Application Of Positron Beams For The Characterization
Of Nano-scale Pores In Thin Films
K. Hirata, K. Ito, Y. Kobayashi, R. Suzuki, and T. Ohdaira
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8565 & 305-8568,
Japan
S. W. H. Eijt, H. Schut, and A. van Veen
Inter/acuity Reactor Institute, Delft University of Technology, Mekelweg 15, NL-2629 JB, Delft, The Netherlands
Abstract. We applied three positron annihilation techniques, positron By-annihilation spectroscopy, positron
annihilation lifetime spectroscopy, and angular correlation of annihilation radiation, to the characterization of nano-scale
pores in thin films by combining them with variable-energy positron beams. Characterization of pores in thin films is an
important part of the research on various thin films of industrial importance. The results of our recent studies on pore
characterization of thin films by positron beams will be reported here.
INTRODUCTION
The control of nano-scale pores is important in
various applications of thin films, examples of which
are high-performance coatings, sensors, separation
membranes, and low-dielectric constant (low-&)
insulators for the next generation of ultralarge-scale
integrated circuits (ULSI). Positronium (Ps), which is
the hydrogen-like bound state between a positron and
an electron, is a powerful probe that can be used in the
characterization of pores in various materials.1 There
are several advantages of positronium porosimetry
over other techniques for pore characterization: it is
nondistractive; it is sensitive to holes of 0.3-50 nm in
size; and it can detect buried, isolated pores that are
undetectable by such conventional techniques as
nitrogen adsorption. In this paper, we explain the
principle and experimental techniques of highsensitivity positronium porosimetry for thin films and
describe several applications to silicon oxide based
thin films.
PRINCIPLE AND EXPERIMENTAL
TECHNIQUE
In many insulating materials, a fraction of positrons
can combine with an electron to form Ps, which is
either spin anti-parallel /rara-positronium (p-Ps) or
spin parallel 6>7t/z6>-positronium (0-Ps). Both p-Ps and
0-Ps can be used for pore characterization.
Para-Ps has an intrinsic self-annihilation lifetime of
125 ps, and it decays into two 511 keV y-rays. When
p-Ps is at rest, the two y-rays are emitted in exactly
opposite directions. If p-Ps has a momentum, the angle
between the two y-rays is deviated, by an amount
proportional to the magnitude of the momentum, from
180 degree. The angular correlation of annihilation
radiation determines the distribution of the deviations
from 180 degree (Fig. la).
In a vacuum, o-Ps annihilates into 3 y-rays (<511
keV) with an intrinsic lifetime of 142 ns. If trapped in
a pore, o-Ps primarily decays into 2 y-rays with a
lifetime shorter than 142 ns upon collision with the
pore wall, where the positron in o-Ps annihilates with
one of the bound electrons having opposite spin. This
2y decay process of o-Ps is called 'pick-off
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
503
annihilation. Since the probability of finding o-Ps on
the pore surface is higher for smaller pores, o-Ps
lifetime is shortened with decreasing pore size.
Therefore, in the case of a trapped o-Ps, the o-Ps
lifetime provides information on the size of the pore
(Fig. Ib). In the presence of open pores, o-Ps trapped
in a pore may escape from the film and undergo the
intrinsic 3y-decay in free space. Hence, the probability
of 3y decay serves as a measure of open porosity (Fig.
Ic).
There are three experimental techniques in
positronium porosimetry. They are angular correlation
of
annihilation radiation
(ACAR), positron
annihilation lifetime spectroscopy (PALS), and
positron Sy-annihilation spectroscopy. As mentioned
above, ACAR gives information on the momentum
distribution of p-Ps, which is sometimes related to
pore connectivity. PALS measures o-Ps lifetime,
which is correlated with the size of a closed or capped
pore. The fraction of Sy-annihilation is obtained from
energy distribution of annihilation radiation, and it
provides information on the open porosity. Combining
of the techniques with variable-energy positron beams
makes it possible to characterize thin films. Variableenergy positron beams suitable for positron 3yannihilation spectroscopy can be obtained with highenergy positrons from a radioactive source.2'3 More
intense beams for ACAR and PALS can be produced
with a linear accelerator and with a nuclear reactor.4"6
based positron beam at the Delft University of
Technology.5'6
Sputter-deposited Silicon Oxide Films 7
Sputter-deposited silicon oxide films have been
applied as sensors 8 and high-performance coatings.9
The former requires open pores to provide paths of gas
molecules, whereas low open porosity is required for
the latter to prevent gas molecules from moving into
materials through open pores. In this study, we
investigated the effect of film deposition condition on
the pore size and structure using positronium
porosimetry.
