Article pubs.acs.org/ac
Nondestructive Speciation Depth Profiling of Complex TiOx Nanolayer Structures by Grazing Incidence X‑ray Fluorescence Analysis and Near Edge X‑ray Absorption Fine Structure Spectroscopy Beatrix Pollakowski* and Burkhard Beckhoff Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany ABSTRACT: An important challenge of modern material science is the depth-sensitive and nondestructive analysis of the chemical binding state of complex structures consisting of multiple thin layers. In general, the correlation of the material functionality and underlying chemical and physical properties is the key question in view of directed device development, performance, and quality control. It has been shown that the combined method grazing incidence X-ray fluorescence analysis (GIXRF) and near edge X-ray absorption fine structure spectroscopy (NEXAFS) can significantly contribute to the nondestructive chemical analysis of buried thin films and interface structures regarding chemical speciation. Recently, we have enhanced the method to allow for a depth-resolved analysis of multilayered nanoscaled thin film structures. By means of appropriate model systems, the methodology has been developed and successfully validated. The model systems basically consist of a carbon cap layer, two titanium layers differing in their oxidation states and separated by a thin carbon layer, and a silicon substrate covered with molybdenum and a carbon layer. A differential approach has been developed to derive the chemical species of each of the titanium layers. present work, for species depth profiling, X-ray absorption fine structure spectroscopy (XAFS) in fluorescence detection mode is used in conjunction with grazing incidence XRS. In the case of stratified materials and depositions on a flat substrate, interference effects of the incoming and reflected beam in the form of an X-ray standing wave field (XSW)4−6 are observable. In stratified materials, a pattern of nodes and antinodes is evolving. This significantly influences the depthdependent excitation conditions for fluorescence generation. One can take advantage of this XSW field as a kind of nanoscaled depth sensor for a selective analysis of certain layers. A dedicated excitation of a specific layer can be ensured and with it the analysis of certain depth regions. Because of the dependence of the XSW field intensity on both the photon energy and the incidence angle, a speciation depth profile needs more elaborate strategies to reveal reliable results. When varying the photon energy during an XAFS measurement, the penetration depth changes. To prevent a variation of the penetration depth during the measurements, the angle of incidence has to vary in a correlated and appropriate manner.
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n nanotechnology, a large variety of advanced material systems consisting of nanolayered structures with complex behavior are employed.1−3 For a directed development of these materials, a complete knowledge of the chemical and physical properties is crucial. For technology implementation of devices on multifunctional platforms, it is important to correlate functionality and the respective chemical and physical material properties. Typical structures used for advanced nanotechnology devices are multielemental stratified specimens with dimensions ranging from a few nanometers, e.g., interface structures, to several of hundreds of nanometers. Advanced stratified materials may consist of various layers, for instance layers of the same element but in a different chemical binding state. To gain access to spatial composition of these nanostructures, X-ray spectrometry (XRS), under grazing incidence conditions, can be applied for a nondestructive and nonpreparative approach to elemental and speciation depth profiling. XRS is based on the excitation of an inner-shell electron by an incident photon followed by the emission of a photon characteristic for an element. In a surface sensitive XRS arrangement, the incoming beam is under grazing incidence and the emitted radiation is detected close to normal incidence. Thus, the penetration depth of the exciting radiation can drive the information depth. In comparison to complementary methods which rely on electron detection, the information depth is significantly increased. In the © XXXX American Chemical Society
Received: March 27, 2015 Accepted: July 8, 2015
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DOI: 10.1021/acs.analchem.5b01172 Anal. Chem. XXXX, XXX, XXX−XXX
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in a way that the intensity of the exciting radiation in a certain depth of interest is sufficiently high and constant. The first step in the proposed procedure is to record a NEXAFS spectrum containing the species information on both layers with almost equal contributions with respect to the repartition of the exciting radiation intensity. This measurement needs a sequence of incidence angles ensuring that both layers are equally excited with respect to the incident radiation intensity. In the following step, a second complementary NEXAFS spectrum is recorded which predominantly contains the species information on the upper layer by choosing a sequence of shallow incidence angles. The major challenge is to calculate the angle of incidence which maximizes the XSW intensity difference between both layers and ensuring a constant integral XSW field intensity at each photon energy of interest. For the sake of clarity, this is explained in detail in the section Simulation of the XSW Intensity. Without a pronounced difference in the XSW intensity, a differential methodology is not applicable. For the identification of the fine structure of the near-edge region of an absorption edge, studies of known chemical compounds are necessary. Reference samples containing only single layers of the involved chemical species have been investigated by NEXAFS. This allows for a validation of each step of the procedure proposed. In good approximation, the aquired NEXAFS spectra of the double layer system can be described as a linear combination of the relevant reference spectra. Furthermore, the analysis of these single layers can be used for the determination of the complex refractive index needed for a more reliable calculation of the XSW intensity distribution and thus of both the mean penetration depth and the adopted angles of incidence for the NEXAFS analysis in view of achieving an even more reliable measurement procedure.
