ISO/TR 23173:2021

Surface chemical analysis - Electron spectroscopies - Measurement of the thickness and composition of nanoparticle coatings

This document provides a description of methods by which the coating thickness and chemical composition of "core-shell" nanoparticles (including some variant and non-ideal morphologies) can be determined using electron spectroscopy techniques. It identifies the assumptions, challenges, and uncertainties associated with each method. It also describes protocols and issues for the general analysis of nanoparticle samples using electron spectroscopies, specifically in relation to their importance for measurements of coating thicknesses. This document focuses on the use of electron spectroscopy techniques, specifically X-ray photoelectron spectroscopy, Auger electron spectroscopy, and synchrotron-based methods. These cannot provide all of the information necessary for accurate analysis and therefore some additional analytical methods are outlined in the context of their ability to aid in the interpretation of electron spectroscopy data.

Analyse chimique des surfaces — Spectroscopies d'électrons — Mesurage de l'épaisseur et de la composition des revêtements de nanoparticules

General Information

• Status: Published
• Publication Date: 24-Jun-2021
• ICS: 07.120 - Nanotechnologies
• Technical Committee: ISO/TC 201/SC 7 - Electron spectroscopies
• Drafting Committee: ISO/TC 201/SC 7 - Electron spectroscopies
• Current Stage: 6060 - International Standard published
• Start Date: 25-Jun-2021
• Completion Date: 25-Jun-2021

Relations

• Consolidated By: ISO/TR 8546:2022 - Hand protection - Guidance for selection and use
• Effective Date: 06-Jun-2022

Overview

ISO/TR 23173:2021 - Surface chemical analysis - Electron spectroscopies - Measurement of the thickness and composition of nanoparticle coatings - describes validated approaches to determine the thickness and chemical composition of coatings on core–shell and related nanoparticle morphologies using electron spectroscopy. The technical report focuses on X‑ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES) and synchrotron‑based electron spectroscopies, identifying assumptions, measurement challenges and sources of uncertainty. It also outlines protocols for nanoparticle sample analysis and lists complementary analytical techniques useful for interpreting electron spectroscopy data.

Key Topics

• Scope and definitions: Terms and symbols consistent with ISO surface‑analysis vocabulary (ISO 18115 series).
• XPS methods: Descriptive formulae for overlayer thickness, numerical modelling, variable excitation energy XPS, inelastic background analysis, near‑ambient‑pressure XPS (NAP‑XPS) and workflows for elemental composition extraction.
• AES methods: Non‑destructive and destructive depth‑profiling, imaging and line‑scan considerations for coated nanoparticles.
• Modelling & software: Use of numerical simulation and specialist packages (example: SESSA) to model XPS intensities and estimate coating thicknesses; Annex A provides an example MATLAB script for XPS modelling.
• Uncertainty & assumptions: Discussion of morphological deviations from ideal concentric core–shell particles, multilayer coatings and the impact of sample format, handling and provenance on surface measurements.
• Complementary analyses: Guidance on supporting techniques (e.g., TEM, SEM, SAXS/SANS, EDX, ICP‑AES, AFM) to improve confidence in thickness and composition interpretation.

Applications

ISO/TR 23173:2021 is directly applicable to laboratories and industries where accurate nanoparticle surface characterisation is critical:

• Nanomaterials research - catalyst design, core–shell syntheses and surface functionalisation studies.
• Biomedical and pharmaceutical development - nanoparticle coatings for drug delivery and biocompatibility.
• Energy and optoelectronics - functional coatings that define device performance.
• Regulatory testing and quality control - verifying coating thickness and surface composition for safety and compliance. The guidance helps users select appropriate electron spectroscopy approaches and combine them with complementary methods to reduce ambiguity in coating thickness and composition measurements.

Who should use this standard

• Surface chemical analysts and metrology labs
• Nanomaterials scientists and R&D teams
• Instrument manufacturers and software developers for XPS/AES modelling
• Regulatory bodies and quality assurance units concerned with nanoparticle characterization

Related Standards

• ISO 18115‑1 / ISO 18115‑2 (surface chemical analysis vocabulary)
• ISO 20579 (sample handling and provenance for nanoparticle surface analysis)
• ISO/TR 14187 (general challenges in surface analysis of nanostructured materials)

Keywords: ISO/TR 23173:2021, nanoparticle coatings, XPS, AES, surface chemical analysis, coating thickness measurement, core‑shell nanoparticles, electron spectroscopies.

