Pore Size Distribution Measurement of
Porous Low-k Dielectrics Using TR-SAXS
Shinichi Terada, Toru Kinashi, and Jennifer Spear*
TECHNOS Co., Ltd. Hirakata, Osaka 5730164 JAPAN
*
TECHNOS International Inc. Tempe, AZ 85283
Abstract. We have developed a method to determine the Pore Size Distribution (PSD) of porous low-k dielectric
materials. The method is based on a modified version of Small Angle X-ray Scattering (SAXS). We fix the incident Xray angle such that it is a larger angle than the total reflection critical angle for the low-k dielectric material, and a
smaller angle than the critical angle for the substrate material. The scattered X-rays are then collected using a two
dimensional position sensitive X-ray detector. Measurements were collected on a set of porous SiLK™, organic, low-k
dielectric, films. The results are compared with Transmission SAXS (T-SAXS) measurements collected using
Synchrotron Radiation (SR) as the X-ray source.
throughput and high precision, high intensity X-ray
irradiation and high Signal-to-Background ratio are
required.
INTRODUCTION
Various sorts of porous low-k dielectric materials
have been developed to meet the dielectric constant
requirements on the ITRS roadmap. A problem for the
integration of porous materials is the lack of fabcompatible methods for pore size distribution (PSD)
measurements. Measuring both the average pore size
and the PSD is important. Determining if large pores
are present is of particular interest, because large pores
can result in defective devices. The goal is to make
PSD measurements in-fab.
This requires high
precision measurements collected using short data
collection times, with a low maintenance sealed X-ray
tube source.
T-SAXS and GISAXS
When SAXS measurements are collected on a thinfilm sample on a thick substrate, there are two typical
X-ray optical arrangements.
SB
S
T
S
R
Film
Substrate
PRINCIPLE OF TR-SAXS
(a)
The objective was to choose an instrumental
configuration that gives a wide range of scattering
momentum, high data precision, and high throughput.
To obtain data over a wide range in scattering
momentum, data needs to be collected over a wide
range of scattering angle. To achieve both high
™
(b)
FIGURE 1. T-SAXS (a) and GISAXS (b) arrangements
T:Transmission, S:Scattering by pores, SB:Scattering by
Substrate, R:Reflection
Fig.1(a) shows the T-SAXS arrangement. In this
case, X-rays reach the film after transmission through
the substrate. Most of the X-ray photons are absorbed
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546
θ Min > θ i > θ c − F
by the substrate. X-ray photons scattered by the
substrate become a source of the background in the
measurement. Optimization of the X-ray wavelength
used in T-SAXS is necessary since decreasing the
wavelength both increases transmission through the
substrate and increase the probability of Compton
scattering in the substrate.
For PSD determination of porous low-k films, TSAXS measurements collected with SR [1] and
GISAXS measurements collected with X-ray tube
sources [2] have been applied.
Fig.1(b) shows the Grazing Incidence SAXS
(GISAXS) arrangement. X-ray irradiation is
performed on the film side of the substrate. Fig. 2
shows the X-rays components coming out from the
sample. For simplification, secondary reflections and
refractions at the film surface are ignored in the figure.
The angle of incidence θi needs to satisfy following
equation.
θ i > θ c−F
Use of Total Reflection at the Interface
To increase the maximum pore size that can be
measured in the PSD measurements, only the
scattering from pores caused by the X-rays that have
been reflected by the interface is detected. To
maximize the reflection at the interface, the angle of
incidence is set below the total reflection critical angle
for the substrate as shown in Fig.3. Hereafter, we call
this method Total Reflection SAXS (TR-SAXS). The
angle of incidence for TR-SAXS must satisfy the
following equation.
(1)
where θc-F is the total reflection critical angle for the
film material. In Fig.2, scattering X-rays that have
different scattering angle are shown as S1, S2 and S3.
Scattering angle θS1, θS2 and θS3 satisfy following
equations.
2θ S1 > 2θ i
2θ i > 2θ S 2 > θ i
θ i > 2θ S 3
θ c−S ≥ θ i > θ c− F
(2)
To maintain the total reflection condition, the angle
of incidence is fixed during measurements. Using a
fixed angle of incidence allows simultaneous detection
of scattered X-rays, with a range of scattering angles,
using a position sensitive X-ray detector.
(3)
(4)
Table 1 shows a comparison of T-SAXS, GISAXS
and TR-SAXS.
