ISO 16413:2020
(Main)Evaluation of thickness, density and interface width of thin films by X-ray reflectometry — Instrumental requirements, alignment and positioning, data collection, data analysis and reporting
Evaluation of thickness, density and interface width of thin films by X-ray reflectometry — Instrumental requirements, alignment and positioning, data collection, data analysis and reporting
This document specifies a method for the evaluation of thickness, density and interface width of single layer and multi-layered thin films which have thicknesses between approximately 1 nm and 1 μm, on flat substrates, by means of X-Ray Reflectometry (XRR). This method uses a monochromatic, collimated beam, scanning either an angle or a scattering vector. Similar considerations apply to the case of a convergent beam with parallel data collection using a distributed detector or to scanning wavelength, but these methods are not described here. While mention is made of diffuse XRR, and the requirements for experiments are similar, this is not covered in the present document. Measurements may be made on equipment of various configurations, from laboratory instruments to reflectometers at synchrotron radiation beamlines or automated systems used in industry. Attention should be paid to an eventual instability of the layers over the duration of the data collection, which would cause a reduction in the accuracy of the measurement results. Since XRR, performed at a single wavelength, does not provide chemical information about the layers, attention should be paid to possible contamination or reactions at the specimen surface. The accuracy of results for the outmost layer is strongly influenced by any changes at the surface. NOTE 1 Proprietary techniques are not described in this document.
Évaluation de l'épaisseur, de la densité et de la largeur de l'interface des films fins par réflectrométrie de rayons X — Exigences instrumentales, alignement et positionnement, rassemblement des données, analyse des données et rapport
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INTERNATIONAL ISO
STANDARD 16413
Second edition
2020-08
Evaluation of thickness, density
and interface width of thin films by
X-ray reflectometry — Instrumental
requirements, alignment and
positioning, data collection, data
analysis and reporting
Évaluation de l'épaisseur, de la densité et de la largeur de l'interface
des films fins par réflectrométrie de rayons X — Exigences
instrumentales, alignement et positionnement, rassemblement des
données, analyse des données et rapport
Reference number
ISO 16413:2020(E)
©
ISO 2020
---------------------- Page: 1 ----------------------
ISO 16413:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
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: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 16413:2020(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Terms and definitions . 1
3.2 Symbols and abbreviated terms. 3
4 Instrumental requirements, alignment and positioning guidelines .4
4.1 Instrumental requirements for the scanning method . 4
4.1.1 Schematic diagrams . 4
4.1.2 Incident beam — Requirements and recommendations . 6
4.1.3 Specimen — Requirements and recommendations . 7
4.1.4 Goniometer — Requirements . 8
4.1.5 Detector — Requirements . 8
4.2 Instrument alignment . 9
4.3 Specimen alignment . 9
5 Data collection and storage .11
5.1 Preliminary remarks .11
5.2 Data scan parameters .11
5.3 Dynamic range.11
5.4 Step size (peak definition) .12
5.4.1 Fixed intervals scan .12
5.4.2 Continuous scan .12
5.5 Collection time (accumulated counts) .12
5.6 Segmented data collection .12
5.7 Reduction of noise .13
5.8 Detectors .13
5.9 Environment .13
5.10 Data storage .13
5.10.1 Data output format .13
5.10.2 Headers .13
6 Data analysis .14
6.1 Preliminary data treatment .14
6.2 Specimen modelling .14
6.2.1 General.14
6.2.2 Interface width models .15
6.3 Simulation of XRR data .16
6.4 General examples .16
6.5 Data fitting .22
7 Information required when reporting XRR analysis .24
7.1 General .24
7.2 Experimental details .24
7.3 Analysis (simulation and fitting) procedures .25
7.4 Methods for reporting XRR curves .26
7.4.1 Independent and dependent variables .26
7.4.2 Graphical plotting of XRR data .26
Annex A (informative) Example of report for an oxynitrided silicon wafer .29
Bibliography .32
© ISO 2020 – All rights reserved iii
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ISO 16413:2020(E)
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 technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
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
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis.
This second edition cancels and replaces the first edition (ISO 16413:2013), of which it constitutes a
minor revision. The changes compared to the previous edition are as follows:
— editorial changes, mainly for a more precise description, e.g. ‘incidence angle’ has been replaced by
‘grazing incidence angle’, ‘intensity’ has been replaced in the appropriate diagrams by ‘reflectivity’ etc.
