Grazing incidence
X-Ray Fluorescence Analysis
and
X-Ray Reflectivity
Giancarlo Pepponi
Fondazione Bruno Kessler
MNF – Micro Nano Facility
MAUD school 2015
Trento, Italy
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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acknowledgements
Fabio Brigidi - Elettra, Trieste, Italy
Christina Streli – Technische Universität Wien – Atominstitut
Dieter Ingerle – Technische Universität Wien – Atominstitut
Florian Meirer – Universiteit Utrecht, Netherlands
Luca Lutterotti – Università degli studi di Trento
Mauro Bortolotti – Università degli studi di Trento
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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XRF configurations
grazing incidence
XRF

bulk
analysis

TXRF
GI-XRF

micro-XRF
XSW
2D - 3D
micrometer spot
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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XRF  GIXRF

Why?
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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XRF  GIXRF
A. H. Compton,
The total Reflection of X-Rays,
Phil. Mag., 45, 1121; 1923
Pictures from the
Nobel Lecture,
December 12, 1927
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Snell’s law – optical region
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Snell’s law – x-ray region
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Snell’s law – x-ray region
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Index of refraction – decrement - delta
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Critical angle for total reflection
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Snell’s law – absorption
Intensity [arbitrary units]
Beer-Lambert‘s Law:
I ( x)  I 0 exp( µx)
1.2
Au sheet
1.0
I
0.8
0.6
I(x)
0
0.4
0.2
0.0
0
50
100 150 200 250 300 350 400 450
distance [µm]
Calculated for E = 17500eV
Linear absorption coefficient:
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Snell’s law – x-ray region – with absorption
heterogeneous wave
medium 1 is vacuum
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
Total external reflection
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Beta – absorption
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Atomic form factor
‘anomalous’ energy dependent terms
photoelectric absorption
corrections for photoabsorption (Kramers-Kronig dispersion)
relativistic effects, nuclear scattering
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Atomic form factor (forward direction)
Grazing incidence, θ close to 0
forward scattering factors (x = theta = q = 0)
photoabsorption
f1 and f2 are directly related to the index of refraction
(reflection, refraction, XRR)
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fresnel – reflected intensity
Propagating electromagnetic field
Photon Energy
Energy of the electromagnetic field, number of photons
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Fresnel – 2 media
Electric vector perpendicular to the plane
of incidence (s, TE, polarisation )
In German senkrecht = perpendicular
Approximations
(ignore quadratic terms):
Same formalism as
for XRR
X-Ray Reflectivity
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Reflectivity
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Reflectivity
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Reflectivity
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Fresnel – x-ray region – exact
Complex dielectric constant
B.L. Henke, Phys. Rev. A, 6, 1, (1972)
M.-R. Lefévère, M. Montel, Opt. Acta 20, 97 (1973)
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fresnel – approximated vs exact - angle of refraction
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fresnel – approximated vs exact - transmission
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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GIXRF - intensity calculation – 1 interface – thin layer
P. Kregsamer, (1991), Spectrochimica Acta Part B, 46(10), 1332–1340. (1991)
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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‘diluted’ dopant profile
optical properties
of the substrate
are used
G. Pepponi et al. / Spectrochimica Acta Part B 59 (2004) 1243–1249
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Multiple layers
L. Parratt, Physical Review, 95(2), 359–369, 1954
X-Ray Reflectivity
(but GIXRF also “given”)
In the optical range:
F. Abeles, Le Journal de Physique et le Radium, "La théorie générale des couches minces", 11, 307–310 (1950)
Recursive transfer matrix method, used also for XRR
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Multiple layers
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‘non ‘diluted’ doping profiles
optical properties calculated for each layer
each layer a different material
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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‘non diluted’ doping profiles
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Total reflection, OK, but practically?
The interference of incident and reflected
beam causes a standing wave field above
the reflectors surface.
Intensity distribution as a
function of incident angle
and depth
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Total reflection, OK, but practically?
