ISO 23170:2022

INTERNATIONAL ISO
STANDARD 23170
First edition
2022-06
Surface chemical analysis — Depth
profiling — Non-destructive depth
profiling of nanoscale heavy metal
oxide thin films on Si substrates with
medium energy ion scattering
Analyse chimique des surfaces — Profilage d'épaisseur — Profilage
d'épaisseur non destructif de films minces d'oxydes de métaux lourds
à l'échelle nanométrique sur des substrats de Si par diffusion d'ions de
moyenne énergie
Reference number
© ISO 2022
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Principle and recommendations of MEIS analysis . 1
5 MEIS analysis .2
6 MEIS spectra simulation .2
7 Reporting MEIS analysis results .5
Annex A (informative) Interlaboratory test report . 6
Annex B (informative) List of MEIS spectra simulation program sources and a procedure of
MEIS spectra simulation using PowerMeis .19
Annex C (informative) Reliability of the IAEA electronic stopping power data .22
Annex D (informative) Fitting parameters A, B, C, D from the IAEA database .24
Bibliography .29
iii
Foreword
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This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis,
Subcommittee SC 4, Depth profiling.
Any feedback or questions on this document should be directed to the user’s national standards body. A
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iv
Introduction
Medium energy ion scattering (MEIS) has been considered to be a quantitative surface and interface
composition analysis method with single atomic depth resolution since its invention in the early of
1980s. MEIS has been widely used for ultrathin films, especially nm gate oxides analysis to determine
its composition, thickness, and the interface. Recently, MEIS has been used for nanoparticle analysis
to determine the size and the composition with the core and shell structure information. In addition
to the toroidal electrostatic energy analyser used in the early stage, different types of energy analyser
such as magnetic energy analyser and time-of-flight (TOF) energy analyser have been used. With the
continued scaling down of electronic devices, demands on accurate and reliable depth profiling have
reached beyond the limit of sputter depth profiling which provides deteriorated depth profiles due
to the sputter damage. Needs have been risen to investigate the consistency between the three types
of energy analyser, ion species, and the different energy range of incident ions used for MEIS analysis
and to set up a procedure for quantitative MEIS analysis. Two international interlaboratory tests were
performed to develop this document which is reported in Annex A.
v
INTERNATIONAL STANDARD ISO 23170:2022(E)
Surface chemical analysis — Depth profiling — Non-
destructive depth profiling of nanoscale heavy metal
oxide thin films on Si substrates with medium energy ion
scattering
1 Scope
This document specifies a method for the quantitative depth profiling of amorphous heavy metal oxide
ultrathin films on Si substrates using medium energy ion scattering (MEIS).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 18115, Surface chemical analysis — Vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 18115 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
electronic stopping power
retarding force acting on charged particles, typically alpha and proton particles, due to interaction with
electrons, resulting in loss of particle energy
4 Principle and recommendations of MEIS analysis
+
4.1 Ultrathin films of thickness less than 10 nm can be analysed with MEIS. (100 to 500) keV H or
+
He ions are used for MEIS analysis. Scattered ion energy and angle are measured precisely so that
measured MEIS spectra be compared with simulated MEIS spectra. MEIS spectra can be simulated with
1 2
various programs from free codes such as PowerMeis and SIMNRA in public websites, MEIS expert
laboratories, and MEIS manufacturers. Simulation programs calculate scattering cross-sections and
electronic stopping powers. Quite often, calculated electronic stopping powers are subject to significant
errors so that tabulated electronic stopping power values in the IAEA website are recommended to
use.
4.2 If not tabulated, it is recommended to measure electronic stopping power by users for more
reliable results. Various types of energy analyzers can be used such as toroidal electrostatic analyser
(TEA), magnetic energy analyser (magnetic), and TOF energy analyser. With MEIS analysis procedures
specified in this document, less than 10 % uncertainty can be expected for ultrathin films under the
guidelines describe in this document. This document is written for amorphous or polycrystalline thin
films but not for crystalline thin films. To reduce the uncertainty of MEIS analysis, additional standards
for calibration of scattering geometry, ion energy, energy resolution, detector efficiency, sample
alignment, are required.
5 MEIS analysis
5.1 Set the ion scattering conditions such as ion energy, scattering angle, incidence angle from the
surface normal, ion species, and ion dose for MEIS analysis. The ion dose is recommended to be in the
15 2
static condition (<10 /cm ) but the static requirement for MEIS analysis is not strict compared to
surface analysis such as XPS and static SIMS.
5.2 For MEIS analysis, specimen should be flat. Slight contamination due to air oxidation and ambient
water and hydrocarbon adsorption does not disturb the MEIS analysis badly. However, if the surface
contamination layer is thicker than 1 nm it shall be cleaned by appropriate methods such as solvent
washing or ion milling.