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 2020 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 16413:2020(E)
Introduction
X-Ray Reflectometry (XRR) is widely applicable to the measurement of thickness, density and interface
width of single layer and multi-layered thin films which have thicknesses between approximately 1 nm
and 1 μm, on flat substrates, provided that the layer, equipment and X-ray wavelength are appropriate.
Interface width is a general term; it is typically composed of interface or surface roughness and/or
density grading across an interface. The specimen needs to be laterally uniform under the footprint of
the X-ray beam. In contrast with typical surface chemical analysis methods which provide information
of the amount of substance and need conversion to estimate thicknesses, XRR provides thicknesses
directly traceable to the unit of length. XRR is very powerful method to measure the thickness of thin
film with SI traceability.
The key requirements for equipment suitable for collecting specular X-ray reflectivity data of high
quality, and the requirements for specimen alignment and positioning so that useful, accurate
measurements may be obtained are described in Clause 4.
The key issues for data collection to obtain specular X-ray reflectivity data of high quality, suitable
for data treatment and modelling are described in Clause 5. The collection of the data is traditionally
conducted by running single measurements under direct operator data input. However, recently data
are often collected by instructing the instrument to operate in multiple runs. In addition to the operator
mode, data can be collected making use of automated scripts, when available in the software program
controlling the instrument.
The principles for analysing specular XRR data in order to obtain physically meaningful material
information about the specimen are described in Clause 6. While specular XRR fitting can be a
complex process, it is possible to simplify the implementation for quality assurance applications to the
extent where it can be transparent to the user. There are many software packages, both proprietary
and non-proprietary available for simulation and fitting of XRR data. It is beyond the scope of this
document to describe details of theories and algorithms. Where appropriate, references are given for
the interested reader.
The information required when reporting on XRR experiments is listed in Clause 7. A brief review of the
possible ways to present XRR data and results is given and, when more than one option is available, the
preferred one is indicated.
This document is not a textbook, it is a standard for performing XRR measurements and analysis.
For a full explanation of the technique, please consult appropriate references [e.g. D. Keith Bowen
and Brian K. Tanner, “X-Ray Metrology in Semiconductor Manufacturing”, Taylor and Francis, London
(2006); M. Tolan, “X-ray Reflectivity from Soft Matter Thin Films“, Springer Tracts in Modern Physics
vol. 148 (1999); U. Pietsch, V. Holy and T. Baumbach, “High Resolution X-Ray Scattering from Thin Films
to Lateral Nanostructures”, Springer (2004); J. Daillant and A. Gibaud, “X-ray and Neutron Reflectivity:
Principles and Applications”, Springer (2009)].
Safety aspects related to the use of X-ray equipment are not considered in this document. During the
measurements, the adherence to relevant safety procedures as imposed by law are the responsibilities
of the user.
© ISO 2020 – All rights reserved v
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INTERNATIONAL STANDARD ISO 16413:2020(E)
Evaluation of thickness, density and interface width of thin
films by X-ray reflectometry — Instrumental requirements,
alignment and positioning, data collection, data analysis
and reporting
1 Scope
This document specifies a method for the evaluation of thickness, density and interface width of single
layer and multi-layered thin films which have thicknesses between approximately 1 nm and 1 μm, on
flat substrates, by means of X-Ray Reflectometry (XRR).
This method uses a monochromatic, collimated beam, scanning either an angle or a scattering vector.
Similar considerations apply to the case of a convergent beam with parallel data collection using a
distributed detector or to scanning wavelength, but these methods are not described here. While
mention is made of diffuse XRR, and the requirements for experiments are similar, this is not covered in
the present document.
Measurements may be made on equipment of various configurations, from laboratory instruments to
reflectometers at synchrotron radiation beamlines or automated systems used in industry.
Attention should be paid to an eventual instability of the layers over the duration of the data collection,
which would cause a reduction in the accuracy of the measurement results. Since XRR, performed at a
single wavelength, does not provide chemical information about the layers, attention should be paid to
possible contamination or reactions at the specimen surface. The accuracy of results for the outmost
layer is strongly influenced by any changes at the surface.
NOTE 1 Proprietary techniques are not described in this document.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions 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 http:// www .electropedia .org/
3.1 Terms and definitions
3.1.1
grazing incidence angle
ω (omega)
angle between the incident beam and the specimen surface
Note 1 to entry: This angle is sometimes called ‘glancing angle’.
