LEUVENInstituut voor
Kern- en Stralingsfysica
Specular reflectivity and off-specular Specular reflectivity and off-specular scatteringscattering
Tools for roughness investigationTools for roughness investigation
Hugues Guerault 15/12/2000Hugues Guerault 15/12/2000
LEUVENInstituut voor
Kern- en StralingsfysicaOutlineOutline
Introduction
Flat surface/interface - Dynamical theoryLayer thickness and electronic density determination
Rough surface/interface - Kinematical theoryRoughness and diffuseness (Non-)periodic roughnessDifferential cross-section Correlation lengths
Investigation geometriesSpecular reflectivity (specular scan)Off-specular scattering (longitudinal, transverse and detector scans)
Conclusions
LEUVENInstituut voor
Kern- en StralingsfysicaIntroductionIntroduction
Increasing ability to structure solids in 1, 2 or 3D at nanoscopic scale Mesoscopic layered superstructures (multilayers, superlattices, layered gratings, quantum wires –and dots)
Perfection depends on Perfection of the superstructure (grating shape, periodicity, layer thickness) Interface quality (roughness, interdiffusion)
Crystalline properties (strain, defects, mosaicity,…)
Roughness affects the physical behavior of interfaces Optical : reduces the specular reflectivity – creates diffuse scattering Magnetic : changes the interface magnetization Electronic : disturbs the band structure in semiconductor devices (resistivity)
LEUVENInstituut voor
Kern- en Stralingsfysica
Transfer Matrix [M]ij M=R01T1R12……………TN-1RNN-1TNRNS
Reflection coefficient r=M12/M22 Absolute Reflectivity R=r.r*
Transmission coefficient t=1/M22
At p,p+1 interface (Rp,p+1 : Refraction Matrix ; pp, mp Fresnel coef.)
Electric field in layer p
)())()(( ykwtipppp
pyezUzUE
Dynamical TheoryDynamical Theory
)()()( 11 pppppp
pppp zUzU
pmmp
zU
1pp,R
Through the layer p (Tp : Translation Matrix)
)()(0
0)(,
,
1 pppphik
hik
pp zUzUe
ezUpzp
pzp
pT
SubstrateN
p+1
p
2
10 Air (n=1)
ZS
Zp
hn- +kn
LEUVENInstituut voor
Kern- en StralingsfysicaN=1 , N=2N=1 , N=2
Single Layer
R=r.r* max. each time
As Then
(Kiessig fringes)
hp
qqqqkz
czzz
212 2
2
11
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.01E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
2
c2
p2
Log(
Refle
ctiv
ity)
Grazing incidence (degree)
W // Si 8 nm 15 nm
0 20 40 60 80
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
W (8 nm) // Si
(/2h)2
4sin4
1 zq2
222
2
hpc
For <c Total external reflection
For p=0, =c leading to el via
Bilayer 2 oscillation frequencies are evidenced
0 1 2 31E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
Grazing incidence (degree)
Log(R
eflec
tivity
)
CuO2 (5,5 nm) // Cu (45 nm) // Si
Cu thickness
CuO2 thickness
hiq
hiq
z
z
errerr
MMr
1
1
21201
21201
22
12
1
el
cel r2
2
LEUVENInstituut voor
Kern- en StralingsfysicaKinematical TheoryKinematical Theory
Born approximations No multiple reflectionsNo refractionR function of d/dz
dzedzzd
qrr ziq
z
z )(2
0 )(4
Rough interfaces Dynamical theory not appropriated anymore
)](')('[)(
)(*. zzTFqRqRrrR
zF
z
100 200 300 400
Aut
ocor
rela
tion
Func
tion
z (A)0 1 2 3 4
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
Log
(Ref
lect
ivity
)
Grazing incidence (degree)
Substrate
100 A
300 A
TF-1 Disturbance of el at interface
LEUVENInstituut voor
Kern- en StralingsfysicaInterface disturbanceInterface disturbance
What kind of disturbance ?
Rough interface Diffuse interface
Diffuseness / Graded interface
Graded composition (electronic density) from j to i layer with l steps
2
0.5 1.0 1.5 2.0
Log
(Refl
ectiv
ity)
Grazing incidence
2
No roughness without diffuseness with diffuseness (3 nm)
Fe (10 nm) / Co (22 nm)
Fe (10 nm) / Ag (22 nm)
LEUVENInstituut voor
Kern- en Stralingsfysica
If Then WiqWiq zz eWpdWe ).(.