For an elemental depth sensitive analysis, the grazing incidence X-ray fluorescence (GIXRF) method has already been employed.5,7 The authors determined the elemental depth profile by analyzing the angular dependent fluorescence intensities of the elements of stratified materials. They have proven that their method is suitable for elemental depth profiling, but no statement about chemical species has been made. For the spectral range of hard X-rays, the depth-sensitive chemical speciation analysis has been reported elsewhere.8,9 For a depthsensitive analysis, either the incidence angle is adapted for a certain depth calculated in advance or the entire layer is embedded in a kind of waveguide structure to ensure a constant penetration depth. One has to note that the chemical speciation of light elements at K edges and transition metals at L edges demands energies in the soft X-ray range. Thereto, we improved the algorithm of de Boer et al.6 for soft X-rays by neglecting angular approximations suitable for the hard X-ray range. This leads to a more accurate calculation of the energy-dependent penetration depth and the incidence angles. With these calculations, it has been confirmed that the combined photon-in photon-out spectroscopic method GIXRFNEXAFS leads to reliable results for the speciation of deeply buried single layers10 and interfaces11 in the soft X-ray range. This is the starting point for the further methodological development toward speciation depth profiling. The model systems introduced here consist of double layer structures of titanium and titanium oxide layers separated by a carbon barrier.
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METHOD FOR STRATIFIED MATERIAL The GIXRF method for sufficiently flat samples is characterized by the occurrence of interference effects of the incident and reflected beams,6 usually referred to as the XSW field. The calculation of the XSW intensity distribution involves the energy dependent complex refraction index including the optical constants n and κ, which are taken from databases,12 layer thicknesses, and incidence angle. In particular, the variation of the angle of incidence and the photon energy has the impact that the nodes and antinodes of the XSW field are moving spatially up and down. This opens up the possibility to tune the position of the nodes and antinodes to a preselected depth. When combining GIXRF with NEXAFS, the energy dependence of the optical properties has to be considered and the angle of incidence adapted correspondingly.10 Hence, it is necessary to first calculate the XSW field and take this knowledge into consideration for the experiments when analyzing statified materials with thicknesses larger than several tens of nanometers. Public domain XSW software13 and our own software “XSWINI”,14 based on the algorithm developed by de Boer et al.6 having been adapted for the soft X-ray range, allow for a reliable and traceable determination of the XSW intensity. In the soft X-ray range, the localization of the intensity distribution of the XSW field is hardly feasible, in particular when varying the photon energy in the vicinity of an absorption edge of a matrix element. This is due to resonant behavior of the optical constants. It follows that the intensity contributions from adjacent depth regions are significant. As a result, a depth profiling of the chemical species in stratified material in the soft X-ray range needs a kind of differential methodology. For each single layer containing the element of interest, a measurement is needed. Therefore, a double layer requires in total at least two near edge X-ray absorption fine structure (NEXAFS) measurements. For such a measurement the incidence angles for the different energies have to be calculated
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EXPERIMENTAL DETAILS All measurements were carried out at the plane grating monochromator (PGM) beamline15,16 for undulator radiation in the PTB laboratory17 at BESSY II. The PGM-U49 beamline15,16 provides tunable radiation both of high photon flux (or radiant power) and of high spectral purity in the soft Xray range. For the analysis of the buried nanolayers, the instrumentation is discussed in detail elsewhere.18 A sketch of the beam geometry in the UHV chamber and of the actual measurement arrangement is shown in Figure 1. The main feature of this UHV chamber is an electrostatic chuck mounted on an 8-axis manipulator allowing for a very precise alignment of the angle of incidence with respect to the wafer surface. The accessible range for the angle of incidence is 0° to more than 45°. Calibrated photodiodes ensure the measurement of the absolute flux or radiant power of the exciting radiation at the chosen photon energy. For the detection of the fluorescence radiation, a calibrated windowless silicon drift detector (SDD) with a well-known response behavior and efficiency19,20 is employed. The nanolayered samples in the present study are deposited on an individual silicon wafer and have been measured one after the other. The sequence of incident angles for the NEXAFS study of each sample has been determined prior to the experiments and will be explained later in more detail. In the following step, the NEXAFS spectra at the titanium L edges (range 450.0−475.0 eV; step width 0.2 eV) of each sample are measured. For each photon energy, a GIXRF spectrum is recorded and the intensity of Lα and Lβ fluorescence lines has B
DOI: 10.1021/acs.analchem.5b01172 Anal. Chem. XXXX, XXX, XXX−XXX
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Table 1. Different Double Layer Depositions on the 200 mm Wafera no. 1 2 3 4 a
layer 2 Q/sccm
layer 1 Q/sccm
species
3
Ti/Ti2O3 Ti2O3/Ti Ti/TiO2 TiO2/Ti
3 9 9
The oxygen flow rate is labeled as Q.
