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Röntgenbeugung und Röntgenstreuung an Multilagenschichten mit diskontinuierlichen Grenzflächen

Röntgenbeugung und Röntgenstreuung an Multilagenschichten mit diskontinuierlichen Grenzflächen. David Rafaja Institut für Metallkunde Struktur und Gefüge von Werkstoffen TU Bergakademie Freiberg http://www.ww.tu-freiberg.de/mk/. Outlines.

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Röntgenbeugung und Röntgenstreuung an Multilagenschichten mit diskontinuierlichen Grenzflächen

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  1. Röntgenbeugung und Röntgenstreuung an Multilagenschichten mit diskontinuierlichen Grenzflächen David Rafaja Institut für Metallkunde Struktur und Gefüge von Werkstoffen TU Bergakademie Freiberg http://www.ww.tu-freiberg.de/mk/

  2. Outlines • Structure model of multilayers with non-continuous interfaces • Experimental methods and theoretical approaches for structure investigation of multilayers • X-ray reflectivity (XRR) • Small-angle X-ray scattering • Reciprocal space mapping • Wide-angle XRD • Applications, Examples (Fe/Au) Physikalisches Kolloquium TUC, 18.6. 2003

  3. Microstructure Model Fe/Au-Multilayer Anticipated changes of the multilayer microstructure (after a temperature treatment) 10 nm TEM courtesy of Prof. J. Zweck, University of Regensburg Physikalisches Kolloquium TUC, 18.6. 2003

  4. Real Structure of Multilayers From SAXS (small-angle X-ray scattering) From WAXS (wide-angle X-ray scattering) • Electron density of individual layers • Thickness of individual layers • Interface roughness • Interface morphology (geometrical and diffuse roughness, lateral correlation length) • Replication of the interference roughness (vertical correlation length) • Interface continuity • Mean thickness of individual layers in the periodic motif • Mean interface roughness • Mean interplanar spacing (residual stresses) • Mean intralayer and interlayer disorder (atomic ordering) • Crystallite size and texture • Interface continuity Physikalisches Kolloquium TUC, 18.6. 2003

  5. Experimental set-up Used for XRR, SAXS, GAXRD and symmetrical XRD Angle of incidence, g Sample Goebel mirror Sample inclination, y X-ray source Diffraction angle, 2q Sample rotation, f Diffraction vector Scintillation detector Normal direction Flat monochromator Physikalisches Kolloquium TUC, 18.6. 2003

  6. Can the interface discontinuities be seen by X-rays?

  7. X-Ray ReflectivityTheoretical background • Multiple (dynamical) scattering of X-rays • Optical theory for smooth interfaces (no interface roughness) Recursive formula Substrate Based on: L.G. Parrat, Phys. Rev. 95 (1954) 359. Physikalisches Kolloquium TUC, 18.6. 2003

  8. X-Ray ReflectivityTheoretical background X-ray reflectivity of multilayers with a certain interface roughness The interfaces must be continuous sj-2 tj-1 tj Change in the Fresnel reflection coefficient (Debye-Waller factor) Substrate L. Névot, P. Croce, Rev. Phys. Appl. 15 (1980) 761. G.H. Vineyard, Phys. Rev. B 26 (1982) 4146. S.K. Sinha, E.B. Sirota, S. Garoff, H.B. Stanley, Phys. Rev. B 38 (1988) 2297. DWBA Physikalisches Kolloquium TUC, 18.6. 2003

  9. Substrate X-ray Diffuse Scatteringon continuous interfaces Distorted wave Born approximation - DWBA Differential cross-section of the diffuse scattering S.K. Sinha, E.B. Sirota, S. Garoff, H.B. Stanley, Phys. Rev. B 38 (1988) 2297. V. Holý, J. Kuběna, I. Ohlídal, K. Lischka, W. Plotz, Phys. Rev. B 47 (1993) 15896. V.Holý, T.Baumbach, Phys. Rev. B 49 (1994) 10668. C (x,y) … In-plane correlation of interface corrugations In a multilayer: additionally the vertical correlation Physikalisches Kolloquium TUC, 18.6. 2003