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 23173
First edition
2021-06
Surface chemical analysis — Electron
spectroscopies — Measurement of
the thickness and composition of
nanoparticle coatings
Analyse chimique des surfaces — Spectroscopies d'électrons —
Mesurage de l'épaisseur et de la composition des revêtements de
nanoparticules
Reference number
©
ISO 2021
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – 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 . 1
5 Overview . 3
6 X-ray photoelectron spectroscopy. 4
6.1 General . 4
6.2 Coating thickness measurement. 4
6.3 Nanoparticle coating thickness . 5
6.4 Numerical methods . 6
6.5 Descriptive formulae. 9
6.6 Modelling and simulation software .11
6.7 Method comparisons .12
6.8 Inelastic background analysis .15
6.9 Elemental composition .16
6.10 Variable excitation energy XPS .18
6.10.1 General.18
6.10.2 Qualitative depth-profiling . .19
6.10.3 Quantitative depth-profiling .22
6.11 Near-ambient-pressure XPS (NAP-XPS) .23
6.11.1 General.23
6.11.2 Internal structure of bimetallic NP catalysts .24
6.11.3 Measurement of NP's in liquid suspension .24
7 Auger electron spectroscopy .26
7.1 General .26
7.2 Coating thickness measurement.26
7.2.1 General.26
7.2.2 Destructive depth-profiling .27
7.2.3 Non-destructive depth-profiling .27
7.2.4 Elemental composition . .27
7.2.5 Imaging and line scans.28
8 Complementary analysis .30
9 Deviations from ideality .33
9.1 General .33
9.2 Multilayered coatings .33
9.3 Other non-ideal cases .35
Annex A (informative) Example script for modelling of XPS data from nanoparticles .40
Bibliography .42
Foreword
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
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iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis,
Subcommittee SC 7, Electron spectroscopies.
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 © ISO 2021 – All rights reserved

