research and production, this is a very interesting chemical element for an experimental determination of the atomic fundamental parameters.
The Physikalisch-Technische Bundesanstalt (PTB) has experimental access to the determination of atomic fundamental parameters by employing the reference-free XRF approach [1,2]. For the experiments, an in-house developed ultrahigh vacuum chamber dedicated to reference-free XRF analysis in various geometries [3] was installed in the focal plane of PTB's plane grating monochromator (PGM) beamline [4] at the BESSY II electron storage ring. The samples were placed in a conventional 45°–45° XRF beam geometry on an X-Y scanning stage in the center of the measurement chamber. The emitted fluorescence radiation is detected by a silicon drift detector (SDD), calibrated with respect to its detection efficiency and response behavior [5]. The energy-dispersive SDD is mounted behind a calibrated diaphragm at a well-defined distance from the sample, which defines the solid angle of detection with a relative uncertainty of 0.7 % [6]. The incident photon flux is determined using calibrated photodiodes, the efficiency of which is known with relative uncertainties below 1 % [7]. For the experimental determination of the oxygen K-shell fluorescence yield, four free-standing thin foil samples were obtained from Lebow Company (Goleta, CA, USA). Two aluminum oxide and two silicon dioxide foils with nominal thicknesses of 100 nm and 500 nm were employed. Both the fluorescence and transmission experiments were conducted in the photon energy range between 380 eV to 850 eV. From the photon energy-dependent transmission of each foil, mass attenuation coefficients can be derived and used for a correction
⁎ Corresponding author. E-mail address: [email protected] (P. Hönicke).
http://dx.doi.org/10.1016/j.sab.2016.08.024 0584-8547/© 2016 Elsevier B.V. All rights reserved.
P. Hönicke et al. / Spectrochimica Acta Part B 124 (2016) 94–98
of the attenuation effects within each sample independently of database values for mass attenuation coefficients. The fluorescence production cross section σO,K−shell(E0) for the oxygen K-shell at a photon energy E0 can be calculated according to Eq. (1), where ωO,K−shell is the fluorescence yield of the O K-shell and τO,K−shell(E0) is the photoionization cross section of the O K-shell for photons of energy E0. The density ρ and thickness d or the mass deposition ρd of the thin foil sample in use does not have to be known here, as only the products of the photoionization cross section and ρd and of the mass attenuation coefficient and ρd need to be known [8]. They can be derived from transmission experiments applying the Lambert-Beer law. σ O;K−shell ðE0 Þρd ¼ ωO;K−shell τO;K−shell ðE0 Þρd ¼
ΦdOKα ðE0 ÞMOKα;E0 Ω Φ0 ðE0 Þ 4π
ð1Þ
The fluorescence photon flux ΦdOKα(E0) is derived from the recorded fluorescence spectra by deconvolving all relevant contributions. The detector response functions for all relevant fluorescence lines as well as relevant background contributions, e.g. bremsstrahlung originating from photo and Auger electrons as well as the resonant Raman scattering background, are used for the spectral deconvolution. The incident Ω photon flux Φ0(E0) and the solid angle of detection 4π are known due to the use of calibrated instrumentation. The attenuation correction factor MOKα,E0 for the incident - as well as the O-Kα fluorescence radiation is determined by Eq. (2), where μS,E0 and μS,EOKα are the mass attenuation coefficients of the foil at the incident photon energy and the fluorescence line energy.
MOKα;E0
μ S;E0 ρd μ S;EOKα ρd þ sinθin sinθout ¼ μ S;E0 ρd μ S;EOKα ρd þ 1− exp − sinθin sinθout
ð2Þ
For a validation of the experimentally determined O K-shell fluorescence yield, different SiO2 layers on silicon were used. The samples with nominal SiO2 layer thicknesses of 2 nm, 6 nm and 10 nm were independently investigated by X-ray reflectometry (XRR). XRR is a wellestablished technique for nanolayer thickness determination which is based on interference effects of X-rays reflected at the layer surface and at the layer-substrate interface. By varying the grazing incidence angle, oscillations in the reflectance are observed and their period relates the layer thickness to the X-ray wavelength. For typically used Cu Ka radiation, the oscillations for SiO2 layers on silicon are relatively weak as the optical constants of Si and SiO2 are very similar at 8 keV. Moreover, the unavoidable carbonaceous contamination layer that covers most surfaces can influence the results for very thin oxide layers. Both limitations can be avoided by using synchrotron radiation, as the measurements can be performed at the Si K-edge at 1.84 keV [9] or even around the O K-edge at 0.53 keV [10]. As only the SiO2 layer contains oxygen, both layers can be separated if the reflectance curves measured at energies below and above the edge are simultaneously modeled. Furthermore, much steeper incidence angles can be used, also enabling the investigation of a strongly curved surface e.g. on a sphere as required for the redefinition of the unit kilogram via the Avogadro constant [11]. Both the thin SiO2-layers used here and the presented XRR methodology were developed within the Avogadro project.
