grazing incidence x-ray fluorescence analysis and x-ray...
TRANSCRIPT
Grazing incidenceX-Ray Fluorescence Analysis
andX-Ray Reflectivity
Giancarlo PepponiFondazione Bruno KesslerMNF – Micro Nano Facility
MAUD school 2018Caen, France
1GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
2
XRF configurations
→
XRF
→
→
bulkanalysis
micro-XRF
2D - 3Dmicrometre spot
grazing incidence
TXRF
GI-XRF
XSW
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
3
XRF → GIXRF
→
Why?
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
4
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 2018 – Giancarlo Pepponi
5
Snell’s law – x-ray region
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
6
Snell’s law – x-ray region
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
7
Index of refraction – decrement - delta
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
8
Critical angle for total reflection
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
9
Snell’s law – absorption
Beer-Lambert‘s Law:
Linear absorption coefficient:
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
10
Snell’s law – x-ray region – with absorption
medium 1 is vacuumTotal external reflection
heterogeneous wave
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
11
Beta – absorption
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
12
Atomic form factor
photoelectric absorption
corrections for photoabsorption (Kramers-Kronig dispersion)relativistic effects, nuclear scattering
‘anomalous’ energy dependent terms
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
13
Atomic form factor (forward direction)
forward scattering factors (x = theta = q = 0)
f1 and f2 are directly related to the index of refraction(reflection, refraction, XRR)
photoabsorption
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
14
Fresnel – reflected intensity
Propagating electromagnetic field
Photon Energy
Energy of the electromagnetic field, number of photons
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
15
Fresnel – 2 media
Electric vector perpendicular to the planeof incidence (s, TE, polarisation ) In German senkrecht = perpendicular
Approximations(ignore quadratic terms):
Same formalism asfor XRRX-Ray Reflectivity
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
16
Reflectivity
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
17
Reflectivity
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
18
Reflectivity
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
19
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 2018 – Giancarlo Pepponi
20
Fresnel – approximated vs exact - angle of refraction
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
21
Fresnel – approximated vs exact - transmission
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
22
GIXRF - intensity calculation – 1 interface – thin layer
P. Kregsamer, (1991), Spectrochimica Acta Part B, 46(10), 1332–1340. (1991)
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
23
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 2018 – Giancarlo Pepponi
24
Multiple layers
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
25
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 2018 – Giancarlo Pepponi
26
Total reflection, OK, but practically?
TXRF – analysis of surface contaminationanalysis of materials deposited onflat reflecting surface
GIXRF – get “positional-structural” (as well as chemical)information through the angular dependence of fluorescence in thegrazing incidence region:above-below surfacefilm-like, particle-likeparticle sizelayered samples
XSW – standing wave field created by interference ofincident and Bragg reflected field but also the study of crystalline like“super-structures” (e.g. Langmuir-Blodgett films)
EDX-
detector
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
27
Quantitative analysis
Empiricalmethods
First principles / fundamental parameters- deterministic- Monte Carlo
PROSNo physical model needed
CONSNeed of SPECIFIC standard samplesOne calibration per experimental condition
APPLICATIONGood for monitoring very similar samples
PROSNON SPECIFIC standard samplesused to evaluate model parametersOne calibration per experimental condition
CONSNeed a physical model to simulate results
APPLICATIONGood if samples keep changing
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
28
Quantitative analysis
PROSNON SPECIFIC standard samplesused to evaluate model parametersOne calibration per experimental condition
CONSNeed a physical model to simulate results
APPLICATIONGood if samples keep changing
Describe/model
- source- detector (efficiency)- sample
Interactions:- scattering- photoelectric absorption- fluorescence/auger
Fundamental Parameters
First principles / fundamental parameters- deterministic- Monte Carlo
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
29
Quantitative analysis
First principles / fundamental parameters- deterministic- Monte Carlo
PROSNON SPECIFIC standard samplesused to evaluate model parametersOne calibration per experimental condition
CONSNeed a physical model to simulate results
APPLICATIONGood if samples keep changing
Peak intensity ExtractionIntensity simulation/comparison/fitting
Spectrum (spectra) simulation/comparison/fitting
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
30
Fundamental parameters
- 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.