Introduction
Recently, there has been increasing development and use of nanoparticles in a wide range of application
[1]–[7]
areas, including catalysis, medicine, energy, optoelectronics and cosmetics . In particular,
nanoparticles having some form of coating layer, which is present either by design or due to incidental
[8]–
processes such as contamination or oxidation, are among the most commonly studied and utilised
[11]
. An essential part of the characterisation of nanoparticles is the measurement of the surface
properties because a large proportion of the material is at a surface or interface. In the case of coated
nanoparticles, the thickness and composition of the coating has a significant role determining its
functional properties and defines the interaction of the particle with its environment. Many applications
require nanoparticles to have coatings that are specifically designed in order to achieve a desired
level of performance. Measurement of surface composition and coating thickness of nanoparticles
is a challenge to which electron spectroscopies are well suited, due to high surface sensitivity, well-
understood physical principles and accessibility. Such measurements can have a significant dependence
on sample format and condition; sample handling and provenance of nanoparticle samples for surface
[12]
chemical analysis are addressed in ISO 20579 . A general introduction to the challenges of surface
[13]
chemical analysis of nanostructured materials is provided in ISO/TR 14187 .
TECHNICAL REPORT ISO/TR 23173:2021(E)
Surface chemical analysis — Electron spectroscopies
— Measurement of the thickness and composition of
nanoparticle coatings
1 Scope
This document provides a description of methods by which the coating thickness and chemical
composition of "core-shell" nanoparticles (including some variant and non-ideal morphologies) can
be determined using electron spectroscopy techniques. It identifies the assumptions, challenges,
and uncertainties associated with each method. It also describes protocols and issues for the general
analysis of nanoparticle samples using electron spectroscopies, specifically in relation to their
importance for measurements of coating thicknesses.
This document focuses on the use of electron spectroscopy techniques, specifically X-ray photoelectron
spectroscopy, Auger electron spectroscopy, and synchrotron-based methods. These cannot provide all
of the information necessary for accurate analysis and therefore some additional analytical methods
are outlined in the context of their ability to aid in the interpretation of electron spectroscopy data.
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 18115-2, Surface chemical analysis — Vocabulary — Part 2: Terms used in scanning-probe microscopy
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 18115-1 and ISO 18115-2
apply.
ISO and IEC maintain terminological 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/
4 Symbols and abbreviated terms
X subscripts denote the material of the overlayer
Y subscripts denote the material of the core
x subscripts denote a specific photoelectron peak from material X
y subscripts denote a specific photoelectron peak from material Y
I
intensity of electrons arising from a peak, i
i
I intensity of electrons from peak i arising from pure material I
iI,
a
vertical thickness of the overlayer material at a given position
b
vertical thickness of the core material at a given position
effective attenuation length of electrons from peak i travelling through material J
L
iJ,
R
nanoparticle core radius
T
thickness of the overlayer
d
horizontal displacement of a specific line of material
angle between the central vertical axis of the particle and the point of the particle's surface
θ
which is at displacement x
normalised intensity ratio of the intensities of peaks x and y
A
xy,
γ
dimensionless scaling factor
T estimated overlayer thickness for a large sphere
∞
T
estimated overlayer thickness for infinitesimally small particles
T
estimated overlayer thickness for a nanoparticle
NP
AES Auger electron spectroscopy
AFM atomic force microscopy
CSNP core-shell nanoparticle
EAL effective attenuation length
EDX energy dispersive X-ray analysis
ICP-AES inductively coupled plasma atomic emission spectroscopy
IMFP inelastic mean free path
KE kinetic energy
MPA mercaptopropanoic acid
NAP-XPS near-ambient-pressure x-ray photoelectron spectroscopy
NP nanoparticle
SAM scanning Auger microscopy
SANS small angle neutron scattering
SAXS small-angle X-ray scattering
SEM scanning electron microscopy
TEM transmission electron microscopy
2 © ISO 2021 – All rights reserved