5.3 Measure a MEIS spectrum of a specimen and generate a MEIS spectrum file with intensity
(counts) vs energy (keV) at a specific angle. Specify all the ion scattering conditions such as ion beam
energy, ion species, incidence angle from the surface normal, scattering angle, ion dose or ion current
with analysis time, beam radius, and the type of energy analyser.
5.4 For MEIS analysis of ultrathin films of approximately 1 nm thickness, a clear plateau does not
appear so that it may have poor reproducibility. It is recommended to express MEIS analysis result in
surface areal density rather than in thickness or concentration for MEIS analysis of ultrathin films of
approximately 1 nm thickness.
5.5 If the primary ion beam current is too high, it can cause multi-hit problems of detector. Under
each MEIS analysis condition, it shall be checked whether the data is affected by the multi-hit problem
by comparing MEIS results from high ion beam current and low ion beam current available from each
MEIS system.
6 MEIS spectra simulation
1)
6.1 MEIS spectra can be simulated with various programs from free codes such as PowerMeis and
2)
SIMNRA in public websites and simulation programs from MEIS laboratories and manufacturers as
listed in Annex B. Detailed procedures for PowerMeis is also given in Annex B as an example. In this
document, general procedures for MEIS spectra simulation are given as a guidance.
Most of MEIS spectra simulation programs are based on Monte Carlo simulation or analytical
calculation of binary scatterings and electronic stopping between binary scatterings. Multiple
scattering is suggested to be included in all MEIS simulations. Thin films thicker than 5 nm are strongly
recommended to be analysed including multiple scattering for the MEIS data obtained by He ions of ion
energy lower than 500 keV. SIMNRA provides multiple scattering simulation so that users can choose
whether including it or not.
Generally, the integration step, and the slab thickness or atom density in MEIS simulations are 0,1 nm,
15 2
and 0,1 nm or 1 x10 atoms/cm , respectively.
In simulation, line shape, cross-section, electronic stopping power, charge neutralization, and energy
straggling shall be selected by users as described below. Electronic stopping power is described in
detail in 6.2
1) http:// tars .if .ufrgs .br
2) https:// home .mpcdf .mpg .de/ ~mam/
Generally, simple Gaussian can be used as basic line shape for the first approximation. For MEIS systems
−4
with high resolution of δE/E approximately 8x10 with proton as a projectile, exponentially modified
Gaussian is recommended for ultrathin films. However, other options can be chosen, if needed. Line
3)
shape parameters for each element, σ (additional parameter), is calculated by Casp version 5.2
o
program for each projectile, projectile energy, and target element. Follow the instructions in Casp
version 5.2.
To calculate cross-sections, interatomic potentials can be chosen from Anderson, L’Ecuyer, Moliere
[1]
potential, or ZBL potential . For MEIS analysis, Moliere potential is widely used. For energy straggling,
[2]
Chu or Yang can be usually chosen. For charge neutralization, Marion and Young’s equation is used for
+ +
30 keV to 150 keV H and for 30 keV to 200 keV He and Armstrong’s equation for 400 keV to 500 keV
+ 3
He . Casp charge-state-fractions algorithm can be used for He with better reliability and for other
heavier ions, if available. PowerMeis provides Marion and Young’s equation and Casp neutralization.
SIMNRA does not include neutralization in simulation.
6.2 Electronic stopping power is automatically calculated by the SRIM 95 or more recent SRIM2013
code, which can be used for non-critical MEIS analysis with inconsistency higher than 10 %. However,
electronic stopping power from the SRIM code can have significant errors in the medium energy range.
For accurate MEIS analysis with consistency lower than 10 %, it is recommended to use the measured
4)
and tabulated electronic stopping power data of elements and compounds from IAEA , as described
in Formula (1). If the IAEA database is insufficient or missing, newly measured electronic stopping
power data by appropriate methods can be added to the IAEA database to improve the accuracy of the
calculated electronic stopping power. The accuracy of electronic stopping power values in the IAEA
database is estimated to be less than 8 % as discussed in Annex C.
The electronic stopping power from IAEA database can be obtained by fitting a set of electronic
stopping power data in which can be used in Formula (1). The equation that can be used to fit the IAEA
database are given in Formula (1). The E is the ion energy, Z is the atomic number of the ion, m is the
2 15
mass of the ion. The unit of S , S , and S is eV·cm /10 atoms, that of E is keV, and that of m is u. For
t l h
fitting to determine A, B, C, and D, Origin or other appropriate fitting programs can be used.
