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Complementary Characterization of Buried Nanolayers by Quantitative X-ray Fluorescence Spectrometry under Conventional and Grazing Incidence Conditions Rainer Unterumsberger,* Beatrix Pollakowski, Matthias M€uller, and Burkhard Beckhoff Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany ABSTRACT:
The determination of the thickness and elemental composition is an important part of the characterization of nanolayered structures. For buried nanolayers, X-ray fluorescence spectrometry is a qualified method for the thickness determination whereas conventional electron emission based methods may reach their limits due to rather restricted information depths. The aim of the presented investigation was the comparison of reference-free X-ray fluorescence spectrometry under conventional and grazing incidence conditions offering complementary information with respect to quantification reliability, elemental sensitivity, and layer sequences. For this purpose, buried boroncarbon layers with nominal thicknesses of 1, 3, and 5 nm have been studied using monochromatized undulator radiation in the laboratory of the Physikalisch-Technische Bundesanstalt (PTB) at the synchrotron radiation facility BESSY II. The results for the two beam geometries are compared and show particulate good agreements, thus encouraging the complementary use of both methodologies.
N
anolayered systems play a major role in structured semiconductor applications. Some materials properties such as the layer thickness can determine the relevant electrical properties of the whole semiconductor system. Destructive analytical methods like secondary ion mass spectrometry (SIMS) can change the properties of the system during the analysis, so a non-destructive and non-preparative investigation of the layers becomes important not only as a reference measurement technique. Reference-free X-ray fluorescence spectrometry (XRF) is a well-established method for the thickness determination.13 It is based on the knowledge of instrumental and experimental parameters such as the efficiency of calibrated X-ray detectors and photodiodes on the one hand and fundamental atomic parameters on the other hand. With the use of high-flux undulator radiation in the soft X-ray energy range enables the thickness determination of buried nanolayers even when composed of light elements like boron and carbon. Under grazing incidence X-ray fluorescence (GIXRF) conditions, the incident X-ray beam can be reflected at the substrate and thereby an X-ray standing wave field (XSW) occurs.4 The total reflection of the incident beam at the substrate prevents the penetration into the substrate. This reduces the substrate contribution and leads to r 2011 American Chemical Society
the possibility of the determination of trace elemental concentrations or minute mass depositions.5 By means of a variation of the incident angle, the sequence of the layers can be revealed.6 The transition from grazing incidence to conventional excitation conditions involves the reduction of spatial and compositional sensitivity in favor of improved quantification reliability. This is due to the angle dependent penetration depth of the excitation radiation on the one hand and the collapse of the XSW field on the other hand.
’ EXPERIMENTAL SECTION The samples for the comparison are composed of silicon wafer substrates covered with boroncarbon layers, varying in nominal thickness of 1, 3, and 5 nm and capped with 2.5 nm silicon dioxide. In addition, two sample systems with a thicker titanium or nickel nanolayer below the boroncarbon layers were investigated. The design of the sample systems allows for Received: August 8, 2011 Accepted: October 3, 2011 Published: October 03, 2011 8623
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Analytical Chemistry the penetration of the boroncarbon layer and for total reflection at the surface or metal nanolayers at the same time. The penetration depth can be tuned by varying the incident angle of the synchrotron radiation on the sample systems. The employed plane grating monochromator (PGM) beamline provides synchrotron radiation of high spectral purity and high photon flux in the energy range of 781860 eV.7 This enables the possibility to analyze light elements like semimetals or transition metals. With respect to the beamline transmittance and detector efficiencies, PTB employs calibration procedures to keep track of any degradation. Taking advantage of calibrated photodiodes and energy-dispersive detectors as well as well-known experimental arrangements, PTB is able to perform completely reference-free fundamental parameter based quantification.8,9 For this purpose, the samples were mounted in a high-vacuum XRF chamber. Figure 1 shows the scheme of the experimental arrangements. The surface of the sample can be adjusted to the optimal position, i.e., the axis of rotation of the XRF instrumentation. The incident angle of the incoming beam with respect to the sample surface can be varied from 0° to 4.5° under grazing incidence conditions or is set constant to 45°, which is the conventional XRF beam geometry. The emitted fluorescence radiation is detected by a calibrated silicon-drift-detector (SDD), which is placed at an angle of 90° with respect to the incoming beam.