TOP trioctylphosphine
UHV ultra-high vacuum
XPS X-ray photoelectron spectroscopy
5 Overview
The methods described in this document are listed by clause and outlined in Table 1. The primary use
detailed is the determination of the thickness of a nanoparticle coating from electron spectroscopy
data, for which three main methods are described, with a specific example given for each. Methods for
coating thickness determination that are described in detail include the use of descriptive formulae
for calculation of coating thicknesses from X-ray photoelectron spectroscopy (XPS) peak intensities;
numerical modelling of XPS intensities from nanoparticles, and general structure and layer thickness
determination by the use of in-depth simulation software. Interpretation of sample composition from
electron spectroscopy data for layered samples is discussed. Rudimentary analysis of the inelastic
background in XPS data is described, alongside the relevant considerations for interpreting inelastic
backgrounds from nanoparticle samples. Discussions of the use and potential benefits of synchrotron-
XPS, near-ambient-pressure XPS (NAP-XPS), and Auger electron spectroscopy (AES) are included, along
with any related issues and considerations. For all methods of analysis, additional characterisation
is required before confident estimates of coating thickness or composition can be made. Therefore, a
range of measurement techniques which are complementary to electron spectroscopy analysis, the
benefits they provide, and any relevant concerns or disadvantages are outlined. A number of alternate
morphologies and deviations from a uniform concentric core-shell structure are described. The effects
these structural variations have on data from such samples are identified, and methods for their
interpretation and analysis are discussed.
Table 1 — Summary of methods and analyses outlined in this document for the measurement of
the thickness and composition of nanoparticle coatings
Clause Details
The use of simple numerical modelling to generate estimated XPS
peak intensities from nanoparticles of a defined morphology. A
6.4 Numerical methods method by which such modelling can be performed is provided,
alongside a simple MathWorks® MATLAB script for performing
such calculations.
The use of methods for calculation of overlayer thicknesses using
empirical or semi-empirical formulae derived from theory or mod-
6.5 Descriptive formulae elling. Typically, these are methods whereby measured data can
be input directly into a set of equations in order to derive a single
calculated coating thickness value.
The use of electron spectroscopy modelling and simulation software.
6.6 Modelling and simulation software SESSA is described in detail as an example, and comparisons between
it and the other methods herein are summarised, with examples.
Overview of the analysis of the inelastic background signal in
6.8 Inelastic background analysis XPS for planar overlayers, and the potential application of this for
coated nanoparticles.
Overview of the extraction of elemental compositions from electron
6.9 Elemental composition spectroscopy data for coated nanoparticles And the challenges
posed by systems with internal structure.
The use of variable-photon-energy XPS (e.g. utilising a synchrotron
6.10 Variable excitation energy XPS light source) for depth profiling of nanoparticles. The capabilities
and applications of such methods are described, with examples.
An outline of the use of NAPXPS to coated nanoparticle systems,
specifically regarding the potential differences between samples
6.11 Near-ambient-pressure XPS (NAPXPS)
analysed in ultra-high vacuum conditions compared to those in an
environment relevant to their application.
Table 1 (continued)
Clause Details
A summary of Auger electron spectroscopy for the analysis of
nanoparticles, including destructive and non-destructive depth
Clause 7 Auger Electron Spectroscopy (AES)
profiling, imaging, and line-scans of individual particles. Several
examples of use are summarised.
A list of supporting measurement techniques which provide infor-
mation that can be useful when analysing electron spectroscopy
Clause 8 Complementary techniques
data from nanoparticles. The benefits and disadvantages of each
suggested technique are outlined.
A summary of how nanoparticle systems might deviate from the ide-
Clause 9 Deviations from ideality alised model of a uniform, concentric, spherical coated nanoparticle,
and the effects of such deviations on electron spectroscopy data.
6 X-ray photoelectron spectroscopy
6.1 General
XPS provides quantitative information of the surface composition of a sample by the collection of
photoelectrons emitted under exposure to an x-ray beam. The information depth of XPS is limited by
the attenuation of the electrons through the sample, which itself is determined by both the properties
of the sample material, and the kinetic energy of the emitted electrons. Lab-based instruments
typically use either aluminium or magnesium K x-rays at a photon energy of 1 486,6 eV or 1 253,6 eV,
α
respectively, this corresponds to a maximum information depth for the elastic photoelectron peaks of
approximately 10 nm. More recently, lab-based instruments with higher energy X-ray sources have also
been developed, with correspondingly larger information depths due to the higher kinetic energies of
the photoelectrons.
Due to this high surface sensitivity, XPS is an inherently nanoscale technique in terms of depth of
analysis and is thus suited to the analysis and characterisation of nano-objects. It is commonly used
to provide quantitative information on the relative concentrations of elements within the surface of a
sample under the assumption of homogeneity, however with a proper understanding of the underlying
theory and appropriate methodology, greater information on the surface structure of samples can be
extracted.
In most lab-based XPS instruments, the analysis area under standard operating conditions is on the
2 2
order of 0,01 mm to 1 mm with some instruments possessing lens-based area-limiting or micro-
,
-4 2
focussed x-ray beams that allow analysis areas down to 10 mm ; thus for samples of nanomaterials
XPS typically serves as a population measurement technique, where the measured intensities are an
average of the material within the analysis area.
Given the high surface sensitivity of XPS, it is also of crucial importance that samples be prepared,
handled, and cleaned with appropriate procedures. The presence of contaminants within a sample
can drastically influence the results of any measurements made. This is of especial importance
for nanomaterial samples, which may often require more careful preparation, or be susceptible to
additional sources of contamination. ISO 20579-4 discusses the issues relating to the handling of nano-
[12]
objects prior to surface analysis .
6.2 Coating thickness measurement
For flat, uniform surfaces measurement of overlayer thickness using XPS has been understood for some
[14]
time. A formula for the calculation of oxide overlayer thicknesses was developed in the 1970s . More
[15]
recently, ISO 14701 ,dealing with the measurement of silicon oxide thickness using XPS, has been
[16]
published. For reporting on measurements of overlayer thicknesses using XPS, ISO 13424 describes
the information to be included. For cases where the overlayer and substrate peaks to be quantified are
[17]
not of similar kinetic energy, a graphical method known as the "Thickogram" was developed. In any
4 © ISO 2021 – All rights reserved