© ISO 2020 – All rights reserved 1
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ISO 16413:2020(E)
3.1.2
critical angle
θ
c
angle between the incident beam and the specimen surface, below which there is total external
reflection of X-rays, and above which the X-ray beam penetrates below the surface of the specimen
Note 1 to entry: The critical angle for a given specimen material or structure can be found by using simulation
software, or approximated from the formula θδ≈ 2 where 1 − δ is the real part of the complex X-ray refractive
c
index n = 1 − δ − iβ.
3.1.3
specimen length
dimension of the specimen in the plane of the incident and reflected X-ray beams and in the plane of the
specimen
3.1.4
specimen width
dimension of the specimen perpendicular to the plane of the incident and reflected X-ray beams and in
the plane of the specimen
3.1.5
specimen height
dimension (thickness) of the specimen perpendicular to the plane of the specimen
3.1.6
layer thickness
thickness of an individual layer on the substrate
3.1.7
beam footprint
area on the specimen irradiated by the X-ray
3.1.8
beam spill-off
effect of grazing incidence that involves the reduction of the measured reflected intensity when part of
the incident beam is not intercepted by the specimen, so that the part spills off the specimen
3.1.9
instrument function
analytical function describing the effects of instrument and resolution on the observed scattered X-ray
intensity
3.1.10
reciprocal space
representation of the physical specimen and X-rays where the distance plotted is proportional to the
inverse of real-space distances, and angles correspond to real-space angles
3.1.11
wave vector
k
vector in reciprocal space describing the incident or scattered X-ray beams
3.1.12
scattering vector
q
vector in reciprocal space giving the difference between the scattered and incident wave vectors
3.1.13
dispersion plane
plane containing the source, detector, incident and specularly reflected X-ray beams
2 © ISO 2020 – All rights reserved
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ISO 16413:2020(E)
3.1.14
specular X-ray reflectivity
reflected X-ray signal detected at an angle with the specimen surface as the incident X-ray beam with
the specimen surface: 2θ/2 = ω
Note 1 to entry: The detected, scattered X-ray intensity is measured as a function of either ω or 2θ or q (usually
z
presented against q or i).
z
3.1.15
diffuse X-ray reflectivity
X-ray scatter arising from the imperfection of the specimen
3.1.16
fringe
one of the repeating maxima in reflectometry data which arise from interference of the X-ray waves
Note 1 to entry: Fringe periods are related to the thickness of a layer (or layers) of contrasting electron density.
Multiple layers give rise to series of superposed interfering fringes.
3.1.17
fringe contrast
qualitative description of the height of a fringe (3.1.16) between its minimum and its maximum
Note 1 to entry: The greater the difference between minimum and maximum, the greater the contrast is said to be.
3.1.18
electron density
ρ
e
electrons per unit volume
3 3
Note 1 to entry: XRR typically measures electron density in electrons per nm or per Å .
Note 2 to entry: This can be calculated from mass density.
3.1.19
mass density
ρ
common density (mass per unit volume)
−3 −3
Note 1 to entry: The unit of the mass density is kg m (or g cm ).
3.1.20
absorption length
L
abs
distance over which the transmitted intensity falls to 1/e of the incident intensity
3.1.21
X,Y,Z coordinate system
orthogonal coordinate system in which X is the direction in the plane of the specimen, parallel to the
incident beam when ϕ = 0; Y is the direction in the plane of the specimen, perpendicular to the incident
beam when ϕ = 0; and Z is the direction normal to the plane of the specimen
3.2 Symbols and abbreviated terms
2θ angle of the detected X-ray beam with respect to the incident X-ray beam
ω angle between the incident X-ray beam and the specimen surface
ϕ angle of rotation about the normal to the nominal surface of the specimen
© ISO 2020 – All rights reserved 3
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ISO 16413:2020(E)
χ angle of tilt of specimen about an axis in the plane of the specimen and in the plane of the
incident X-ray beam, X-ray source and detector
θ critical angle
c
λ wavelength of the incident X-ray beam
ρ mass density
ρ electron density
e
k wave vector
q scattering vector
q scalar magnitude of the component of the scattering vector in reciprocal space normal to
Z
the specimen surface (corrected or uncorrected for refraction). q = sin(θ) × 4π/λ
Z
σ root mean square height of the scale-limited surface (according to ISO 25178-2) or
interface width
L absorption length in the specimen
abs
XRR X-Ray Reflectometry or X-Ray Reflectivity
4 Instrumental requirements, alignment and positioning guidelines
4.1 Instrumental requirements for the scanning method
4.1.1 Schematic diagrams
The principal requirements are on the beam size and beam positioning over the coaxial centres of
rotation of specimen (ω) and detector (2θ) axes.