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SIMULATION OF THE XSW INTENSITY The simulation of the intensity of the XSW field IXSW is based on the optical properties involving the complex refractive index, which can either be found in databases, e.g., of the Center for Xray Optics (CXRO)12 or experimentally determined by spectroscopic X-ray reflectometry (XRR), as it is the case in the present work. The optical properties n and κ have been determined by XRR for pure titanium and for the different titanium oxides in the energy range from 450 to 475 eV. Figure 3 shows the XSW intensity distributions of the samples Ti/Ti2O3 and Ti2O3/Ti dependent on the grazing incidence angle θ and the depth d for a constant photon energy of 450 eV, where differences in the respective XSW distributions are most prominent. Such calculations serve as the basis for the determination of the incidence angles of each photon energy of the NEXAFS analysis. As mentioned in the previous section, two sets of incident angles are required to fully probe the double layer structures. The criterion to calculate the angle of incidence for analyzing the entire double layer system was chosen, so that the mean intensity IXSW in the lower and upper layer are almost equal and, in addition, constant in the energy range from 450 to 475 eV (nearedge region of the Liii,ii of Ti), which is the more relevant constraint. This ensures that the acquired spectrum is deconvoluable by means of the NEXAFS spectra of wellknown single layers10 in an optimal manner. The more challenging part of the procedure is to define a second criterion to probe predominately only the upper layer (L2). Again, the mean intensity IXSW,L2 should remain constant independently from the photon energy. In addition, the intensity IXSW,L1 in the lower layer (L1) should be minimal, in the best case negligible. For the layered structures presented here, calculations have been shown that only a ratio IXSW,L1/IXSW,L2 of about 0.5 ensures constant mean penetration depth for all used photon energies. It becomes apparent that it is a matter of optimization to find a suitable criterion to calculate the incident angle sequence for the GIXRF-NEXAFS analysis of the upper layer. For the case that the upper layer is optically denser than the lower layer, the fulfillment of the criteria is hardly possible due to strong variations of the integral XSW field intensity with the photon energy. Thereby, an intensity minimum in the upper layer and a maximum in the lower layer are simultaneously observable, as shown in Figure 3. Steeper incidence angles are needed to almost fulfill the second criterion. With decreasing layer thickness, the effect becomes smaller. Figure 4 exhibits the dependence of the required angles of incidence θ with the photon energy, calculated for experimentally determined optical properties and assuming an intensity ratio of the lower to the upper layer of about 0.5. The determination of the energy-dependent incidence angle was carried out for the relevant energy range from 455 to 465 eV. This restricted energy range is due to the fact that first, the generation of fluorescence radiation below the absorption edge is unlikely, and second,
Figure 1. Sketch of the beam geometry of the analysis chamber, mounted at PGM-U49 beamline for undulator radiation in the PTB laboratory. The incident beam is monochromatic radiation of high spectral purity and of well-known flux.