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For the determination of the solid angle of detection, two different techniques are used with respect to the respective quantification methods. Under conventional XRF conditions, a calibrated diaphragm in front of the detector is defining the solid angle of detection. Under grazing incidence conditions, the solid angle of detection is calculated for every incident angle knowing the distance of the detector and the beam spot profile as well as the collimating geometry of the detector.5 The radiant power of the incidence undulator radiation and the photon flux is measured by means of calibrated photodiodes before and after recording each fluorescence spectrum. In order to avoid high background contributions and interfering fluorescence lines, the excitation energy was chosen to 510 eV, thus below the K absorption-edge of oxygen.
’ X-RAY FLUORESCENCE ANALYSIS The recorded fluorescence spectra were deconvoluted employing the experimentally derived and physically modeled response functions of the SDD.10 The model spectrum includes the fluorescence lines and background contributions from resonant Raman scattering (RRS)11 and bremsstrahlung effects. Figure 2 (left side) shows the XRF spectrum of the sample with a nominal 5 nm boroncarbon layer without a metal layer, and Figure 2 (right side) shows the respective GIXRF spectrum as described below.
Figure 1. Schematic view of the experimental setup in the two beam geometries employed. Under grazing incidence conditions (left side) the sample can be rotated. For conventional XRF beam geometry (right side) the sample is set constant to 45°.
Figure 2. XRF spectrum of the sample: nominal 2.5 nm SiO2/5 nm BC/Si-substrate (left side). GIXRF spectrum of the same sample (right side). 8624
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edge Xi, and jXi is the jump ratio at the absorption edge Xi:
In general, in conventional geometry the RRS and substrate fluorescence contributions are increased and have an unfavorable impact on the deconvolution of the spectrum, due to reduced signal to background ratios. By means of the knowledge of the relevant instrumental and atomic fundamental parameters, the mass deposition mi/Fi of the elements boron and carbon with unit area Fi can be determined using the following equation:12 2
μtot, i ¼
7 7 7 1 5
Pi
P0 τi, E0 Q
Ωdet 1 4π sin Ψin μtot, i
μi, E0 μi, Ei þ sin Ψin sin Ψout
ð1Þ
The components are shown in Table 1. For conventional incidence geometries, Ψin and Ψout are 45° with respect to the wafer surface. The factor Q is composed of fundamental parameters of the respective element. Xi is the absorption edge, ωXi is the fluorescence yield of the absorption edge Xi, gl,Xi is the transition probability of the fluorescence line l belonging to the absorption Table 1. Overview of All Experimental and Atomic Fundamental Parameters Used in Equation 1 E0
excitation energy of the incident radiation
Ei
photon energy of the fluorescence line l of the element i
S0
signal of the photodiode
σdiode,E0
spectral responsitivity of the photodiode
P0 = S0/σdiode,E0
radiant power of the incident radiation
Ri
count rate of the fluorescence line l of the element i
εdet,Ei
detection efficiency of the SDD at the photon energy Ei
Pi = Ri/εdet,Ei τi,E0
effective count rate of the fluorescence line l photoelectric cross section of the element i at the
Ωdet
effective solid angle of detection
photon energy E0 Ψin
angle of incidence with respect to the wafer surface
Ψout
angle of observation
F
density
Q
fluorescence production cross section
μtot,i
absorption correction factor
jX i 1 jX i
ð2Þ
The fundamental parameters were taken from Elam et al.,13 for the K fluorescence yields of the boron and carbon, data experimentally determined at PTB were used.14 To determine the layer thickness d of the calculated mass deposition, the density F of the element has to be known. The relation between d and mi/Fi is as follows d = mi/Fi/F. Usually the bulk density of the respective element is used, but for thin layers and unknown chemical speciation the uncertainty of the density is increased up to 10%. A further aspect is the surface contamination of carbon. Under conventional incidence conditions it is hard to distinguish between the surface and layer contributions to the total mass deposition. Beside the primary excitation radiation, fluorescence radiation from one element with an energy above the absorption edge of a second element can excite the element and cause secondary fluorescence radiation. In particular, the energy of the carbon Kα fluorescence radiation is above the K-edge of boron and has the ability to induce additional boron Kα fluorescence radiation. However, in the present case this effect is negligible because of the low mass deposition of carbon and the low fluorescence yields in the soft X-ray range.15 If the excitation energy is above the silicon K-edge, secondary fluorescence radiation could be excited by the silicon fluorescence radiation from the silicon substrate. The upper limit of this effect is estimated to 2.5%.15 The measurements were performed with an excitation energy below the silicon K-edge. Considering potential higher-order and stray light radiation of the PGM beamline, which is about 0.5%,7 any additional secondary fluorescence excitation by the substrate is in the range of 104 or less. The absorption of the elemental specific fluorescence radiation induced below the wafer surface is taken into account with the exponential decrease involving the term μi,Ei/sin Ψout.5 The determined mass depositions of boron and carbon can be converted into layer thicknesses with the assumption of bulk density. For the sake of comparison, the nominal thicknesses of the boron carbide layers are fragmented into the boron and carbon parts. An overview of the quantification is given in Table 2. The estimated relative uncertainty (k = 1) of the quantification in XRF geometry is about 25%. It is composed of the following contributions, shown in Table 3.