11 1
=+
D D D
SE() SE() SE()
t l h
SE()=A E (1)
l
zmB CE
 
SE =+ln 1
()
 
h
E  m 
where
S (E) is the total electronic stopping power;
t
S (E) is the electronic stopping power of low energy electrons;
l
S (E) is the electronic stopping power of high energy electrons;
h
A, B, C, D are the fitting parameters;
E is the ion energy;
z is the atomic number of the ion;
m is the mass of the ion.
3) Available from: http:// www/ casp -program .org/
4) Available from: https:// www -nds .iaea .org/ stopping/
From the IAEA data , available fitting parameters A, B, C, and D are calculated and tabulated in Annex D
for the convenience of the users of this document.
For straggling correction factor, just use 1,0, if the correction factor is not available, which is generally
the case.
6.3 In output, energy channel width and angular channel width can be adjusted according to the
energy and angular resolution for each MEIS analysis. Energy channel width is generally used as 0,1 keV
and angular channel width should be same to the detector angular width when obtaining 1D spectrum.
In beam, atomic number, atomic mass, beam energy, and incidence angle from the surface normal are
given. Projectile number can be adjusted to fit the experimentally measured MEIS spectrum of well-
defined internal reference.
Analyser type is chosen among electrostatic, TOF, and magnetic. For electrostatic and magnetic analyser
type, energy resolution full width half maximum (FWHM) (δE), scattering angle, and angular width
(Δθ) specified from each MEIS measurements are given. For TOF analyser type, TOF length (L), time
resolution (δt), are additionally given according to specific TOF MEIS scattering conditions. Out of plane
angle and angular width are used when MEIS scattering data are obtained from out of plane region or
large detector. Energy resolution FWHM (δE) or time resolution (δt) can be measured by fitting the
leading edge of a MEIS peak from a clean surface peak of heavy metal specimen.
6.4 After all the input parameters for simulation and experimental parameters are given, the structure
of a specimen is to be built. Firstly, list up elements used in simulation. Then, construct layered thin film
structures with the thickness and composition for each layer. Generally, a substrate layer is included
in simulations. If necessary, a surface contamination layer or an interface layer between ultrathin film
layers can be introduced to improve the fitting.
6.5 After all the specified and appropriate values are given, start a simulation. If all the input
parameters are appropriate, then simulated spectra are given. Adjust the parameter of the projectile
number in beam to fit the overall intensity or the intensity of a reference layer for example between
measured and simulated MEIS spectra when an internal reference layer is used. Then adjust the
thickness and composition of each layer manually and iteratively to get the best agreement between
measured and simulated MEIS spectra. A chi-square test can be used to find the best agreement with
a properly chosen energy range of spectrum. The low limit of an energy range in χ calculation is
recommended to be not lower than 10 keV from the substrate surface peak. In case that a reference
layer of known stoichiometry is included in the sample, the height of reference layer can be chosen to
generate minimum χ calculation to determine the projectile number and then the composition and the
thickness of unknown layers can be determined by changing fitting energy range to the unknown layer
2 2
peak position to calculate and minimize χ . In case of no reference layer, overall χ calculation with an
appropriate fitting range can be used to get the best agreement between measured and simulated MEIS
spectra.
15 2
6.6 MEIS simulation programs generate composition and surface areal density (10 atoms/cm ) for
each layer. Therefore, to convert the areal density to the thickness of each layer, the density of each
layer is required. If the density of thin films used in the MEIS analysis is known, use the number. But,
generally the number is not known so that the bulk density can be used. In the case of non-stoichiometric
compounds or mixtures, the sum rule can be used. According to the sum rule, the density of a non-
stoichiometric compound ρ(A B ) can be estimated by the Formula (2).
x+δx y+δy
ρ(A B ) = [(x+δx)m(A) +(y+δy)m(B)[/{[x m(A) + y m(B)]/ρ(A B)} (2)
x+δx y+δy x y
where
ρ(A B ) is the density of a non-stoichiometric compound with A constituent of x+δx composition
x+δx y+δy
and B constituent of y+δy composition;
m(A) is the mass of A constituent;
m(B) is the mass of B constituent;
ρ(A B ) is the density of a stoichiometric compound with A constituent of x composition and
x y
B constituent of y composition.
For mixtures of A and B, the density of the mixture A(x%) and B(y%) can be estimated by the
Formula (3).
ρ(x%A+y%B) = [x m(A) + y m(B)]/[x m(A)/ρ(A) + y m(B)/ρ(B)] (3)
In Formulae (2) and (3), the m is the mass of each element or a compound in u.
By dividing the simulated areal atomic density of each layer with the estimated density of each layer,
the thickness of each layer can be obtained. The use of bulk density values or the density estimated by
the sum rule can generate errors in the depth from MEIS analysis.
