Basic Principles of X-ray Reflectivity in Thin Films ...beaucag/Classes/Characterization...Feb 24,...
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Basic Principles of X‐ray Reflectivity in Thin Films Félix Jiménez‐Villacorta 02-24-2011
Transcript of Basic Principles of X-ray Reflectivity in Thin Films ...beaucag/Classes/Characterization...Feb 24,...
Basic Principles of X‐ray Reflectivity in Thin Films
Félix Jiménez‐Villacorta
02-24-2011
Outline
• X‐ray diffraction• X‐ray diffraction in thin films: high angle vs low angle
• XRR as structural characterization• Diffuse scattering: specular vs off‐specular reflectivity
• Summary
William Lawrence Bragg
William Henry Bragg
X‐ray diffraction
Bragg s law: angle where constructive interference of scattered X‐rays produces a diffraction peak:
nλ = BC + CD = 2dhklsinθ
where dhkl is the vector drawn from the origin of the unit cell to intersect the crystallographic plane.
High angle vs Low angleProbing ranges in x-ray diffraction on thin filmsnλ = 2dsinθ
λ = 2dhklsinθ nλ = 2tsinθ
θ ~ 1/d
2θω=θ
ki kfQ2θ
ω=θki kfQ
k (incident)
k’(diffracted)
Q
θ
d
High θ (high Q) = Low d Low θ (low Q) = High d
X‐ray Reflectivity
0 1 2 3 41E-6
1E-4
0,01
1
θ2
αc2
m2
Log(
Ref
lect
ivity
)
Grazing incidence (degree)
8 nm 15 nm
0 20 40 60 80
0,000
0,001
0,002
W (8 nm) // Si
(λ/2d)2
2222
2⎟⎠⎞
⎜⎝⎛=−
dmc
λαθ
44
22 116)(z
yxz
el
qqq
qQR ∝= δδρπReflectivity (background)
At every interface, a portion of x‐rays is reflected. Interference of these partialy reflected x‐ray beams creates a reflectometry pattern.
Kiessig fringes
X‐ray 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 σVacuum/CoSi
2
=0
* Rough interface σCoSi
2/Si
no roughness 5A 10 A
∙ X‐ray reflectivity can be used for:‐ Layer thickness of thin films and multilayers.‐ Surface and interface roughness. ‐ Surface density gradients and layer density.
X‐ray ReflectivitySpecial case: bilayers and multilayers
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(
Reflec
tivity
)
CuO2 (5,5 nm) // Cu (45 nm) // Si
Cu thickness
CuO2thickness
Multilayer: n‐1 Kiessig fringes between 2 Bragg Peaks
1 2 310
100
1000
10000
100000
Inte
nsity
(c.p
.s.)
2-Theta
CoSN2
Diffuse scatteringSpecular vs off-specular reflectivity
‐ Specular contribution of the diffuse scattering‐ Same oscillations than reflectivity curve
Longitudinal diffuse scattering
Diffuse scattering
0 1 2 3 4 5
10
100
1000
10000
100000
1000000
Inte
nsity
2 theta (º)
XRR specular long. diff (Δω=0.05º) long. diff (Δω=0.1º)
Off Specular XRR - (s2 - Au Cold)
0 1 2 3 4 5
10
100
1000
10000
100000
1000000
Off Specular XRR - (s6 - Au Hot)
Inte
nsity
2 theta
XRR specular long. diff. (Δω=0.05º) long. diff. (Δω=0.1º)
Longitudinal diffuse scatteringFeRh thin films + cap
Um+1(x,y)
Um (x,y)
Um (x’,y’)hm
ideal
zm+1
zm
Q ≠ qzQ = qz
Diffuse scatteringTransverse diffuse scan (ω‐rocking curve)
0 1 2
Log
[Int
ensity
(ar
b. u
nits
)]
ω scan
ξ=7000 A ξ=2000 A ξ=500 A
Yoneda Wingsαc
αc
Specular
Various ξ : Large lateral correlation ξ at interface⇓
Specular peak
Yoneda wings : each time αi or αf = αc
Summary
‐At every interface, a portion of x‐rays is reflected. Interference of these partialy reflected x‐ray beams creates a reflectometry pattern.
‐ X‐ray reflectivity is a useful techinque for structural characterization of thin films. Information about the thickness and the roughness of such samples can be obtained.
‐ Diffuse scattering of x‐rays give also information about the roughness, correlation length (fractal parameters) in surfaces and interfaces.
