ISO 16413:2020

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 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

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
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
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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
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on the ISO list of patent declarations received (see www .iso .org/ patents).
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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

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.
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’.
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

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
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

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
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

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 analysis.
The positions of fringes are unaffected, so thickness analysis can proceed successfully.
Figure 3 — Simulated specular reflectivity of 20,0 nm Si N on bulk Si, with and without
3 4
instrument function
c) If the above recommended condition cannot be met, provided that spill-off does not continue much
beyond the critical angle, fringes in the reflectometry data will still give an accurate measure of
layer thicknesses.
d) That portion of the X-ray beam measured at the detector should not spill off the specimen
perpendicular to the dispersion plane (the dispersion plane is perpendicular to the plane of
Figure 1) in the case where measuring the direct beam intensity is used to align the specimen
accurately over the centre of rotation of ω and 2θ.
4.1.3 Specimen — Requirements and recommendations
4.1.3.1 Specimen — Requirements
The following basic requirements shall be verified.
— XRR is a near-surface-sensitive technique. The specimen shall therefore be handled or treated only
in such ways that the surface is not modified or that any modification is taken into account in the
interpretation of the data. Modifications could include touching, mechanical or chemical polishing.
4.1.3.2 Specimen — Recommendations
The following basic recommendations should be followed.
a) The specimen should be laterally uniform under the beam footprint observed by the detector.
b) The specimen should fill the incident beam from a specimen angle significantly below the critical
angle and for angles above this. It is recommended that the specimen should fill the beam from a
maximum of 75 % of the critical angle.
c) The specimen should not be significantly bowed, or alignment precision and data quality are
compromised. The effect of curvature can be minimized by minimizing the beam footprint on the
specimen. It is recommended that the specimen should fill the beam from a maximum of 75 % of
the critical angle. It may be possible to proceed with data analysis from curved specimens. Some
data fitting models can take specimen curvature into account. Thickness values may be obtained
with sufficient accuracy, but the accuracy of interface widths and density is poorer.
d) The specimen surface and interfaces (where applicable) should be smooth, with a root mean square
(rms) roughness or interface width less than or similar to L /θ . Refer to 5.2.1 for a more detailed
abs c
description of roughness and interface width. Typically, this means σ < 5 nm maximum (above
which, special models must be applied for the analysis) and preferably σ < 3,5 nm. Where the
surface or interfaces are too rough, reflected intensity falls too rapidly with increasing specimen
angle, and reflectometry data give no useful material information. Models used to fit data are also
less reliable at very high interface widths.
4.1.4 Goniometer — Requirements
The following basic requirements shall be verified.
a) A mechanically well-aligned and stable X-ray goniometer is required.
b) For a scanning configuration, the ω and 2θ axes shall be capable of being moved such that intervals
can be maintained in the ratio Δ(2θ) = 2(Δω). Maintaining the ratio to one part in 1 000 is typically
sufficient.
c) The intervals of ω and 2θ shall be capable of being small enough that at least five data points may be
collected over a single thickness fringe. More data points are required for more complex specimens.
d) The specimen height (Z) shall be capable of being set accurately on the centre of rotation of ω and
2θ axes.
e) The specimen stage angle of tilt (χ) shall enable setting the specimen parallel to the incident
beam slits.
4.1.5 Detector — Requirements
The following basic requirements shall be verified.
a) The detector response shall be stable within the time-frame of the experiment.
b) For the specular reflectivity data to be collected in a single scan, the angular resolution of the
detector shall be such as to allow discrimination between the specular and diffuse reflectivity. It is
usual and recommended that the acceptance slits at the detector (where applicable) be set to match
the incident beam width and divergence.
c) Either the detector shall be capable of linear (or linearized) response over the whole reflected
intensity range (several orders of magnitude) or a system of calibrated attenuators to limit the
detected intensity is required over appropriate parts of the data range in order that the detector
can be linear (or linearized) in that range. Data in the different sections are then normalized using
the attenuation factors.
8 © ISO 2020 – All rights reserved