3
mi 1 6 6 ¼ ln61 μtot, i 4 Fi
with
Q ¼ ωXi gl, Xi
Table 2. Determined Thicknesses of Boron and Carbon in XRF- and GIXRF-Geometry nominal thickness of buried layers (nm) layered systems SiO2/BC
SiO2/BC/Ti
SiO2/BC/Ni
boron
carbon
determined thickness in XRF (nm)
determined thickness in GIXRF (nm)
boron
carbon
boron
carbon
0.8
0.2
0.9 ( 0.2
0.4 ( 0.1
0.9 ( 0.3
0.6 ( 0.2
2.5
0.7
2.6 ( 0.7
0.8 ( 0.2
2.5 ( 0.8
0.9 ( 0.3
4.2
1.2
4.2 ( 1.1
1.2 ( 0.3
4.0 ( 1.2
1.3 ( 0.4
0.8
0.2
0.8 ( 0.2
1.1 ( 0.3
0.7 ( 0.2
1.3 ( 0.4
2.5 4.2
0.7 1.2
2.5 ( 0.7 4.0 ( 1.0
1.4 ( 0.4 1.2 ( 0.3
2.4 ( 0.7 3.9 ( 1.2
1.3 ( 0.4 1.4 ( 0.5
0.8
0.2
1.0 ( 0.3
1.2 ( 0.3
0.6 ( 0.4
0.5 ( 0.3
2.5
0.7
2.7 ( 0.7
1.4 ( 0.4
2.0 ( 1.0
0.7 ( 0.4
4.2
1.2
4.3 ( 1.1
1.6 ( 0.4
3.5 ( 1.8
1.0 ( 0.5
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’ GRAZING INCIDENCE X-RAY FLUORESCENCE ANALYSIS The XRF under grazing incidence conditions has several advantages for near-surface investigations. In general, because of an incident angle below the critical angle of total reflection at the substrate, the contribution of the RRS, produced by substrate silicon atoms, to the background of the fluorescence spectrum and the substrate fluorescence are considerably reduced. Figure 2 (right side) shows a GIXRF spectrum of the present measurement. Here, in general, two effects decrease the reduction of the background compared to the XRF measurement. First, the favorable excitation conditions, i.e., the low excitation energy, leads to a good peak to background ratio, due to low scattering cross sections and only production of silicon Ll substrate fluorescence even in XRF geometry. At higher excitation energies above 1 keV, the peak to background ratio of GIXRF is favorable in comparison to XRF due to higher scattering cross sections. An example is shown in Figure 3, where the peak to background ratio is about 3:1 in XRF geometry and about 130:1 in GIXRF geometry. Table 3. Relative Uncertainties of the Quantification in XRF Geometry relative uncertainty parameter
(102)
Second, in the silicon dioxide cap layer, RRS is produced by oxygen and silicon atoms. At small incident angles, this contribution dominates the RRS, whereas it can be neglected in XRF geometry. Because of these effects, the level of the background in GIXRF geometry is comparable to the respective level in XRF geometry. In the angular range of the GIXRF geometry, the distance of the SDD to the sample-surface can be minimized, which also increases the solid angle of detection. This increases the detection sensitivity and reduces the lower limits of detection. Furthermore, the reflected beam can interfere with the incoming beam and an XSW field occurs.4,16 The relative excitation intensity above the surface17 and in the upper layers will be modified.18 The modification of the resulting XSW intensity has to be calculated because of the dependency on the excitation energy and the incident angle. The calculation of the modified excitation intensity has been performed by the software package IMD.19 Figure 4 shows the calculated XSW field for an ideal sample with the assumption that the boroncarbon layer is a homogeneous boron carbide layer and roughnesses at the surface and between the layers of 0.3 nm (root-mean-square, rms). The effective excitation intensity is proportional to the XSW intensity. Because of the depth-dependent modification of the excitation radiation, it is possible to reveal information about the sequence of the layers by measuring the fluorescence radiation as a function of the incident angle.20 The normalized count rates of boron,
comment
S0
0.01
signal of the photodiode
σdiode,E0
1