Figure 1 shows a diagram of a basic collimated beam, scanning configuration for an XRR experiment.
The case of a convergent beam and distributed detector is not shown.
4 © ISO 2020 – All rights reserved
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ISO 16413:2020(E)
Key
ω angle between the specimen surface and the incident X-ray beam
2θ angle between the detected beam and 2θ = 0 (the extension of the incident X-ray beam)
(i) X-ray source
(ii) collimated incident x-ray beam
(iii) specimen
(iv) centre of rotation
(v) reflected x-ray beam
(vi) detection system
NOTE The centre of rotation, where incident and reflected beams, the specimen surface and the rotation
axes of ω and 2θ coincide, is highlighted as grey disc.
Figure 1 — Schematic layout of a typical scanning XRR experimental configuration, projected
into the plane of the source, detector, incident and specularly-reflected X-ray beams (the
dispersion plane)
Figure 2 shows a schematic diagram of scanning configuration XRR in a three-dimensional view,
indicating the diffuse scatter as well as the specularly reflected X-ray beam.
Key
ω angle between the specimen surface and the incident X-ray beam
2θ angle between the detected beam (at 2θ = 0) and whichever part of the reflected beam is of interest (the
detected beam)
(i) X-ray source
(ii) collimated incident x-ray beam
(iii) specimen
(iv) diffusely scattered x-rays
(v) specularly reflected x-ray beam
Figure 2 — Schematic diagram showing specular and diffusely reflected X-ray beams
© ISO 2020 – All rights reserved 5
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ISO 16413:2020(E)
4.1.2 Incident beam — Requirements and recommendations
4.1.2.1 Incident beam — Requirements
The following requirements shall apply to the collimated beam, scanning method. Similar considerations
apply to the convergent beam, parallel data collection method.
a) The incident beam shall be stable (or can be compensated) within the time-frame of the experiment.
b) The incident beam shall be nominally monochromatic. The wavelength dispersion dλ shall fulfil
the following condition: dλ < λdθ/tan(θ ) where dθ is the beam divergence and θ is typically the
m m
maximum incidence angle where fringes are still observed.
EXAMPLE If using an incident beam of Cu Kα radiation (λ = 0,154 1 nm) with an angular divergence of
50 arc seconds, and if fringes are to be observed out to an incident angle of 3,5°, then dλ needs to be less than
0,035 nm.
c) If the beam is not sufficiently collimated, the divergence of the beam limits the maximum detectable
thickness. Practically, the maximum measurable thickness is less than λ/6sin(dθ) where dθ is
the beam divergence for a suitable specimen. For typical laboratory equipment, the limit is a few
hundred nm.
d) The incident intensity shall be such as to allow several orders of magnitude intensity range above
background, since reflected intensity falls rapidly above the critical angle. Below the critical
angle, there is total external reflection. Above the critical angle, reflected intensity falls at a rate
−4
proportional to q for a perfectly smooth surface, and more rapidly than this for rough or/and
z
graded surfaces.
4.1.2.2 Incident beam — Recommendations
The following recommendations concern the collimated beam, scanning method. Similar considerations
concern the convergent beam, parallel data collection method.
a) The specimen should be laterally uniform under the area irradiated (the beam footprint) and
observed by the detector. This may be achieved by control of incident and scattered beam slits and/
or, for example, inserting a knife-edge near the specimen.
b) Beam spill-off should be minimized. This is especially important when the specimen angle is near
and above the critical angle. The beam width compared to the specimen length should be such that
there is no beam spill-off for a specimen angle which is above about 75 % (preferably less) of the
critical angle. (See Figure 3.)
NOTE With the specimen parallel to the beam (ω = 0), the beam covers all of the specimen. The beam
footprint varies with incident angle unless slits or knife-edge position are varied through the scan).
1) The maximum acceptable beam width for a given specimen size can then be found by geometry.
2) If there are very small specimens, it may not be practical to meet the recommended
requirements. In this case, the accuracy and precision of densities and interface widths
deduced may be compromised.
3) This is necessary so that the position of the critical angle can be ascertained with reasonable
confidence, so that, if data analysis includes layer density and interface width parameters,
these can be deduced with reasonable accuracy.