NOTE For the requirements of specular reflectometry, as here, there is no discrimination in the plane
perpendicular to the dispersion plane (i.e. in the plane perpendicular to the diagram in Figure 1). Reflected
intensity is integrated in this direction.
4.2 Instrument alignment
Alignment checks may be part of automated routines available on particular equipment. Slit collimation
of the scattered radiation is assumed. The procedure below describes one approach to align the
instrument 2θ axis
a) Set the X-ray source slit width to minimize spill off (typically 0,1 mm to 0,2 mm in a laboratory
system).
b) Make sure that nothing unwanted obstructs the beam between the source and detector. The
specimen and specimen mounting shall be out of the beam.
c) Start with the detector slits significantly wider than the source slits (many times wider).
d) The incident X-ray beam shall be accurately centred on the centre of rotation of the specimen and
detector axes.
NOTE It is possible, with modern control software, that corrections to axes motions take into account a
non-ideal instrument alignment.
e) Set the detector slit width so that the acceptance angle is similar to the incident beam divergence.
This typically means that the detector slit width is set the same as the source slit width in a
laboratory system or about 20 % wider.
f) Scan the detector angle across the incident beam. The peak should be an approximately symmetric
single maximum. Locate the position of the centre of the peak maximum (approximately at the
centre of mass). Move the detector to this position to set the 2θ = 0 position accurately.
4.3 Specimen alignment
Equipment and its controls may include automatic specimen alignment, data collection and analysis
routines, and may make use of other methods of alignment, e.g. range finders or position monitors.
The procedure below describes one approach to specimen alignment relative to the X-ray beam in an
aligned instrument.
a) The instrument shall be aligned correctly, with appropriate slit widths, with the incident beam
accurately over the centre of rotation and the detector angle 2θ = 0 correctly set on the incident beam.
b) The angle, ω, between specimen surface and incident beam shall be calibrated so that zero sets the
specimen surface approximately parallel to the incident beam.
c) If using a knife-edge, its position in Z, X, and tilt perpendicular to the beam direction (where
available) shall be carefully set. This is done after adjusting the specimen position. The
manufacturer’s recommended operating instructions should be consulted.
d) Mount the specimen on the specimen stage, in a suitable and repeatable orientation as far as
possible, e.g. notch or flat down, or cleaved edge parallel or perpendicular to the beam direction.
e) Where applicable, set the X-ray generator power to the manufacturer’s recommended operating
level. Ensure stable operation.
f) Move χ such that the specimen surface is nominally perpendicular to the plane containing the
source, incident beam and detector.
g) Move the specimen to the X, Y, ϕ position required for the measurement. Make sure that nothing
unwanted (such as the means of specimen mounting) can interfere with the incident or reflected
beams.
h) Initially, make sure that Z is such that the incident beam initially passes unhindered past the
specimen.
i) If required, insert an attenuator in the beam so that the detected intensity is well within the linear
or linearized regime of the detector. Note the full beam intensity, I .
full
j) Move Z to move the specimen into the beam until about one quarter to one fifth of the full beam
intensity is observed, i.e. move Z until I ~I /4 to ~I /5.
observed full full
k) Adjust ω until a maximum intensity is observed. If the maximum intensity is more than half the full
beam intensity, go back to step (j).
l) Scan ω to find more precisely the position of maximum intensity. Set ω here.
m) Now set χ. Move Z until the incident beam is nearly eclipsed (to about 2 % of full beam intensity).
n) Scan χ both sides of the nominal position.
o) Set χ to the minimum of the scan profile.
p) Move Z until I = I /2.
observed full
q) Scan ω again, and set ω at the intensity maximum, which should be I /2.
full
r) Make small adjustments in Z and ω if required until the maximum intensity on an ω scan is I /2.
full
The specimen is now parallel to the incident beam and half way into it. Since the beam is over the
centre of rotation of ω and 2θ, the surface of the specimen is now also over the centre of rotation.
s) It is standard practice on some XRR equipment to fit a knife-edge close to the specimen to define
the beam and reduce scatter, although this is not essential on all equipment for obtaining high
quality data. If a knife-edge is in use, it is set and adjusted at this point. Procedures are specific to
the particular equipment configuration in use, and so are not discussed here.
t) Move 2θ to an angle significantly above the critical angle but such that there is sufficient intensity
in the specularly reflected beam, i.e. well above the background level of the detector. Move ω to
half 2θ.
NOTE In general, moving 2θ to ~0,5° to 1,0° (~1 800 to 3 600 arc sec) will be appropriate if using Cu Kα
radiation or similar.
u) Reflected intensity is generally much weaker than the direct incident beam. Adjust or remove the
attenuator (if applicable) in order that a clear intensity within the linear or linearized response of
the detector is measurable. If the intensity is too low, decrease 2θ until a significant signal appears,
but do not get too close to the critical angle.
v) Scan the ω axis over a sufficient range to see a clear peak as the specimen passes through the
specular reflection condition. Then set ω to the point of highest intensity (Figure 4). This refines
the specimen angle setting on a specular reflection and is more precise than relying on setting the
specimen surface parallel to the incident beam.
w) Go back to step p) and recheck the half beam position. If the half beam position changes, retract the
knife edge (if used) and re-check the procedure from step p) onward.
x) The instrument may have an axis called ω - 2θ or θ - 2θ, in which case it may be helpful to recalibrate
this axis to half the 2θ value. Or it may have an axis called 2θ - θ, in which case it may be helpful to
recalibrate this at the 2θ value. However, the instrument controls may not permit this.
The specimen is now aligned and ready to scan.
10 © ISO 2020 – All rights reserved