SS
R1
S
S1
R1
SB
θi
2θS2
Film
Substrate
θi
R2
S2
Film
θi
θi
Substrate
S3
2θS3
R2
2θs
θi
2θS1
(6)
where θc-S is the total reflection critical angle for the
substrate.
Thus, the X-ray scattering that has a scattering
angle greater than the incidence angle is detected at a
higher exit angle than the reflections. Therefore, the
fundamental lower limit of scattering angle that can be
detected by this method is the critical angle of total
reflection for the thin film.
SS
(5)
θi
FIGURE 3. X-rays Components coming out of the sample
(TR-SAXS) R1:Surface reflection R2:Interface reflection
S: Scattering by pores SS: Scattering by surface roughness
FIGURE 4. X-rays Components coming out of the sample
(GISAXS) R1:Surface reflection R2:Interface reflection
S1,S2,S3: Scattering by pores SS: Scattering by surface
roughness SB: Scattering by substrate
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TABLE 1. Comparison of various SAXS methods
T-SAXS
GISAXS
TR-SAXS
Absorption by
++
Substrate
Scattering by
++
+
Substrate
Lowest Limit of
0
0
θc-F
Scattering Angle
for Detection
X-ray Optics Arrangement
Fig.4 shows the X-ray optics arrangement used for
TR-SAXS. The point focus of a sealed X-ray tube was
chosen because of its advantages over the line focus.
Fig.5 shows a TR-SAXS image. The image
includes the radial SAXS signal and the planar
scattering signal from surface roughness. There is only
a small region of the diffraction cone where scattering
from roughness overlaps the scattering from the pores.
When the line focus is used, there is a much larger
region of overlap between the scattering from pores
and the scattering from roughness. Therefore, the point
focus configuration was chosen so the SAXS intensity
distribution can be calculated excluding the region of
data affected by scattering from roughness.
EXPERIMENTS
Another reason to choose the point focus
configuration was to increase the detection efficiency
of the high angle data. The scattering at higher angles
is weaker than at lower angle and occurs on a cone of
a larger radius. With the arrangement shown in Fig.4,
about half of the diffraction cone can be detected for
high scattering angles. In a contrast, Fig 6 shows the
small slice of the diffraction cone that can be detected
when the line focus of an x-ray tube is used with
parallel beam geometry. In this case a soller collimator
stops most of the scattering X-ray photons that have
higher scattering.
FIGURE 4. Arrangement of Point Focus TR-SAXS
Detected
(Others Lost)
Reflection
Beam Center
Reflection
beam center
Angle Accepted by
Soller Collimator
X-ray Scattering caused
by surface roughness
FIGURE 6. Loss of Scattering X-rays by Soller Collimator
FIGURE 5. TR-SAXS Image
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X -ray Intensity (arb.U nit)
Data Processing
The scattering momentum distribution of the
scattering X-ray intensity is calculated from the
collected image. First, the pixel which represents
reflected beam center is determined analyzing X-ray
image collected using beam attenuator. Second, for
each pixel which is not masked, distance r from the
reflected beam center is calculated and then converted
to scattering momentum q following the equations,
r = p ⋅ (i − i0 ) 2 + ( j − j0 ) 2
(7)
200
150
100
50
0
0.0
0.2
0.4
0.6
0.8
1.0
q (nm -1)
r
(8)
l
4π sin θ
tan 2θ =
q=
250
FIGURE 7. Scattering X-ray Intensity Distribution
(9)
λ
where, p is the pixel pitch of the X-ray image sensor,
(i,j) is the index of the pixel, (i0,j0) is the pixel index of
the reflected beam center, l is the distance between the
position of X-ray reflection and the detector, θ is the
scattering angle and λ is the wavelength of the Xrays. For the integration, the area on the detector
which is close to the diffraction plane is masked since
surface roughness scattering is dominant in this area.
This mask area is shown as dark area in Fig.5. Fig.7
shows the distribution calculated from the image
shown in Fig.5.
RESULTS AND DISCUSSIONS
Measurements were done on a set of porous SiLK,
organic, low-k, film samples. Another set of samples
prepared using the same conditions was measured
using T-SAXS at the Argonne SR facility.
Table 2 shows the average pore diameter obtained
using TR-SAXS and T-SAXS. Fig.8 shows the PSD
determined from the TR-SAXS data, of films that were
processed at normal temperature with varying amounts
of poragen loading. Fig.9 shows the PSD of films
with the same amounts of poragen loading (30%) that
were processed at various temperatures.
The pore size distribution and the void fraction
were determined by fitting data with a theoretical
model after backgrounds were subtracted from the data.