calculation of an overlayer thickness, it is necessary that the peak areas corresponding to the overlayer
and substrate materials are identifiable and measurable.
For samples which are not flat, such methods will be in error due to the effects of sample geometry
on the path-length of electrons through the overlayer. Under the assumption of a uniform overlayer
thickness, a sample with a flat surface oriented for normal emission to the detector presents the
shortest possible direct path for electrons through the overlayer. For a conformal, uniform overlayer
any topography therefore increases this path length, in a manner equivalent to tilting the sample.
Analytical methods to determine the "effective average tilt" of the sample which results from the
[18]
topography have been developed if the topography is either known or can be measured, for example
by atomic force microscopy (AFM). For generic morphologies such as spheres and cylinders, a simpler
[19]
method using the concept of "topofactors" has been shown . In methods of this type, a calculation
is made treating the sample as if flat, and then the relevant "topofactor" is applied to correct for the
[19]–[21]
known topography .
Such methods for measurement of overlayers on topographic samples apply only in the case where the
topography is on the macroscopic scale – that is, they cannot account for topography on the scale of the
electron IMFP’s within the material. At this length scale the volumetric contribution of the coating to the
XPS data becomes significant and the assumption of a continuous underlying substrate becomes invalid.
For nanoparticle samples, the presence of overlayer material on the sides and underside of the particles,
and potentially even particles beneath the outermost layer, can contribute to the measurement result.
6.3 Nanoparticle coating thickness
Several methods for the determination of nanoparticle coating thicknesses from XPS data are
available. These can broadly be categorised into three types: simple numerical modelling, empirically
determined formulae and the use of more rigorous simulation software. When any analysis of XPS data
from nanoparticles is considered however, there are several assumptions which are typically made.
Hereafter, particles conforming to these assumptions are described as "ideal" core-shell particles.
— The analysis area is assumed to be representative of the whole sample, exhibiting no macroscopic
variation. In situations where this is not the case, multiple non-overlapping analysis areas can be
used to assess the effect of any variation.
— Unless specifically accounted for, the nanoparticles are assumed to be randomly deposited, with
[22]
no large-scale ordering . This assumption is not necessary if the analysis method requires, or is
capable of modelling, particles in a specific distribution.
— All of the measured XPS peak intensities are assumed to arise from the nanoparticles, with no
[10]
significant contribution from the substrate or contaminants .
— The core material and coating are each assumed to be uniform in density, i.e. possess no gaps,
density gradients, or similar. It follows from this assumption that the boundary between the core
and coating materials is abrupt, with no mixing layer.
— The core and coating are assumed to form a pair of concentric spheres.
— All the particles in the analysed population are identical in both chemical and physical structure.
— There is no significant contribution to the signal from particles below the outermost layer, i.e. the
electron path lengths do not exceed the particle size.
Depending on the analysis method selected, some of these assumptions might not be necessary, or
deviations can be accounted for. This is particularly true for more advanced simulation methods,
as these can be capable of accounting for many possible structural variations. Because there are a
large number of possible structural variations which are indistinguishable directly from XPS data, it
is important that deviations from the typical assumed case are understood and characterised using
relevant analytical techniques. In some cases, variation in the XPS measurements taken can be used
to corroborate or disprove these assumptions; for example the use of multiple separate analysis areas
to judge sample homogeneity. Sample rotation (with respect to the analyser) may be used to identify
the presence, or lack, of signal arising from the substrate, or to indicate structural discrepancies; for
spherical, randomly deposited particles, angle-dependant XPS should not observe differences in the
relative signal observed from the core and shell. Any discrepancy would therefore be due either to
signal from the substrate, or structural deviations.
In most realistic scenarios, many of these assumptions are invalid to some degree. The effects of
deviations from the assumed morphology are discussed in Clause 9.
6.4 Numerical methods
In general, a numerical modelling approach involves writing a simple script or program to calculate
relative XPS intensities for the core and overlayer materials arising from a nanoparticle. By performing
such calculations programmatically, for a large array of core/shell sizes, and then comparing to
experimental data, an estimate of overlayer thickness can be made. Numerical modelling of the
attenuation of electrons through material can be used in order to generate expected XPS peak intensities
for any given material and can be applied to a broad range of sample morphologies. Despite this, there
[23]–[25]
are relatively few examples of numerical modelling in the literature . An understanding of the
attenuation of electrons through material is required in order to correctly apply this method; this
[14],[17],[19],[22]–[25]
information can be readily found throughout the literature . Likewise, a rudimentary
understanding of the relevant geometrical calculations is necessary, particularly if non-ideal
morphologies are being considered.
Numerical modelling of this type can be performed using a broad range of software. Scientific scripting
environments such as MATLAB are ideally suited, however the procedure can be translated to the
majority of common programming languages and is simple enough to be implemented within common
spreadsheet manipulation software. It is suited for use with most types of nanoparticle system and is
particularly beneficial for systems which cannot be resolved using any descriptive formula, but which
still possess a well-understood geometry.
Typically, the first step in using numerical modelling involves calculating the relative XPS intensities for
the core and overlayer materials arising from a vertical line through the particle. The signal from this
line can be considered equivalent to a stack of planar overlayers. The effects of elastic scattering can be
corrected for by the use of effective attenuation lengths (EALs) in calculations of electron attenuation
through the material. In this case, the intensities for the core and overlayer materials arising from a
single line of material within an ideal particle are given by Formulae (1) and (2):
     