Key
X omega, in degrees
Y normalized intensity
Figure 4 — Scan of ω through the specular condition, with 2θ fixed at 1°
5 Data collection and storage
5.1 Preliminary remarks
The X-ray generator shall be operating stably to the manufacturer's specification in an appropriate
environment. Particular care shall be taken on switching on an X-ray generator, to allow a reasonable
time to establish stable working conditions of electronics and X-ray beam. Refer to the manufacturer’s
start-up procedures.
5.2 Data scan parameters
For data collection, ω and 2θ angles are required to be moved or scanned. The specular angular
condition ω = θ shall be fulfilled at each data collection point.
The scanning time is the time necessary to obtain the entire scan. Whenever possible, it is recommended
to calculate, or at least estimate, the scanning time. This is particularly important when multiple scans
or automated scripts are used for the data collection.
The collection time at each point may be kept fixed or variable (accumulated counts) (see 4.5).
5.3 Dynamic range
It is recommended that scans shall begin at ω = θ = 0° and end when reaching the background level.
Following this recommendation will allow the best data analysis. However, to reduce scanning time, for
particular requirements, limited range data scans can be collected.
A reliable alternative method to reduce the scanning time is the use of multiple scans for the data
collection. Multiple scans allow the average of the data collected over different scans, taken at the same
conditions, improving the statistics.
5.4 Step size (peak definition)
5.4.1 Fixed intervals scan
The intervals of ω and 2θ shall be capable of being small enough that at least five data points may be
collected over a single thickness fringe. More data points are required for more complex specimens.
a) Five points on a fringe are sufficient for rapid analysis of a well-defined single-layer specimen
where there is good fringe contrast.
b) Seven points is typically recommended over a single fringe. More data points may be collected if
desired.
c) If the specimen structure has multiple layers giving overlapping and interfering fringes in the
reflectometry data, more points per fringe may be required in order to define the shape accurately
and so enable analysis to distinguish between multiple layers.
Scanning in step size at fixed intervals is rather common.
5.4.2 Continuous scan
Alternatively, instead of a scan in intervals with data collection at each point, ω and 2θ can be
continuously moved at a constant speed, while the data are collected with a fixed sampling rate
(sampling time).
The same conditions on points over fringe as in 5.4.1 shall be fulfilled also in the continuous scan
approach.
This approach is recommended when a simple specimen structure is measured over a large dynamic
range (2θ > 10°) in the presence of a fast-dynamic detector, because it optimizes the collection and
scanning time.
5.5 Collection time (accumulated counts)
The collection time may be kept fixed or variable. The latter is also known as accumulated counts
approach.
In the fixed collection time approach, each data point is collected over the same time interval.
In the accumulated counts approach, the collecting time at each data
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