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measured mass attenuation around the O K-edge by means of a corresponding separation of the various contributions. Due to the use of compound thin foils, an additional contribution to the measured mass attenuation around the O K-edge from the respective bonding partner must be taken into account in order to derive the required product of the photoionization cross section from the O K-edge and ϱd (τO−K(E0)ϱd). As both Si and Al do not have any absorption edges in the relevant photon energy range, their contribution to the total mass attenuation of the sample is a simple exponential decay in the first approximation (see Fig. 1). Moreover, the normalized difference between the contribution of the higher oxygen shells and the relevant shells of the respective bonding partner does not change significantly in the photon energy range of the O K-edge. Instead of having to take into account both the sample stoichiometry and the resulting combined mass attenuation, this allows a deconvolution of the experimentally determined mass attenuation into a combined contribution from scattering and the higher shells of oxygen and the bonding partner as well as the photoelectric cross section of the O K-absorption edge. The combined contribution can be approximated well enough using the tabulated energy dependence of the bonding partner's mass attenuation coefficient multiplied with a fictitious ϱd⁎, which is derived from the experimental data below the O K-edge. The product of the photoionization cross section from the O K-edge and ϱd (τO,K−shell(E0)ϱd) can then be derived using the extrapolated mass attenuation contribution of all higher shells (μAl,Si+O⁎(E0)ϱd⁎) according to Eq. (3). This is depicted in Fig. 2.
τO;K−shell ðE0 Þϱd ¼ μ ðE0 Þϱd−μ Al;SiþO ðE0 Þϱd
ð3Þ
The fluorescence intensities of the O-Kα line are derived from the SDD spectra by deconvolution using the known detector response functions [5] as well as relevant background contributions for bremsstrahlung from photoelectrons and resonant Raman scattering [13]. The bremsstrahlung originates from photo and Auger electrons, whereas the resonant Raman background originates from O-Kα fluorescence photons being Raman scattered at the O K-absorption edge on their way through the sample. In Fig. 3, a fluorescence spectrum obtained on the 100 nm SiO2 foil at an excitation energy of 620 eV as well as a modeled spectrum are shown. The derived count rate DOKα for the O-Kα fluorescence line from the deconvoluted spectra is used to determine the detected fluorescence photon flux ΦdOKα(E0) by normalization of the SDD's detection efficiency for O-Kα photons.
2.1. Data evaluation For the experimental determination of the K-shell fluorescence yield of oxygen, also the photoionization cross section for oxygen at the chosen incident photon energies has to be known. Taking into account that the mass attenuation coefficient is the sum of all shells' photoionization probabilities as well as of the cross sections for coherent and incoherent scattering, one can derive the K-shell ionization cross section from the
Fig. 1. Comparison of the tabulated relevant contributions [12] to the measured mass attenuation in the photon energy range of the O K-edge. For oxygen, only the sum of the relevant higher shells and the scattering contribution is plotted (μO⁎). On the right axis, the depicted normalized differences are plotted.
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Fig. 2. Experimentally determined product of attenuation coefficients, layer thickness and density (black dots and grey asterisks) around the O K-absorption edge on the SiO2 foil with a nominal thickness of 500 nm. The extrapolated contribution of higher shells (grey+) and of the O K-shell are also marked.
3. Results and discussion The derived values for the product of the photoionization cross section from the O K-edge and mass deposition τO,K−shell(E0)ϱd and the derived fluorescence photon fluxes ΦdOKα(E0) can then be used to calculate the fluorescence yield for the O K-edge according to Eq. (1). This was done for each excitation energy and sample. In Fig. 4, the results for the 100 nm SiO2 sample are shown as a function of the incident photon energy. The good agreement between results obtained at different incident photon energies indicates that the approximated higher shell contribution to the total mass attenuation coefficient is appropriate within this limited excitation energy range. Only the value obtained at 540 eV is slightly lower which is due to the fact that this excitation energy is very close to the π*-resonance (see Fig. 2), where higher harmonic contributions of the undulator and the plane grating monochromator [4] can influence the measured foil transmittance. The same procedure was applied to the other oxide foil samples in order to derive experimental values of the O K-fluorescence yield. For each sample, the weighted mean of all values determined at the different excitation photon energies was calculated and is shown in Fig. 5 in
Fig. 3. Fluorescence spectrum obtained on the 100 nm SiO2 foil at an excitation energy of 620 eV. The green curve represents the modeled spectrum using detector response functions for the relevant fluorescence lines (dotted lines) as well as a resonant Raman background (blue) and a pile-up contribution (red).