  10. Capping layer Layer X z Layer C Layer B Layer A Substrate X-ray Reflectivity Structure model , t,  (top) , t,  (X) , t,  (C) , t,  (B) , t,  (A) ,  (S) J.H. Underwood, T.W. Barbee, Appl. Opt. 20 (1981) 3027. P. Lee, Appl. Opt. 22 (1983) 1241. B. Vidal, P. Vincent, Appl. Opt. 23 (1984) 1794. S.K. Sinha, E.B. Sirota, S. Garoff, H.B. Stanley, Phys. Rev. B 38 (1988) 2297. V. Holý, J. Kuběna, I. Ohlídal, K. Lischka, W. Plotz, Phys. Rev. B 47 (1993) 15896. Physikalisches Kolloquium TUC, 18.6. 2003

  11. XRR Curve of a Periodic Multilayer • Total reflection  Electron density of the uppermost layer • Decrease of the reflected Intensity  interface roughness • Kiessig oscillations thickness of the whole multilayer • Bragg-like peaks  thickness of the periodic motif • Extinction of the Bragg-like peaks  thickness of the individual layers in the multilayer system Physikalisches Kolloquium TUC, 18.6. 2003

  12. X-ray Diffuse Scattering of a Periodic Multilayer • Observed phenomena • Yoneda Peaks  Maximum of Fresnel transmissions coefficients, t (kin) or t (kout) • Y.Yoneda, Phys. Rev 131 (1963) 2010. • Maximum of resonant diffuse scattering (RDS, Holy‘s bananas)  kinematical effect (periodicity of the multilayer) • Bragg-like lines  dynamical effect (vertical correlation of corrugations) • Crossing of the RSD and Bragg-like lines • V.Holý, T.Baumbach, Phys. Rev. B 49 (1994) 10668. Reciprocal space mapping Q/2Q (arcsec) Sample inclination (arcsec) Information on the mesoscopic Structure in the lateral direction and on the vertical correlation of disturbances qx-qz scan at qy = 0 Coplanar diffraction geometry Physikalisches Kolloquium TUC, 18.6. 2003

  13. Fe/Au MultilayersExperimental example Fe/Au (27Å/23Å)x10 Si/Au(100Å) Refined parameters t (Fe) (27 ± 2) Å t (Au) (23 ± 1) Å L 50 Å s (Fe) 5 Å s (Au) 5 Å r (Fe) (1.4 ± 0.2) r (Au) (0.9 ± 0.1) Physikalisches Kolloquium TUC, 18.6. 2003

  14. Binary System Fe – Au Au Fe Physikalisches Kolloquium TUC, 18.6. 2003

  15. XRR on Multilayers with Non-Continuous Interfaces Interfaces Continuous Discontinuous Regions Continuous Discontinuous Amplitude and Phase shift Reflectivity Physikalisches Kolloquium TUC, 18.6. 2003

  16. XRR on Multilayers with Non-Continuous Interfaces Fe/Au (30Å/10Å) x 8 Simulation Changes in the XRR curve • Intensity of Bragg peaks decreases • The fringes near the TER are shifted • The structure refinement using the classical model yields closer electron densities of the alternating materials and larger roughness of all interfaces c = 100% Consequences c = 60% c = 30% Physikalisches Kolloquium TUC, 18.6. 2003

  17. Diffuse Scattering from Multilayers with Non-continuous Interfaces DWBA: Differential cross-section Continuous Interfaces Discontinuous Form-factor The integration is performed only in the continuous regions Physikalisches Kolloquium TUC, 18.6. 2003

  18. Diffuse Scattering from Multilayers with Non-continuous Interfaces Consequences Decrease of the intensity of the Yoneda peaks  modified Fresnel transmission coefficients Broadening of the specular peak in the longitudinal scans  „convolution“ with the form-factor D. Rafaja, H. Fuess, D. Šimek, J. Kub, J. Zweck, J. Vacínová, V. Valvoda, J. Phys.: Condensed Matter 14 (2002) 5303-5314. Physikalisches Kolloquium TUC, 18.6. 2003

  19. Diffuse Scattering from Multilayers with Non-continuous Interfaces Fe/Au (70Å/21Å)13 / 280Å Au / SiO2 As deposited 2h/200°C 2h/300°C 4h/300°C Physikalisches Kolloquium TUC, 18.6. 2003

  20. Wide-Angle X-ray Scattering Structure model tB Intralayer disorder Continuous and discrete interface roughness tA Average d-spacing Interlayer distance • Jahn-Teller-Method (layered structures) • Additional information on the atomic ordering (interplanar distances, intralayer disorder, texture) E.E. Fullerton, I.K. Schuller, H. Vanderstraeten and Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. Physikalisches Kolloquium TUC, 18.6. 2003