−a −b −a
   
     
     
   
L L L
xX,,xY xX,
     
II=−11ee−−1 e (1)
  
xx,X  
   
   
   
−a  −b 
   
     
L L
yX,,yY
   
II=−ee1 (2)
 
yy, Y
 
 
 
where
X, Y are the materials of the overlayer and core, respectively;
x and y are the specific photoelectron peaks from materials X and Y;
I
is the intensity of electrons arising from a peak, i;
i
I
is the intensity of electrons from peak i arising from pure material I;
iI,
6 © ISO 2021 – All rights reserved

a
is the vertical thickness of the overlayer material at a given position;
b
is the vertical thickness of the core material at a given position;
L
is the effective attenuation length of electrons from peak, i, travelling through material J.
iJ,
For lines which do not pass through the core, where b=0, Formulae (1) and (2) are still valid. For
situations in which one of the elements within a sample is present within both the core and overlayer,
simply summing the outputs of both equations will provide the total intensity for that element.
Figure 1 — Schematic illustration of the equivalence of the XPS intensity observed from an
infinitesimal line at a fixed horizontal displacement to that of the hollow cylinder describing all
lines at identical horizontal displacement
This calculation is repeated for an array of parallel lines through the particle and the intensities for
each line summed across the entire geometry of the particle with appropriate weighting for the area
represented by each line. For spherically symmetrical particles, the relative intensities arising from a
vertical line of material are equivalent to those originating from the hollow cylinder described by the
rotation of this line around the central vertical axis of the particle, as shown in Figure 1. Therefore,
the calculation reduces to a one-dimensional summation of displacements from the central axis of the
particle, with correction factors applied to account for the differing circumferences of the cylinders.
Figure 2 — Schematic of the geometry relevant to calculation of intensities from a specific line
of material at a horizontal displacement x from the central vertical axis of the particle
Figure 2 depicts the relevant geometry for calculating the dimensions of an individual line of material,
It is most efficient to perform the intensity calculations given in Formulae (1) and (2) in a loop from
π
θ = 0 rad to θ = rad. Using this method, the parameters in Figure 2 are related by Formulae (3) to (6).
dR=+()T sinθ (3)
22ab+= ()RT+ cosθ (4)

