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Analysis,Vol.44
MICRO-DIFFRACTION
WITH MONO-CAPILLARIES
M.J. Fransen, J.H.A. Vasterink
and J. te Nijenhuis
Philips Analytical, Lelyweg 1, 7602 EA Almelo, The Netherlands
ABSTRACT
The use of glass capillaries (the so-called mono-capillaries) as incident beam optical module for
X-ray micro-diffraction is evaluated. These mono-capillaries show a gain in intensity with a
typical factor of three over traditional pinhole collimators. Procedures to improve the particle
statistics of the measurement are discussed. Examples are shown on phase identification and
preferred orientation analysis of diamond films grown with a combustion flame and residual
stress analysis of a copper damascene structure grown on a silicon substrate.
INTRODUCTION
When the size of the sample to be investigated is below 1 mm2, the term micro-diffraction is
generally used. It is clear that in this situation not only the time for acquiring a diffractogram will
increase with respect to a standard sample size, but also the number of crystallites participating
in the diffraction process may become too low to meet the isotropy criterion. The recently
introduced glass capillaries (the so-called ‘mono-capillaries’) offer a gain in intensity over the
traditional pinhole collimators, alleviating at least the first of these problems.
In this study we explore the (im)possibilities for micro-diffraction on polycrystalline samples
using mono-capillaries. We will discuss ways to overcome the statistical problem of the limited
number of crystallites. Application examples of phase analysis, preferred orientation analysis and
the determination of residual stress in a thin film are given.
PHYSICAL
PROPERTIES
OF THE MONO-CAPILLARY
A mono-capillary is a hollow glass tube used as incident beam X-ray optical module [ 11. The
point focus of the X-ray source is used. Photons entering the mono-capillary at a small angle
with respect to the inner surface of the capillary are reflected by means of total reflection. In this
way, the mono-capillary acts as a wave guide for X-rays. Compared with pinholes, a larger
portion of the divergence of the source is used. The divergence of the exit beam is around 0.3”,
set by the properties of the glass used. Radiation with a higher energy is absorbed; and thus the
white radiation is strongly suppressed by the mono-capillary.
The final spot size on the specimen will depend on the inner diameter of the mono-capillary
(which can be chosen between 2 mm and 10 pm), the divergence of the exit beam, the distance
from the end of the mono-capillary to the sample, the angle of incidence o and the sample tilt
angle UT.With a 100 pm mono-capillary, a factor of three in intensity is gained over a pinhole
with the same diameter, as measured by recording a rocking curve using a (1 11)-oriented Si
crystal.
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This document was presented at the Denver X-ray
Conference (DXC) on Applications of X-ray Analysis.
Sponsored by the International Centre for Diffraction Data (ICDD).
This document is provided by ICDD in cooperation with
the authors and presenters of the DXC for the express
purpose of educating the scientific community.
All copyrights for the document are retained by ICDD.
Usage is restricted for the purposes of education and
scientific research.
DXC Website
– www.dxcicdd.com
ICDD Website
- www.icdd.com
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PARTICLE
STATISTICS
IN MICRO-DIFFRACTION
In X-ray diffraction analysis on small areas, the number of crystallites available for reflection
may become too low for the assumption of an isotropic distribution. As an example of this we
show in Figure 1 a series of short measurements on the (101) peak of a-quartz. All scans were
recorded with a mono-capillary with an inner diameter of 100 urn. The scans printed with dashed
lines were recorded with a Position-Sensitive Detector (PSD) set at an angle of 26.65” 28 and a
stationary sample. Between the scans, the sample was rotated about 45” around the surface
normal. In each measurement, the contribution from only a few crystallites is visible. The
situation improves dramatically when the sample is rotated continuously around the surface
normal during the measurement (spinning). A further improvement is obtained when the PSD is
used in scanning mode. This has the same effect as an oscillation of the incident beam angle (u.
counts/s
Quartz (101) reflection
"2Theta
Figure 1. Scans on the (101) vejlection of a-quartz powder with different sample orientations
(dashed lines) and a scan obtained with spinning sample and scanning PSD (solid line).
In Figure 1 the result of these improvements can be observed in the measurement drawn with a
solid line. The width of the peak is an addition of the broadening from the crystallites (about 0.1”
20) and the divergence of the mono-capillary (about 0.3” 20). The peak has now a symmetrical
shape with a peak position close to 26.652” 20 as given in ICDD pattern PDF 33-l 161.
