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 Freiberghttp://www.ww.tu-freiberg.de/mk/

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)


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


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)


Experimental set-up

Scintillationdetector

Flat monochromator

SampleGoebel 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?


X-Ray ReflectivityTheoretical background

Substrate

- Multiple (dynamical) scattering of X-rays

- Optical theory for smooth interfaces (no interface roughness)

22

1

11,

212

1,

21,

11

1

cos4

sin4

2exp;

1

jjj

jjjjj

jjjj

jjjjj

jjjjj

j

Rj

nq

tiqfqq

qqr

fAfr

AfrA

E

E

Based on: L.G. Parrat, Phys. Rev. 95 (1954) 359.

Recursive formula

2NRI

12

1 0

2

jjjatj

ej fiffN

rn


X-Ray ReflectivityTheoretical background

Substrate

22

21,

1

11,

212

1,

21,

11

1

cos4

;2exp

2exp

1

jjjjj

jjjjj

jjjj

jjjjj

jjjjj

j

Rj

nqtiqf

qqq

qqr

fAfr

AfrA

E

E

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) 4146.S.K. Sinha, E.B. Sirota, S. Garoff, H.B. Stanley, Phys. Rev. B 38 (1988) 2297.

DWBA

The interfaces must be continuous

tj

tj-1

j-2


X-ray Diffuse Scatteringon continuous interfaces

S

yqxqiyxCq

jjjjj

jjj

yxz eedxdyF

kkkk

kt

1~

8exp2

,

221

11,

2

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.

Substrate

C (x,y) … In-plane correlation of interface corrugations

In a multilayer: additionally the vertical correlation


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) 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.

0;0 zyx qqq

z

, t, (top)

, t, (X)

, t, (C)

, t, (B)

, t, (A)

, (S)


XRR Curve of a Periodic Multilayer

0 2 4 6 8 1010

-8

10-6

10-4

10-2

100

102

104

106

108

Au/Al, 10x, tA+t

B=7.5nm

t(A)/t(B)=1/1

t(A)/t(B)=1/2

t(A)/t(B)=1/3

t(A)/t(B)=1/4

Re

fle

cti

vit

y

Glancing angle (o2)

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

12

1 0

2 fiff

rn e

e

2exp 224 qqI

mntqt 2cos224

mn 22 cos2

01 AB ttnI


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)

10668.

Information on the mesoscopic Structure in the lateral direction and on the vertical correlation of disturbances

Sample inclination (arcsec)

(a

rcse

c)

-6000 -4000 -2000 0 2000 4000 6000

4000

6000

8000

qx-qz scan at qy = 0

Coplanar diffraction geometry


Fe/Au MultilayersExperimental example

1 2 3 4 5 6 7100

101

102

103

104

105

106

107

108

Inte

nsi

ty (

a.u

.)

Glancing angle (o2)

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


Binary System Fe – AuA ssessed A u-F e phase diagram. C alculated.

Au Fe


XRR on Multilayers with Non-Continuous Interfaces

Continuous Discontinuous

Regions

ContinuousDiscontinuous

12

1 jjj AfA

2NAR

Reflectivity

Amplitude and Phase shift

Interfaces


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

0 2 4 6 8 1010-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

(c)

(b)

(a)

Ref

lect

ivity

(ar

b.un

its)

Glancing angle (°2)

c = 100%

c = 60%

c = 30%

Changes in the XRR curve

Consequences

Fe/Au (30Å/10Å) x 8

Simulation


Diffuse Scattering from Multilayers with Non-continuous Interfaces

Interfaces

Continuous Discontinuous

S

yqxqiyxCq

jjjjj

jjj

yxz eedxdyF

kkkk

kt

1~

8exp2

,

221

11,

2

kS k

yqxqiyxCq

jjjjjj

yxeedxdyF

ctct

yxz ,1~

1

,

1,1,

2

1

0, yxk 1, yxk Form-factor

DWBA:Differential cross-section

The integration is performed only in the

continuous regions



D. Rafaja, H. Fuess, D. Šimek, J. Kub, J. Zweck, J. Vacínová, V. Valvoda, J. Phys.: Condensed Matter 14 (2002) 5303-5314.

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

-1.0 -0.5 0.0 0.5 1.0100

101

102

103

104

105

106

107

Inte

nsity

(cp

s)

Sample inclination (deg)


0 1 2 3 4 5 6 7100

102

104

106

108

1010

1012

Inte

nsi

ty (

cps)

Diffraction angle (°2)


Fe/Au (70Å/21Å)13 / 280Å Au / SiO2

As deposited2h/200°C2h/300°C4h/300°C


Wide-Angle X-ray Scattering

Structure model

tA

tB

Continuous and discrete interface

roughness

Intralayer disorder

Average d-spacingInterlayer 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.


