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

2Physikalisches Kolloquium TUC, 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)

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

4Physikalisches Kolloquium TUC,  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  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 From SAXS (small-angle X-ray scattering) Real Structure of Multilayers From WAXS (wide-angle X-ray scattering)

5Physikalisches Kolloquium TUC, Experimental set-up Scintillation detector Flat monochromator Sample Goebel mirror X-ray source Sample rotation,  Normal direction Diffraction vector Diffraction angle, 2  Angle of incidence,  Sample inclination,  Used for XRR, SAXS, GAXRD and symmetrical XRD

Can the interface discontinuities be seen by X-rays?

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

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

9Physikalisches Kolloquium TUC, X-ray Diffuse Scattering on 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) V. Holý, J. Kuběna, I. Ohlídal, K. Lischka, W. Plotz, Phys. Rev. B 47 (1993) V.Holý, T.Baumbach, Phys. Rev. B 49 (1994) Substrate C (x,y) … In-plane correlation of interface corrugations In a multilayer: additionally the vertical correlation

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

11Physikalisches Kolloquium TUC, 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

12Physikalisches Kolloquium TUC, X-ray Diffuse Scattering of a Periodic Multilayer Reciprocal space mapping Observed phenomena  Yoneda Peaks  Maximum of Fresnel transmissions coefficients, t (k in ) or t (k out )  Y.Yoneda, Phys. Rev 131 (1963)  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) Information on the mesoscopic Structure in the lateral direction and on the vertical correlation of disturbances Sample inclination (arcsec)  (arcsec) q x -q z scan at q y = 0 Coplanar diffraction geometry

13Physikalisches Kolloquium TUC, Fe/Au Multilayers Experimental example t (Fe) (27 ± 2) Å t (Au) (23 ± 1) Å  50 Å  (Fe) 5 Å  (Au) 5 Å  (Fe) (1.4 ± 0.2)  (Au) (0.9 ± 0.1) Fe/Au (27Å/23Å)x10 Si/Au(100Å) Refined parameters

14Physikalisches Kolloquium TUC, Binary System Fe – Au AuFe

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

16Physikalisches Kolloquium TUC, XRR on Multilayers with Non- Continuous Interfaces  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% c = 60% c = 30% Changes in the XRR curve Consequences Fe/Au (30Å/10Å) x 8 Simulation

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

18Physikalisches Kolloquium TUC, Diffuse Scattering from Multilayers with Non-continuous Interfaces D. Rafaja, H. Fuess, D. Šimek, J. Kub, J. Zweck, J. Vacínová, V. Valvoda, J. Phys.: Condensed Matter 14 (2002) 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

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

20Physikalisches Kolloquium TUC, Wide-Angle X-ray Scattering Structure model tAtA tBtB Continuous and discrete interface roughness Intralayer disorder 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.

21Physikalisches Kolloquium TUC, 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:

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

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

24Physikalisches Kolloquium TUC, WAXS on Multilayers with Non- Continuous Interfaces D. Rafaja, H. Fuess, D. Simek, L. Zdeborova and V. Valvoda, J. Phys.: Condens. Matter 14 (2002) f … atomic scattering factors, F … structure factors, c … continuity of interfaces, R … positions of precipitates, E 0 … amplitude of the Thomson scattering, z … origin of the layer A, t … thickness of the layer A MatrixMultilayerInterference Term

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

26Physikalisches Kolloquium TUC, Combined Refinement SAXS/WAXS Virgin 2h/200°C XRR XRD XRR XRD t(Fe) t(Au)  d(Fe) d(Au)   (Fe)  (Au)  (surf) c(%) Fe/Au (26Å/24Å)10

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

28Physikalisches Kolloquium TUC, Combined Refinement SAXS/WAXS Virgin 4h/300°C XRR XRD XRR XRD t(Fe) t(Au) t(int)  d(Fe) d(Au)   (Fe)  (Au)  (surf)  (Fe1) c(%) Fe/Au (70Å/21Å)13

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

30Physikalisches Kolloquium TUC, 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 q x =0 WAXS  Satellite Peaks are overlapped by the Diffraction Peak from Matrix

31Physikalisches Kolloquium TUC, 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)