It is clear that special attention must be paid to the statistical aspects of the data collection when
setting up a micro-diffraction experiment. Spinning or oscillation of the sample and the use of a
PSD can improve the results dramatically. When these measures cannot be taken or do not yield
an acceptable result, one has to increase the analysis area or to reduce the sample’s particle size.
PREFERRED
ORIENTATION
OF FLAME-GROWN
DIAMOND
PARTICLES
As an example of the use of mono-capillaries for the measurement of preferred orientation we
have a look at the texture in diamond films grown on a molybdenum substrate using a
combustion flame [2]. The method yields diamond films with a circular shape with a total radius
of about 1 cm (see insert in Figure 2). The properties of the film vary strongly between the center
of the film and the outer regions. An important factor determining the morphology of the films is
the nitrogen concentration in the flame. In Ref. [2], the texture in a series of samples grown with
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increasing N2 concentration was studied by analyzing the back-reflected spots from a laser beam
illuminating the sample and by Scanning Electron Microscopy (SEM). In the present paper, the
preferred orientation is determined with X-rays, using a mono-capillary.
As a starting point for the analysis we measured the phases present in the center of the samples
using a 100 pm mono-capillary. The sample was spun during the measurement. A scanning PSD
was used. Two scans were recorded, a symmetrical 8-28 scan and one scan in which the angle of
incidence was fixed to 2”. Both scans are shown in Figure 2. The scans are both shifted in the
vertical direction for clarity: 1.5 counts/s and 0.75 counts/s, respectively.
counts/s
3.5
3.0
2.5
Symmetrical
2.0
scan
Grazing Incidence
A
: C (Diamond)
7Theta
Figure 2. Measurements on the central area of aflame-grown
drawing of the sample is shown in the insert.
diamondfilm. A schematic
Upon comparison of both scans one can clearly observe the layered structure of the sample: in
the symmetrical scan peaks originating from the substrate are clearly visible. The Mo2C signal is
also suppressed in the grazing incidence scan, suggesting that this phase forms the interface
between the substrate and the diamond film.
b)
Figure 3. PoleJigures of the (I 1 I) reflection of diamond, recorded on the central area of six
different samples, each grown with a larger addition of N2 gas.
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We used the diamond (111) reflection at 43.9” 20 for the preferred orientation analysis. In Figure
3, pole figures measured on six samples with an increasing N2 addition are displayed. The
maximum v angle was 90”. In the first three pole figures, labeled a) to c), corresponding to N2
additions of 15 seem, 20 seem and 40 seem respectively, it can be seen that the reflections are
located around w = 55”. This is a clear indication that the diamond film has a fiber texture in the
(001) direction. From the limited number of spots in the ring it can be concluded that the
crystallites are fairly large. When the N:! concentration is increased further from 60 seem through
80 seem to 100 seem (Fig. 4 d)-f)), th e morphology of the film changes: the preferred orientation
almost disappears. From the much smoother pole figure it can be concluded that the crystallite
size decreases as well. This observation is in accordance with the SEM pictures from Ref. [2].
RESIDUAL
STRESS IN COPPER DAMASCENE
STRUCTURE
Copper, historically feared as a highly mobile contaminant in silicon, is now widely used as a
conductor in semiconductor devices. X-ray diffraction can be used to determine the orientation
of the copper grains as well as the residual stress in the Cu film. In general, the structures to be
evaluated are small, so the mono-capillary is a logical choice for this type of samples.
The sample we analyzed was a copper damascene structure with a size of 1 mm x 1.5 mm on a
silicon (001) substrate. We used a 0.5 mm mono-capillary for the recording of the data. The
stress of the sample was measured parallel and perpendicular to the lines of the structure (q = 0”
and <p= 90”, respectively).
The Cu layer is (1 1 1)-oriented and exhibits a fiber texture. In this case, the pole figures of other
reflections of copper will show rings with a constant intensity. These rings are found on tilt
angles w = 22”, 48.5” and 82.4” for the (331) reflection and w = 39.2” and 75” for the (420)
reflection. Figure 4 shows three scans of the (331) reflection at 136.5” 28
counts/s
"2Theta
Figure 4. Measurements of the Cu (331) reflection at different tilt angles.
