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
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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
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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
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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
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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
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14. Physikalisches Kolloquium TUC, 18.6. 2003
Binary System Fe – Au Au Fe 14
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15. XRR on Multilayers with Non-Continuous Interfaces
Discontinuous
Regions
Continuous
Discontinuous
Amplitude and Phase shift
Reflectivity 15
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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
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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
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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
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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
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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
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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
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23. WAXS on Multilayers with Non-Continuous Interfaces
Kinematical Theory
Matrix + Precipitates
Structure model
substrate
buffer 23
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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 Discontinuity25
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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
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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
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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
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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
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