Fig. 4. Determined values for the fluorescence yield of the O K-edge for the different excitation energies on the 100 nm SiO2 sample including their total experimental uncertainty.
comparison to available literature data [14–17]. The data is also shown in Table 1. The results for each sample agree very well with each other. The total experimental uncertainty for the two foils with a nominal thickness of 500 nm (~ 5.4 %) is slightly larger than for the 100 nm foils (~ 5.0 %), due to an additional contribution to the uncertainty budget from pile-up effects in the SDD spectra. When comparing the small amount of available literature data, best agreement can be found with the value determined by Tawara et al. [16]. The authors of that work used gaseous samples, excited by electron impact, to experimentally determine the oxygen-K edge fluorescence yield. In comparison to the widely used value from Krause's tables [14], the agreement is less good as the Krause value is too low. A similar difference between our experimental data and the value from Cullen et al. [15] can be found. The theoretically calculated value by McGuire [17] is too high in comparison to our experimental data. The uncertainties of the literature values, if provided, are all larger than the determined total uncertainty budget of the experimental data presented here. The largest difference can be found in comparison to the estimated uncertainty of Krause [14]. The present reduction in the uncertainty of the O K-edge fluorescence yield allows to significantly improve the accuracy and to reduce the uncertainty of fundamental parameter-based quantification results.
Fig. 5. Comparison of the determined values for the O K-shell fluorescence yield to various available literature values [14–17] including their respective uncertainty if provided.
P. Hönicke et al. / Spectrochimica Acta Part B 124 (2016) 94–98 Table 1 Determined values for the O K-shell fluorescence yield in comparison to literature values including their respective uncertainty if provided. ωK Al2O3 100 nm Al2O3 500 nm SiO2 100 nm SiO2 500 nm Weighted mean Krause [14] Cullen [15] Tawara [16] McGuire [17]
0.00682 ± 0.00034 0.00704 ± 0.00038 0.00679 ± 0.00034 0.00687 ± 0.00037 0.00688 ± 0.00036 0.0058 ± 0.00174 0.00571 0.00645 ± 0.0011 0.0094
The uncertainty budget of the presented results is calculated on the basis of the relative uncertainty contributions of the relevant parameters. The main contributors to the total uncertainty budget are the determined ionization cross sections (~2.5 %), the attenuation correction factors (2 %) and the determination of the fluorescence intensities by spectral deconvolution (3 %). The latter is higher compared to e.g. [18] for the case of oxygen, due to the significant contribution of the RRS scattering background and the related uncertainty. More details on the experimental uncertainty budget can be found in [18,19]. For validation of the new experimental value for the oxygen K-shell fluorescence yield, the SiO2 layers on Si can be used, as the layer thickness is independently determined using X-ray reflectometry. The results for the layer with a nominal thickness of 6 nm are shown in Fig. 6. The reflectance at 529 eV was measured at the beginning and at the end of the sequence to verify that particularly the contamination layer thickness did not change during the measurements. Obviously, the reflectance curves vary drastically around the O K-edge. The obtained oxide layer thicknesses are summarized in Table 2. The uncertainty contributions due to the photon energy and the incidence angle are b0.1 %. For the 10 nm layer, the total layer thickness can be determined from the period of the oscillations; the optical constants of the involved materials are not required. For very thin layers, only the first minimum in the reflectance is observed and the optical constants obtained from transmission measurements and other reflectance measurements are necessary. Therefore the relative uncertainty of the layer thickness increases from 2 % to 10 % while the absolute uncertainty remains constant.
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Table 2 Comparison of the different XRF quantification results when using Krause's value or our experimentally determined value for the O K-shell fluorescence yield including the respective total uncertainty as well as X-ray reflectivity derived thicknesses for the SiO2 layers. Nominal thickness / nm
XRR thickness / nm
XRF thickness (using Krause [14] value) / nm
XRF thickness (using new data) / nm
2 6 10
3.6 ± 0.2 7.0 ± 0.2 9.2 ± 0.2
4.4 ± 1.4 8.4 ± 2.6 11.0 ± 3.4
3.7 ± 0.3 7.0 ± 0.5 9.2 ± 0.7
Each oxide layer sample is again measured using the same geometry and setup but at an excitation energy of 675 eV and the thereby obtained fluorescence intensity of O-Kα radiation is used to quantify the mass deposition of oxygen present on the sample. Assuming the stoichiometric composition and the bulk density of SiO2, this value can be converted to a layer thickness of SiO2. This was done for all three samples using the Krause value for the O K-fluorescence yield and the new experimentally determined value. The results are compared to the XRR determined layer thicknesses and shown in Table 2. For both quantifications, the Ebel values [20] for the K-shell ionization cross section of oxygen were used, as they were expected to be the most reliable [21]. The agreement between XRR and XRF values determined by using the new experimentally obtained fluorescence yield is much better than for the values quantified using the Krause O K-yield. In addition, the achievable experimental uncertainty for such an XRF thickness determination is drastically reduced due to the small uncertainty of the determined fluorescence yield. This allows a significantly increased reliability of quantification results in fundamental parameter based XRF applications where oxygen species are involved. 4. Conclusions The fluorescence yield for the oxygen K shell has been experimentally determined using the reference-free XRF setup of PTB and free-standing thin foils of SiO2 and Al2O3. The presented experimental value is also experimentally validated by comparison of XRF determined thicknesses of SiO2 layers on Si to results from X-ray reflectometry. In conjunction with the drastically lower and reliable uncertainty of the presented experimentally determined fluorescence yield value in comparison to the usually used Krause data and their estimated uncertainties, this work substantially contributes to applications of X-ray analytical techniques, where quantitative information is to be derived using fundamental parameter based quantification algorithms. This is in particular important when such methods are indispensable due to missing reference materials or calibration samples at the nanoscale. Acknowledgements This research was performed within the EMRP projects ThinErgy and SolCell. The financial support of the EMRP program is gratefully acknowledged. It is jointly funded by the European Metrology Research Programme (EMRP) and participating countries within the European Association of National Metrology Institutes (EURAMET) and the European Union. References
Fig. 6. XRR results for the SiO2 layer with a nominal thickness of 6 nm. The reflectance measured at different photon energies around the oxygen K edge is shown together with a simultaneous fit at all energies, resulting in an oxide thickness of 7.0 nm. The reflectance at 529 eV was measured at the beginning and at the end of the sequence to verify that the contamination layer did not change during the measurements.