7 Reporting MEIS analysis results
7.1 Report all the MEIS analysis conditions such as ion beam energy, ion species, ion current,
incidence angle from the surface normal, scattering angle, ion dose, analysis time, beam radius, sample
descriptions including surface contamination and surface flatness, sample preparation, MEIS analysis
chamber pressure, energy analyser type and specifications, detector type and specifications.
7.2 Details of MEIS spectra simulations shall be specified including simulation program name and all
of simulation parameters.
7.3 It is recommended to report MEIS analysis results in the quantity with unit of surface areal
15 2
density (10 atoms/cm ), or concentration (atomic fraction) as a function of depth in the unit of areal
15 2
density (10 atoms/cm ). Using the bulk density, it can be reported as concentration (atomic fraction)
as a function of depth in the unit of thickness (nm), but it shall be clearly stated that the bulk densities
are assumed for ultrathin films.
Annex A
(informative)
Interlaboratory test report
A.1 Overview
This annex gives a report of an interlaboratory test on non-destructive depth profiling of nanoscale
thin films with medium energy ion scattering.
A.2 Principle
MEIS spectra of HfO thin films with nominal thickness of 1 nm, 3 nm, 5 nm, and 7 nm on a substrate
12 nm SiO on a Si substrate were measured precisely by 12 participants. Three different types of MEIS
detector were used such as electrostatic, magnetic, and TOF. Measured MEIS spectra were simulated
by each participant laboratories, resulting in the poor consistency of approximately 15 %. They were
simulated again by one key laboratory, K-MAC, Korea and sources of poor consistency such as electronic
stopping power and neutralization correction were investigated, which improved the consistency of
MEIS analysis results less than 8 %.
A.3 Sample description
Samples were prepared at National Nano Fab Center in Daejeon, Korea. Nominally, 1, 3, 5, and 7 nm HfO
were deposited by atomic layer deposition method on a 12 nm thermal SiO layer on a 6 inch Si(001)
wafer. A 12 nm thermal SiO layer that assists the uniform and flat growth of HfO layer is used as an
2 2
internal reference in the MEIS analysis. The uniformity of the thickness over a 6 inch wafer was tested
by measuring 7 points of the wafer 5 times with ellipsometer. As a result, the standard deviations of
thickness were estimated to approximately 0,5 %. The thickness of HfO /SiO /Si samples was also
2 2
measured by transmission electron microscopy (TEM). TEM images of HfO /SiO /Si thin films are
2 2
shown in Figure A.1 and the average thickness of samples are summarized in Table A.1.
a) 1 nm HfO on a 12 nm thermal SiO /Si sub- b) 3 nm HfO on a 12 nm thermal SiO /Si sub-
2 2 2 2
strate strate
c) 5 nm HfO on a 12 nm thermal SiO /Si sub- d) 7 nm HfO on a 12 nm thermal SiO /Si sub-
2 2 2 2
strate strate
NOTE The scale bar at the bottom left of the image is 2 nm.
Figure A.1 — TEM images of HfO on a 12 nm thermal SiO /Si substrate
2 2
Table A.1 — Thickness of 1 nm, 3 nm, 5 nm and 7 nm HfO measured by TEM
Thickness (nm)
Samples
Average Standard deviation
1 nm HfO 1,72 0,12
3 nm HfO 3,29 0,10
5 nm HfO 4,86 0,18
7 nm HfO 6,39 0,06
A.4 Measurement procedure
A.4.1 Measurement
For MEIS analysis, the energy and the angle of scattered ions are measured to analyse depth profiles
of ultrathin films. A MEIS instrument consists of an ion source, an accelerator, an energy analyser,
and a detector. A schematic diagram is shown in Figure A.2. Ions generated from an ion source are
accelerated to impinge on a sample surface. The energy of projectile ions scattered by target atom
nuclei is measured by an energy analyser. The scattering angle is determined by the geometry of an ion
source, a sample, and a detector. Electrostatic analyser, and magnetic, TOF are widely used as energy
analysers.
Key
+ +
1 ion source (H or He )
2 scattered particles
3 particles to detector
4 accelerator
5 analyser (electrostatic, magnetic or TOF)
6 sample
α incident angle
θ scattering angle
Figure A.2 — Schematic diagram of a MEIS system
Twelve (12) participants in this RRT are UFRGS (Brazil), IBM Watson (US), Western Ontario University
(Canada), Kyoto University (Japan), Global Foundry (US), Samsung Advanced Institute of Technology
(R. O. Korea), Samsung Electronics (R. O. Korea), SK hynix (R. O. Korea), K-MAC, (R. O. Korea), DGIST (R.
