ISO 18118:2024
(Main)Surface chemical analysis — Auger electron spectroscopy and X-ray photoelectron spectroscopy — Guide to the use of experimentally determined relative sensitivity factors for the quantitative analysis of homogeneous materials
Surface chemical analysis — Auger electron spectroscopy and X-ray photoelectron spectroscopy — Guide to the use of experimentally determined relative sensitivity factors for the quantitative analysis of homogeneous materials
This document gives guidance on the measurement and use of experimentally-determined relative sensitivity factors for the quantitative analysis of homogeneous materials by Auger electron spectroscopy and X-ray photoelectron spectroscopy. The methods described only apply to polycrystalline and amorphous materials, as effects inherent to single-crystal samples are not addressed.
Analyse chimique des surfaces — Spectroscopie des électrons Auger et spectroscopie de photoélectrons — Lignes directrices pour l'utilisation de facteurs expérimentaux de sensibilité relative pour l'analyse quantitative de matériaux homogènes
General Information
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Standards Content (Sample)
International
Standard
ISO 18118
Third edition
Surface chemical analysis — Auger
2024-02
electron spectroscopy and X-ray
photoelectron spectroscopy —
Guide to the use of experimentally
determined relative sensitivity
factors for the quantitative analysis
of homogeneous materials
Analyse chimique des surfaces — Spectroscopie des électrons
Auger et spectroscopie de photoélectrons — Lignes directrices
pour l'utilisation de facteurs expérimentaux de sensibilité relative
pour l'analyse quantitative de matériaux homogènes
Reference number
© ISO 2024
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms. 4
5 General information . 5
6 Measurement conditions . 6
6.1 General .6
6.2 Excitation source .7
6.3 Energy resolution .7
6.4 Energy step and scan rate .7
6.5 Signal intensity . .7
6.6 Gain and time constant (for AES instruments with analogue detection systems) .7
6.7 Modulation to generate a derivative spectrum .7
7 Data-analysis procedures . 7
8 Spectrometer response function . 8
9 Determination of chemical composition using relative sensitivity factors . 8
9.1 Calculation of chemical composition .8
9.1.1 General .8
9.1.2 Composition determined from elemental relative sensitivity factors .9
9.1.3 Composition determined from atomic relative sensitivity factors or average
matrix relative sensitivity factors .9
9.2 Uncertainties in calculated compositions .9
Annex A (informative) Formulae for relative sensitivity factors .10
Annex B (informative) Information on uncertainty of the analytical results.16
Bibliography . 19
iii
Foreword
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This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis, Subcommittee
SC 7, Electron spectroscopies.
This third edition cancels and replaces the second edition (ISO 18118:2015), which has been technically
revised.
The main changes are as follows:
— The main equation for the use of sensitivity factors for analysis has been moved from Annex A to the
main text
— Defined symbols and abbreviated terms from the Annexes have been consolidated to Clause 4.
— Several terms have been modified for formatting purposes, and some have been removed due to no
longer being required.
— Several formulae have been removed from Annex A and replaced by references to formulae and
databases of parameters that are more accurate. Such databases are now the recommended source for
the parameters calculated using the removed formulae.
— Annex A has been redefined as an informative Annex.
— Multiple small additions have been made to provide new and updated sources for information.
— Editorial changes have been made throughout.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
Introduction
Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) are surface-analytical
techniques that are sensitive to the composition in the surface region of a material to depths of, typically,
a few nanometres (nm). Both techniques yield a surface-weighted signal, averaged over the analysis
volume. Most samples have compositional variations, both laterally and with depth, and quantification is
often performed with approximate methods since it can be difficult to determine the magnitude of any
compositional variations and the distance scale over which they can occur. The simplest sample for analysis
is one that is homogeneous. Although this situation occurs infrequently, it is often assumed, for simplicity in
the analysis, that the sample material of interest is homogeneous. This document provides guidance on the
measurement and use of experimentally determined relative sensitivity factors for the quantitative analysis
of homogeneous materials by AES and XPS.