[1] B. Beckhoff, R. Fliegauf, M. Kolbe, M. Müller, J. Weser, G. Ulm, Reference-free total reflection X-ray fluorescence analysis of semiconductor surfaces with synchrotron radiation, Anal. Chem. 79 (2007) 7873–7882. [2] B. Beckhoff, Reference-free X-ray spectrometry based on metrology using synchrotron radiation, J. Anal. At. Spectrom. 23 (2008) 845–853. [3] J. Lubeck, B. Beckhoff, R. Fliegauf, I. Holfelder, P. Hönicke, M. Müller, B. Pollakowski, F. Reinhardt, J. Weser, A novel instrument for quantitative nanoanalytics involving complementary X-ray methodologies, Rev. Sci. Instrum. 84 (2013) 045106.
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[4] F. Senf, U. Flechsig, F. Eggenstein, W. Gudat, R. Klein, H. Rabus, G. Ulm, A plane-grating monochromator beamline for the PTB undulators at BESSY II, J. Synchrotron Radiat. 5 (1998) 780–782. [5] F. Scholze, M. Procop, Modelling the response function of energy dispersive X-ray spectrometers with silicon detectors, X-Ray Spectrom. 38 (4) (2009) 312–321. [6] M. Kolbe, B. Beckhoff, M. Krumrey, G. Ulm, Thickness determination for Cu and Ni nanolayers: comparison of reference-free fundamental-parameter based X-ray fluorescence analysis and X-ray reflectometry, Spectrochim. Acta B 60 (2005) 505–510. [7] M. Krumrey, G. Ulm, High-accuracy detector calibration at the PTB four-crystal monochromator beamline, Nucl. Instrum. Methods A 467-468 (2001) 1175–1178. [8] B. Beckhoff, G. Ulm, Determination of fluorescence yields using monochromized undulator radiation of high spectral purity and well known flux, Adv. X-ray Anal. 44 (2001) 349–354. [9] M. Krumrey, M. Hoffmann, G. Ulm, K. Hasche, P. Thomsen-Schmidt, Thickness determination for SiO2 films on Si by X-ray reflectometry at the Si K edge, Thin Solid Films 459 (1–2) (2004) 241–244. [10] M. Krumrey, G. Gleber, F. Scholze, J. Wernecke, Synchrotron radiation-based X-ray reflection and scattering techniques for dimensional nanometrology, Meas. Sci. Technol. 22 (2011) 094032. [11] I. Busch, Y. Azuma, H. Bettin, L. Cibik, P. Fuchs, K. Fujii, M. Krumrey, U. Kuetgens, N. Kuramoto, S. Mizushima, Surface layer determination for the Si spheres of the Avogadro project, Metrologia 48 (2011) S62–S82. [12] T. Schoonjans, A. Brunetti, B. Golosio, M. Sanchez del Rio, V.A. Solé, C. Ferrero, L. Vincze, The xraylib library for X-ray–matter interactions. Recent developments, Spectrochim. Acta B 66 (2011) 776–784.