The applied theoretical model was the local monodisperse approximation [3],
In Fig.8, the results on the samples which have 2030% poragen loading show very similar PSD. Also,
the average pore size values shown in Table 2 are in
good agreement with the T-SAXS results. The PSD
results for the 10% poragen loading sample differ from
the other samples. Additionally, the average pore size
does not compare as well with the T-SAXS result. It is
believed that the fitting calculation was not as
successful for this wafer due to low signal-tobackground ratio. SAXS signal amplitude is
proportional to the void fraction, which is the lowest in
the case of 10% poragen loading.
∞
dσ
= A∆ρ 2 ∫ Φ (q, R) 2 S (q, R) N ( R)dR (10)
dΩ
0
where, Φ (q, R ) and S ( q, R ) were the form factor
of a sphere of radius R , and the inter-particle
structure factor of the mono-disperse hard-sphere
model. The probability distribution N ( R ) was
assumed to be a log-normal distribution. The fitted
parameters were, the effective intensity ( A∆ρ ) , the
volume fraction of the hard-spheres, and two
parameters (a peak radius and a 'width') of the lognormal distribution.
2
As shown in Fig.9, the TR-SAXS results show
changes
in PSD for the different processing
temperatures.
549
diameter and the void fraction were 2.04% and 2.06%
respectively.
TABLE 2. Comparison of results using TR-SAXS
and T-SAXS with SR
Poragen
Processing
Average Pore
Temp.
Loading
Diameter (nm)
(%)
TRSR
(oC)
SAXS
1
9.0
8.6
Optimal
30
2
8.9
8.9
Optimal
25
3
9.3
9.2
Optimal
20
4
6.7
9.3
Optimal
10
5
10.0
9.8
+115
30
6
10.8
12.4
+135
30
7
10.6
12.9
+135
20
8
7.6
13.1
+135
10
9
12.3
15.7
+250
30
10
9.8
15.6
+250
20
11
9.9
15.6
+250
10
TABLE 3. Repeatability of Average Pore Size
(5minutes acquisition, 5 measurements)
Average Pore
Void Fraction
Diameter (nm)
(%)
Average
8.9
32.0
Maximum
9.2
32.8
Minimum
8.7
31.0
Standard
0.182
0.660
Deviation
Relative Standard
2.04
2.06
Deviation (%)
CONCLUSIONS
0.2
Optimal Processing Temp.
Probability
0.15
The GISAXS arrangement was modified to TRSAXS to extend the detectable scattering angle, which
in turn increases the largest pore diameter that can be
detected. The instrument was built using all fab-ready
parts such as a sealed X-ray tube. Measurements were
collected on a set of porous, organic, low-k, film
samples. The results have good agreement with TSAXS using a SR X-ray source. The repeatability
achieved is 2% R.S.D. for 5 minute data acquisition
time.
30%
25%
20%
10%
0.1
0.05
0
0
5
10
15
20
25
Pore Diameter(nm)
ACKNOWLEDGMENTS
FIGURE 8. Calculated PSD for samples processed at
the optimal temperature
Probability
0.2
Technos would like to thank the Dow Chemical
Company for providing a well controlled set of porous
SiLK wafers with different void fractions and average
pore sizes.
Poragen Loading 30%
optimal
+115
+135
+250
0.15
0.1
REFERENCES
0.05
1. Huang, E., Toney, M., Lurio, L.B., Volksen, W., Hawker,
C.J., Hedrick, J., Lee, V., Magbitang, T., Mecerreyes, D. ,
Brock, P., and Miller, R.D., “Pore Size Distributions in
Nanoporous Methylsilsesquioxanes (MSSQ) Films for
Low Dielectric Constant Layers”, an APS Annual Report
from IMMYT-Whitehead-CAT, Argonne, Argonne
National Laboratory, 2000
0
0
5
10
15
20
25
Pore Diameter(nm)
FIGURE 9. Calculated PSD for samples that have
30% poragen loading and were processed at varying
temperatures
2. Kawamura, S., Maekawa, K., Ohta, T., Omote, K.,
Suzuki, R., Ohdaira T., Tachibana, M., and Suzuki K.,
Proceedings of the 2001 International Interconnect
Technology Conference, 2001, pp. 195-197.
Table 3 shows the repeatability of average pore
size and void fraction determined using TR-SAXS.
These measurements were done on the sample with
30% poragen loading and an 11 nm target pore
diameter. The relative standard deviation of the pore
3. Pedersen, J. S., J. Appl. Cryst. 27, 595 (1994).
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