O. Korea), KIST (R. O. Korea), and Huddersfield (UK). PowerMeis simulations were performed by W. Min
at K-MAC. The experimental conditions of 12 participants are summarized in Table A.2.
Table A.2 — MEIS analysis conditions for each participant
Incident energy incident angle scattering angle
Participants Incident ion analyser
o o
(keV) ( ) ( )
A H 100 0 120 Electrostatic
B H 100 54,7 110 Electrostatic
C H 94 45 135 Electrostatic
D He 400 31,5 74,1 Magnetic
E He 400 44,5 83,6 Magnetic
F He 500 44,2 78,2 Magnetic
G He 450 54,6 70,5 Magnetic
H He 400 45 68 Magnetic
I He 100 45 130 TOF
J He 80 45 90 TOF
Table A.2 (continued)
Incident energy incident angle scattering angle
Participants Incident ion analyser
o o
(keV) ( ) ( )
K He 100 2 120 Electrostatic
L He 100 54,7 70,5 Electrostatic
A.4.2 MEIS Spectrum simulation
[3]
The PowerMeis program was used as a simulation tool for analysis . It was developed mainly by
Mauricio A. Sortica and Gabriel M. Marmitt at the Pedro Grande group of the Universidade Federal
do Rio Grande do Sul (UFRGS), Brazil. PowerMeis uses the Monte-Carlo method to simulate a MEIS
spectrum by summing individual scattering spectrum from randomly selected scattering points of a
sample. The scattered ion energy is calculated by the kinematic factor for each scattering event and
by the electronic stopping energy loss according to the ion beam path in the medium. The peak shape
of each event is calculated by the straggling according to the beam path for each location and a system
resolution.
In this report, the scattering cross-section was calculated by Moliere potential. For the electronic
stopping power, both SRIM95 electronic stopping power and the new refitted electronic stopping power
were used for comparison, and the Chu model was used for the straggling. Neutralization correction
should be applied to the data from electrostatic analyser and magnetic sector. Neutralization of Marion
+ +[2] +[4]
is applied to 100 keV H and He and that of Armstrong is applied to 400 keV to 500 keV He . Casp
[5]
program can be used for both cases with better reliability . The density of HfO used in the simulations
3 3
was 9,68 g/cm , and that of SiO was 2,2 g/cm for the thickness calculation.
The stoichiometry of a thermal SiO layer, (Si:O = 1:2) was used as a reference layer. The number of
incident particles was determined by the Si height of the thermal SiO layer below the HfO layer in
2 2
the sample. When determining the number of incident particles by fitting the Si peak height of the SiO
layer, background signals between Hf and Si peaks should be subtracted. Background signal is caused
by the multiple scattering or the roughness. Given the TEM images of the samples, the background
seems to originate from the multiple scattering rather than the roughness. The background signal
is almost constant at the energy range between Si and Hf peaks. Since the simulation is based on the
single binary scattering, subtracting the multiple scattering contribution to the Si or Hf peak was done
before analysis by simulation.
MEIS analysis is performed by changing the model structure of a sample in a simulation to match the
experimental Hf peak until the difference between the experimental data and the simulation results
minimize. For simplicity, the interfaces between the HfO layer and the SiO layer and that between
2 2
the SiO layer and the Si substrate were ignored. The thickness of HfO is mainly adjusted to fit the full
2 2
width half maximum of the Hf peak. In Figure A.3, the solid black line is the experimental data and the
red line is a simulation of a fixed HfO composition (Hf:O = 1:2) with a number of incident particles that
can fit the SiO height from 293 keV to 300 keV. The Hf peak shows a slight difference between the black
and red lines, and the red line is multiplied by a constant, C to the Hf height to generate the green line
in a good agreement with the black line so that the composition of Hf increased to 0,33 * C. For all the
simulations, the same electronic stopping power for HfO calculated from the SRIM 95 or the refitted
electronic stopping power are used as described below.
Key
X energy in keV
Y scattered ion intensity in counts
Figure A.3 — Example of MEIS analysis to determine the thickness and the concentration of a
HfO /SiO /Si ultrathin film
2 2
A.4.3 SRIM electronic stopping power
The Hf concentration and the thickness of the HfO layer are obtained in the RRT using the SRIM95
electronic stopping power calculated automatically by the PowerMeis simulation program. Scattering
[6] [7]
cross-sections from Moliere potential and Chu straggling were used. Results are summarized
in Table A.3. The average value of the 7 nm sample data are 32,3 % in Hf concentration, 6,52 nm in
16 2
thickness, and 1,74 × 10 atoms/cm in the amount. The standard deviation of the 7 nm sample data
15 2
are 1,7 % in concentration, 1,00 nm in thickness, and 2,31 × 10 atoms/cm in quantity or the surface
areal density of Hf. The relative standard deviations are 5,3 % for concentration, 15 % for thickness,
and 13,3 % for the amount of Hf, which are too high to be a routine practical analysis method.