[13] M. Müller, B. Beckhoff, G. Ulm, B. Kanngießer, Absolute determination of cross sections for resonant Raman scattering on silicon, Phys. Rev. A 74 (2006) 012702. [14] M. Krause, Atomic radiative and radiationless yields for K and L shells, J. Phys. Chem. Ref. Data 8 (2) (1979) 307–327. [15] D.E. Cullen, J.H. Hubbell, L. Kissel, EPDL97: The Evaluated Photo Data Library, UCRL50400-Vol.6-Rev.5, 1997. [16] H. Tawara, K.G. Harrison, F.J. De Heer, X-ray emission cross sections and fluorescence yields for light atoms and molecules by electron impact, Physica 63 (2) (1973) 351–367. [17] E. McGuire, K-shell auger transition rates and fluorescence yields for elements ArXe, Phys. Rev. A 2 (1970) 273–278. [18] M. Kolbe, P. Hönicke, M. Müller, B. Beckhoff, L-subshell fluorescence yields and Coster-Kronig transition probabilities with a reliable uncertainty budget for selected high- and medium-Z elements, Phys. Rev. A 86 (2012) 042512. [19] M. Kolbe, P. Hönicke, Reliable determination of fundamental parameters of Zr and Ti for a reliable quantitative X-ray fluorescence analysis, X-Ray Spectrom. 44 (4) (2015) 217–220. [20] H. Ebel, R. Svagera, M.F. Ebel, A. Shaltout, J.H. Hubbell, Numerical description of photoelectric absorption coefficients for fundamental parameter programs, X-Ray Spectrom. 32 (2003) 442–451. [21] P. Hönicke, M. Kolbe, M. Müller, M. Mantler, M. Krämer, B. Beckhoff, Experimental verification of the individual energy dependencies of the partial L-shell photoionization cross sections of Pd and Mo, Phys. Rev. Lett. 113 (16) (2014) 163001.
Contents lists available at ScienceDirect
Spectrochimica Acta Part B journal homepage: www.elsevier.com/locate/sab
Experimental determination of the oxygen K-shell fluorescence yield using thin SiO2 and Al2O3 foils P. Hönicke ⁎, M. Kolbe, M. Krumrey, R. Unterumsberger, B. Beckhoff Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany
a r t i c l e
i n f o
Article history: Received 25 July 2016 Received in revised form 23 August 2016 Accepted 24 August 2016 Available online 28 August 2016 Keywords: Atomic fundamental parameters X-ray fluorescence spectroscopy Fluorescence yield X-ray reflectometry Quantitative analysis
a b s t r a c t In this work, the K-shell fluorescence yield for oxygen ωO,K−shell is determined experimentally, employing the radiometrically calibrated X-ray fluorescence instrumentation of the Physikalisch-Technische Bundesanstalt (PTB), Germany's National Metrology Institute. Four free-standing thin foils with two different thicknesses of both SiO2 and Al2O3 were used in order to derive an experimental value for this atomic fundamental parameter. Multiple excitation photon energies were applied to record fluorescence spectra of all four samples. The resulting value (ωO,K−shell = 0.00688 ± 0.00036) is almost 20 % higher than the commonly used value from the Krause tables [M. Krause, Atomic Radiative and Radiationless Yields for K and L shells, J. Phys. Chem. Ref. Data 8(2), 307–327 (1979)]. In addition, the achieved total uncertainty budget for the new experimental value is reduced significantly in comparison to available literature data. For validation purposes, thin SiO2 layers on Si samples were used. Here, the layer thicknesses derived from X-ray reflectometry are well in line with our X-ray fluorescence quantification results based on the new experimental value for the O K-shell fluorescence yield. © 2016 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
The ongoing development of thin film materials for applications in different fields of research and production often require an accurate and reliable analysis. If a non-destructive quantitative characterization of the elemental composition is needed, often only fundamental parameter-based – or even reference-free X-ray fluorescence (XRF) spectroscopy is available as an analytical method due to the extremely low availability of reference materials or calibration samples with sufficient similarity to the analytical problem in terms of the matrix elemental and spatial composition. This is particularly the case for nanoscaled material systems, where the variety of element combinations and analytical questions increases steadily and at a much faster pace than that at which reference materials can currently be developed. However, the achievable accuracy of the quantitative results is often limited by the uncertainty of the fundamental parameters involved. Especially for low-Z elements, they are large and often only estimated. This drastically limits the feasibility of fundamental parameter based quantification for light elements such as oxygen. As particularly oxides are very much present in many fields of research and production, this is a very interesting chemical element for an experimental determination of the atomic fundamental parameters.
The Physikalisch-Technische Bundesanstalt (PTB) has experimental access to the determination of atomic fundamental parameters by employing the reference-free XRF approach [1,2]. For the experiments, an in-house developed ultrahigh vacuum chamber dedicated to reference-free XRF analysis in various geometries [3] was installed in the focal plane of PTB's plane grating monochromator (PGM) beamline [4] at the BESSY II electron storage ring. The samples were placed in a conventional 45°–45° XRF beam geometry on an X-Y scanning stage in the center of the measurement chamber. The emitted fluorescence radiation is detected by a silicon drift detector (SDD), calibrated with respect to its detection efficiency and response behavior [5]. The energy-dispersive SDD is mounted behind a calibrated diaphragm at a well-defined distance from the sample, which defines the solid angle of detection with a relative uncertainty of 0.7 % [6]. The incident photon flux is determined using calibrated photodiodes, the efficiency of which is known with relative uncertainties below 1 % [7]. For the experimental determination of the oxygen K-shell fluorescence yield, four free-standing thin foil samples were obtained from Lebow Company (Goleta, CA, USA). Two aluminum oxide and two silicon dioxide foils with nominal thicknesses of 100 nm and 500 nm were employed. Both the fluorescence and transmission experiments were conducted in the photon energy range between 380 eV to 850 eV. From the photon energy-dependent transmission of each foil, mass attenuation coefficients can be derived and used for a correction
⁎ Corresponding author. E-mail address: [email protected] (P. Hönicke).
http://dx.doi.org/10.1016/j.sab.2016.08.024 0584-8547/© 2016 Elsevier B.V. All rights reserved.
