ISO 16413:2013

INTERNATIONAL ISO
STANDARD 16413
First edition
2013-02-15
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 2013
© ISO 2013
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ii © ISO 2013 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Terms, definitions, symbols and abbreviated terms . 1
2.1 Terms and definitions . 1
2.2 Symbols and abbreviated terms. 4
3 Instrumental requirements, alignment and positioning guidelines .4
3.1 Instrumental requirements for the scanning method . 4
3.2 Instrument alignment . 9
3.3 Specimen alignment . 9
4 Data collection and storage .11
4.1 Preliminary remarks .11
4.2 Data scan parameters .11
4.3 Dynamic range.11
4.4 Step size (peak definition) .12
4.5 Collection time (accumulated counts) .12
4.6 Segmented data collection .12
4.7 Reduction of noise .13
4.8 Detectors .13
4.9 Environment .13
4.10 Data storage .13
5 Data analysis .14
5.1 Preliminary data treatment .14
5.2 Specimen modelling .14
5.3 Simulation of XRR data .16
5.4 General examples .16
5.5 Data fitting .19
6 Information required when reporting XRR analysis .21
6.1 General .21
6.2 Experimental details .21
6.3 Analysis (simulation and fitting) procedures .22
6.4 Methods for reporting XRR curves .23
Annex A (informative) Example of report for an oxynitrided silicon wafer .26
Bibliography .30
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International
Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies
casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 16413 was prepared by Technical Committee ISO/TC 201, Surface chemical analysis.
iv © ISO 2013 – All rights reserved

Introduction
X-Ray Reflectometry (XRR) is widely applicable to the measurement of thickness, density and interface
width of single layer and multilayered 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)].
Note that proprietary techniques are not described in this International Standard.
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 16413:2013(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 International Standard specifies a method for the evaluation of thickness, density and interface
width of single layer and multilayered 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.
2 Terms, definitions, symbols and abbreviated terms
2.1 Terms and definitions
2.1.1
incidence angle
angle betwen the incident beam and the specimen surface
2.1.2
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.
2.1.3
specimen length
dimension of the specimen in the plane of the incident and reflected X-ray beams and in the plane
of the specimen
2.1.4
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
2.1.5
specimen height
Z
dimension (thickness) of the specimen perpendicular to the plane of the specimen
2.1.6
layer thickness
thickness of an individual layer on the substrate
2.1.7
beam footprint
area on the specimen irradiated by the X-ray
2.1.8
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
2.1.9
instrument function
analytical function describing the effects of instrument and resolution on the observed scattered
X-ray intensity
2.1.10
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
2.1.11
wave vector
k
vector in reciprocal space describing the incident or scattered X-ray beams
2.1.12
scattering vector
q
vector in reciprocal space giving the difference between the scattered and incident wave vectors
2.1.13
dispersion plane
plane containing the source, detector, incident and specularly reflected X-ray beams
2.1.14
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 ω).
z
2.1.15
diffuse X-ray reflectivity
X-ray scatter arising from the imperfection of the specimen
2.1.16
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.
2 © ISO 2013 – All rights reserved

2.1.17
fringe contrast
qualitative description of the height of a fringe 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.
2.1.18
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.
2.1.19
mass density
ρ
common density (mass per unit volume)
−3 −3
Note 1 to entry: It is measured in kg m (or sometimes in g cm ).
2.1.20
absorption length
L
abs
distance over which the transmitted intensity falls to 1/e of the incident intensity
2.1.21
2theta
2Θ
angle of the detected X-ray beam with respect to the incident X-ray beam direction
2.1.22
omega
ω
angle between the incident X-ray beam and the specimen surface
2.1.23
phi
Φ
angle of rotation about the normal to the nominal surface of the specimen
2.1.24
chi
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
2.1.25
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
2.2 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
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 x sin(θ)
z
σ root mean square height of the scale-limited surface (according to ISO 25178-2) or inter-
face width
L Absorption length in the specimen
abs
XRR X-Ray Reflectometry or X-Ray Reflectivity
Z specimen height
3 Instrumental requirements, alignment and positioning guidelines
3.1 Instrumental requirements for the scanning method
3.1.1 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 2013 – All rights reserved

