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David Rafaja Institut für Metallkunde

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Presentation on theme: "David Rafaja Institut für Metallkunde"— Presentation transcript:

1 Röntgenbeugung und Röntgenstreuung an Multilagenschichten mit diskontinuierlichen Grenzflächen
David Rafaja Institut für Metallkunde Struktur und Gefüge von Werkstoffen TU Bergakademie Freiberg

2 Physikalisches Kolloquium TUC, 18.6. 2003
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) 2 Physikalisches Kolloquium TUC,

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 3 Physikalisches Kolloquium TUC,

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 4 Physikalisches Kolloquium TUC,

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

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

7 X-Ray Reflectivity Theoretical 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. 7 Physikalisches Kolloquium TUC,

8 X-Ray Reflectivity Theoretical background
The interfaces must be continuous X-ray reflectivity of multilayers with a certain interface roughness sj-2 tj-1 tj Substrate Change in the Fresnel reflection coefficient (Debye-Waller factor) 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 8 Physikalisches Kolloquium TUC,

9 X-ray Diffuse Scattering on continuous interfaces
Distorted wave Born approximation - DWBA Differential cross-section of the diffuse scattering Substrate 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) V.Holý, T.Baumbach, Phys. Rev. B 49 (1994) C (x,y) … In-plane correlation of interface corrugations In a multilayer: additionally the vertical correlation 9 Physikalisches Kolloquium TUC,

10 Physikalisches Kolloquium TUC, 18.6. 2003
X-ray Reflectivity Structure model , t,  (top) , t,  (X) , t,  (C) , t,  (B) , t,  (A) ,  (S) Substrate Layer A Layer B Layer C Layer X Capping layer z 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) 10 Physikalisches Kolloquium TUC,

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 11 Physikalisches Kolloquium TUC,

12 X-ray Diffuse Scattering of a Periodic Multilayer
Reciprocal space mapping 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) 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 12 Physikalisches Kolloquium TUC,

13 Fe/Au Multilayers Experimental example
Fe/Au (27Å/23Å)x10 Si/Au(100Å) Refined parameters t (Fe) (27 ± 2) Å t (Au) (23 ± 1) Å L Å s (Fe) Å s (Au) Å r (Fe) (1.4 ± 0.2) r (Au) (0.9 ± 0.1) 13 Physikalisches Kolloquium TUC,

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

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

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% 16 Physikalisches Kolloquium TUC,

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 17 Physikalisches Kolloquium TUC,

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) 18 Physikalisches Kolloquium TUC,

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 19 Physikalisches Kolloquium TUC,

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. 20 Physikalisches Kolloquium TUC,

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: 21 Physikalisches Kolloquium TUC,

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

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

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) 24 Physikalisches Kolloquium TUC,

25 WAXS – Simulation of Interface Discontinuity
25 Physikalisches Kolloquium TUC,

26 Combined Refinement SAXS/WAXS
Fe/Au (26Å/24Å)10 Virgin h/200°C XRR XRD XRR XRD t(Fe) t(Au) L d(Fe) d(Au) d s(Fe) s(Au) s(surf) c(%) 26 Physikalisches Kolloquium TUC,

27 Fe/Au (26Å/24Å)10 Large 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) 27 Physikalisches Kolloquium TUC,

28 Combined Refinement SAXS/WAXS
Fe/Au (70Å/21Å)13 Virgin h/300°C XRR XRD XRR XRD t(Fe) t(Au) t(int) L d(Fe) d(Au) d s(Fe) s(Au) s(surf) r(Fe1) c(%) 28 Physikalisches Kolloquium TUC,

29 Fe/Au (70Å/21Å)13 Low 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) 29 Physikalisches Kolloquium TUC,

30 Comparison of the Scattering Phenomena
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 30 Physikalisches Kolloquium TUC,

31 Physikalisches Kolloquium TUC, 18.6. 2003
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) 31 Physikalisches Kolloquium TUC,


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