2 Rd−<, dR
b= (5)


0, dR>

aR=+()Tbcos/θ − 2 (6)
where
R is the nanoparticle core radius;
T is the thickness of the overlayer;
d is the horizontal displacement of a specific line of material;
a is the vertical thickness of the overlayer at displacement d;
b is the vertical thickness of the core at displacement d;
θ is the angle between the central vertical axis of the particle and the point of the particle's surface
which is at displacement d.
If performing the geometry summation in this way (i.e. summing for a range of values of θ) two
correction factors need to be applied. Firstly, the intensities from each individual line will be equivalent
8 © ISO 2021 – All rights reserved

to those from a hollow cylinder of variable radius. The intensity sum therefore needs to be corrected
for the increasing circumference with increasing d. The circumference is linearly proportional to d', and
thus from Formula (3), to sinθ. Secondly, a correction is applied to account for the variation in thickness
of each hollow cylinder, which is equivalent to the differential change in d, d′. As d is proportional to sinθ,
d varies as cosθ. Thus, with both corrections applied, the intensities for each line need to be multiplied
by a factor of sinθcosθ.
An example MATLAB script with commentary explaining the steps is given in Annex A.
This method can be used to generate accurate estimates of overlayer thickness by performing the
calculation over a range of overlayer thicknesses, plotting the resulting intensity ratio, and comparing
to experimentally observed values. Typically the most significant contributor to the uncertainty is
[24],[26]
the ~10 % uncertainty in the estimation of effective attenuation lengths . The method assumes
a straight-line trajectory for all detected electrons, i.e. elastic scattering is corrected for by the use
of EALs. For nanoparticles with organic or low-Z element overlayer materials, this assumption is
reasonably valid. However, for high-Z overlayers, the effect of elastic scattering can become significant.
This method can be extended to cover non-ideal nanoparticle systems such as those with a non-
central core, or significant polydispersity. In such cases it is important to have an otherwise complete
characterisation of the particles. For example, in the case of a non-central core, the diameters of both
the core and the complete particle are required to estimate the displacement of the core. Likewise,
if quantification of the amount of overlayer material for such a system was needed, core diameter
and displacement would be required. In all such cases of particle asymmetry, the distribution of
nanoparticle orientations within the sample deposit is also required and any ordering with respect to
the asymmetry will need to be accounted for. In all cases except fully aligned particles, the full range of
particle orientations will need to be calculated with appropriate geometric weightings.
6.5 Descriptive formulae
The most accessible method to enable the general XPS analyst to efficiently estimate overlayer
[23],[24],[27]
thicknesses is through the use of descriptive formulae , for which the only expertise required
is moderate mathematical literacy. Typically, such methods are either developed by empirically or semi-
[24]
empirically fitting data obtained from a more complex modelling or a simulation-based approach ,
[28]
or in some more constrained conditions, approximate analytical formulae have been derived . The
[24]
most well-known method in current use is the "T " method . This method can be applied simply by
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methodical application of the required formulae, which, for efficiency, can be readily encapsulated by a
simple spreadsheet. The ease of use and repeatability of this method have been demonstrated through
its application by many of the participants of an interlaboratory study into measurement of coating
[10]
thicknesses .
The T method for the determination of shell thicknesses of core-shell nanoparticles is an empirical
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method developed by comparison to numerical modelling, similar to that described previously in 6.4.
Formulae for a distinct set of size regimes or limits were determined, and in combination are used
to produce a general formula for estimation of overlayer thicknesses on nanoparticles. The resulting
expression is encapsulated in Formulae (7) to (11), which are mathematically identical to those in the
[24]
original work , but are slightly simplified.
II
xy ,Y
A = (7)
xy,
II
xX, y
36, 09, 01, 04, 10,,59
07,l44AAn,LL + 2AL L
()
xy, xy, xy,
yX, xX, yX, xX,
T = (8)
∞
36,
A +89,
xy,
 
 
AL
 xy,,xX 
 
TR=+11− (9)
 