P. Hönicke et al. / Spectrochimica Acta Part B 124 (2016) 94–98
of the attenuation effects within each sample independently of database values for mass attenuation coefficients. The fluorescence production cross section σO,K−shell(E0) for the oxygen K-shell at a photon energy E0 can be calculated according to Eq. (1), where ωO,K−shell is the fluorescence yield of the O K-shell and τO,K−shell(E0) is the photoionization cross section of the O K-shell for photons of energy E0. The density ρ and thickness d or the mass deposition ρd of the thin foil sample in use does not have to be known here, as only the products of the photoionization cross section and ρd and of the mass attenuation coefficient and ρd need to be known [8]. They can be derived from transmission experiments applying the Lambert-Beer law. σ O;K−shell ðE0 Þρd ¼ ωO;K−shell τO;K−shell ðE0 Þρd ¼
ΦdOKα ðE0 ÞMOKα;E0 Ω Φ0 ðE0 Þ 4π
ð1Þ
The fluorescence photon flux ΦdOKα(E0) is derived from the recorded fluorescence spectra by deconvolving all relevant contributions. The detector response functions for all relevant fluorescence lines as well as relevant background contributions, e.g. bremsstrahlung originating from photo and Auger electrons as well as the resonant Raman scattering background, are used for the spectral deconvolution. The incident Ω photon flux Φ0(E0) and the solid angle of detection 4π are known due to the use of calibrated instrumentation. The attenuation correction factor MOKα,E0 for the incident - as well as the O-Kα fluorescence radiation is determined by Eq. (2), where μS,E0 and μS,EOKα are the mass attenuation coefficients of the foil at the incident photon energy and the fluorescence line energy.
MOKα;E0
μ S;E0 ρd μ S;EOKα ρd þ sinθin sinθout ¼ μ S;E0 ρd μ S;EOKα ρd þ 1− exp − sinθin sinθout
ð2Þ
For a validation of the experimentally determined O K-shell fluorescence yield, different SiO2 layers on silicon were used. The samples with nominal SiO2 layer thicknesses of 2 nm, 6 nm and 10 nm were independently investigated by X-ray reflectometry (XRR). XRR is a wellestablished technique for nanolayer thickness determination which is based on interference effects of X-rays reflected at the layer surface and at the layer-substrate interface. By varying the grazing incidence angle, oscillations in the reflectance are observed and their period relates the layer thickness to the X-ray wavelength. For typically used Cu Ka radiation, the oscillations for SiO2 layers on silicon are relatively weak as the optical constants of Si and SiO2 are very similar at 8 keV. Moreover, the unavoidable carbonaceous contamination layer that covers most surfaces can influence the results for very thin oxide layers. Both limitations can be avoided by using synchrotron radiation, as the measurements can be performed at the Si K-edge at 1.84 keV [9] or even around the O K-edge at 0.53 keV [10]. As only the SiO2 layer contains oxygen, both layers can be separated if the reflectance curves measured at energies below and above the edge are simultaneously modeled. Furthermore, much steeper incidence angles can be used, also enabling the investigation of a strongly curved surface e.g. on a sphere as required for the redefinition of the unit kilogram via the Avogadro constant [11]. Both the thin SiO2-layers used here and the presented XRR methodology were developed within the Avogadro project.
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measured mass attenuation around the O K-edge by means of a corresponding separation of the various contributions. Due to the use of compound thin foils, an additional contribution to the measured mass attenuation around the O K-edge from the respective bonding partner must be taken into account in order to derive the required product of the photoionization cross section from the O K-edge and ϱd (τO−K(E0)ϱd). As both Si and Al do not have any absorption edges in the relevant photon energy range, their contribution to the total mass attenuation of the sample is a simple exponential decay in the first approximation (see Fig. 1). Moreover, the normalized difference between the contribution of the higher oxygen shells and the relevant shells of the respective bonding partner does not change significantly in the photon energy range of the O K-edge. Instead of having to take into account both the sample stoichiometry and the resulting combined mass attenuation, this allows a deconvolution of the experimentally determined mass attenuation into a combined contribution from scattering and the higher shells of oxygen and the bonding partner as well as the photoelectric cross section of the O K-absorption edge. The combined contribution can be approximated well enough using the tabulated energy dependence of the bonding partner's mass attenuation coefficient multiplied with a fictitious ϱd⁎, which is derived from the experimental data below the O K-edge. The product of the photoionization cross section from the O K-edge and ϱd (τO,K−shell(E0)ϱd) can then be derived using the extrapolated mass attenuation contribution of all higher shells (μAl,Si+O⁎(E0)ϱd⁎) according to Eq. (3). This is depicted in Fig. 2.