The scans clearly show a shift in 28 with increasing tilt angle, indicating that the film is in a
stressed state. The rise in intensity with the tilt angle is due the fact that the illuminated area gets
larger, resulting in a larger sample volume in the case of a thin film. Note that due to the absence
of defocusing even the reflection at \c,= 82.4” can well be used. Similar results were obtained for
the (420) reflection.
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In the analysis of the residual stress in the thin film we follow the method described by
Vermeulen et al. [3]. In the case of a thin surface layer with a rotationally symmetric stress state,
i.e. with equal principle stresses, a Sin2 v plot can be made. When a perfect (111) fiber texture is
assumed, the X-ray elastic constants St and %S2 can be calculated from the single-crystal elastic
constants Stt, St2 and SJ~taken from Ref. [4]. This yields St = -1.42 TPa-’ and %S2= 6.65 TPa-’ ,
values that are treated as L&Z-independent. A verification of this assumption can be obtained by
plotting the results as a function of the parameter a, given by:
av=d~~~
(1)
When plotting a y as a function of sin2 Y for different reflections, the results should be on a
straight line. In Figure 5 this plot is shown. It can be seen that the data points originating from
the (420) reflection fit in between the (33 1) data points, showing that St and ?/z& can indeed be
treated as J&Z-indenendent.
0.3622 ,
0.362
II
0 Phi=O”
0.3618
E
% 0.3616
S
3
0.3614
0.3612
0
0.2
0.4
0.6
0.8
1
1.2
Sin’ Psi
Figure 5. Sin2 y plot of the correctedposition
recorded at different tilt angles.
of the (331) and (420) reflections of copper
In order to calculate the residual stress present in the film a value for the strain-free lattice
spacing is necessary. As an estimate we used the as-measured lattice spacing of the (33 1)
reflection at v = 48.5” and converted this to a value for a.using Eq. (1). The mean peak position
of the two measurements at this tilt angle is 136.49” 20, which is close to the value of 136.50“ 28
given by ICDD in reference pattern PDF 04-0836 for high-purity Cu powder.
When all the considerations in the previous paragraph are taken into account, the residual stress
in the Cu film can be calculated, yielding a value of 458 + 14 MPa at cp= 0” and 454 + 14 MPa at
cp= 90”.
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CONCLUSIONS
Mono-capillaries can well be used for the analysis of sub-millimeter spots on a sample. The
intensity gain of a 100 pm mono-capillary over a single pinhole with the same diameter is a
factor of three.
When measuring small spots on a sample, care has to be taken that the number of crystallites that
are brought in reflection condition is not too small. Possible solutions (except increasing the
sample area or decreasing the size of the crystallites) are spinning or oscillation of the sample.
The examples discussed in this paper demonstrate that micro-diffraction analysis with monocapillaries can be performed for several applications, such as phase analysis, with symmetrical or
grazing incidence scans, texture analysis and determination of the residual stress in thin films.
Texture measurements on diamond films grown with combustion flame-assisted chemical vapor
deposition show that increasing the addition of N2 in the flame yields a transition in morphology
of the film: from a small number of large crystallites oriented in the (001) direction to a larger
number of small crystallites with a more random orientation.
Residual stress measurements on a copper damascene structure with an area of 1 mm x 1.5 mm
show that the stress is 458 + 14 MPa parallel and 454 + 14 MPa perpendicular to the lines of the
structure. Due to the absence of defocusing with this geometry, results obtained at tilt angles
exceeding 80” can be used successfully for further analysis.
ACKNOWLEDGEMENT
The authors want to thank J.J. Schermer [5] for providing us with the diamond film samples.
REFERENCES
[l] Mtiller, J.J.; Gomy, H.-E.; Schmalz, J.; Heinemann, U., J. Appl. Cry&. 1995,28, 853-855.
[2] J.J. Schermer and F.K. de Theije, Diamond and Related Materials 1999,9,2127-2139.
[3] A.C. Vermeulen, R. Delhez, Th.H. de Keijser and E.J. Mittemeijer, J. Appl. Phys. 1995, 77
(I 0), 5026-5049.
[4] I.C. Noyan and J.B. Cohen, Residual Stress. Springer Verlag: New York, NJ, 1987.
[5] University of Nijmegen, Nijmegen, The Netherlands
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