been determined absolutely. Furthermore, the intensities of the respective fluorescence lines were normalized to both incident radiant power and the effective solid angle of detection.18
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SAMPLE PREPARATION Using the ion beam sputtering deposition (IBSD) technique,21 the double layer structures consisting of titanium and titanium oxide layers, respectively, were produced by the Fraunhofer Institute for material and beam technology (IWS) Dresden, Germany. The advantage of this technique is that parameters such as energy, flux, incident direction, and charge state can be easily regulated and moreover the deposition process can take place at lower temperatures.22 The deposition were carried out in a “Large Area Dual IBSD” facility,23 employing a primary argon source for sputtering the target and a secondary source for an assisting gas. This enabled the production of layered structures like titanium oxides by adding oxygen as reactive gas. The roughness of the deposited layers was below 0.5 nm rms. The layered samples have the following configuration: as substrate, a polished 200 mm silicon wafer was used and coated with 50 nm Mo and then with 5 nm C. Afterward two titanium layers varying in the oxidation state and separated by a 1.5 nm thick carbon layer were deposited. These layers were then covered by 5 nm of carbon to prevent further unintentional oxidation processes. From a previous study, it was established which oxygen flow rate Q in the assisting source leads to the desired target oxidation state of titanium.10 Figure 2 exhibits the
Figure 2. Schematic view of the buried TiOx nanolayer system, prepared with IBSD.
stratified samples. In total there were four samples, which contain two different pairs consisting of the same layers but with an inverted deposition sequence (see Table 1). The specified thicknesses are nominal values, calculated from single reference layer samples measured with X-ray reflectometry (XRR). C
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Figure 3. Calculation of the X-ray standing wave field intensity distribution dependent on the grazing incidence angle θ and the depth d for a constant photon energy of 450 eV using own software. Left: calculation for the sample Ti/Ti2O3. Right: calculation for the sample Ti2O3/Ti.
Figure 4. Set of incident angles calculated for experimentally determined optical properties for GIXRF-NEXAFS measurements of the upper layer. The run of the curves for the samples Ti/Ti2O3 and Ti2O3/Ti is shown.
previous experiments proved that above 465 eV the integral XSW intensity varies in a less pronounced way. One can clearly see that the curve is dominated by the corresponding absorption κ of the element titanium.12 As shown in Figure 4, above the Ti-Liii and Ti-Lii absorption edges the desired incidence angle is significantly increased for all layered structures. In Figure 5 the total intensity ratio of the lower layer (L1) and the upper layer (L2) depending on the incidence angle θ for different photon energies is depicted. This figure illustrates the procedure for the determination of the required angles of incidence θ: for a chosen ratio the angle of incidence for the NEXAFS measurement of the upper layer can be directly deduced for the respective energy. As already mentioned, the ratio of about 0.5 is suitable for these bilayers, but a smaller value would be better to reduce the contribution originating from the lower layer. A very small ratio indicates less excitation of the lower layer, but the stability of the mean intensity IXSW,L2 as a function of energy is not ensured. Moreover, smaller ratio values lead to incident angles not ensuring to probe the entire upper layer. Figure 5 shows the calculation of the intensity ratios of the sample systems consisting of Ti 2 O 3 /Ti and Ti/Ti 2 O 3 , respectively. For all other samples, these kinds of calculations have been carried out too. On the basis of these calculations, the angles of incidence were determined, as exhibited in Figure 4.
Figure 5. Illustration of the procedure to determine the incidence angle θ ensuring sufficient intensity in the respective layer and a constant intensity ratio between the upper and lower layers, IXSW,L1/IXSW,L2 = 0.5 for the systems Ti2O3/Ti and Ti/Ti2O3 the. The ratio of both intensities IXSW,L1/IXSW,L2 is exhibited depending on the incidence angle for relevant photon energies.