4) Some modelling and data fitting software allow the specimen size and beam size to be input,
which allows data fitting where there is significant beam spill-off, but even so it is recommended
that the specimen fill the incident beam from below the critical angle in order to have high
confidence in fitting this region and obtaining good density information.
6 © ISO 2020 – All rights reserved
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ISO 16413:2020(E)
Key
−1
X q , in nm simulated specular reflectivity of 20,0 nm Si N (with
Z 3 4
Y reflectivity 0,6 nm surface roughness) on bulk Si (with 0,3 nm
interface width), without instrument function
simulated specular reflectivity of 20,0 nm Si N (with
3 4
0,6 nm surface roughness) on bulk Si (with 0,3 nm
interface width), with instrument function (0,5 mm
source and detector slits and a 10 mm specimen)
NOTE The position of the critical angle for the small specimen is unclear and possibly apparently shifted,
and the rate of decrease of reflected intensity with increasing specimen angle is affected. This affects the
roughness or interface width deduced if the instrument function is not accurately taken into account in ana
...
FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 16413
ISO/TC 201
Evaluation of thickness, density
Secretariat: JISC
and interface width of thin films by
Voting begins on:
20200311 X-ray reflectometry — Instrumental
requirements, alignment and
Voting terminates on:
20200506
positioning, data collection, data
analysis and reporting
Évaluation de l'épaisseur, de la densité et de la largeur de l'interface
des films fins par réflectrométrie de rayons X — Exigences
instrumentales, alignement et positionnement, rassemblement des
données, analyse des données et rapport
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO
ISO/FDIS 16413:2020(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN
DARDS TO WHICH REFERENCE MAY BE MADE IN
©
NATIONAL REGULATIONS. ISO 2020
---------------------- Page: 1 ----------------------
ISO/FDIS 16413:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
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
CH1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 16413:2020(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms . 1
3.1 Symbols and abbreviated terms. 3
4 Instrumental requirements, alignment and positioning guidelines .4
4.1 Instrumental requirements for the scanning method . 4
4.1.1 Schematic diagrams . 4
4.1.2 Incident beam — Requirements and recommendations . 5
4.1.3 Specimen — Requirements and recommendations . 7
4.1.4 Goniometer — Requirements . 8
4.1.5 Detector — Requirements . 8
4.2 Instrument alignment . 9
4.3 Specimen alignment . 9
5 Data collection and storage .11
5.1 Preliminary remarks .11
5.2 Data scan parameters .11
5.3 Dynamic range.11
5.4 Step size (peak definition) .12
5.4.1 Fixed intervals scan .12
5.4.2 Continuous scan .12
5.5 Collection time (accumulated counts) .12
5.6 Segmented data collection .12
5.7 Reduction of noise .13
5.8 Detectors .13
5.9 Environment .13
5.10 Data storage .13
5.10.1 Data output format .13
5.10.2 Headers .13
6 Data analysis .14
6.1 Preliminary data treatment .14
6.2 Specimen modelling .14
6.2.1 General.14
6.2.2 Interface width models .15
6.3 Simulation of XRR data .16
6.4 General examples .16
6.5 Data fitting .22
7 Information required when reporting XRR analysis .24
7.1 General .24
7.2 Experimental details .24
7.3 Analysis (simulation and fitting) procedures .25
7.4 Methods for reporting XRR curves .26
7.4.1 Independent and dependent variables .26
7.4.2 Graphical plotting of XRR data .26
Annex A (informative) Example of report for an oxynitrided silicon wafer .29
Bibliography .32
© ISO 2020 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO/FDIS 16413:2020(E)
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 technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
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
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis.
This second edition cancels and replaces the first edition (ISO 16413:2013), of which it constitutes a
minor revision. The changes compared to the previous edition are as follows:
— editorial changes, mainly for a more precise description, e.g. ‘incidence angle’ has been replaced by
‘grazing incidence angle’, ‘intensity’ has been replaced in the appropriate diagrams by ‘reflectivity’ etc.
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 2020 – All rights reserved
---------------------- Page: 4 ----------------------
ISO/FDIS 16413:2020(E)
Introduction
X-Ray Reflectometry (XRR) is widely applicable to the measurement of thickness, density and interface
width of single layer and multi-layered thin films which have thicknesses between approximately 1 nm
and 1 μm, on flat substrates, provided that the layer, equipment and X-ray wavelength are appropriate.
