ISO 18118:2004

INTERNATIONAL ISO
STANDARD 18118
First edition
2004-05-15
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
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 2004
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©  ISO 2004
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ii © ISO 2004 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 1
4 Symbols and abbreviated terms. 2
5 General information . 3
6 Measurement conditions. 4
6.1 General. 4
6.2 Excitation source . 4
6.3 Energy resolution. 4
6.4 Energy step and scan rate . 4
6.5 Signal intensity. 4
6.6 Gain and time constant (for AES instruments with analogue detection systems) . 4
6.7 Modulation to generate a derivative spectrum . 4
7 Data-analysis procedures . 5
8 Intensity-energy response function . 5
9 Determination of chemical composition using relative sensitivity factors . 5
9.1 Calculation of chemical composition . 5
9.2 Uncertainties in calculated compositions. 6
Annex A (normative) Equations for relative sensitivity factors. 7
A.1 Symbols and abbreviated terms. 7
A.2 Principles . 9
A.3 Relative sensitivity factors. 10
Annex B (informative) Information on uncertainty of the analytical results . 17
B.1 Symbols and abbreviated terms. 17
B.2 Introduction . 17
B.3 Matrix effects . 17
B.4 Sample morphology. 18
B.5 Surface topography . 18
B.6 Radiation damage . 18
B.7 Ion-sputtering effects . 18
B.8 Surface contamination . 19
Bibliography . 20

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
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established has the right to be represented on that committee. International organizations, governmental and
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International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 18118 was prepared by Technical Committee ISO/TC 201, Surface chemical analysis, Subcommittee
SC 5, Auger electron spectroscopy.
iv © ISO 2004 – All rights reserved

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 may 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 International Standard provides guidance on the
measurement and use of experimentally determined relative sensitivity factors for the quantitative analysis of
homogeneous materials by AES and XPS.

INTERNATIONAL STANDARD ISO 18118:2004(E)

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 International Standard 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.
2 Normative references
The following referenced documents are indispensable for the application 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
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 apply. The definitions of
absolute elemental sensitivity factor and relative elemental sensitivity factor from ISO 18115 are given for
convenience in 3.1 and 3.2. Definitions of average matrix relative sensitivity factor and pure-element relative
sensitivity factor from a future amendment to ISO 18115 are given in 3.3 and 3.4.
3.1
absolute elemental sensitivity factor
coefficient for an element with 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 The choice of use of atomic concentration or atomic fraction should be made clear.
NOTE 2 The type of sensitivity factor used should be appropriate for the equations used in the quantification process
and for the type of sample analysed, for example, of homogeneous samples or segregated layers.
NOTE 3 The source of the sensitivity factors should be given in order that the correct matrix factors or other
parameters have been used.
NOTE 4 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.
3.2
relative elemental sensitivity factor
coefficient proportional to the absolute elemental sensitivity factor, where the constant of proportionality is
chosen such that the value for a selected element and transition is unity
NOTE 1 Elements and transitions commonly used are C 1s or F 1s for XPS and Ag M VV for AES.
4,5
NOTE 2 The type of sensitivity factor used should be appropriate for the analysis, for example, of homogeneous
samples or segregated layers.
NOTE 3 The source of the sensitivity factors should be given in order that the correct matrix factors or other
parameters have been used.
NOTE 4 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.
3.3
average matrix relative sensitivity factor
coefficient proportional to the intensity calculated for a pure element in an average matrix with 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 The choice of use of atomic concentration or atomic fraction should be made clear.
NOTE 2 The type of sensitivity factor used should be appropriate for the equations used in the quantification process
and for the type of sample analysed, for example, of homogeneous samples or segregated layers.
NOTE 3 The source of the sensitivity factors should be given. Matrix factors are taken to be unity for average matrix
relative sensitivity factors.
NOTE 4 Sensitivity factors depend on parameters of the excitation source, the spectrometer and the orientation of the
sample to these parts of the instrument.
3.4
pure-element relative sensitivity factor
coefficient proportional to the intensity measured for a pure sample of an element with 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 The choice of use of atomic concentration or atomic fraction should be made clear.
NOTE 2 The type of sensitivity factor used should be appropriate for the equations used in the quantification process
and for the type of sample analysed, for example, of homogeneous samples or segregated layers.
NOTE 3 The source of the sensitivity factors should be given in order that the correct matrix factors or other
parameters have been used. Matrix factors are significant and should be used with pure-element relative sensitivity factors.
NOTE 4 Sensitivity factors depend on parameters of the excitation source, the spectrometer and the orientation of the
sample to these parts of the instrument.
4 Symbols and abbreviated terms
AES Auger electron spectroscopy
AMRSF average matrix relative sensitivity factor
ARSF atomic relative sensitivity factor
ERSF elemental relative sensitivity factor
2 © ISO 2004 – All rights reserved