v
International Standard ISO 18118:2024(en)
Surface chemical analysis — Auger electron spectroscopy
and X-ray photoelectron spectroscopy — Guide to the use of
experimentally determined relative sensitivity factors for the
quantitative analysis of homogeneous materials
1 Scope
This document gives guidance on the measurement and use of experimentally-determined relative
sensitivity factors for the quantitative analysis of homogeneous materials by Auger electron spectroscopy
and X-ray photoelectron spectroscopy. The methods described only apply to polycrystalline and amorphous
materials, as effects inherent to single-crystal samples are not addressed.
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 18115-1, Surface chemical analysis — Vocabulary — Part 1: General terms and terms used in spectroscopy
ISO 21270, Surface chemical analysis — X-ray photoelectron and Auger electron spectrometers — Linearity of
intensity scale
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 18115-1 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
absolute elemental sensitivity factor
coefficient for an element by which the measured intensity for that element is divided to yield the atomic
concentration or atomic fraction of the element present in the sample
Note 1 to entry: See relative elemental sensitivity factor.
Note 2 to entry: The choice of atomic concentration or atomic fraction should be made clear.
Note 3 to entry: The type of sensitivity factor utilized should be appropriate for the formulae used in the quantification
process and for the type of sample analysed, for example homogeneous samples or segregated layers.
Note 4 to entry: The source of sensitivity factors should be given to ensure that the correct matrix factors or other
parameters are used.
Note 5 to entry: Sensitivity factors depend on parameters of the excitation source, the spectrometer, and the orientation
of the sample to these parts of the instrument. Sensitivity factors also depend on the matrix being analysed, and in
SIMS this has a dominating influence.
[SOURCE: ISO 18115-1]
3.2
elemental relative sensitivity factor
coefficient proportional to the absolute elemental sensitivity factor (3.1), where the constant of
proportionality is chosen such that the value for a selected element and transition is unity
Note 1 to entry: Elements and transitions commonly used are C 1s or F 1s for XPS and Ag M VV for AES.
4,5
Note 2 to entry: The type of sensitivity factor used should be appropriate for the type of sample analysed, for example
homogeneous samples or segregated layers.
Note 3 to entry: The source of sensitivity factors should be given to ensure that the correct matrix factors or other
parameters are used.
Note 4 to entry: Sensitivity factors depend on parameters of the excitation source, the spectrometer, and the orientation
of the sample to these parts of the instrument. Sensitivity factors also depend on the matrix being analysed, and in
SIMS this has a dominating influence.
[SOURCE: ISO 18115-1]
3.3
average matrix relative sensitivity factor
AMRSF
coefficient, proportional to the intensity, calculated for an element in an average matrix, by
which the measured intensity for that element is divided in calculations to yield the atomic concentration or
atomic fraction of the element present in the sample
Note 1 to entry: See sensitivity factor, elemental relative sensitivity factor (3.2) and pure element relative sensitivity
factor (3.4).
Note 2 to entry: The choice of atomic concentration or atomic fraction should be made clear.
Note 3 to entry: The type of sensitivity factor utilized should be appropriate for the formulae used in the quantification
process and for the type of sample analysed, for example homogeneous samples or segregated layers.
Note 4 to entry: The source of sensitivity factors should be given. Matrix factors are taken to be unity for average
matrix relative sensitivity factors.
Note 5 to entry: Sensitivity factors depend on parameters of the excitation source, the spectrometer, and the
orientation of the sample to these parts of the instrument. The numerical values of the sensitivity factors can also
depend on the method used to measure the peak intensities.
[SOURCE: ISO 18115-1]
3.4
pure-element relative sensitivity factor
PERSF
coefficient, proportional to the intensity measured for a pure sample of an element, by which the
measured intensity for that element is divided in calculations to yield the atomic concentration or atomic
fraction of the element present in the sample
Note 1 to entry: See sensitivity factor, elemental relative sensitivity factor (3.2), and average matrix relative sensitivity
factor (3.3).