 
LL
yX,,xY
  
 
05, 04, 01,
LL L
yX, xY, xX,
γ = (10)
01,
AR
xy,
35,,25
TL ++γγ0,565 RT
()
∞ xX, 0
T = (11)
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35,,25
()11+ ,,80γγL ++ 565γ R
( ))
xX,
where
X and Y are the materials of the shell and core, respectively;
x and y are specific photoelectron peaks from materials X andY;
A
is the normalised intensity ratio of the intensities of peaks x and y;
xy,
I
is the intensity of electrons from peak i;
i
I
is the intensity of electrons from peak i arising from pure material I;
iI,
L
is the effective attenuation length of electrons from peak i travelling through material J;
iJ,
R
is the nanoparticle core radius;
γ
is a dimensionless scaling factor;
T
is the estimated overlayer thickness for a large sphere;
∞
T
is the estimated overlayer thickness for infinitesimally small particles;
T
is the estimated overlayer thickness for a nanoparticle.
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The information required is the particle core size, R, and the measured XPS peak intensities for the
core, I , and overlayer, I . The measured relative intensity from pure reference materials of the core
y x
and the shell, I :I is also recommended, however in cases where this is difficult to obtain, estimated
y,Y x,X
values can suffice. A step by step procedure for applying this method is given below.
[26],[29]–[31]
a) Determine or retrieve values for the effective attenuation lengths L .
iJ,
b) Measure I and I from XPS data.
x y
c) Measure, or estimate, pure material intensities I and I .
xX, yY,
d) Calculate A from Formula (8).
xy,
e) Calculate T , T , and γ using Formulae (8) to (10).
0 ∞
f) Determine T using Formula (11).
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The T method encapsulates the straight-line-approximation for most ideal core-shell particles and
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compensates for the effects of elastic scattering by the use of EALs. Thus, the uncertainty in estimated
overlayer thickness will be greatest for nanoparticle systems in which the coating is formed of high-Z
elements or for which photoelectron peaks with relatively low energies are measured. The magnitude
of elastic scattering effects can be usefully described using the albedo parameter detailed by Powell
[32]
and Jablonski .
For the vast majority of practical cases, the uncertainty due to the use of this method will be less than
[24],[26]
the ~10 % uncertainty in the estimation of EALs . Figure 3 shows the distribution of thicknesses
calculated by T , for 10 000 randomly generated nanoparticles modelled using numerical methods as
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described previously within this document. Parameters for these particles were varied uniformly over
the following ranges: core radii from 1 nm to 100 nm; overlayer thickness from 1 nm to 10 nm; electron
kinetic energies (core or overlayer) from 200 eV to 1 400 eV; and Z values (core or overlayer) from
i
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3-83. Within this regime, more than 80 % of the calculated overlayer thicknesses lie within ±10 % of
the modelled value, and the standard deviation in the ratio of calculated to modelled thickness is ~8 %.
It is worth noting that this dataset will contain a significant number of cases at the extremes of the
physically plausible parameters which are unrepresentative of real particles.
Key
X modelled overlayer thickness (nm)
Y ratio of calculated to modelled overlayer thickness
NOTE Dashed lines indicate ±10 % deviation from the modelled value. More than 80 % of the points fall
within these lines.
Figure 3 — Plot of the ratio of the T calculated overlayer thickness vs the thickness from the
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model, for 10 000 randomly generated nanoparticles
6.6 Modelling and simulation software
In some scenarios, descriptive formulae, or simple numerical modelling using the straight-line
approximation can prove unsuitable. In situations where complex, varied morphologies are known to
exist within a sample, numerical modelling can still be utilised, but will be quite arduous. In situations
where elastic scattering can play a significant role, use of the straight-line approximation, and formulae
based upon it, can become less accurate. To adequately interpret data from such systems, more in-depth
simulations of electron transport and material properties are required. Software packages designed
to allow the general analyst ready access to such simulations are available; the NIST database for the
Simulation of Electron Spectra for Surface Analysis (SESSA) is currently one of the most well-known,
[33]–[36]
and has been shown to be effective for the purpose of nanoparticle analysis .
SESSA itself contains databases for the majority of the parameters required for modelling electron
spectroscopy data, (for example various interaction cross-sections, inelastic mean free paths, lineshapes)
often from multiple sources including theoretical and empirical data. Many values can be adjusted by
the user to fit their particular case, and all values are traceable to their literature source, with many
including a statement concerning their reliability. This allows the user to determine for themselves
their confidence in any given simulation result. The simulation itself is performed using Monte Carlo
calculations based on the ‘trajectory reversal’ model in w
...