Interface width is a general term; it is typically composed of interface or surface roughness and/or
density grading across an interface. The specimen needs to be laterally uniform under the footprint of
the X-ray beam. In contrast with typical surface chemical analysis methods which provide information
of the amount of substance and need conversion to estimate thicknesses, XRR provides thicknesses
directly traceable to the unit of length. XRR is very powerful method to measure the thickness of thin
film with SI traceability.
The key requirements for equipment suitable for collecting specular X-ray reflectivity data of high
quality, and the requirements for specimen alignment and positioning so that useful, accurate
measurements may be obtained are described in Clause 3.
The key issues for data collection to obtain specular X-ray reflectivity data of high quality, suitable
for data treatment and modelling are described in Clause 4. The collection of the data is traditionally
conducted by running single measurements under direct operator data input. However, recently data
are often collected by instructing the instrument to operate in multiple runs. In addition to the operator
mode, data can be collected making use of automated scripts, when available in the software program
controlling the instrument.
The principles for analysing specular XRR data in order to obtain physically meaningful material
information about the specimen are described in Clause 5. While specular XRR fitting can be a
complex process, it is possible to simplify the implementation for quality assurance applications to the
extent where it can be transparent to the user. There are many software packages, both proprietary
and non-proprietary available for simulation and fitting of XRR data. It is beyond the scope of this
document to describe details of theories and algorithms. Where appropriate, references are given for
the interested reader.
The information required when reporting on XRR experiments is listed in Clause 6. A brief review of
the possible ways to present XRR data and results is given and, when more than one option is available,
the preferred one is indicated.
This document is not a textbook, it is a standard for performing XRR measurements and analysis.
For a full explanation of the technique, please consult appropriate references [e.g. D. Keith Bowen
and Brian K. Tanner, “X-Ray Metrology in Semiconductor Manufacturing”, Taylor and Francis, London
(2006); M. Tolan, “X-ray Reflectivity from Soft Matter Thin Films“, Springer Tracts in Modern Physics
vol. 148 (1999); U. Pietsch, V. Holy and T. Baumbach, “High Resolution X-Ray Scattering from Thin Films
to Lateral Nanostructures”, Springer (2004); J. Daillant and A. Gibaud, “X-ray and Neutron Reflectivity:
Principles and Applications”, Springer (2009)].
Safety aspects related to the use of X-ray equipment are not considered in this document. During the
measurements, the adherence to relevant safety procedures as imposed by law are the responsibilities
of the user.
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 16413:2020(E)
Evaluation of thickness, density and interface width of thin
films by X-ray reflectometry — Instrumental requirements,
alignment and positioning, data collection, data analysis
and reporting
1 Scope
This document specifies a method for the evaluation of thickness, density and interface width of single
layer and multi-layered thin films which have thicknesses between approximately 1 nm and 1 μm, on
flat substrates, by means of X-Ray Reflectometry (XRR).
This method uses a monochromatic, collimated beam, scanning either an angle or a scattering vector.
Similar considerations apply to the case of a convergent beam with parallel data collection using a
distributed detector or to scanning wavelength, but these methods are not described here. While
mention is made of diffuse XRR, and the requirements for experiments are similar, this is not covered in
the present document.
Measurements may be made on equipment of various configurations, from laboratory instruments to
reflectometers at synchrotron radiation beamlines or automated systems used in industry.
Attention should be paid to an eventual instability of the layers over the duration of the data collection,
which would cause a reduction in the accuracy of the measurement results. Since XRR, performed at a
single wavelength, does not provide chemical information about the layers, attention should be paid to
possible contamination or reactions at the specimen surface. The accuracy of results for the outmost
layer is strongly influenced by any changes at the surface.
NOTE 1 Proprietary techniques are not described in this document.
2 Normative references
There are no normative references in this document.
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the following terms and definitions 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 http:// www .electropedia .org/
3.1
grazing incidence angle
ω (omega)
angle between the incident beam and the specimen surface
Note 1 to entry: This angle is sometimes called ‘glancing angle’.
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ISO/FDIS 16413:2020(E)
3.2
critical angle
θ
c
angle between the incident beam and the specimen surface, below which there is total external
reflection of X-rays, and above which the X-ray beam penetrates below the surface of the specimen
Note 1 to entry: The critical angle for a given specimen material or structure can be found by using simulation
software, or approximated from the formula θδ≈ 2 where 1 − δ is the real part of the complex X-ray refractive
c
index n = 1 − δ − iβ.
