ISO 16413:2013
(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
ISO 16413:2013 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.
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
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 16413:2013(E)
©
ISO 2013
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ISO 16413:2013(E)
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© ISO 2013
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ISO 16413:2013(E)
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
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ISO 16413:2013(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.
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.
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ISO 16413:2013(E)
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.
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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
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ISO 16413:2013(E)
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.
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ISO 16413:2013(E)
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
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ISO 16413:2013(E)
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.
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ISO 16413:2013(E)
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 relected
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.
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ISO 16413:2013(E)
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.
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ISO 16413:2013(E)
Y
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
10
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.
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ISO 16413:2013(E)
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
...
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