Differential cross-sectionDifferential cross-section
)'(20 )'()(' rrQierrdrdrr
dd
dd
qLLrrQR
zyx
2
4*.)(
))','(),(())(2
220 yxUyxUiqYqXqi
z
el mmzyx dxdyedXdYeq
rdd
))','(),(( yxUyxUiqyx
mmzeLL
Um+1(x,y)
Um (x,y)
Um (x’,y’)hm
ideal
zm+1
zm
Q qz
Differential cross-section (detected intensity) depends on p(W=Um(x,y)) (Height distribution at
interfaces)
)','(),( yxUyxUW mm
kin ksc
Q
q//(x,y)
qz
LEUVENInstituut voor
Kern- en Stralingsfysica
Discrete Height Distribution
Kiessig fringes function of D
Flat substrate
Pure specular
)2)(2...(... yxYiqXiq qqdYeeXd
dd yx
1 Wiqze
44
22 116)(z
yxz
el
qqq
qQR
)()()( 2211 UpUpWp
Periodic RoughnessPeriodic Roughness
1)0( Wp
SubiQDiQdp
coh ReppeQR )()( 212
U1
U2
D
LEUVENInstituut voor
Kern- en Stralingsfysica
Two contributions
Specular contribution observed in the specular direction
Diffuse contribution observed when Q(x,y)0
Random Height Distribution
Gaussian height distribution
Non-periodic RoughnessNon-periodic Roughness
0),( yxUm
2))','(),((),( yxUyxUYXg mm
)','(),(22),( 2 yxUyxUYXg
Height-Height correlation function
22 ),( yxUm
2
2
2
21)(
u
eWp
2)(
2
22 RgqWqWiq
zz
z eee
dd
flat
qyx
q
z
yxel
spe ddeqqe
qLLr
dd
zz
2222
2
220
24
)(),(2
220 1
222 YqXqiYXCqq
z
yxel
diff
yxzz eedXdYeq
LLrdd
+
),(22)( 2 YXCRg zz
LEUVENInstituut voor
Kern- en Stralingsfysica
Height-Height correlation function
where h : roughness exponent : lateral correlation length
hR
zz eRC
2
2)(
Correlation LengthsCorrelation Lengths
Increasing and decreasing roughness in periodic multilayers
: vertical correlation length No Increasing Partial Identical replication roughness replication replication
kj ZZ
kk
jj
j
kjk eRCRCRC )()(
21)(
LEUVENInstituut voor
Kern- en StralingsfysicaSpecular reflectivitySpecular reflectivity
0 1 2 3 41E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
Grazing incidence angle (degree)
Log(
Ref
lect
ivity
)
CoSi2 (15 nm) // Si * Flat surface Vacuum/CoSi2
=0
* Rough interface CoSi2/Si no roughness 5A 10 A
0 1 2 3 41E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10 CoSi2 (15 nm) // Si
Log(
Ref
lect
ivity
)
Grazing incidence angle (degree)
* Rough Surface Vacuum/CoSi2 no roughness 5A 10 A
* Flat interface CoSi2/Si=0
0 1 2 3 4 51E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10[a-Si / W] multilayersN=20 d=70 A =20
Log(R
eflec
tivity
)
Incident angle (degree)
No roughness [W/a-Si]=5 A
LEUVENInstituut voor
Kern- en Stralingsfysica
Transverse scan (Rocking curve) at 2=2º
Si layer (64 nm) on Si substrate =7A , h=0.2 , various
Large lateral correlation at interface
Specular peak
Yoneda wings : each time i or f = c
Off-specular (diffuse) scatteringOff-specular (diffuse) scattering
-2.0x10-3 -1.0x10-3 0.0 1.0x10-3 2.0x10-3
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Longitudinaldiffuse scan
0=0.1
Specularreflectivity
qx(A-1)
q z(A-1)
inaccessible q-area inaccessible q-area
rocking curve2=1.5
detector scan=0.9
0 1 2
Log
[Inte
nsity
(arb
. unit
s)]
scan
=7000 A =2000 A =500 A
Yoneda Wings
LEUVENInstituut voor
Kern- en Stralingsfysica
Si (30 nm) // Ge (50 nm) // SiO2 (1.5 nm)Schlomka et al. PRB 51(4) 1995
Offset (longitudinal) scan Detector scan
Longitudinal and detector scansLongitudinal and detector scans
Curve depends on i (penetration depth)i < c No penetration
Increasing i different modulations
Specular contribution of the diffuse scattering
Same oscillations than reflectivity curve
LEUVENInstituut voor
Kern- en StralingsfysicaConclusionsConclusions
Grazing Incidence X-Ray Reflection Surface/interface investigation at atomic scale Non destructive technique
Vertical periodicity & in-plane morphology Layer thickness, electronic density profile (composition
profile) Surface and interface roughness In-plane and between plane correlations No information on the crystalline structure
Application 01/2001: Collaboration IKS / VSM / IMEC Roughness characterization of Co1-xNixSi2 layers
(MBE) Roughness influence on the resistivity
Top Related