A
15
10
11
_-a- Sfp?
w"""
1.0 Pa
--•- 1.5 Pa
--•- 2.0 Pa
5
0
o-Ps
5
10
15
20
Positron energy (keV)
FIGURE 2. I3r as a function of incident positron energy for
(a) uncapped and (b) capped samples.
FIGURE 1. Schematic diagram of positronium porosimetry.
(a) 2D-ACAR provides information on the pore style
through p-Ps momentum, (b) Ortho-Ps lifetime is a measure
of the size of closed and capped pores, (c) By-annihilation
of oPs is a probe for open pores.
Silicon oxide films were deposited on Si substrates
at different argon pressures ranging from 0.25 to 2.0
Pa using a magnetron sputtering system (ANELVA
L332S-FHS).7 Not only the as-deposited (uncapped)
samples but also the samples with capping layer were
prepared. A 100 nm thick silicon oxide capping layer
without open porosity was deposited on top of the
films. Figure 2 shows the argon pressure dependence
of the 3y o-Ps decay fraction (I3) as a function of
incident positron energy E (hfE plot) for the
uncapped and capped samples. We can see in Fig. 2a
APPLICATIONS
Here, we present some applications of positronium
porosimetry to silicon oxide based thin films. The data
were obtained with an isotope-based positron beam at
the National Institute of Advanced Industrial Science
and Technology (AIST),2'3 an accelerator-based
intense pulsed positron beam at AIST,4 and a reactor-
504
TABLE 1. Ortho-Ps lifetime and characteristic pore size
( R) for capped samples. Also included in the table is
refractive index at a wavelength of 630 nm of the
uncapped films
that I3r is very small at E>20 keV. This is because
most of the positrons are injected in the Si substrate
and annihilate there without Ps formation.
With decreasing E from 20 keV, more positrons are
implanted into the silicon oxide film. We note that I3r
values at 2-7 keV are different for films prepared at
different argon pressures; I3y significantly increases
with increasing argon pressure from 0.25 to 1.5 Pa.
The enhancement of I3r with argon pressure indicates
that film porosity increases with argon pressure. Fig.
2b clearly shows that the I3r values at 2-7 keV are
reduced by the capping. From this result, we can
conclude that the films have open pores; the o-Ps
atoms that would otherwise escape into the vacuum
through open pores are confined in the pores by the
capping and decay into 2y rays by the pick-off
annihilation process, which reduces I3r
To investigate the effect of argon pressure on pore
size, we conducted PALS of the capped samples at
£=5.5KeV (Fig. 3). The 6>-Ps lifetime obtained by
three-component analysis is summarized in Table 1,
along with refractive index of uncapped films. The
lower refractive index for the films deposited at higher
argon pressure is consistent with higher porosity
mentioned above. Also included in Table 1 are the
characteristic pore sizes estimated from the o-Ps
lifetime using a simple empirical equation between the
pore size and o-Ps lifetime.10 The pore size increases
with increasing argon pressure from 0.25 to 1.5 Pa,
and the characteristic pore size shows a maximum
radius of 2.6 nm at 1.5 Pa. The variation of the pore
size as a function of argon pressure is correlated with
the decrease of the refractive index, which indicates
that film open porosity increases with total porosity.
Ar pressure
(Pa)
0.25
0.5
1.0
1.5
2.0
0-Ps
lifetime (ns)
13.7 ±0.2
28.9 ±0.2
46.1 ±0.2
49.5 ±0.3
42.7 ±0.2
R
(nm)
0.8
1.3
2.3
2.6
2.1
Refractive index
1.457
1.430
1.390
1.376
1.401
Pore-introduced Hydrogen-silsesquioxane
(HSQ) Spin-on-glass Films
In order to develop next-generation ULSI devices,
researchers are trying to produce low dielectric
constant (low-&) materials, which reduce the
interconnect RC (resistance R and capacitance C)
delay. Pore-introduction to material reduces its
dielectric constant, and pore-introduced hydrogensilsesquioxane (HSQ) spin-on-glass film is one of the
candidates for the low-£ material. As pore structures
strongly affect film properties including mechanical
strength and moisture uptake, characterization of the
pore structure is important in the development of new
low-A: materials.
^
—
KN50
4
YU65
— YK48
—*- KI31
Cap ->
(SiOx)
50
100
150
Time (ns)
0
5
10
15
20
Positron energy (keV)
FIGURE 3. Positron lifetime spectra at £=3keV of capped
samples.
FIGURE 4. I3r as a function of incident positron energy for
(a) uncapped and (b) capped samples.