Table A.3 — Analysis results by using SRIM95 electronic stopping, Moliere potential, and Chu
a
straggling
Concentration of Hf Thickness Quantity of Hf
15 2
(nm) (1x10 atoms/cm )
Partici- 1 nm 3 nm 5 nm 7 nm 1 nm 3 nm 5 nm 7 nm 1 nm 3 nm 5 nm 7 nm
pants
A 0,133 0,297 0,29 0,318 1,60 2,60 4,0 5,9 1,77 6,41 9,64 15,61
B 0,29 0,29 0,31 2,50 4,50 6,38 6,02 10,84 16,61
C 0,21 0,303 0,30 0,303 1,07 2,55 4,20 5,95 1,87 6,43 10,47 15,00
D 0,23 0,343 0,343 0,352 0,88 2,45 3,95 5,85 1,71 6,99 11,27 17,09
E 0,205 0,322 0,35 0,347 1,10 2,50 4,18 5,90 1,87 6,68 12,16 16,69
F 0,273 0,328 0,323 0,35 0,78 2,41 3,78 5,45 1,77 6,57 10,16 15,85
G 0,26 0,306 0,324 0,327 0,78 2,55 4,15 5,75 1,69 6,50 11,18 15,61
H 0,205 0,307 0,31 0,317 0,92 2,27 3,80 5,55 1,57 5,78 9,79 14,60
I 0,295 0,305 0,305 0,307 0,95 3,10 5,30 7,55 2,33 7,86 13,43 19,26
J 0,237 0,303 0,31 0,31 1,25 3,40 5,60 8,20 2,46 8,57 14,42 21,58
K 0,2 0,31 0,312 0,327 1,12 3,60 5,20 7,75 1,86 9,27 13,47 21,03
L 0,213 0,267 0,305 0,298 1,20 3,20 5,50 8,05 2,13 7,09 13,94 19,95
Average 0,224 0,307 0,314 0,323 1,06 2,76 4,51 6,52 1,89 7,00 11,53 17,43
Standard 0,041 0,018 0,018 0,017 0,23 0,42 0,66 1,00 0,27 1,00 1,64 2,31
deviation
(18 %) (5,9 %) (5,7 %) (5,3 %) (22 %) (15 %) (15 %) (15 %) 14 %) (14,3 %) (14,2 %) (13,3 %)
a + +
For the results by magnetic sector and electrostatic analyser, neutralization of Marion is used for 100 keV H and He ,
+
and that of Armstrong for 400 keV to 500 keV He .
A.4.4 Newly fitted electronic stopping power
Among the factors affecting the MEIS analysis results, the scattering cross-section and the electronic
stopping power have high influence. The models for the cross-sections of Hf and Si are reliable and are
[8]
in good agreement with the measurement data . On the other hand, electronic stopping power values
of HfO and SiO from SRIM95 do not fit well with the measurement data set of black lines in Figure A.4.
2 2
+
In fact, there is no data available in the range of 15 keV to 100 keV for He on SiO in the IAEA database.
+ +
To eliminate the ambiguity, the electronic stopping powers of 62,3 keV He and 100 keV He on SiO
+
were measured and added to the public electronic stopping power data set of He on SiO from IAEA to
obtain a new fitted electronic stopping curve. Two newly measured electronic stopping power values
+
were added, which were obtained by measuring the height of the MEIS spectrum using 100 keV He
[9]
with two different incidence angles and the same scattering angle .
A new fitted electronic stopping power was calculated by refitting a set of electronic stopping power
data. The equation used to fit the data are shown in Formula (1) and the fitting results are shown in
Table A.4. The E is the ion energy, Z is the atomic number of the ion, m is the mass of the ion. The unit of
2 15
S , S , and S is eV·cm /10 atoms, that of E is keV, and that of m is u.
t l h
+ +
a) H on SiO b) H on HfO
2 2
+ +
c) He on SiO d) He on HfO
2 2
Key
X energy (keV)
-15 2
Y electronic stopping power [10 eVcm /atom]
stopping data set
1 fitted electronic stopping power from the IAEA experimental data (scattered dot)
2 SRIM 95
3 added experimental results (KMAC)
a
Newly measured additional electronic stopping values.