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RESULTS: SPECIES DEPTH PROFILING OF A BURIED NANOLAYER Starting with the deconvolution of the spectra recorded at an incidence angle of about 45°, the procedure allows for the identification of all chemical species involved. Reference spectra from standards or similar samples are necessary to calculate the superposition and determine the contributions of each species. D
DOI: 10.1021/acs.analchem.5b01172 Anal. Chem. XXXX, XXX, XXX−XXX
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Analytical Chemistry This may lead to difficulties because of the lack of such standards with well-known chemical species information. Here, these measurements have been carried out at θ = 45° assuming that both layers are nearly equally excited and contribute to the NEXAFS spectrum in a similar way. The TiLiii,ii XRF-NEXAFS spectra in Figure 6 can be successfully
Figure 7. Ti-Liii,ii GIXRF-NEXAFS spectra measured at shallow incidence angles. The near-edge fine structure of the samples is dominated by expected chemical species of the top layer, but there are still some contributions of the species of the lower layer observable. For the sake of clarity, the spectra are shifted on the y-axis and correspondingly scaled to the results presented in Figures 8 and 9. Figure 6. Ti-Liii,ii NEXAFS spectra recorded in conventional XRF geometry at an angle of incidence of about 45°. The red and the green curves arise from samples consisting of Ti2O3 and Ti differing in the sequence of the layers. The blue and the purple ones are from samples consisting of TiO2 and Ti. For the sake of clarity, the spectra are shifted on the y-axis and correspondingly scaled to the results presented in Figures 8 and 9.
achievable excitation scheme in order to predominately measure the upper layer is a ratio of about 0.5. That means, that the recorded spectrum consists of two-third of the upper layer information and one-third originate from the lower layer. These measurements confirm the difficulties occurred when calculating the mean penetration depth and consequently the energydependent angle of incidence. Because of the kind of deposition technique used, it is rather unlikely that a mix of the different titanium species has occurred within any of the layers. Comparing the samples with inverted layer sequences show clear differences in the fine structure. It becomes now identifiable which species belongs to the upper layer. Figures 8 and 9 illustrate the procedure of the differential approach proposed by means of the samples consisting of Ti2O3 and Ti. The two curves plotted in the bottom shows the measured Ti-Liii,ii X-ray absorption fine structure spectra at different varying shallow and steep incidence angles to probe different depth regions. Furthermore, the normalized count rates are scaled by a factor, which takes into account the ratio derived from the data explained in detail below. The results of the species depth profile and the corresponding reference single layer measurements are plotted at the two upper graphs in this picture. To determine the depth-sensitive chemical species, a ratio of 1 is assumed for the measurements at steep angles. In addition, for measurements at varying shallow incidence angles, the fractions of both layers are assumed to be a fixed ratio to be determined by a fit each species contribution. The ratio derived in this way is about 0.25, which differs from previously calculated ratio of 0.5. However, this fitting approach involving two constraints allows to well separate the different species contributions as shown in Figures 8 and 9. Using the differential X-ray absorption fine structure spectra, the type of chemical binding state can be identified by means of the reference fine structure and the related chemical shift of the absorption edge. The observed peak structure allows for sufficient discrimination of species, but it is noticeable that the peaks at the Ti-Lii absorption edge are not as pronounced as those of the Ti-Liii edge region. In fact, the differential spectra are
deconvoluted by the usage of a linear deconvolution. Because of the knowledge of the relationship between oxidation state and the oxygen flow rate during the deposition process and due to the buried single layer study,10 an identification of the species is easily feasible. It has been clearly confirmed that the first two systems consist of Ti and Ti2O3 and the last two consist of Ti and TiO2 (see Table 1). However, this method does not provide any information about the sequence of the layers in the multilayered system. Different layer sequences may lead to variations in the superposed NEXAFS fine structure. However, for very thin layers, self-absorption effects24 are negligible, as shown in Figure 6. Comparing the spectra of the samples with different layer sequences, the measured absorption fine structures of both are very similar. Furthermore, no significant contribution from interfacial species has been observed. GIXRF-NEXAFS measurements at varying shallow incidence angles have been carried out to analyze the upper layer species. The incidence angle dependence on the photon energy for the samples consisting of Ti2O3 and Ti are shown in Figure 4. Figure 7 exhibits the respective Ti-Liii,ii GIXRF-NEXAFS spectra. Because of the variation of the incident angle, the spectra have been normalized to the number of excited atoms and corrected for self-absorption effects.24 These NEXAFS spectra are dominated by the characteristic fine structure for the expected titanium or titanium compound in the upper layer, but there are distinctive fractions of the fine structure originating from the lower layer chemical species.The simulations presented in the previous section reveals that it is barely unavoidable to partially excite also the lower layers for these specimens. The best E
DOI: 10.1021/acs.analchem.5b01172 Anal. Chem. XXXX, XXX, XXX−XXX
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Figure 8. By means of the samples Ti/Ti2O3 the method proposed is applied to derive chemical species depth profile for a buried double layer structure. The two curves depicted in the bottom shows the measured Ti-Liii,ii X-ray absorption fine structure spectra at different varying incidence angles to analyze different depth regions. In addition, the normalized count rates are scaled by a factor, which takes into account the ratio from the derived from the data. The results of the deconvolution and the corresponding reference single layer measurements are plotted at the top two graphs in this picture.