Note 2 to entry: The choice of atomic concentration or atomic fraction should be made clear.
Note 3 to entry: The type of sensitivity factor used should be appropriate for the formulae used in the quantification
process and for the type of sample analysed, for example homogeneous samples or segregated layers.
Note 4 to entry: The source of sensitivity factors should be given to ensure that the correct matrix factors or other
parameters are used. Matrix factors are significant and should be used with pure-element relative sensitivity factors.
Note 5 to entry: Sensitivity factors depend on parameters of the excitation source, the spectrometer, and the
orientation of the sample to these parts of the instrument. The numerical values of the sensitivity factors can also
depend on the method used to measure the peak intensities.
[SOURCE: ISO 18115-1]
3.5
spectrometer response function
quotient of the number of particles detected with a spectrometer by the number of such particles per solid
angle and per interval of the dispersing parameter available for measurement as a function of the dispersing
parameter
Note 1 to entry: See spectrometer étendue.
Note 2 to entry: The dispersing parameter is commonly energy, mass, or wavelength.
Note 3 to entry: The units of the spectrometer response function can be sr⋅eV, sr⋅amu, or sr⋅m.
Note 4 to entry: The spectrometer response function is similar to the spectrometer transmission function (3.6) or
étendue but includes the efficiencies of all other components of the measurement chain, such as detectors and the
electronic processing and recording equipment.
Note 5 to entry: For some methods of quantitative analysis, the energy dependence of the response function is needed in
order to use relative sensitivity factors. For these cases, a function is determined which is proportional to the absolute
response function, where the proportionality constant is not necessarily important.
[SOURCE: ISO 18115-1]
3.6
spectrometer transmission function
analyser transmission function
quotient of the number of particles transmitted by the analyser by the number of such particles per
solid angle and per interval of the dispersing parameter (e.g. energy, mass, or wavelength) available for
measurement as a function of the dispersing parameter
Note 1 to entry: See spectrometer response function (3.5).
Note 2 to entry: The units of transmission can be sr⋅eV, sr⋅amu, or sr⋅m.
Note 3 to entry: Often, an incomplete use of the term occurs where just the solid angle of acceptance of the spectrometer,
in sr, or a fraction of the 2π solid angle of available space is given. This usage is deprecated, cf. solid angle of analyser.
Note 4 to entry: This term is often used incorrectly instead of spectrometer response function, which includes
contributions from the detector and the signal-processing system.
[SOURCE: ISO 18115-1]
3.7
atomic relative sensitivity factor
ARSF
coefficient, proportional to the intensity measured for a single atom of an element, by which the measured
intensity for that element is divided in calculations to yield the atomic concentration or atomic fraction of
the element present in the sample.
Note 1 to entry: See elemental relative sensitivity factor (3.2).
Note 2 to entry: The choice of atomic concentration or atomic fraction should be made clear.
Note 3 to entry: The type of sensitivity factor utilized should be appropriate for the formulae used in the quantification
process and for the type of sample analysed, for example homogeneous samples or segregated layers.
Note 4 to entry: The source of sensitivity factors should be given to ensure that the correct matrix factors or other
parameters are used.
Note 5 to entry: Sensitivity factors depend on parameters of the excitation source, the spectrometer, and the orientation
of the sample to these parts of the instrument. Sensitivity factors also depend on the matrix being analysed, and in
SIMS this has a dominating influence.