  21. Kinematical Theory of WAXS for Multilayers with Continuous Interfaces Intensity: Positions of interfaces (Gauss-like distribution): Positions of individual atoms (correlated displacements): Structure factor of individual layers: Interatomic distances and their fluctuations: Physikalisches Kolloquium TUC, 18.6. 2003

  22. WAXS Diffraction Pattern of a Periodic Multilayer Fe/Au (3.24nm/1.41nm)  12 Fe: 16  0.20268 nm, Au: 6  0.2355 nm Positions of Satellites: Periodicity of a bi-layer: Mean interplanar spacing: Physikalisches Kolloquium TUC, 18.6. 2003

  23. buffer substrate WAXS on Multilayers with Non-Continuous Interfaces Kinematical Theory Matrix + Precipitates Structure model Physikalisches Kolloquium TUC, 18.6. 2003

  24. WAXS on Multilayers with Non-Continuous Interfaces f … atomic scattering factors, F … structure factors, c … continuity of interfaces, R … positions of precipitates, E0 … amplitude of the Thomson scattering, z … origin of the layer A, t … thickness of the layer A Matrix Multilayer Interference Term D. Rafaja, H. Fuess, D. Simek, L. Zdeborova and V. Valvoda, J. Phys.: Condens. Matter 14 (2002) 10021-10032. Physikalisches Kolloquium TUC, 18.6. 2003

  25. WAXS – Simulation of Interface Discontinuity 20 % Interface discontinuity 40 % Physikalisches Kolloquium TUC, 18.6. 2003

  26. Combined Refinement SAXS/WAXS Fe/Au (26Å/24Å)10 Virgin 2h/200°C XRR XRD XRR XRD t(Fe) 26.5 25.6 26.5 27.0 t(Au) 24.0 24.6 22.0 27.8 L 50.5 50.2 48.5 54.8 d(Fe) 2.031 2.027 d(Au) 2.359 2.353 d 0.09 0.13 s(Fe) 6.51.07.02.0 s(Au) 6.51.28.0 2.4 s(surf) 6.5 9.0 c(%) 90 100 85 80 Physikalisches Kolloquium TUC, 18.6. 2003

  27. Fe/Au (26Å/24Å)10Large correlation of the interface roughness Well-pronounced maxima of the resonant diffuse scattering Large difference between (XRR) and (XRD) Diffraction angle (arcsec) Sample inclination from the normal direction (arcsec) Physikalisches Kolloquium TUC, 18.6. 2003

  28. Combined Refinement SAXS/WAXS Fe/Au (70Å/21Å)13 Virgin 4h/300°C XRR XRD XRR XRD t(Fe) 69.7 63.5 69.9 61.8 t(Au) 20.4 24.3 19.4 25.8 t(int) 2.2 2.1 L 90.1 90.0 89.3 89.7 d(Fe) 2.036 2.027 d(Au) 2.339 2.327 d 0.076 0.040 s(Fe) 8.0 4.5 12.0 6.5 s(Au) 9.5 5.0 13.0 7.5 s(surf) 12 20 r(Fe1) 1.0 0.6 c(%)90100 8580 Physikalisches Kolloquium TUC, 18.6. 2003

  29. Fe/Au (70Å/21Å)13Low correlation of the interface roughness Weak maxima of the resonant diffuse scattering Small difference between (XRR) und (XRD) Diffraction angle (arcsec) Sample inclination from the normal direction (arcsec) Physikalisches Kolloquium TUC, 18.6. 2003

  30. Continuous Interfaces XRR Total External Reflection Kiessig Oscillations Bragg Peaks SAXS Yoneda Peaks Resonant Diffuse Scattering WAXS Satellite Peaks Non-continuous Interfaces XRR Total External Reflection Kiessig Oscillations Bragg Peaks are weaker SAXS Yoneda Peaks are weaker Resonant Diffuse Scattering is concentrated at qx=0 WAXS Satellite Peaks are overlapped by the Diffraction Peak from Matrix Comparison of the Scattering Phenomena Physikalisches Kolloquium TUC, 18.6. 2003

  31. Acknowledgement Deposition of Fe/Au multilayers • Prof. R. Krishnan and Prof. A. Das, CNRS Meudon/ Paris (F) Transmission electron microscopy • Prof. J. Zweck, University of Regensburg (D) Physikalisches Kolloquium TUC, 18.6. 2003

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