3.3
specimen length
dimension of the specimen in the plane of the incident and reflected X-ray beams and in the plane of the
specimen
3.4
specimen width
dimension of the specimen perpendicular to the plane of the incident and reflected X-ray beams and in
the plane of the specimen
3.5
specimen height
dimension (thickness) of the specimen perpendicular to the plane of the specimen
3.6
layer thickness
thickness of an individual layer on the substrate
3.7
beam footprint
area on the specimen irradiated by the X-ray
3.8
beam spill-off
effect of grazing incidence that involves the reduction of the measured reflected intensity when part of
the incident beam is not intercepted by the specimen, so that the part spills off the specimen
3.9
instrument function
analytical function describing the effects of instrument and resolution on the observed scattered X-ray
intensity
3.10
reciprocal space
representation of the physical specimen and X-rays where the distance plotted is proportional to the
inverse of realspace distances, and angles correspond to realspace angles
3.11
wave vector
k
vector in reciprocal space describing the incident or scattered X-ray beams
3.12
scattering vector
q
vector in reciprocal space giving the difference between the scattered and incident wave vectors
3.13
dispersion plane
plane containing the source, detector, incident and specularly reflected X-ray beams
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ISO/FDIS 16413:2020(E)
3.14
specular X-ray reflectivity
reflected X-ray signal detected at an angle with the specimen surface as the incident X-ray beam with
the specimen surface: 2θ/2 = ω
Note 1 to entry: The detected, scattered X-ray intensity is measured as a function of either ω or 2θ or q (usually
z
presented against q or i).
z
3.15
diffuse X-ray reflectivity
X-ray scatter arising from the imperfection of the specimen
3.16
fringe
one of the repeating maxima in reflectometry data which arise from interference of the X-ray waves
Note 1 to entry: Fringe periods are related to the thickness of a layer (or layers) of contrasting electron density.
Multiple layers give rise to series of superposed interfering fringes.
3.17
fringe contrast
qualitative description of the height of a fringe (3.16) between its minimum and its maximum
Note 1 to entry: The greater the difference between minimum and maximum, the greater the contrast is said to be.
3.18
electron density
ρ
e
electrons per unit volume
3 3
Note 1 to entry: XRR typically measures electron density in electrons per nm or per Å .
Note 2 to entry: This can be calculated from mass density.
3.19
mass density
ρ
common density (mass per unit volume)
−3 −3
Note 1 to entry: The unit of the mass density is kg m (or g cm ).
3.20
absorption length
L
abs
distance over which the transmitted intensity falls to 1/e of the incident intensity
3.1 Symbols and abbreviated terms
2θ 2Theta, the angle of the detected X-ray beam with respect to the incident X-ray beam
ω Omega, the angle between the incident X-ray beam and the specimen surface
ϕ Phi, the angle of rotation about the normal to the nominal surface of the specimen
χ Chi, the angle of tilt of specimen about an axis in the plane of the specimen and in the plane
of the incident X-ray beam, X-ray source and detector
θ Critical angle
c
λ Wavelength of the incident X-ray beam
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ISO/FDIS 16413:2020(E)
ρ Mass density
ρ Electron density
e
k Wave vector
q Scattering vector
q Scalar magnitude of the component of the scattering vector in reciprocal space normal to
z
the specimen surface (corrected or uncorrected for refraction). q = 4π/λ × sin(θ)
z
σ root mean square height of the scale-limited surface (according to ISO 25178-2) or
interface width
L Absorption length in the specimen
abs
XRR X-Ray Reflectometry or X-Ray Reflectivity
Z specimen height
4 Instrumental requirements, alignment and positioning guidelines
4.1 Instrumental requirements for the scanning method
4.1.1 Schematic diagrams
The principal requirements are on the beam size and beam positioning over the coaxial centres of
rotation of specimen (ω) and detector (2θ) axes.
Figure 1 shows a diagram of a basic collimated beam, scanning configuration for an XRR experiment.
The case of a convergent beam and distributed detector is not shown.
Key
ω angle between the specimen surface and the incident X-ray beam
2θ angle between the detected beam and 2θ = 0 (the extension of the incident X-ray beam)
(i) X-ray source
(ii) collimated incident x-ray beam
(iii) specimen
(iv) centre of rotation
(v) reflected x-ray beam
(vi) detection system
NOTE The centre of rotation, where incident and reflected beams, the specimen surface and the rotation
axes of ω and 2θ coincide, is highlighted as grey disc.