τO;K−shell ðE0 Þϱd ¼ μ ðE0 Þϱd−μ Al;SiþO ðE0 Þϱd
ð3Þ
The fluorescence intensities of the O-Kα line are derived from the SDD spectra by deconvolution using the known detector response functions [5] as well as relevant background contributions for bremsstrahlung from photoelectrons and resonant Raman scattering [13]. The bremsstrahlung originates from photo and Auger electrons, whereas the resonant Raman background originates from O-Kα fluorescence photons being Raman scattered at the O K-absorption edge on their way through the sample. In Fig. 3, a fluorescence spectrum obtained on the 100 nm SiO2 foil at an excitation energy of 620 eV as well as a modeled spectrum are shown. The derived count rate DOKα for the O-Kα fluorescence line from the deconvoluted spectra is used to determine the detected fluorescence photon flux ΦdOKα(E0) by normalization of the SDD's detection efficiency for O-Kα photons.
2.1. Data evaluation For the experimental determination of the K-shell fluorescence yield of oxygen, also the photoionization cross section for oxygen at the chosen incident photon energies has to be known. Taking into account that the mass attenuation coefficient is the sum of all shells' photoionization probabilities as well as of the cross sections for coherent and incoherent scattering, one can derive the K-shell ionization cross section from the
Fig. 1. Comparison of the tabulated relevant contributions [12] to the measured mass attenuation in the photon energy range of the O K-edge. For oxygen, only the sum of the relevant higher shells and the scattering contribution is plotted (μO⁎). On the right axis, the depicted normalized differences are plotted.
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Fig. 2. Experimentally determined product of attenuation coefficients, layer thickness and density (black dots and grey asterisks) around the O K-absorption edge on the SiO2 foil with a nominal thickness of 500 nm. The extrapolated contribution of higher shells (grey+) and of the O K-shell are also marked.
3. Results and discussion The derived values for the product of the photoionization cross section from the O K-edge and mass deposition τO,K−shell(E0)ϱd and the derived fluorescence photon fluxes ΦdOKα(E0) can then be used to calculate the fluorescence yield for the O K-edge according to Eq. (1). This was done for each excitation energy and sample. In Fig. 4, the results for the 100 nm SiO2 sample are shown as a function of the incident photon energy. The good agreement between results obtained at different incident photon energies indicates that the approximated higher shell contribution to the total mass attenuation coefficient is appropriate within this limited excitation energy range. Only the value obtained at 540 eV is slightly lower which is due to the fact that this excitation energy is very close to the π*-resonance (see Fig. 2), where higher harmonic contributions of the undulator and the plane grating monochromator [4] can influence the measured foil transmittance. The same procedure was applied to the other oxide foil samples in order to derive experimental values of the O K-fluorescence yield. For each sample, the weighted mean of all values determined at the different excitation photon energies was calculated and is shown in Fig. 5 in
Fig. 3. Fluorescence spectrum obtained on the 100 nm SiO2 foil at an excitation energy of 620 eV. The green curve represents the modeled spectrum using detector response functions for the relevant fluorescence lines (dotted lines) as well as a resonant Raman background (blue) and a pile-up contribution (red).
Fig. 4. Determined values for the fluorescence yield of the O K-edge for the different excitation energies on the 100 nm SiO2 sample including their total experimental uncertainty.
comparison to available literature data [14–17]. The data is also shown in Table 1. The results for each sample agree very well with each other. The total experimental uncertainty for the two foils with a nominal thickness of 500 nm (~ 5.4 %) is slightly larger than for the 100 nm foils (~ 5.0 %), due to an additional contribution to the uncertainty budget from pile-up effects in the SDD spectra. When comparing the small amount of available literature data, best agreement can be found with the value determined by Tawara et al. [16]. The authors of that work used gaseous samples, excited by electron impact, to experimentally determine the oxygen-K edge fluorescence yield. In comparison to the widely used value from Krause's tables [14], the agreement is less good as the Krause value is too low. A similar difference between our experimental data and the value from Cullen et al. [15] can be found. The theoretically calculated value by McGuire [17] is too high in comparison to our experimental data. The uncertainties of the literature values, if provided, are all larger than the determined total uncertainty budget of the experimental data presented here. The largest difference can be found in comparison to the estimated uncertainty of Krause [14]. The present reduction in the uncertainty of the O K-edge fluorescence yield allows to significantly improve the accuracy and to reduce the uncertainty of fundamental parameter-based quantification results.
Fig. 5. Comparison of the determined values for the O K-shell fluorescence yield to various available literature values [14–17] including their respective uncertainty if provided.