spectral responsitivity of the photodiode
P0
1.0
consist of S0 and σdiode,E0
Ri
1.0
count rate of the fluorescence line l of the
εdet,Ei
1.5
element i detection efficiency of the SDD at the photon
Pi
1.8
consist of Ri and εdet,Ei
energy Ei Ωdet
0.7
solid angle of detection
F
10.0
bulk value used for B4C
τi,E0
13.0
see ref 5
μtot,i
13.0
see ref 5
Q total
15.5 26.1
see ref 5
Figure 4. Calculated XSW field for an ideal sample 2.5 nm SiO2/5 nm B4C/Si-substrate and the assumption of 0.3 nm roughness (rms).
Figure 3. XRF spectrum of the sample: nominal 2.5 nm SiO2/5 nm BC/Si-substrate at an excitation energy of 1060 eV (left side) and the respective GIXRF spectrum (right side). In this example, the peak to background ratio is increased by the factor 40. 8626
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Figure 5. Relative fluorescence count rate as a function of the incident angle (left side). It is normalized to the solid angle of detection and the sinus of the incident angle to have a comparison to the calculated excitation intensities in the respective layer (right side).
carbon, and oxygen Kα fluorescence radiation as well as of the silicon Ll substrate signal are shown in Figure 5 (left side). The run of the curves identifies the oxygen-, carbon-, and borondepositions as thin films, and the silicon signal is characteristic for a bulklike concentration.6 The angle at half-maximum of the fluorescence radiation peak is 1.19° for oxygen, 1.28° for carbon, and 1.39° for boron, which reveals the sequence of the layers. To get information about the effective excitation intensity in a layer, the mean value of the XSW intensity in the respective layer has to be calculated for every incident angle. The result of this calculation is shown in Figure 5 (right side). With comparison of the count rates and the calculated excitation intensities, the run of the curves are similar. However, the peak value of the curves is higher for the calculated curves. This can be explained by surface contamination of light elements like carbon which attenuates the XSW intensity in the other layers. A second indication of surface contamination of carbon is that at very small incident angles (0.1°), the count rates of carbon Kα fluorescence are higher than the oxygen Kα fluorescence count rates, shown in the inlet of Figure 5 (left side). It was expected that the oxygen signal emerge first being the top layer of the system. The third indication is the evaluation of the carbon count rate compared to the calculated curves. It is shifted to smaller incident angles which could be explained by a superposition of surface signal and signal of the buried layer of carbon. This confirms the results of the carbon quantification under conventional incidence conditions, where the mass deposition of carbon is higher than the nominal value on each sample. Considering the modified excitation intensity IWsurf, eq 1 is extended to5 2 3 mi 1 6 6 ¼ ln61 μtot, i 4 Fi
7 Pi 7 7 Ωdet 1 1 5 P0 IWsurf τi, E0 Q 4π sin Ψin μtot, i
ð3Þ
In addition to the uncertainties as described in Table 3, the uncertainty of the relative excitation intensity IWsurf has to be taken into consideration for the GIXRF quantification. The assumed density of the elements in the layers has a direct impact on the calculation of the XSW intensity. On the other hand, IMD calculations show a small dependency of the XSW intensity on
Table 4. Comparison of GIXRF Quantification at 2.4° and 4.4°a nominal thickness incident angle Ψin
boron
carbon
0.8 nm 2.5 nm 4.2 nm 0.2 nm 0.7 nm 1.2 nm
2.4°
0.6
1.9
3.3
0.7
0.9
1.5
4.4°
0.9
2.5
4.0
0.6
0.9
1.3
a
Differences are due to the XSW intensity calculated for the ideal sample.