4 Symbols and abbreviated terms
AES Auger electron spectroscopy
A atomic mass of element i
i
E binding energy of core level for element i
b,i
E band-gap energy
g
E kinetic energy of an auger electron or photoelectron from element i
i
E free-electron plasmon energy
p
E primary electron energy
pr
F matrix correction factor for element i
i
F matrix correction factor for element j
j
H(cosα, ω ) Chandrasekhar function for parameters cosα and ω
i i
I measured intensity of the chosen peak in the key material
key
C number of atoms of element i in the molecular formula of the compound
i
I measured intensity of element i in the reference sample
i,ref
I
measured intensity of element i in the unknown sample
i,unk
I
measured intensity of element j in the reference sample
j,ref
I measured intensity of element j in the unknown sample
j,unk
J excitation beam intensity
M molecular mass of the compound containing element i
i
n number of identified elements in the unknown sample
N Avogadro constant
A
N atomic density for the average matrix sample
av
N atomic density of element i
i
N
atomic density of the reference sample
ref
N
atomic density of the key element
key
N atomic density of the unknown sample
unk
N number of valence electrons per atom or molecule
v
elastic-scattering correction factor for the average matrix sample at the electron energy E for
i
Q
av
the particular Auger-electron or photoelectron peak of interest
elastic-scattering correction factor for element i at the electron energy E for the particular
i
Q
i
Auger-electron or photoelectron peak of interest
elastic-scattering correction factor for element i at emission angle α = 0 with respect to the
Q (0)
i
surface normal
Q elastic-scattering correction factor for element i in the reference sample
i,ref
Q
elastic-scattering correction factor for element i in the unknown sample
i,unk
R backscattering correction factor for the average matrix sample
av
R backscattering correction factor for element i
i
backscattering correction factor for element i in the reference sample (these terms are unity for
R
i,ref
XPS)
backscattering correction factor for element i in the unknown sample (these terms are unity for
R
i,unk
XPS)
RSF relative sensitivity factor
S atomic relative sensitivity factor for element i
i,At
S
average matrix relative sensitivity factor for element i
i,Av
S
elemental relative sensitivity factor for element i in a specified compound
i,Ec
S pure-element relative sensitivity factor for element i
i,Ep
S
relative sensitivity factor for element i
i,RSF
S elemental relative sensitivity factor for element i
i,E
S
relative sensitivity factor for element j
j,RSF
T
spectrometer response function (SRF)
XPS X-ray photoelectron spectroscopy
Z atomic number
Z atomic number of the average matrix sample
av
α emission angle with respect to the surface normal
θ angle of incidence of electron beam
X
atomic fraction of element i in the reference sample
i,ref
X atomic fraction of element i in the unknown sample
i,unk
λ
electron inelastic mean free path for element i in the reference sample
i,ref
λ electron inelastic mean free path for element i in the unknown sample
i,unk
λ electron inelastic mean free path for the average matrix sample
av
λ electron inelastic mean free path for element i
i
−3
ρ density of the solid (kg⋅m )
5 General information
It is convenient in many quantitative applications of AES and XPS to utilize relative sensitivity factors (RSFs)
for quantitative analyses. Three types of RSF have been used for this purpose: elemental relative sensitivity
factors (ERSFs), atomic relative sensitivity factors (ARSFs), and average matrix relative sensitivity
factors (AMRSFs). Formulae defining these three types of RSF are given in A.2 and the principles on which
these formulae are based on are given in A.2.
While the ERSFs are the simplest and easiest to apply, they are the least accurate because no account is
taken of matrix correction factors (as described in A.2). The matrix correction factors for AES can vary
[1] [2]
between 0,1 and 8 while they can vary between 0,3 and 3 for XPS. The ARSFs are more accurate than
ERSFs in that they take account of differences in atomic densities, generally the largest single matrix
correction. The AMRSFs are the most reliable RSFs in that there is almost complete correction of matrix
effects. It is recommended that ERSFs be used only for semi-quantitative analyses (that is, rough estimates
of composition) and that ARSFs or preferably, AMRSFs be used for quantitative analyses. For the latter
applications, ARSFs shall be used only in situations for which it is not possible to make use of AMRSFs (for
example, measurements involving Auger electrons or photoelectrons at energies for which inelastic mean
free paths cannot be reliably determined).