EDXdetector
TXRF
–
analysis of surface contamination
analysis of materials deposited on
flat reflecting surface
GIXRF –
get “positional-structural” (as well as chemical)
information through the angular
dependence of fluorescence in the
grazing incidence region:
above-below surface
film-like, particle-like
particle size
layered samples
XSW
standing wave field created by interference of
incident and Bragg reflected field
but also the study of crystalline like
“super-structures” (e.g. Langmuir-Blodgett films)
–
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Quantitative analysis
Empirical
methods
PROS
No physical model needed
CONS
Need of SPECIFIC standard samples
One calibration per experimental condition
APPLICATION
Good for monitoring very similar samples
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
First principles /
fundamental parameters
- deterministic
- Monte Carlo
PROS
NON SPECIFIC standard samples
used to evaluate model parameters
One calibration per experimental condition
CONS
Need a physical model to simulate results
APPLICATION
Good if samples keep changing
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Quantitative analysis
First principles /
fundamental parameters
- deterministic
- Monte Carlo
PROS
NON SPECIFIC standard samples
used to evaluate model parameters
One calibration per experimental condition
CONS
Need a physical model to simulate results
Describe/model
- source
- detector (efficiency)
- sample
Interactions:
- scattering
- photoelectric absorption
- fluorescence/auger
Fundamental Parameters
APPLICATION
Good if samples keep changing
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Quantitative analysis
First principles /
fundamental parameters
- deterministic
- Monte Carlo
Peak intensity
Extraction
Intensity
simulation/comparison/fitting
PROS
NON SPECIFIC standard samples
used to evaluate model parameters
One calibration per experimental condition
CONS
Need a physical model to simulate results
Spectrum (spectra)
simulation/comparison/fitting
APPLICATION
Good if samples keep changing
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Quantitative analysis
Monochromatic
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Fundamental parameters
https://data-minalab.fbk.eu/txrf/xraydata/
- Standard Atomic Weight: IUPAC recommended values
- Elemental densities: J. H. Hubbell and S. M. Seltzer
- Electron binding energies, Edge Jump, X-Ray lines, Transition probabilities, Fluorescence yield,
Cascade effect: xraylib, T. Schoonjans et al.
- Atomic energy level widths: J. L. Campbell, T. Papp
- Fluorescence yield, Coster-Kronig probabilities: M. O. Krause
- Atomic scattering factors (150eV-30000eV): B. L. Henke et al.
- Atomic scattering factors (30000eV - 300000 eV): S. Brennan et al.
- Phoelectric (shell-specific and total), elastic and inelastic scattering cross sections: H.Ebel et al.
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fundamental parameters
Elements
Materials
Layers
( Contamination/dopant
Profile )
Sample
Simulation
Nanoparticles
Experimental
Parameters
Data Fitting
Experimental
Set-up
(primary beam, detector)
Geometrical
Configuration
Experimental Data
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fundamental parameters
Elements
Materials
In XRF:
Cross sections are tabulated in cm^2/g
For single elements
Layers
( Contamination/dopant
Profile )
Nanoparticles
To define a material in XRF you must provide:
Weight fractions and density
In XRD:
you just need the phase parameters
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
Phases
Layers
( Contamination/dopant
Profile )
Nanoparticles
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Example : doped silicon surface
Arsenic concentration
Si (bulk)
SiO2 (native)
atoms / cm^3
SiO2 (native)
20nm
Si (bulk)
cm
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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GIXRF quantitative analysis
0.1 deg simulated spetrum
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GIXRF quantitative analysis
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XRR
GIXRF vs XRR ?
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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GIXRF - intensity calculation – 1 interface
sensitive to electron density and
its changes:
- material density
- film thickness
- optical constants
- roughness
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
reveals elemental surface
concentrations:
- material composition
- in depth elemental
information
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GIXRF vs XRR
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GIXRF - ambiguity problem - As doping profile
14
x 10
21
Depth distribution of Arsenic
fit result
SIMS
concentration [atoms/cm3]
12
GIXRF fit result looks very good,
almost no difference between
calculation and measurement
… but the result for the depth
distribution is unrealistic
-> GIXRF is ambiguous
10
8
6
4
2
0
0
5
10
15
depth [nm]
courtesy of Dieter Ingerle
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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GIXRF - ambiguity problem – Hf thin film
GIXRF measurement data fitted to calculated values. This
comparison shows the ambiguity of GIXRF concerning density
and thickness. For the left side a layer-density of 6.7 g/m3 was
used, while on the right 6.1 g/m3 was used
GIXRF can only determine surface mass concentration!
Ambiguity thickness vs. density (XRR probably better)
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
courtesy of Dieter Ingerle
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GIXRF - intensity calculation – 1 interface
Si wafers implanted with 1E15
atoms/cm2 of Arsenic by beamline
ion implantation with different
implantation energies:
• As1 – 0.5keV
• As3 – 2keV
• As4 – 3keV
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Roughness
Multiply reflectivity and transmission by a damping factor
P. Croce and L. Nevot, Rev. Phys. Appl. 11, 113 (1976)
L. Nevot, P. Croce, Revue de physique appliquée, 15, 761 (1980)
factors multiplying the
Fresnel coefficient
All good for XRR but what about
Fluorescence???
interface layers with changing index of refraction
- error function , linear
Can we model it as particles?