the boroncarbon layer thickness. The estimation for the relative uncertainty of the XSW intensity is about 15%, mainly caused by the uncertainties of the respective optical constants. Finally, the uncertainty of the solid angle of detection is about 4% for the GIXRF beam geometry.6 According to that, the total relative uncertainty of the GIXRF quantification is about 30%.
’ COMPARISON OF XRF AND GIXRF In order to get a comparison with the XRF quantification, in GIXRF geometry all sample systems were investigated at the same excitation energy of 510 eV at an incident angle of 4.4°. The comparison of the GIXRF and XRF results is shown in Table 1. In both geometries, the determined thicknesses for boron are in line with the nominal values. This is an indication that the correct amount of boron was used during the deposition process. The sample system with the nickel interlayer has the largest deviation. This can be explained by a strong interaction of nickel with the other layers and possible diffusion of nickel during the production of the samples. These effects may modify the depth depending XSW intensity and the deviation from the calculated excitation intensity increases. The carbon contamination on the sample surface has an additional impact on the XSW intensity. A comparison of the present GIXRF quantification at 4.4° for the sample system SiO2/BC (first column in Table 2) and the respective quantification at 2.4° illustrates this impact. The determined boron thicknesses are reduced while the carbon thicknesses are increased, it is shown in Table 4. The additional carbon top layer lowers the XSW intensity in the boroncarbon layer, which is not considered in the calculation. Thereby the boron thickness is apparently reduced. 8627
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Analytical Chemistry The increased carbon thickness is due to the combination of surface and buried carbon. That increases the XSW intensity for carbon which is also not considered in the calculation. The differences of the quantification at 4.4° and 2.4° are within the uncertainties. An iterative calculation of the XSW intensity according to the determined layer thicknesses and possible contaminations could correct these differences. Because of these effects, the uncertainties of the effective excitation intensity are increased for the GIXRF quantification. With the assumption of a typical carbon contamination cap layer of 0.2 nm, the thickness determination of carbon in XRF geometry results in the expected thicknesses for the buried nanolayers of the samples without a titanium or nickel nanolayer. For the sample systems with a metal nanolayer, the determined carbon thicknesses in XRF are much higher than the nominal values, which could be caused by increased surface carbon contamination. The carbon quantification in GIXRF is sophisticated due to two components of carbon, the surface contamination, and the boroncarbon layer. Limited to the ideal sample systems in the calculation, the relative excitation intensity, which has an impact on the determined carbon thickness, has a large uncertainty. As mentioned above, the sample system with the nickel interlayer has the largest deviation due to the unknown interaction of nickel. This is even stronger for the determined carbon thickness. Here, an estimate of the respective total uncertainty is about 50%.