In analytical applications of AES and XPS, it is essential that Auger-electron and photoelectron intensities be
measured using exactly the same procedure as that used for measurement of the RSFs. For some applications
of AES (e.g. sputter depth profiles), it is convenient to use peak-to-peak heights of Auger-electron signals in
the differential mode as measures of Auger-electron intensities. For other applications of AES (e.g. scanning
Auger microscopy), the Auger-electron intensity can be determined from the difference between the
intensity at a peak maximum in the direct spectrum and the intensity of a nearby background signal. Finally,
for many applications in XPS and for some applications of AES, areas of peaks in direct spectra are used as
measures of photoelectron or Auger-electron intensities.
Relative sensitivity factors depend on the parameters of the excitation source (for example, the incident
electron energy in AES and the choice of X-ray energy in XPS), the spectrometer configuration (for example,
the angle of incidence of the electron beam in AES, the angle between the X-ray source and the analyser
axis in XPS, the sample area viewed by the analyser, and the acceptance solid angle of the analyser), and the
[3]
orientation of the sample to these parts of the instrument. The sample area viewed by the analyser and
the analyser acceptance solid angle can depend on analyser settings (for example, selection of apertures,
whether the analyser is operated in the constant analyser energy mode or the constant retardation ratio
mode, and the corresponding choices of analyser pass energy or retardation ratio). Finally, the measured
Auger-electron or photoelectron intensities can depend on the instrumental parameters described in
Clause 6. Therefore, it is essential that Auger-electron and photoelectron intensities be determined using
exactly the same instrumental settings and the same sample orientation as those employed for the ERSF
measurements. It is also essential that the same data-analysis procedures (described in Clause 7) be
used in measurements of signal-electron intensities for the unknown sample as those used in the ERSF
measurements.
Commercial AES and XPS instruments are generally supplied with a set of ERSFs for one or more common
operating conditions. These ERSFs were typically determined on an instrument of the same type or, in
some cases, on similar instruments. It is recommended that an analyst check the ERSFs supplied with
the instrument for those elements expected to be of analytical interest to ensure that the supplied ERSFs
are correct. In addition, the spectrometer response function (SRF) of the instrument can change with
time, as described in Clause 8. Such changes can be detected and corrective actions be taken by regular
[5][6]
measurement of the SRF using appropriate reference materials. Alternatively, an analyst can check for
possible changes in SRF with time by measuring selected ERSFs as described in Clause 8.
6 Measurement conditions
6.1 General
The same measurement conditions (for example, instrumental configuration, sample orientation, and
instrumental settings) shall be used for the measurement with the unknown sample as those chosen for the
ERSF measurements. Particular attention shall be given to the following parameters.
6.2 Excitation source
The incident-electron energy in AES and the X-ray source in XPS shall be the same for the measurement of
the unknown sample as that chosen for the measurement of the ERSFs.
6.3 Energy resolution
Unless peak areas are used to measure the signal intensities, the energy resolution of the electron-energy
analyser (that is determined by choice of aperture sizes, pass energy, or retardation ratio) shall be the same
[7]
for the unknown-sample measurement as for the measurement used to generate the ERSFs .
6.4 Energy step and scan rate
The size of the energy step (energy per channel) used to acquire spectral data and the spectral scan rate
shall be chosen so that there is negligible spectral distortion in the acquired data for the selected energy
resolution.
6.5 Signal intensity
The incident-electron current (in AES) or the X-ray intensity (in XPS) shall be adjusted together with the
voltage applied to the detector so that the measured signal intensity is proportional to the incident current
or X-ray intensity to within 1 % as described in ISO 21270. Alternatively, the measured signal intensity that
is corrected for counting losses, as described in ISO 21270, shall be proportional to the incident current or
X-ray intensity to within 1 %.