Figure 9. By means of the samples Ti2O3/Ti, the method proposed is applied to derive chemical species depth profile for a buried double layer structure. The two curves depicted in the bottom shows the measured Ti-Liii,ii X-ray absorption fine structure spectra at different varying incidence angles to analyze different depth regions. In addition, the normalized count rates are scaled by a factor, which takes into account the ratio derived from the data. The results of the deconvolution and the corresponding reference single layer measurements are plotted at the top two graphs in this picture.
somewhat noisy, but the peak structure is already sufficient for a clear identification. A comparison to the corresponding buried single layer study confirms the chemical state that exists in each of the layers.
or experimentally determined. Because of the lack of reliable data in the soft X-ray range, the complex refractive index was measured here by X-ray reflectometry in order to improve the accuracy of the depth profiling. Criteria have to be formulated to appropriately define the excitation condition for fluorescence generation at sufficiently high incidence angles for X-ray absorption fine structure spectroscopy. It has been shown that for a complex layered structure, a criterion that solely relies on the equally emitted intensity repartition within a two layer system is not sufficient. In particular, for the calculation of an incidence angle sequence suitable for the upper layer analysis, the ratio between the total excitation intensity in the upper and in the lower layer has to be taken into account. This has to be minimized and remain as constant as possible when tuning the photon energy during the NEXAFS measurement. The differential method leads to reliable results for chemical species depth profiling. The measurements on the model systems Ti/TiO2 and Ti/Ti2O3, including the inverted sequences, have been successfully carried out. For each of the layers, the chemical species was determined nondestructively and nonpreparatively.
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CONCLUSION A differential method have been employed to determine speciation depth profiles, which is based on simulating the Xray standing wave field affecting the excitation condition for fluorescence generation. The Ti-Liii,ii GIXRF-NEXAFS analysis was carried out at varying incidence angles to predominately excite a preselected depth region. For our model systems, two GIXRF-NEXAFS measurements at different mean penetration depths are necessary to fully probe the system. A first measurement at varying shallow angles probes only the top layer species and a second one at varying steeper angles analyzes both layers. If the number of relevant layers is increased, the number of measurements has to be increased in a corresponding manner. The calculation of the XSW field intensity uses the complex refractive index which can be found in databases such as CXRO12 F
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(19) Scholze, F.; Procop, M. X-Ray Spectrom. 2001, 30, 69−76. (20) Krumrey, M.; Gerlach, M.; Scholze, F.; Ulm, G. Nucl. Instrum. Methods Phys. Res., Sect. A 2006, 568, 364−368. (21) Cuomo, J. J., Rosnagel, S. M., Kaufman, H. R., Eds. Handbook of Ion Beam Processing Technology; Noyes Publications: Park Ridge, NJ, 1989. (22) Cevro, M.; Carter, G. J. Phys. D: Appl. Phys. 1995, 28, 1962−1976. (23) Gawlitza, P.; Braun, S.; Leson, A.; Lipfert, S.; Nestler, M. Vak. Forsch. Prax. 2007, 19, 37−43. (24) Tröger, L.; Arvanitis, D.; Baberschke, K.; Michaelis, H.; Grimm, U.; Zschech, E. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 3283−3289.
Further improvements are necessary to optimize the excitation conditions and, consequently, the angles of incidence to excite the upper layer while minimizing the contribution from the layer below. The current status of this method allows for a reliable chemical speciation of layered systems consisting of only a few layers of the same element but different chemical binding state. The contribution of the lower layers is obvious and has to be decreased. Because of the strong dependence of the XSW field intensity on the layered structure and their material properties, a general statement regarding the criteria for the determination of the incidence angles is rather challenging. One may expect that the procedure has to be adapted for every class of samples in view to use this technique as a reference measurement technique for validation.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful for the financial support by Deutsche Forschungsgemeinschaft (DFG), Grants EN 207/25-1 and BE 1372/6-1. The authors thank Terrence Jach for fruitful discussions.
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