Figure A.4 — SRIM95 and new fitted electronic stopping power
Table A.4 — Fitting results of electronic stopping power
A B C D
-0,5 2 16.5 2 2 12
[eV ·cm /10 [eV ·cm /u·10 atoms] [u/keV]
atoms]
Value Std. Err Value Std. Err Value Std. Err Value Std. Err
−2 3 2 −2 −3 −1
H on SiO 2,70 3,73 × 10 2,47 × 10 2,76 × 10 1,29 × 10 2,95 × 10 2,74 3,86 × 10
−2 3 2 −2 −3 −1
H on HfO 2,91 4,56 × 10 3,17 × 10 2,73 × 10 1,12 × 10 2,09 × 10 3,27 4,80 × 10
3 2 −2 −2 −1
He on SiO 3,16 0,04 2,11 × 10 8,02 × 10 2,62 × 10 3,94 × 10 1,29 4,19 × 10
3 4 −2 −1
He on HfO 4,48 3,35 4,89 × 10 3,57 × 10 9,72 × 10 2,56 × 10 1,15 9,94
The PowerMeis program introduced a correction factor for electronic stopping power to use a new fitted
electronic stopping power. Newly fitted electronic stopping power values are applied by multiplying the
correction factor for each layer to the value from SRIM95 already installed in the PowerMeis program.
The electronic stopping power depends on the projectile ion energy, the projectile ion species, and the
composition of a sample so that it varies before and after the collision event. Therefore, the correction
factor is determined by taking into consideration for the incident and scattered ion beam path, the
electronic stopping power from SRIM95, and the new fitted electronic stopping power for E and KE .
0 0
The correction factor for the unit layer was obtained by Formula (A.1). K is the kinematic factor for the
scattering angle, α is the incident angle, β is the exit angle, and E is the initial energy of the ion. Since
the sample for this interlaboratory test is thin enough and there is no grazing angle experiment, the
ion beam energy change during the ion beam path is not very significant except for scattering events.
Therefore, it is assumed that the electronic stopping power does not change significantly from the value
of E during the intake path and the value of KE in the outgoing path.
0 0
SE() SK()E
ss00
SK= +
s
cosc± os²
SE SKE
() ()
NN00
SK= + (A.1)
N
cosc± os²
S
N
C =
S
S
where
C is the correction factor;
S is the electronic stopping power calculated by SRIM;
s
S is the newly fitted electronic stopping power.
N
The MEIS analyses were performed again with the newly fitted electronic stopping power as shown in
Table A.5. The average value of the 7 nm HfO layer is 31,5 % in the Hf concentration, 6,25 nm in the
16 2
thickness, and 1,63 × 10 atoms/cm in the amount of Hf. The standard deviation of the 7 nm sample
15 2
is 2,3 % for the concentration, 0,28 nm for the thickness, and 1,15 × 10 atoms/cm for the amount of
Hf. The relative standard deviation is 7,3 % for concentration, 4,5 % for thickness, 7,0 % for Hf quantity,
which showed a significant improvement compared to the former one in Table A.3. The improvement of
the consistency by using the new refitted electronic stopping power is quite clear, which demonstrates
that the use of accurate electronic stopping powers is critical for quantitative and reliable MEIS
analysis. It should be mentioned that the relative standard deviation of the concentration of Hf for
1 nm HfO is still poor compared to HfO layers thicker than 3 nm in contrast to those of the thickness
2 2
and the quantity of Hf. For 1 nm HfO layer, the plateau of the Hf peak did not appear clearly so that
the reliability of MEIS analysis of ultrathin films thinner than 1 nm is not enough. It is recommended
to express MEIS analysis result in surface areal density rather than in thickness or concentration for
ultrathin films of approximately 1 nm thickness.