IERF intensity-energy response function
At
S atomic relative sensitivity factor for element i
i
Av
S average matrix relative sensitivity factor for element i
i
E
S elemental relative sensitivity factor for element i
i
RSF relative sensitivity factor
XPS X-ray photoelectron spectroscopy
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). Equations defining these three types of RSF are given in A.3 of Annex A, and the principles on
which these equations are based are given in A.2 of Annex A.
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.3). The matrix correction factors for AES can vary
[1] [2]
between 0,1 and 8 while for XPS they can vary between 0,3 and 3 . 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 may 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. It is
therefore 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 intensity-energy response function (IERF) of the instrument may change with time as
described in Clause 8. Such changes can be detected and corrective actions taken using calibration software
[4]
available from the UK National Physical Laboratory . Alternatively, an analyst can check for possible
changes in IERF 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
In AES, the incident-electron energy and in XPS the X-ray source 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
[5]
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
[6]
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.
NOTE Procedures to check for linear detector response in pulse-counting systems are described in ISO 21270. The
first method described there may 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 by
[7,8]
applying a modulation energy to the analyser or by numerical processing of a measured direct
[9,10]
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.
4 © ISO 2004 – All rights reserved

NOTE The details of the peak attenuation in numerical differentiation and of the Savitzky and Golay differentiation
method in AES can be obtained from References [9] and [10].
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
[11]
subtracted from the measured spectrum (see ASTM E 995 ). The backgrounds most commonly used for
[12] [13] [14]
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 the reference
[11,15]
samples used to determine the ERSFs . See also 6.7.
[11]
NOTE 1 Details of background-subtraction procedures are given in ASTM E 995 .
NOTE 2 Details of peak attenuation in numerical differentiation and of the Savitzky and Golay differentiation method in
AES can be obtained from References [9] and [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 Intensity-energy response function
The intensity-energy response function (IERF) is a measure of the efficiency of the electron-energy analyser
[1,17,18]
in transmitting electrons and of the detector system in detecting them as a function of electron energy .
In general, the IERF 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) may have different
IERFs 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
intervals (for example, every six months) using calibration software available from the UK National Physical
[4]
Laboratory 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.
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 may be determined using Equations (A.5) and (A.6) or one
of the other equations given in Annex A. Equation (A.6) is commonly used but ignores matrix terms. For some
types of relative sensitivity factor, these matrix terms are effectively unity, and may be ignored but, when other
[1] [2]
types of sensitivity factor are used, the matrix factors may be as high as 8 in AES and 3 in XPS . The
accuracy of calculated chemical compositions thus depends significantly on the type of sensitivity factor used.
This is discussed in Annex A.
NOTE 1 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.
NOTE 2 In some applications, it may 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 and reference samples, and the composition is calculated from Equation (A.4) of Annex A. If the two
materials are close in composition, matrix correction factors can be ignored and Equation (A.4) 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 International Standard. Scraping, fracturing or cleaving of the
reference sample, where feasible, may 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
E
The composition of the unknown sample can be obtained from Equation (A.6) using ERSFs, S , supplied by
i
the instrument manufacturer or as measured by the analyst.
9.1.3 Composition determined from atomic relative sensitivity factors or average matrix relative
sensitivity factors
At
The composition of the unknown sample can be obtained from Equation (A.6) using ARSFs, S , or AMRSFs,
i
Av
S .
i
NOTE 1 The ARSFs may be supplied by the instrumental manufacturer or be calculated by the analyst using
Equation (A.9).
NOTE 2 The AMRSFs can be obtained from Equation (A.10) together with Equations (A.11) to (A.34).
9.2 Uncertainties in calculated compositions
[19]
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.
6 © ISO 2004 – All rights reserved