Figure 1 — Schematic layout of a typical scanning XRR experimental configuration, projected
into the plane of the source, detector, incident and specularly-reflected X-ray beams (the
dispersion plane)
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ISO/FDIS 16413:2020(E)
Figure 2 shows a schematic diagram of scanning configuration XRR in a three-dimensional view,
indicating the diffuse scatter as well as the specularly reflected X-ray beam.
Key
ω angle between the specimen surface and the incident X-ray beam
2θ angle between the detected beam (at 2θ = 0) and whichever part of the reflected beam is of interest (the
detected beam)
(i) X-ray source
(ii) collimated incident x-ray beam
(iii) specimen
(iv) diffusely scattered x-rays
(v) specularly reflected x-ray beam
Figure 2 — Schematic diagram showing specular and diffusely reflected X-ray beams
4.1.2 Incident beam — Requirements and recommendations
4.1.2.1 Incident beam — Requirements
The following requirements shall apply to the collimated beam, scanning method. Similar considerations
apply to the convergent beam, parallel data collection method.
a) The incident beam shall be stable (or can be compensated) within the time-frame of the experiment.
b) The incident beam shall be nominally monochromatic. The wavelength dispersion dλ shall fulfil
the following condition: dλ < λdθ/tan(θ ) where dθ is the beam divergence and θ is typically the
m m
maximum incidence angle where fringes are still observed.
EXAMPLE If using an incident beam of Cu Kα radiation (λ = 0,154 1 nm) with an angular divergence of
50 arc seconds, and if fringes are to be observed out to an incident angle of 3,5°, then dλ needs to be less than
0,035 nm.
c) If the beam is not sufficiently collimated, the divergence of the beam limits the maximum detectable
thickness. Practically, the maximum measurable thickness is less than λ/6sin(dθ) where dθ is
the beam divergence for a suitable specimen. For typical laboratory equipment, the limit is a few
hundred nm.
d) The incident intensity shall be such as to allow several orders of magnitude intensity range above
background, since reflected intensity falls rapidly above the critical angle. Below the critical
angle, there is total external reflection. Above the critical angle, reflected intensity falls at a rate
−4
proportional to q for a perfectly smooth surface, and more rapidly than this for rough or/and
z
graded surfaces.
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ISO/FDIS 16413:2020(E)
4.1.2.2 Incident beam — Recommendations
The following recommendations concern the collimated beam, scanning method. Similar considerations
concern the convergent beam, parallel data collection method.
a) The specimen should be laterally uniform under the area irradiated (the beam footprint) and
observed by the detector. This may be achieved by control of incident and scattered beam slits and/
or, for example, inserting a knife-edge near the specimen.
b) Beam spill-off should be minimized. This is especially important when the specimen angle is near
and above the critical angle. The beam width compared to the specimen length should be such that
there is no beam spill-off for a specimen angle which is above about 75 % (preferably less) of the
critical angle. (See Figure 3.)
NOTE With the specimen parallel to the beam (ω = 0), the beam covers all of the specimen. The beam
footprint varies with incident angle unless slits or knife-edge position are varied through the scan).
1) The maximum acceptable beam width for a given specimen size can then be found by geometry.
2) If there are very small specimens, it may not be practical to meet the recommended
requirements. In this case, the accuracy and precision of densities and interface widths
deduced may be compromised.
3) This is necessary so that the position of the critical angle can be ascertained with reasonable
confidence, so that, if data analysis includes layer density and interface width parameters,
these can be deduced with reasonable accuracy.
4) Some modelling and data fitting software allow the specimen size and beam size to be input,
which allows data fitting where there is significant beam spill-off, but even so it is recommended
that the specimen fill the incident beam from below the critical angle in order to have high
confidence in fitting this region and obtaining good density information.
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ISO/FDIS 16413:2020(E)
Key
−1
X q , in nm simulated specular reflectivity of 20,0 nm Si N (with
Z 3 4
Y reflectivity 0,6 nm surface roughness) on bulk Si (with 0,3 nm
interface width), without instrument function
simulated specular reflectivity of 20,0 nm Si N (with
3 4
0,6 nm surface roughness) on bulk Si (with 0,3 nm
interface width), with instrument function (0,5 mm
source and detector slits and a 10 mm specimen)
NOTE The position of the critical angle for the small specimen is unclear and possibly apparently shifted,
and the rate of decrease of reflected intensity with increasing specimen angle is affected. This affect
...
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