’ CONCLUSIONS AND PERSPECTIVES It could be confirmed that reference-free X-ray fluorescence analysis is a well established method for the non-destructive and non-preparative thickness determination of surface contaminations and thin layers.1,5 We have shown that reference-free X-ray fluorescence analysis in conventional and grazing incidence conditions gives complementary information about the layer composition and sequence and that the combination of the methods allows for reliable thickness determination of nanolayered systems. The results confirm that in conventional XRF geometry, the uncertainties are small, but due to the signal-to-noise ratio, the sensitivity is low. This leads to the quantification of the total mass deposition of a respective element in the sample. It could be shown that in GIXRF beam geometry, the sequence of the layers (and partial diffusion into an adjacent layer) can be revealed by measuring the fluorescence radiation as a function of the incident angle. The quantification under grazing incidence conditions showed that the uncertainties are higher mainly due to the influence of the XSW intensity. However, the background is lower than for XRF beam geometry, and the solid angle of detection is increased which leads to improved limits of detection. Independent of the geometry, the uncertainties of the fundamental parameters have a large impact on the total uncertainties. To reduce the uncertainty of the XSW, an iterative calculation of the relative excitation intensity according to the determined layer thicknesses and possible contaminations is intended. The comparison of XRF and GIXRF exhibited that the potential of each method can compensate the restriction of the other method. Here, under conventional beam geometry the total carbon and boron thickness could be determined with small uncertainties. In addition, the measurements in GIXRF offered the sequence of the layers and the existence of additional carbon
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contamination. Thus, the combination of both methods enables a reliable quantification of buried nanolayers consisting of light elements. One may expect the combined XRF/GIXRF methodology to be able to substantially contribute to the reliable characterization of buried nanolayers of technologically relevant materials.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors B.P and B.B. acknowledge the financial support granted by the German Research Foundation (DFG) for the Research Project BE 1372/6-1. ’ REFERENCES (1) Kolbe, M.; Beckhoff, B.; Krumrey, M.; Ulm, G. Spectrochim. Acta, Part B 2005, 60, 505–510. (2) Kolbe, M.; Beckhoff, B.; Krumrey, M.; Reading, M. A.; den Berg, J. V.; Conard, T.; Gendt, S. D. ECS Trans. 2009, 25, 293–300. (3) den Berg, J. V.; Reading, M. A.; Parisini, A.; Kolbe, M.; Beckhoff, B.; Ladas, S.; Fried, M.; Petrik, P.; Bailey, P.; Noakes, T.; Conard, T.; Gendt, S. D. ECS Trans. 2009, 25, 349–361. (4) de Boer, D. K. G. Phys. Rev. B 1991, 44, 498–511. (5) Beckhoff, B.; Fliegauf, R.; Kolbe, M.; M€uller, M.; Weser, J.; Ulm, G. Anal. Chem. 2007, 79, 7873–7882. (6) Bubert, H.; Riviere, J. In Surface and Thin Film Analysis: Principles, Instrumentation, Applications; Bubert, H., Jenett, H., Eds.; Wiley-VCH Verlag GmbH: Weinheim, Germany, 2002; Chapter 2. (7) Senf, F.; Flechsig, U.; Eggenstein, F.; Gudat, W.; Klein, R.; Rabus, H.; Ulm, G. J. Synchrotron Rad. 1998, 5, 780–782. (8) Beckhoff, B. J. Anal. At. Spectrom. 2008, 23, 845–853. (9) Kolbe, M.; Beckhoff, B.; Krumrey, M.; Ulm, G. Appl. Surf. Sci. 2005, 252, 49–52; 13th Applied Surface Analysis Workshop - AOFA 13. (10) Scholze, F.; Procop, M. X-Ray Spectrom. 2009, 38, 312–321. (11) M€uller, M.; Beckhoff, B.; Ulm, G.; Kanngießer, B. Phys. Rev. A 2006, 74, 012702. (12) Beckhoff, B.; Kanngießer, B.; Langhoff, N.; Wedell, R.; Wolff, H. Handbook of Practical X-Ray Fluorescence Analysis; Springer-Verlag: Berlin, Germany, 2006; Chapter 5. (13) Elam, W. T.; Ravel, B.; Sieber, J. R. Radiat. Phys. Chem. 2002, 63, 121–128. (14) Beckhoff, B.; Ulm, G. Adv. X-Ray Anal. 2001, 44, 349–354. (15) Zschornack, G. Handbook of X-Ray Data; Springer Verlag: Berlin, Germany, 2007. (16) Klockenk€amper, R.; von Bohlen, A. Spectrochim. Acta, Part B: At. Spectrosc. 2001, 56, 2005–2018. (17) Kr€amer, M.; von Bohlen, A.; Sternemann, C.; Paulus, M.; Hergenr€oder, R. Appl. Surf. Sci. 2007, 253, 3533–3542. (18) Pollakowski, B.; Beckhoff, B.; Reinhardt, F.; Braun, S.; Gawlitza, P. Phys. Rev. B 2008, 77, 235408. (19) Windt, D. L. Comput. Phys. 1998, 12, 360. (20) Lommel, M.; H€ onicke, P.; Kolbe, M.; M€uller, M.; Reinhardt, F.; M€obus, P.; Mankel, E.; Beckhoff, B.; Kolbesen, B. O. Solid State Phenom. 2009, 145146, 169.
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