Annex A
(normative)
Equations for relative sensitivity factors
A.1 Symbols and abbreviated terms
AES Auger electron spectroscopy
A atomic mass of element i
i
C number of atoms of element i in the molecular formula of the compound
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
unk
I measured intensity of element i in the unknown sample
i
unk
I measured intensity of element j in the unknown sample
j
ref
I measured intensity of element i in the reference sample
i
ref
I measured intensity of element j in the reference sample
j
I measured intensity of the key material
key
M molecular mass of the compound containing element i
i
N Avogadro constant
A
N atomic density for the average matrix sample
av
N atomic density of element i
i
N number of valence electrons per atom or molecule
v
key
N atomic density of the key element
ref
N atomic density of the reference sample
unk
N atomic density of the unknown sample
n number of identified elements in the unknown sample
Q elastic-scattering correction factor for the average matrix sample
av
Q elastic-scattering correction factor for element i
i
Q (0) elastic-scattering correction factor for element i at emission angle α = 0 with respect to the
i
surface normal
ref
Q elastic-scattering correction factor for element i in the reference sample
i
unk
Q elastic-scattering correction factor for element i in the unknown sample
i
ref
r backscattering factor for element i in the reference sample
i
unk
r backscattering factor for element i in the unknown sample
i
r backscattering factor for the average matrix sample
av
r backscattering factor for element i
i
RSF relative sensitivity factor
E
S elemental relative sensitivity factor for element i
i
At
S atomic relative sensitivity factor for element i
i
Av
S average matrix relative sensitivity factor for element i
i
RSF
S relative sensitivity factor for element i
i
RSF
S relative sensitivity factor for element j
j
Ep
S pure-element relative sensitivity factor for element i
i
Ec
S elemental relative sensitivity factor for element i in a specified compound
i
U over-voltage ratio, given by the ratio of the primary energy to the binding energy of the
electrons in a particular shell or subshell
unk
X atomic fraction of element i in the unknown sample
i
ref
X atomic fraction of element i in the reference sample
i
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
ζ ratio of the transport mean free path to the inelastic mean free path for element i
i
−3
ρ density of the solid (kg⋅m )
ω single-scattering albedo for element i
i
θ angle of incidence of electron beam
8 © ISO 2004 – All rights reserved

Γ a coefficient for determining ζ for element i
i,0 i
Γ a coefficient for determining ζ for element i
i,1 i
Γ a coefficient for determining ζ for element i
i,2 i
Γ a coefficient for determining ζ for element i
i,3 i
λ electron inelastic mean free path for the average matrix sample
av
λ electron inelastic mean free path for element i
i
ref
λ electron inelastic mean free path for element i in the reference sample
i
unk
λ electron inelastic mean free path for element i in the unknown sample
i
A.2 Principles
Quantitative analysis of a homogeneous sample can be accomplished through comparison of an Auger-
unk
electron or photoelectron peak intensity, I , from an unknown sample (the sample material whose surface
i
ref
composition is to be determined) with the corresponding peak intensity, I , from a reference sample with
i
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
[1,20,21,22,23,24]
a single phase and to be atomically flat, the measured intensity ratio is given by :
unk unk unk unk unk
unk
XN Q (1+r )λ
I
ii ii
i
= (A.1)
ref ref ref ref ref ref
IXNQ (1+r )λ
ii i ii
unk ref
where X and X are the atomic fractions of the element i in the unknown and reference samples,
i i
unk ref unk ref
respectively, N and N are the corresponding atomic densities, Q and Q are the corresponding
i i
unk ref
[25]
corrections for elastic-electron scattering , r and r are the corresponding backscattering factors for
i i
unk ref
AES (these terms are zero for XPS), and λ and λ are the corresponding electron inelastic mean free
i i
paths. It should be understood that the elastic-scattering correction terms and the inelastic mean free paths in
Equation (A.1) are determined at the electron energy E for the particular Auger-electron or photoelectron peak
i
of interest. The backscattering factor terms are determined at the electron energy E for the binding energy E
i b,i
corresponding to the initial ionization that was responsible for the Auger peak of element i being measured.
unk
From Equation (A.1), X can be obtained as follows:
i
unk ref ref ref ref ref unk
 