505
HSQ films with a thickness of ca. 500 nm were
fabricated by spin-coating of precursor solutions of
triethoxysilane and porogen with an acidic catalyst on
Si substrates followed by subsequent curing. By
varying the porogen concentration, the samples with
different porosities (KN50, YU65, YK48, and KI31 in
the order of increasing additive concentration) were
prepared.11 Porogen was not added to the precursor
solution for KN50. The atomic density of the films
was determined by Rutherford backscattering
spectrometry (RBS) using a software 12 on the
assumption that the composition of the film was
Si2O3H3, and the film thickness was measured by
spectroscopic ellipsometry. The atomic density
decreases with increasing porogen concentration, so
the total porosity increases in the order of KN50,
YU65, YK48, and KI31. Capped samples were
prepared by sputter-deposition of a silicon oxide layer
with a thickness of 60 nm on top of each sample.
ouu
250
.
"
1
| 200 < \
£150 •
1
^100
50
-
•
:
n
0.8
, , , , . , , , , l,f,, . , , , , . , A ,
0.9
1
1.1
1.2 1.3
Density (g/cm3)
1.4
FIGURE 5. L0.Ps as a function of film atomic density.
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
FIGURE 6. 2D-ACAR spectra for (a) KI31 and (b) KN50 at a positron energy of 3keV. The indications px and py represent
momentum parallel and perpendicular to the sample surface, respectively.
506
SUMMARY
Fig. 4a and 4b show the I3fE plots for the
uncapped and capped samples, respectively. Capping
considerably reduces I3y for the films, except KN50,
and we conclude that these films have open porosity.
As the 0-Ps atoms escape through the open pore to a
vacuum, the escaping ability of o-Ps characterized by
the 0-Ps escaping length L0.Ps gives information about
open pore connectivity.13 L0.Ps can be obtained by data
analysis program for variable-energy positron beam
experiment.14 Figure 5 shows L0.Ps as a function of the
atomic density of the film. The L0.Ps value for the
sample with the highest atomic density (KN50) is ca. 2
nm, which is close to the 0-Ps diffusion length in SiO2
obtained from V-Dr, where D is the Ps diffusion
coefficient in bulk SiO2 (1.45xlO~5 cm2/s) 15 and T is
the 0-Ps lifetime in the HSQ film of the sample (4.0 ns
at E=3 keV). Therefore, the 0-Ps atoms do not escape
through interconnected open pores for KN50. The L0.Ps
value increases as the film atomic density decreases.
The pronounced enhancement in L0.Ps around 1.1
g/cm3 suggests that the open pore interconnectivity
rises rapidly when the density becomes lower than this
value.
Information on the connectivity of open pores in
the films is also provided by two-dimensional
distribution of p-Ps momentum, which is obtained by
the combined use of a variable-energy positron beam
with a two-dimensional ACAR (2D-ACAR) system.
Figure 6 shows 2D-ACAR spectra for KI31 and KN50
samples at E=3 keV. In the figure, px and py represent
momentum parallel and perpendicular to the sample
surface, respectively. A narrow peak in the central
position for each spectrum is due to p-Ps annihilation.
An asymmetric broadening is observed for KI31; the
cross-sectional momentum distribution for py is
broader than that for px. Furthermore, for KI31, the
two-dimensional momentum distribution is offcentered toward the positive py (film surface) direction.
On the assumption that the spectrum is superimposed
by Gaussian components, a centered component due to
p-Ps annihilation in closed pores and an off-centered
component with a momentum of ca. 1.5xlO"3 m0c in
the direction toward the surface due to p-Ps flying
were obtained. Thus, some of the p-Ps atoms formed
in the HSQ film of KI31 fly toward the film surface
direction through interconnected pores. The
asymmetry of 2D-ACAR spectrum is not observed for
KN50, indicating that the sample has no open pore.
The results obtained by 2D-ACAR are consistent with
those by positron 3y-annihilation measurement.
We have demonstrated the usefulness of
positronium porosimetry for the characterization of
nano-scale pores in thin films. The combined use of
variable-energy positron beams with positron 3yannihilation spectroscopy, PALS, and ACAR gives
information on open pores, their connectivity, and the
pore size, which are essential for optimizing the film
fabrication conditions but otherwise difficult to be
characterized by the other technique. The positronium
porosimetry is a powerful tool for the characterization
of nanoporosity in thin films of industrial importance.
ACKNOWLEDGMENTS
We are grateful to Profs. W. Zheng and T. B.
Chang for their help in the study of sputter-deposited
silicon oxide films.
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