P. Hönicke et al. / Spectrochimica Acta Part B 124 (2016) 94–98 Table 1 Determined values for the O K-shell fluorescence yield in comparison to literature values including their respective uncertainty if provided. ωK Al2O3 100 nm Al2O3 500 nm SiO2 100 nm SiO2 500 nm Weighted mean Krause [14] Cullen [15] Tawara [16] McGuire [17]
0.00682 ± 0.00034 0.00704 ± 0.00038 0.00679 ± 0.00034 0.00687 ± 0.00037 0.00688 ± 0.00036 0.0058 ± 0.00174 0.00571 0.00645 ± 0.0011 0.0094
The uncertainty budget of the presented results is calculated on the basis of the relative uncertainty contributions of the relevant parameters. The main contributors to the total uncertainty budget are the determined ionization cross sections (~2.5 %), the attenuation correction factors (2 %) and the determination of the fluorescence intensities by spectral deconvolution (3 %). The latter is higher compared to e.g. [18] for the case of oxygen, due to the significant contribution of the RRS scattering background and the related uncertainty. More details on the experimental uncertainty budget can be found in [18,19]. For validation of the new experimental value for the oxygen K-shell fluorescence yield, the SiO2 layers on Si can be used, as the layer thickness is independently determined using X-ray reflectometry. The results for the layer with a nominal thickness of 6 nm are shown in Fig. 6. The reflectance at 529 eV was measured at the beginning and at the end of the sequence to verify that particularly the contamination layer thickness did not change during the measurements. Obviously, the reflectance curves vary drastically around the O K-edge. The obtained oxide layer thicknesses are summarized in Table 2. The uncertainty contributions due to the photon energy and the incidence angle are b0.1 %. For the 10 nm layer, the total layer thickness can be determined from the period of the oscillations; the optical constants of the involved materials are not required. For very thin layers, only the first minimum in the reflectance is observed and the optical constants obtained from transmission measurements and other reflectance measurements are necessary. Therefore the relative uncertainty of the layer thickness increases from 2 % to 10 % while the absolute uncertainty remains constant.
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Table 2 Comparison of the different XRF quantification results when using Krause's value or our experimentally determined value for the O K-shell fluorescence yield including the respective total uncertainty as well as X-ray reflectivity derived thicknesses for the SiO2 layers. Nominal thickness / nm
XRR thickness / nm
XRF thickness (using Krause [14] value) / nm
XRF thickness (using new data) / nm
2 6 10
3.6 ± 0.2 7.0 ± 0.2 9.2 ± 0.2
4.4 ± 1.4 8.4 ± 2.6 11.0 ± 3.4
3.7 ± 0.3 7.0 ± 0.5 9.2 ± 0.7
Each oxide layer sample is again measured using the same geometry and setup but at an excitation energy of 675 eV and the thereby obtained fluorescence intensity of O-Kα radiation is used to quantify the mass deposition of oxygen present on the sample. Assuming the stoichiometric composition and the bulk density of SiO2, this value can be converted to a layer thickness of SiO2. This was done for all three samples using the Krause value for the O K-fluorescence yield and the new experimentally determined value. The results are compared to the XRR determined layer thicknesses and shown in Table 2. For both quantifications, the Ebel values [20] for the K-shell ionization cross section of oxygen were used, as they were expected to be the most reliable [21]. The agreement between XRR and XRF values determined by using the new experimentally obtained fluorescence yield is much better than for the values quantified using the Krause O K-yield. In addition, the achievable experimental uncertainty for such an XRF thickness determination is drastically reduced due to the small uncertainty of the determined fluorescence yield. This allows a significantly increased reliability of quantification results in fundamental parameter based XRF applications where oxygen species are involved. 4. Conclusions The fluorescence yield for the oxygen K shell has been experimentally determined using the reference-free XRF setup of PTB and free-standing thin foils of SiO2 and Al2O3. The presented experimental value is also experimentally validated by comparison of XRF determined thicknesses of SiO2 layers on Si to results from X-ray reflectometry. In conjunction with the drastically lower and reliable uncertainty of the presented experimentally determined fluorescence yield value in comparison to the usually used Krause data and their estimated uncertainties, this work substantially contributes to applications of X-ray analytical techniques, where quantitative information is to be derived using fundamental parameter based quantification algorithms. This is in particular important when such methods are indispensable due to missing reference materials or calibration samples at the nanoscale. Acknowledgements This research was performed within the EMRP projects ThinErgy and SolCell. The financial support of the EMRP program is gratefully acknowledged. It is jointly funded by the European Metrology Research Programme (EMRP) and participating countries within the European Association of National Metrology Institutes (EURAMET) and the European Union. References
Fig. 6. XRR results for the SiO2 layer with a nominal thickness of 6 nm. The reflectance measured at different photon energies around the oxygen K edge is shown together with a simultaneous fit at all energies, resulting in an oxide thickness of 7.0 nm. The reflectance at 529 eV was measured at the beginning and at the end of the sequence to verify that the contamination layer did not change during the measurements.
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