6.6 Gain and time constant (for AES instruments with analogue detection systems)
The settings of the detector system shall be the same in the unknown-sample measurement as in the
[8]
measurement used to generate the ERSFs. The time constant in the measurements shall be sufficiently
short so that shapes of spectral features are not significantly distorted during data acquisition. The gain of
the detector system shall be adjusted so that the intensities measured for the relevant peaks are within the
range for linear detector response.
Procedures to check for linear detector response in pulse-counting systems are described in ISO 21270.
The first method described there(ISO 21270:2004, 6.6) can be used for analogue AES systems if there are
sufficient instrumental controls.
6.7 Modulation to generate a derivative spectrum
It is often convenient in AES to utilize the differential spectrum. The derivative spectrum can be acquired
[9][10]
by applying a modulation voltage to the analyser or by numerical processing of a measured direct
[11][12].
spectrum For this purpose, a modulation or numerical differential of between 2 eV and 10 eV (peak-
to-peak) is commonly used. The same modulation energy shall be used for the measurements with the
unknown sample as that used to determine the ERSFs.
NOTE 1 The details of the peak attenuation in numerical differentiation and of the Savitzky and Golay differentiation
method in AES can be obtained from Reference [9] and Reference [10]. Discussion of improvements to this method,
and the effects of the number of points used in this method can be obtained from Reference [68]
NOTE 2 Corrections for the effects of analyser modulation on peak intensity in derivative Auger spectra can be
obtained from Reference [69].
7 Data-analysis procedures
The same procedures shall be used for the analysis of the spectra measured for the unknown sample and for
the ERSF measurements.
To obtain a peak area or a peak height from a measured direct spectrum, a background shall be chosen and
subtracted from the measured spectrum (see Reference [11]). The backgrounds most commonly used for
[14] [15] [16]
this purpose are a linear background, a Shirley background, or a Tougaard background .
In AES, it is often convenient to measure a peak-to-peak height or a peak-to-background height in a
differential spectrum. The differential spectrum can be recorded (in analogue detection instruments)
or a measured direct spectrum can be numerically differentiated for this purpose. The same numerical
procedure and choices shall be made in the differentiation of the spectra for the unknown sample and for
[13][17].
the reference samples used to determine the ERSFs See also 6.7.
NOTE 1 Details of background-subtraction procedures are given in Reference [11].
NOTE 2 Details of peak attenuation in numerical differentiation and of the Savitzky and Golay differentiation
method in AES can be obtained from Reference [9] and Reference [10].
NOTE 3 Reference [16] gives information on procedures to obtain consistent results in the use of differentiation
for measurements with different chemical states of an element. This reference provides similar information for the
determination of peak areas.
8 Spectrometer response function
The spectrometer response function (SRF) is a measure of the efficiency of the electron-energy analyser in
[1][19][20]
transmitting electrons and of the detector system in detecting them as a function of electron energy.
In general, the SRF will change if the analyser pass energy, retardation ratio, and aperture sizes are modified.
In addition, different instruments of the same type (and from the same manufacturer) can have different
SRFs for the same instrumental settings because the detector efficiency as a function of energy will often
change during its service life. As a result, it is recommended that the intensity scale be calibrated at regular
[5][6]
intervals (for example, every six months) using an appropriate method or that ERSFs be measured for
selected elements (having Auger-electron or photoelectron peaks over the working range of the energy
scale). Such checks should also be made if the detector surface has been exposed to any environment that
could affect its efficiency and if insulating films (e.g. from sputtering of non-conducting samples) have been
deposited on analyser surfaces. Local measurements of ERSFs for selected elements shall be recorded in
the log book for the instrument and plotted as a function of time so that changes can be easily detected. For
NAP-XPS systems, due to the additional attenuation of the signal potentially changing the effective SRF, any
set of RSFs should only be considered valid for measurements taken under identical NAP conditions.
9 Determination of chemical composition using relative sensitivity factors
9.1 Calculation of chemical composition
9.1.1 General
The chemical composition of an unknown sample can be determined using Formula (A.6) and Formula (1)
or one of the other formulae given in Annex A. Formula (1) is commonly used but ignores matrix terms. For
some types of relative sensitivity factor, these matrix terms are effectively unity, and can be ignored but,
[1]
when other types of sensitivity factor are used, the matrix factors can be as high as 8 in AES and 3 in XPS.