Kinematical Theory of WAXS for Multilayers with Continuous

Interfaces

2

2

*

22

1

;

c

aa

caP

eFFFFI

LL

L

atiqLSLSLSL

LL

4

1

1

4exp

:,,

22

1

22

10

1

2

2

qiqd

e

ef

qiqdnfF

ddeePefefF

dnndyxr

L

N

n

N

nLnL

N

n

ddniqiqnd

n

N

n

rqinL

L

LL

L

L

L

Intensity:

Positions of interfaces (Gauss-like distribution):

Positions of individual atoms (correlated displacements):

Structure factor of individual layers:

Interatomic distances and their fluctuations:


WAXS Diffraction Pattern of a Periodic Multilayer

30 32 34 36 38 40 42 44 46 48 500

5

10

15

20

25

30

35

dBd

A

+2

+1-4

-3-2

-1d

0

Inte

nsi

ty (

a.u

.)

Diffraction angle (o2)

n

dn 1sin2

Positions of Satellites:

BABA

BBAA

NNNN

dNdNd

BBAA dNdN

Periodicity of a bi-layer:

Mean interplanar spacing:

Fe/Au (3.24nm/1.41nm) 12Fe: 16 0.20268 nm, Au: 6 0.2355 nm


WAXS on Multilayers with Non-Continuous Interfaces

substrate

buffer

k

Pqik

k

rqiPqi

k

rPqirqi

jP

rqiMP

RqijV

rqiM

jP

rqiM

RqijV

rqiMM

rqiM

jP

rqiP

Rqij

jP

rRqijPP

rqiP

Prqi

PMrqi

MVrqi

kkk

j

j

j

j

efrdeerderde

rdeeRErderEE

rdeeRErderErderE

rdeeRE

rderRErderE

rderErderErderEE

00

000

0

00

000

Structure model

Kinematical Theory

Matrix + Precipitates


WAXS on Multilayers with Non-Continuous Interfaces

MLMMLM

MLM

j

iqtBjAj

iqzML

j

iqtBjAj

iqzM

j k

PqiMP

RqiPqiM

FFccFcFcEI

EEIcFFcEE

eFFeF

eFFecFcEE

effeefEE

Ajj

Ajj

kjjM

Re121

;1

1

222220

0

0

Sample0

,

D. Rafaja, H. Fuess, D. Simek, L. Zdeborova and V. Valvoda, J. Phys.: Condens. Matter 14 (2002) 10021-10032.

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


WAXS – Simulation of Interface Discontinuity

MLM

ML

M

FFcc

Fc

Fc

EI

Re12

122

22

2

0

32 36 40 44 48

0

200

400

600

800

1000

2

10

-1

-2

-3

-4

(a)

Inte

ns

ity

(a

.u.)

D iffraction angle (o2)

32 36 40 44 48

0

200

400

600

800

1000

(b)


20 % Interface discontinuity 40 %


Combined Refinement SAXS/WAXS

0 2 4 610

0

102

104

106

108

1010

Inte

nsi

ty (

cps)

Scattering angle (°2)

Virgin 2h/200°C XRR XRD XRR XRDt(Fe) 26.5 25.6 26.5 27.0t(Au) 24.0 24.6 22.0 27.8 50.5 50.2 48.5 54.8d(Fe) 2.031 2.027d(Au) 2.359 2.353 0.09 0.13(Fe) 6.5 1.0 7.0 2.0(Au) 6.5 1.2 8.0 2.4(surf) 6.5 9.0c(%) 90 100 85 80

30 35 40 45 5010

2

103

104

Inte

nsi

ty (

arb

.un

its)


Fe/Au (26Å/24Å)10


Fe/Au (26Å/24Å)10Large correlation of the interface roughness

-6000 -4000 -2000 0 2000 4000 60002000

4000

6000

8000

Sample inclination from the normal direction (arcsec)

Diff

ract

ion a

ngle

(a

rcse

c)

Well-pronounced maxima of the resonant diffuse scattering

Large difference between (XRR) and (XRD)


Combined Refinement SAXS/WAXS

0 2 4 610

0

102

104

106

108

1010

1012

Inte

nsity

(cp

s)

Scattering angle (°2)

30 35 40 45 50

102

103

104

Inte

nsi

ty (

arb

.un

its)


Virgin 4h/300°C XRR XRD XRR XRDt(Fe) 69.7 63.5 69.9 61.8t(Au) 20.4 24.3 19.4 25.8t(int) 2.2 2.1 90.1 90.0 89.3 89.7d(Fe) 2.036 2.027d(Au) 2.339 2.327 0.076 0.040(Fe) 8.0 4.5 12.0 6.5(Au) 9.5 5.0 13.0 7.5(surf) 12 20(Fe1) 1.0 0.6c(%) 90 100 85 80

Fe/Au (70Å/21Å)13


Fe/Au (70Å/21Å)13Low correlation of the interface roughness

-6000 -4000 -2000 0 2000 4000 60002000

4000

6000

Sample inclination from the normal direction (arcsec)

Diff

ract

ion a

ngle

(a

rcse

c)

Weak maxima of the resonant diffuse scattering

Small difference between (XRR) und (XRD)


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


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)

röntgenbeugung und röntgenstreuung an multilagenschichten mit diskontinuierlichen grenzflächen...

Documents