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Roughness
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Depth resolution – buried layers and interfaces
Definition of depth resolution:
- different at different depths
Sample 10nm In2O3 / 4nmAg / 10nm In2O3
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0.10
0.08
0.06
0.04
0.02
0
2
4
6
8
10
12
14
16
normalised As concentration [a.u.]
normalised As concentration [a.u.]
Depth resolution – junction depth
0.1
0.01
1E-3
0
2
difference among angular
fluorescence intensities
fluorescence intensity [a.u.]
5
4
3
2
1
0
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
4
6
8
10
12
14
16
depth [nm]
depth [nm]
0.014
0.012
0.010
0.008
blu - black
blu - red
0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
angle [rad]
angle [rad]
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fluorescence intensity
cascade effect – secondary fluorescence
Cascade photon
Photoelectron
Incident photon
Secondary
fluorescence
photon
Fluorescence
photon
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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Fluorescence intensity
cascade effect – secondary fluorescence
GaAs solution deposited on silicon – Cascade – No Secondary Fluo
GaAs Wafer – No Cascade – No Secondary Fluo
GaAs Wafer – Cascade – Secondary Fluo
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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GIXRF - secondary fluorescence
200 nm of ZnSe on Ge
ZnK
SeKa1
GeK
GeKa1
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Geometric corrections
Conway, John T. , Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment 614.1 (2010): 17-27.
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Divergence
Divergence 0.5 mrad
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‘Strange’ angular fluorescence dependencies
????
And the happy end!
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GIXRF on plasma immersion doped samples
P2 As PIII (7s/ 50mTorr) Si as implanted
P1 As PIII (7s/ 50mT0rr) Si RTA 1050°C
Very strange angle scan!!!
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GIXRF on plasma immersion doped samples
Confronting GI-XRF with theory reveals that it is hiding As containing
surface particles/residues.
Characteristic shapes due the
angular dependence of the
fluorescence radiation for
three different cases of atomic
locations.
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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GIXRF - particles
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GIXRF - particles
Result: about 1/3 of the As is in particles
and 2/3 in the film-like doped layer
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Arsenolite crystals on the surface
Following the trace of breadcrumbs
we found that the particles are
actually micro- and nano-crystals…
… crystals that are
made of Arsenic
and Oxygen …
Si
As
O
… and melt in
the electron
beam.
Total exposure
time:
1h10min
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Extension of the wavefield - coherence
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Extension of the wavefield - coherence
courtesy of Dieter Ingerle
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Extension of the wavefield - coherence
courtesy of Dieter Ingerle
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Example Ge:Sn
 SIMS measured profile
 Beta curve
Si
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
Ge
Sn
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Example Al2O3 protective layers
Experimental Data
University of Maryland
Prof. Ray Phaneuf
Amy Marquardt
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
Simulation
Ag - La
Background
Si - Ka
Al - Ka
S - Ka
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Example Al2O3 protective layers
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Example Al2O3 protective layers
 Nanoparticles Composition:
𝐴𝑔4 𝐶𝑢1.5 𝑆1.5
 Nanoparticles Size:
 Multiple Layers
 Diffusion Profile
 Nanoparticles
Gaussian distrib. - xc: 30 nm ; σ 6 nm
(good agreement with AFM measurements)
 Sulphur
Estimation
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Grazing exit x-ray fluorescence
GI-XRF
R. Becker, J. Golovchenko,
J. Patel, PRL 50(3), 153–156
GE-XRF
“the principle of microscopic reversibility predicts that the results of
absorption- and emission-type experiments should be identical were
they performed with the same wavelength radiation.”
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
Advantage:
- higher lateral resolution
Disadvantage:
- reduced sensitivity
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Grazing exit
SSRL beamline 10-2 mesoprobe setup
pinhole: spotsize 500µm2
Motivation:
Check spatial homogeneity
Scan
180
S2R6C11
190
“the principle of microscopic reversibility predicts that the
results of absorption- and emission-type experiments should
be identical were they performed with the same wavelength
radiation.” Becker et al.
S2R6C10
200
Y [mm]
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Grazing exit
Motivation:
Check spatial homogeneity of annealing
increasing angle
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
Motor position
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GIXRF/XRR software - JGIXA
Dieter Ingerle – ATI - TuWien
courtesy of Dieter Ingerle
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XRF/GIXRF/XRR software - GIMPY
SciPy library
Computation/Simulation
• ED-XRF
• GI-XRF
• GE-XRF
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
• Spectrum Simulation
• XRR
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The Software
GIXRF and XRR– MAUD school 2015 – Giancarlo Pepponi
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THANKS
FOR YOUR
ATTENTION
76
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