[2]
The accuracy of calculated chemical compositions thus depends significantly on the type of sensitivity
factor used. This is discussed in Annex A.
NOTE AES and XPS cannot directly detect hydrogen or helium. A quantitative analysis of an unknown sample that
is likely to contain one of these elements (e.g. organic compounds) will have a systematic error unless some method is
devised to overcome this limitation.
In some applications, it can be satisfactory to determine the composition of an unknown sample if a reference
sample of similar composition is available. For this situation, measurements are made of signal-electron
intensities from the unknown samples and reference samples, and the composition is calculated using
Formula (A.5). If the two materials are close in composition, matrix correction factors can be ignored and
Formula (A.5) is valid. The analyst should nevertheless be aware that it can be difficult to prepare reference
samples of known composition; for example, compounds cleaned by ion sputtering will generally have a
surface composition different from the bulk composition due to preferential-sputtering effects. This can be
helpful if the sample to be analysed has been similarly sputtered. However, artefacts due to sputtering are
beyond the scope of this document. Scraping, fracturing, or cleaving of the reference sample, where feasible,
can be a suitable means of generating a suitable surface for comparisons with the unknown sample.
9.1.2 Composition determined from elemental relative sensitivity factors
The composition of the unknown sample can be obtained from Formula (1) using ERSFs, S , supplied by
i,E
the instrument manufacturer or as measured by the analyst.
I
i,unk
S
iR, SF
X = (1)
i,unk
I
n
j,unk
∑
j=1
S
j,RSF
9.1.3 Composition determined from atomic relative sensitivity factors or average matrix relative
sensitivity factors
The composition of the unknown sample can be obtained from Formula (1) using ARSFs, S , or
i,At
AMRSFs, S .
i,Av
NOTE 1 The ARSFs can be supplied by the instrumental manufacturer or be calculated by the analyst using
Formula (A.9).
NOTE 2 The AMRSFs can be obtained using methods described in A.2.4.
9.2 Uncertainties in calculated compositions
[21]
Many factors can contribute to the uncertainty of a chemical composition determined from RSFs.
Information on possible uncertainties in such measurements is given in Annex B.
Annex A
(informative)
Formulae for relative sensitivity factors
A.1 Principles
Quantitative analysis of a homogeneous sample can be accomplished through comparison of an Auger-
electron or photoelectron peak intensity, I , from an unknown sample (the sample material whose
i,unk
surface composition is to be determined) with the corresponding peak intensity, I , from a reference
i,ref
sample with known surface composition (either a pure element or a suitable compound) in order to remove
instrumental and, in some cases, matrix factors. This comparison can only be made if the analytical
conditions for both measurements are identical. In the simplest analytical case, when the sample surface is
assumed to consist of a single phase and to be atomically flat, the measured intensity is given by
[1][22][23][24][25][26]:
Formula (A.1), and the intensity ratio is given by Formula (A.2)
IJ= TX NQ R λ (A.1)
ii,,unkunk unkuii,,nk unkui, nk
I XN QR λ
i,unk ii,,unkunk unkuii,,nk unk
= (A.2)
I XN QR λ
i,ref ii,,refref ref iii,,refref
where
J
is the X-ray photon (for XPS) or electron beam (for AES) intensity on the sample, which should
be identical for both the reference and unknown samples
T
is the spectrometer response function (SRF) which should be identical for both the reference
and unknown samples
X
is the atomic fraction of the element i in the unknown samples;
i,unk
X
is the atomic fraction of the element i in the reference samples;
i,ref
N
is the atomic density of the unknown sample;
unk
N
is the atomic density of the reference sample;
ref
Q
is the elastic-scattering correction factor for element i in the unknown sample;
i,unk
Q
is the elastic-scattering correction factor for element i in the reference sample;
i,ref
R
is the backscattering correction factor for element i in the unknown sample (these terms are
i,unk
unity for XPS);
R
is the backscattering correction factor for element i in the reference sample (these terms are
i,ref
unity for XPS);
λ
is the electron inelastic mean free path for element i in the unknown sample;
i,unk
λ
is the electron inelastic mean free path for element i in the reference sample.