https://data-minalab.fbk.eu/txrf/xraydata/
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
31
Fundamental parameters
Sample
Experimental Parameters
Elements
Materials
Layers
( Contamination/dopant Profile )
Nanoparticles
Experimental Set-up
(primary beam, detector)
Geometrical Configuration
Simulation
Experimental Data
Data Fittin
g
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
32
Fundamental parameters
Elements
Materials
Layers
( Contamination/dopant Profile )
Nanoparticles
In XRF:Cross sections are tabulated in cm^2/gFor single elements
To define a material in XRF you must provide:Weight fractions and density
In XRD:you just need the phase parameters
Phases
Layers
( Contamination/dopant Profile )
Nanoparticles
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
SiO2 (native)
Si (bulk)
33
Example : doped silicon surface
Si (bulk)
SiO2 (native)
Arsenic concentration
cmat
om
s /
cm^3
20nm
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
34
GIXRF quantitative analysis
0.1 deg simulated spetrum
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
35
GIXRF quantitative analysis
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
36
XRR
GIXRF vs XRR ?
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
37
GIXRF - intensity calculation – 1 interface
sensitive to electron density andits changes:- material density
- film thickness- optical constants- roughness
reveals elemental surfaceconcentrations:- material composition
- in depth elementalinformation
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
38
GIXRF vs XRR
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
39
GIXRF - ambiguity problem - As doping profile
0 5 10 150
2
4
6
8
10
12
14x 10
21
depth [nm]
co
nc
en
tra
tio
n [
ato
ms
/cm
3]
Depth distribution of Arsenic
fit result
SIMS 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
courtesy of Dieter Ingerle
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
40
GIXRF - ambiguity problem – Hf thin film
GIXRF can only determine surface mass concentration!Ambiguity thickness vs. density (XRR probably better)
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
courtesy of Dieter Ingerle
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
41
GIXRF - XRR combined
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 2018 – Giancarlo Pepponi
42
Roughness
L. Nevot, P. Croce, Revue de physique appliquée, 15, 761 (1980)
P. Croce and L. Nevot, Rev. Phys. Appl. 11, 113 (1976)
interface layers with changing index of refraction- error function , linear
factors multiplying theFresnel coefficient
All good for XRR but what about Fluorescence???
Can we model it as particles?
Multiply reflectivity and transmission by a damping factor
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
43
Roughness
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
44
Depth resolution – buried layers and interfaces
Definition of depth resolution:
- different at different depths
Sample 10nm In2O3 / 4nmAg / 10nm In2O3
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
45
Depth resolution – junction depth
0 2 4 6 8 10 12 14 16
0.02
0.04
0.06
0.08
0.10n
orm
alis
ed
As c
on
ce
ntr
atio
n [
a.u
.]
depth [nm]
0 2 4 6 8 10 12 14 161E-3
0.01
0.1
no
rmalis
ed
As c
on
ce
ntr
ation
[a
.u.]
depth [nm]
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
0
1
2
3
4
5
flu
ore
sce
nce
in
ten
sity [
a.u
.]
angle [rad]0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
diffe
ren
ce
am
on
g a
ng
ula
r
flu
ore
sce
nce
in
ten
sitie
s
angle [rad]
blu - black
blu - red
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
46
Fluorescence intensitycascade effect – secondary fluorescence
Incident photon
Photoelectron
Fluorescence
photon
Incident photonIncident photon
PhotoelectronPhotoelectronPhotoelectron
Fluorescence
photon
Fluorescence
photon
Fluorescence
photon
Cascade photon
Secondary
fluorescence
photon
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
47
Fluorescence intensitycascade 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 2018 – Giancarlo Pepponi
48
GIXRF - secondary fluorescence
200 nm of ZnSe on GeZnK
GeKa1
SeKa1
GeK
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
49
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.
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
50
Divergence
Divergence 0.5 mrad
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
51
Grazing exit x-ray fluorescence
R. Becker, J. Golovchenko, J. Patel, PRL 50(3), 153–156
“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.”
GI-XRF
GE-XRF
Advantage:- higher lateral resolution
Disadvantage:- reduced sensitivity
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi
5252
52
Thank you for your attention!
For any further question or doubt:[email protected]
GIXRF and XRR– MAUD school 2018 – Giancarlo Pepponi