IXNQ (1+r )λ I
unk ref
ii i i i i
XX== F (A.2)
iii
ref unk unk unk unk ref
 
INQ (1+r )λ I
ii ii i
 
where F is a matrix correction factor for element i in the comparison of measurements made with a particular
i
unknown sample and a particular reference sample. For AES, if the reference intensities are for pure elements
ref
[1]
with X values of unity, the F are in the range 0,1 to 8 with one-third of the values outside the range 0,5
i
i
[2]
to 1,5. For XPS, the F are closer to unity and range from 0,3 to 3 .
i
[1,24]
The atomic fraction of the element i in an unknown sample with n identified elements is then given by :
unk

I
i
F
i
ref

I
i
unk 
X = (A.3)
i
unk
n

I
j

F
∑ j
ref

I
j
j=1

This equation must be solved iteratively since the matrix factors depend on the composition of the material.
This composition is, of course, unknown until Equation (A.3) is solved. If, for simplicity, it is assumed that the
atomic densities, backscattering factors and inelastic mean free paths are the same for the two samples
ref
considered in Equation (A.2), the matrix correction factors F = 1 and the reference atomic fractionsX = 1.
i i
For these assumptions, if the unknown sample consists of n elements, the atomic fractions X of these
i
[24]
elements can be obtained from :
unk

I
i

ref

I
i
unk 
X = (A.4)
i
unk
n

I
j

∑
ref

I
j
j=1

While Equation (A.4) 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
unk
elements in the unknown sample are unity. In reality, F values (calculated for X for pure elements) in
i
i
[1]
AES are between 0,1 and 8 (with one-third of the values outside the range 0,5 to 1,5) while for XPS the F
i
[2]
values range from 0,3 to 3 .
ref unk
Values of I are needed for a quantitative analysis to obtain the fractional compositions X from
i i
unk ref
measured values of I for an unknown sample using Equation (A.3) or (A.4). The I values can be
i i
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
ref
halogens that are gases at room temperature), the I values can be estimated from similar measurements
i
with compounds containing the desired elements. Unless corrections can be made for matrix effects [the
matrix correction factor F in Equation (A.3) and the additional matrix effects discussed in B.2], values of
i
ref
[26,27]
I for the same element i from different compounds may 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
[1,7,28,29,30,31,32,33]
particular peak from a selected key element . In XPS, the 1s photoelectron line of fluorine in
lithium fluoride has been generally used for this purpose while the silver M VV Auger-electron line has been
4,5
commonly used in AES.
A.3 Relative sensitivity factors
A.3.1 Introduction
Defining equations are given here for three different types of relative sensitivity factor (RSF) that can be
ref RSF
obtained from I values. The RSFs, S , for an element i in an unknown material containing n elements,
i i
unk
can be used to evaluate the atomic fraction, X , of the element i from the following equation:
i
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unk

IF
ii

RSF

S
unki
X = (A.5)
i
unk
n

IF
jj

∑
RSF

S
j=1 j

RSF ref
Equation (A.5) can be obtained from Equation (A.3) by equating S with normalized values of I . If, for
i i
simplicity, the matrix correction factors are neglected, Equation (A.5) becomes:
unk