i,ref
From Formula (A.2), X can be obtained using Formula (A.3):
i,unk
I XN QR λ I
i,unk ii,,refref refrii,,ef ref i,unk
X = =X F (A.3)
i,unk i,ref i
I NQ R λ I
i,ref unk iii,,unkunk i,unk i,ref
where F is the matrix correction factor for element i in the comparison of measurements made with a
i
particular unknown sample and a particular reference sample.
The atomic fraction of the element i in an unknown sample with n identified elements is then given by
[1][26]:
Formula (A.4)
I
i,unk
X
i,ref
I
i,ref
X = (A.4)
i,unk
I
n
j,unk
X
∑ j,ref
j=1
I
j,ref
This formula should be solved iteratively since the matrix factors depend on the composition of the material.
This composition is, of course, unknown until Formula (A.4) is solved. If, for simplicity, it is assumed that the
atomic densities, elastic-scattering correction factors, backscattering correction factors, and inelastic mean
free paths are the same for the two samples considered in Formula (A.3) and the reference sample is pure
elemental solids, the matrix correction factors F = 1 , and the reference atomic fractions X =1 . For these
i i,ref
assumptions, if the unknown sample consists of n elements, the atomic fractions X of these elements can be
i
[26]
obtained from Formula (A.5) :
I
i,unk
I
i,ref
X = (A.5)
i,unk
I
n
j,unk
∑
j=1
I
j,ref
While Formula (A.5) is simple and is often used for quantitative surface analysis by AES and XPS, it should
be emphasized that it is based on the simplifying assumption that the matrix correction factors F for the
i
elements in the unknown sample are unity. In reality, F values (calculated using pure elements) range from
i
[1]
0,1 to 8 (with one-third of the values outside the range 0,5 to 1,5) for AES. The F values range from 0,3 to
i
[2]
3 for XPS.
Values of I are needed for a quantitative analysis to obtain the fractional compositions X from
i,ref i,unk
measured values of I for an unknown sample using Formula (A.4) or Formula (A.5). The I values
i,unk i,ref
can be obtained from a series of measurements for those elements that can be conveniently prepared as
solids with a sufficiently high degree of purity (generally better than 99 %) and with clean surfaces in an
AES or XPS instrument. For other elements (e.g. the alkali metals and elements such as oxygen, nitrogen, and
the halogens that are gases at room temperature), the I values can be estimated from similar
i,ref
measurements with compounds containing the desired elements. Unless corrections can be made for matrix
effects [the matrix correction factor F in Formula (A.4) and the additional matrix effects discussed in B.2],
i
[28][29]
values of I for the same element i from different compounds can be different .
i,ref
It is generally convenient in practice to make use of I values that have been normalized to unity for a
i,ref
[1][9].[30][31][32][33][34][35]
particular peak from a selected element, hereafter referred to as the key element In
XPS, the 1s photoelectron line of fluorine in lithium fluoride has been generally used for this purpose while
the silver M4,5VV Auger-electron line has been commonly used in AES.
A.2 Relative sensitivity factors
A.2.1 Introduction
Defining formulae are given here for three different types of relative sensitivity factor (RSF) that can be
obtained from I values. The RSFs, S , for an element i in an unknown material containing n elements,
i,ref i,RSF
can be used to evaluate the atomic fraction, X , of the element i from Formula (A.6):
i,unk
IF
ii,unk
S
i,RSF
X = (A.6)
i,unk
IF
n
jj,unk
∑
j=1
S
j,RSF
...
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