Table A.5 — Analysis results with newly fitted electronic stopping power
Concentration of Hf Thickness Quantity of Hf
15 2
(nm) (1x10 atoms/cm )
Partici- 1 nm 3 nm 5 nm 7 nm 1 nm 3 nm 5 nm 7 nm 1 nm 3 nm 5 nm 7 nm
pants
A 0,127 0,263 0,267 0,29 1,69 2,93 4,38 6,30 1,78 6,41 9,70 15,18
B 0,26 0,268 0,275 2,65 4,78 6,88 5,87 10,66 15,67
C 0,205 0,29 0,278 0,297 1,10 2,70 4,48 6,35 1,87 6,51 10,36 15,65
D 0,217 0,323 0,288 0,295 0,92 2,55 4,10 6,05 1,66 6,85 9,82 14,83
E 0,21 0,317 0,343 0,346 1,15 2,60 4,35 6,18 2,01 6,84 12,41 17,75
F 0,264 0,317 0,326 0,35 0,85 2,58 4,02 5,85 1,86 6,79 10,89 17,01
G 0,243 0,312 0,323 0,333 0,90 2,72 4,42 6,12 1,82 7,04 11,87 16,69
H 0,203 0,316 0,313 0,303 0,96 2,31 3,95 5,80 1,62 6,07 10,28 14,62
I 0,215 0,32 0,323 0,325 1,03 2,55 4,30 6,17 1,84 6,78 11,55 16,70
J 0,247 0,333 0,33 0,343 1,03 2,64 4,38 6,50 2,11 7,31 12,01 18,54
K 0,213 0,305 0,322 0,31 0,96 2,87 4,20 6,27 1,70 7,27 11,23 16,15
L 0,220 0,273 0,287 0,313 0,98 2,60 4,50 6,55 1,79 5,90 10,72 17,05
Average 0,214 0,303 0,306 0,315 1,06 2,64 4,32 6,25 1,83 6,64 10,96 16,34
Standard 0,033 0,023 0,025 0,023 0,02 0,15 0,22 0,28 0,14 0,47 0,83 1,15
deviation
(15 %) (7,6 %) (8,2 %) (7,3 %) (2 %) (5,7 %) (5,1 %) (4,5 %) (7,7 %) (7,1 %) (7,6 %) (7,0 %)
[6] [7]
NOTE 1  Moliere potential , and Chu straggling were applied.
[2] +
NOTE 2  For the magnetic sector and electrostatic analyser results, Marion neutralization was applied for 100 keV H and
+ [4] +
He , and Armstrong's neutralization was applied for 400 keV to 500 keV He .
A.4.5 Comparison
Shown in Figure A.5 are the concentration, the thickness, and the amount of Hf for the 7 nm HfO
sample analysed by SRIM95 electronic stopping power and a new fitted electronic stopping power
for comparison. As shown in Figure A.5, the concentration determined by using SRIM95 electronic
stopping power show relatively good agreement. However, the thickness and the amount of Hf show
+
poor agreement. MEIS analysis results by using 80 keV to 100 keV He are higher than those by 100 keV
+ +
H or 400 keV to 500 keV He regardless of the analyser type. On the other hand, the use of newly
fitted electronic stopping powers significantly reduces the standard deviation of the thickness and the
quantity of Hf, while the standard deviation of the concentration increases slightly. This demonstrates
that accurate electronic stopping power is critical for quantitative MEIS analysis. Electronic stopping
power from SRIM95 can be the starting point but if experimentally determined values are available
from the IAEA home page, it is strongly recommended to use the electronic stopping power from the
IAEA. If electronic stopping powers are not available or not sufficient from the IAEA home page, they
may be measured by each user for more reliable MEIS analysis.
a) Concentration result of 7 nm HfO sample by b) Concentration result of 7 nm HfO sample by
2 2
using SRIM 95 using newly fitted electronic stopping power
c) Thickness of 7 nm HfO sample by using d) Thickness of 7 nm HfO sample by using
2 2
SRIM 95 newly fitted electronic stopping power
e) Quantity of Hf of 7 nm HfO sample by using f) Quantity of Hf of 7 nm HfO sample by using
2 2
SRIM 95 newly fitted electronic stopping power
Key
X participants
Y1 concentration of Hf
Y2 thickness of HfO (nm)
15 2
Y3 quantity of Hf (1x10 atoms/cm )
+
100 keV He
+
300 keV to 500 keV He
+
80 keV to 100 keV He
average
Figure A.5 — Concentration, thickness, and quantity of Hf results of 7 nm HfO sample by using
SRIM95 and newly fitted electronic stopping power
A.4.6 Measurement of electronic stopping power
+
This report includes the newly measured 62,3 keV He+ and 100 keV He electronic stopping powers
[9] +
for SiO . Since there were no data for 15 keV to 100 keV He in SiO , measurements were required
2 2
to increase the accuracy of the electronic stopping power in the range of approximately 100 keV. This
+
value was added to the IAEA electronic stopping power data of He on SiO to obtain a newly fitted
electronic stopping curve.
Two newly measured electronic stopping power values were obtained by measuring the height of the
+
MEIS spectrum using 100 keV He with two different incidence angles at the same scattering angle. The
spectral height at energy KE of the MEIS measurement is given by Formula (A.2). It is affected by the
stopping power as well as the incident angle, the cross-section at the scattering angle, the number of
incident particles and the detector efficiency. K is the kinematic factor, S is the stopping power of E
1 0
in the intake path, S is the stopping power of KE in the exit path, α is the incident angle, and β is the
2 0
exit angle. C is the concentration of the element, A is a constant, Q is the number of incident ions, ΔE is
ch
the channel width of th
...