I
i

RSF

S
unk i
X = (A.6)
i
unk
n

I
j

∑
RSF

S
j=1 j

The three types of RSF defined below (elemental RSFs, atomic RSFs and average matrix RSFs that are
E At Av
designated S , S , and S , respectively) give analytical results of increasing accuracy. These RSFs can
i i i
RSF
be used for surface analyses in place of S in Equation (A.6).
i
It should be emphasized that the values of all RSFs depend on how the line intensities are measured and on
the experimental conditions such as the parameters of the excitation source, the spectrometer configuration
and the orientation of the sample with respect to these parts of the instrument. Surface analyses made with
particular sets of RSFs shall be based on AES or XPS measurements that were made with the same method
E At
of intensity measurement and with identical experimental conditions. Also, a consistent set of RSFs (S , S
i i
Av
or S ) shall be used in an analysis.
i
A.3.2 Elemental relative sensitivity factors (with no correction for matrix effects)
A.3.2.1 General
As noted in A.2, elemental RSFs can be obtained from measurements made with pure elements or with
compounds containing the desired element, as indicated in A.3.2.2 and A.3.2.3, respectively.
A.3.2.2 Pure-element relative sensitivity factors
Ep
ref
The pure-element relative sensitivity factor (PERSF), S , can be obtained from measurements of S for
i i
the selected element and a measurement of the peak intensity for the selected key material, I :
key
ref
I
Ep i
S = (A.7)
i
I
key
The use of these sensitivity factors in Equation (A.5) requires that the matrix factors F given in Equation (A.2)
i
ref
are evaluated for pure elements (i.e. X = 1). The use of these sensitivity factors in Equation (A.6) leads to
i
[1] [2]
errors in AES between 0,1 and 8 in AES and 0,3 and 3 in XPS .
A.3.2.3 Elemental relative sensitivity factors from measurements with compounds
Ec
The elemental relative sensitivity factor for element i in a specified compound, S , can be obtained from
i
ref
measurements of I for the selected element in that compound and of I for the particular key material:
i key
ref
I
Ec
i
S = (A.8)
i
ref
XI
i key
ref Ec
where X is the atomic fraction of element i in the compound. As noted in A.2, values of S for the same
i i
element i in different compounds may be different due in part to uncorrected matrix factors and in part to
limitations of the experimental measurements (such as different attenuations of peaks of different energies
due to surface contamination on un-cleaned samples or to preferential sputtering effects if the sample
surfaces were cleaned by ion bombardment. It was hoped in early measurements that, by measuring many
compounds, the effects of surface contamination could be averaged out. For example, ratios of RSFs
obtained for two elements from measurements with different compounds containing those elements showed a
[34]
standard deviation of typically 14 % . In addition, evaluations of the RSFs from different data sets indicated
[26,35]
a poor correlation with theoretical predictions .
The use of these sensitivity factors in Equation (A.5) requires that the F matrix factors given in Equation (A.2)
i
ref
are evaluated for compounds where, in each matrix factor, the X values may differ. These matrix factor
i
values may differ from those for pure elements. The use of these sensitivity factors in Equation (A.6) leads to
errors likely to be slightly lower than those given above for pure elements.
A.3.2.4 Sets of elemental relative sensitivity factors
Ep
Ec
Measurements of S and S for a particular instrument and for particular experimental conditions have
i i
E
often been combined to yield a set of elemental RSFs, S .
i
NOTE Instrument suppliers may provide a set of elemental RSFs.
A.3.3 Atomic relative sensitivity factors (with partial correction of matrix effects)
The ratio of atomic densities in Equation (A.2) is generally the most important contribution to the matrix
[20,31]
correction factor F. Atomic relative sensitivity factors (ARSFs) can be defined that include ratios of
i
At
atomic densities to provide in this way a partial correction of matrix effects. The ARSFs, S , can be obtained
i
E
from the elemental relative sensitivity factors obtained from pure elements and from compounds, S , using
i
the following equation:
key

N
At E
SS (A.9)
=
ii

N
i

key
where N and N are the atomic densities for the key element and for element i, respectively.
i
These sensitivity factors are used with Equation (A.6) with errors significantly lower than those for
pure-element relative sensitivity factors.
A.3.4 Average matrix relative sensitivity factors (with nearly complete correction of matrix
effects)
Additional corrections for matrix effects can be made by consideration of all of the parameters in
Av
Equation (A.1). The average matrix relative sensitivity factors (AMRSFs), S , are obtained from elemental
i
E
[1,2,36]
RSFs, S , with the following equation :
i
NQ (1+r )λ
Av E
av av av av
SS= (A.10)
ii
NQ (1+r )λ
ii i i

where the terms N , Q , r and λ are the atomic density, the elastic-scattering correction, the
av av av av
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