Incident
Specimen
X-ray beam, collimated
ω
2θ = 0
2θ
X-ray source
Detection
system
Relected
Centre of rotation
X-ray beam
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)
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 an orange 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.
X Diffusely
scattered
Specularly re
lected
X-rays
Z Y
X-ray beam
Incident
X-ray beam
2θ
n
2θ = 0
ω
X-ray source
Specimen
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)
Figure 2 — Schematic diagram showing specular and diffusely reflected X-ray beams
3.1.2 Incident beam — Requirements and recommendations
3.1.2.1 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 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 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.
3.1.2.2 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 2013 – All rights reserved

Y
-1
-2
-3
-4
-5
-6
-7
-8
01 23 4 5 6
Key
−1
X q , in nm — simulated specular reflectivity of 20,0 nm Si N
Z 3 4
(with 0,6 nm surface roughness) on bulk Si (with
Y intensity, in a.u.
0,3 nm interface width), without instrument
function
--- simulated specular reflectivity of 20,0 nm Si N
3 4
(with 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.
3.1.3 Specimen — Requirements and recommendations
3.1.3.1 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.
3.1.3.2 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
/θ . Refer to 5.2.1 for a more detailed
(rms) roughness or interface width less than or similar to L
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.
3.1.4 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.
3.1.5 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
8 © ISO 2013 – All rights reserved

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.
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.
3.2 Instrument alignment
Alignment checks may be part of automated routines available on particular equipment. Slit collimation
of the scattered radiation is assumed. The following basic requirements shall be verified.
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 may 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.
3.3 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 2013 – All rights reserved

Y
1 500 1 600 1 700 1 800 1 900 2 000 2 100 2 200
Key
X omega, in arc seconds
Y intensity, in cps
NOTE Since raw data are usually collected in angular units and a raw intensity scale, this figure is not shown
as normalized intensity versus q .
z
Figure 4 — Scan of ω through the specular condition, with 2θ fixed at 3 600 arc seconds (1°)
4 Data collection and storage
4.1 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.
4.2 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).
4.3 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.
4.4 Step size (peak definition)
4.4.1 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.
4.4.2 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 4.4.1 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.
4.5 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 point is stopped when a threshold
number of counts is achieved. In this case, an algorithm taking into account the detector dead time
correction is used to re-normalize the collected data. Whenever possible, a mixed approach is
recommended, where the maximum collection time is fixed and a threshold counts is considered. The
threshold value shall be chosen to grant the linearity of the detector.
For example, because of the fast exponential decay of the specularly reflected intensity, when starting the
data collection from 0°, in the initial part of the scan, a high count rate is registered, then the accumulated
counts limit is a great advantage to reduce the total scanning time. On the contrary, far from the critical
angle region, for high angles or with rough specimens, the fixed collection time approach is envisaged,
otherwise the accumulated count limit would require much longer time to be achieved without any
improvement in the signal to noise ratio.
4.6 Segmented data collection
It is recommended that, whenever possible, a single scan shall begin at ω = θ = 0° and end when reaching
the background level is acceptable to collect data in segment.
A segment, or limited range data scan, is intended as a partial scan over a limited region of the dynamic
range which covers a limited angular range defined by an initial and a final angle specular condition.
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It is recommended that at least one overlapping collected point exists for each segmented scan to proper
allow the joint of the segmented scans and the re-construction of a full range scan.
4.7 Reduction of noise
In data collection, the number of counts follows a Poisson statistic. Controlling the count time becomes
a critical parameter to reduce the noise. However, the minimum noise acceptable for a quantitative XRR
analysis depends on a number of analytical situations, including but not limited to
— the base purpose of the XRR experiment (i.e. quality control versus fundamental scientific research),
— the complexity of the sample (i.e. ideal uniform single layer versus complex multi-material thin film
stack),
— the intensity of the available X-ray source (i.e. laboratory sealed X-ray tube versus synchrotron
source), and
— the time available for the experiment (i.e. high throughput environment versus long-term research
environment).
Because this International Standard cannot account for all potential situations, no quantitative guidance
regarding a minimum acceptable noise for a specific experiment can be given. However, users should
recognize that a reduction in noise by increased count time and/or X-ray intensity will increase the
ultimate reliability of any XRR structural determination.
4.8 Detectors
For most instrumental set-ups using laboratory X-ray sources, counting detectors (based e.g. on NaI
scintillators) are used. For sources with high intensity (e.g. synchrotron radiation), semiconductor
photodiodes can be employed in the photovoltaic mode. The dark current needs to be low (<1 pA) and
constant. All remarks in this document referring to count rates do not apply to these detectors.
4.9 Environment
Care shall be taken of the environment in which the data collection is performed. The general,
conservative principle to adopt is
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