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SURFACE AND INTERFACE ANALYSIS
Surf. Interface Anal. 29, 330–335 (2000)
Experimental determination of electron effective
attenuation lengths in silicon dioxide thin films
using synchrotron radiation
I. Data analysis and comparisons
M. Suzuki,1 * H. Ando,1 Y. Higashi,1 H. Takenaka,1 H. Shimada,2 N. Matsubayashi,2
M. Imamura,2 S. Kurosawa,1 S. Tanuma3 and C. J. Powell4
1
Center for Materials Development and Analytical Technology, NTT Advanced Technology Corporation,
Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
2
National Institute of Materials and Chemical Research, Tsukuba, Ibaraki 305-8565, Japan
3
Japan Energy Co., Ltd., Niizo-Minami, Toda, Saitama 335-8503, Japan
4
National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
We have measured effective attenuation lengths (EALs) of 140–1100 eV electrons in ultrathin silicon dioxide
layers using synchrotron radiation. These EALs were generally smaller than those reported previously,
although there was agreement with the values measured by Hochella and Carim (Surf. Sci. Lett. 1988; 197:
L260). Our measured EALs were ~37% smaller than the corresponding inelastic mean free paths calculated
from optical data by Tanuma et al. Part of this difference is believed to be due to uncertainty in measurements
of the oxide thickness and the remainder to the effects of elastic electron scattering. Copyright  2000 John
Wiley & Sons, Ltd.
KEYWORDS: effective attenuation length; silicon dioxide; synchrotron radiation; photoemission; inelastic mean free path
INTRODUCTION
Values of effective attenuation lengths (EALs) and inelastic mean free paths (IMFPs) of electrons are needed in
quantitative investigations by Auger electron spectroscopy
(AES) and x-ray photoelectron spectroscopy (XPS). The
EALs have been measured by the overlayer-film method,
and semi-empirical expressions have been published for
EALs in different materials.1,2 The IMFPs have been calculated from experimental optical data for many materials
by Tanuma et al.,3 – 5 and have been utilized to develop the
TPP-2M predictive IMFP equation.3 The IMFPs can be
measured by elastic peak electron spectroscopy, and an
evaluation of calculated and measured IMFPs has been
published recently.6 Although IMFPs are expected to be
greater than the corresponding EALs by up to ¾40% due
to the effects of elastic electron scattering, the actual EAL
value will depend on the measurement conditions.7
An important practical application of XPS is measuring
the thicknesses of gate oxides in metal-oxide semiconductor devices. Silicon dioxide thicknesses of 2–5 nm
are required in current and planned devices, and EALs
are required for thickness measurements by XPS. We
present here new EAL measurements in SiO2 for electron
* Correspondence to: M. Suzuki, Center for Materials Development
and Analytical Technology, NTT Advanced Technology Corporation,
Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan.
E-mail: [email protected]
Contract/grant sponsor: New Energy and Industrial Technology
Development Organization.
Copyright  2000 John Wiley & Sons, Ltd.
energies of 140–1100 eV from XPS measurements with
synchrotron radiation (SR). A key factor in these measurements is the determination of the effective thickness
of the oxide films. We also analyse the EAL dependence
on electron energy.
EXPERIMENTAL
Oxide films with thicknesses of 100 nm (sample A) and
11.3 nm (sample B) were formed on Si(100) wafers by
thermal oxidation in dry oxygen. These thicknesses are
averaged values of ellipsometry measurements, and both
values were also confirmed with a stylus profiler. In
addition, an essentially identical oxide thickness of 11.4š
0.5 nm for sample B was found from AES depth profiling
analysis in which the sputtering rate was calibrated using
a NIST SiO2 /Si substrate standard reference material
(SRM 2536). Three samples for the XPS measurements
with thinner oxide layers were prepared from sample
B by etching with a dilute HF solution. Prior to the
preparation of these samples, it was confirmed that the
11.3 nm oxide film of sample B was completely removed
by careful immersion in the acid solution for 40 s; the
etching rate was estimated at ¾0.283 nm s 1 . Oxide
films of varying thickness for the XPS experiments were
prepared by similar immersions for varying times: 22 s for
sample C, 33 s for sample D and 36 s for sample E; the
corresponding nominal oxide thicknesses were 5, 2 and
1 nm, respectively. Sputter depth profiling experiments
were conducted to measure the actual thicknesses using
Received 15 December 1999
Revised 28 February 2000; Accepted 28 February 2000
EFFECTIVE ATTENUATION LENGTH IN SiO2 . I
secondary ion mass spectrometry (SIMS) and AES (see
below). Surface roughnesses of the films were measured
by atomic force microscopy (AFM), and the root-meansquare (RMS) roughnesses were estimated to be between
0.44 and 0.53 nm for areas of 5 µm ð 5 µm. An Si
reference specimen with a very thin oxide film (sample F)
was prepared in a solution of H2 SO4 and H2 O2 after HF
treatment; these are conventional procedures in silicon
large-scale integration device fabrication processes.
The SR-XPS measurements were performed at beamline 13C of the Photon Factory of the High Energy
Accelerator Research Organization in Japan.8 The SR was
produced by a 13-period undulator, and a high-resolution
spherical grating monochromator (SGM) system could
provide high flux and high-energy-resolution soft x-rays
from 150 to 1200 eV with a 750 grooves mm 1 grating.
The relative energy resolution was better than 3000 for xray energies below 400 eV, and was 1500–2000 for x-ray
energies over 400 eV. The SR x-rays from the beamline
were almost completely linearly polarized in the horizontal plane.9 Silicon 2p photoelectron spectra were measured
by a Physical Electronics 1600C hemispherical analyser
with a mean diameter of 279.4 mm. The analysis area
was circular with a diameter of 0.8 mm, and the analyser
acceptance angle was š7° . The angle between the incident
x-rays and analyser axis was set at 55° . The measurements
were performed with two different configurations, either
normal incidence of the x-rays and an average photoelectron emission angle D 55° , or x-rays at an incidence
angle of 55° and D 0° . The pressure of the chamber was
kept at <1 ð 10 7 Pa during the measurements. Sample A
and sample F were used as reference materials for SiO2
and Si, respectively. These samples were lightly sputtered
before the XPS measurements to remove surface contamination and, in the case of sample F, the thin surface oxide.
DETERMINATION OF EFFECTIVE
ATTENUATION LENGTHS
The EALs were calculated from the following equations,
which were derived after assuming that the effects of
elastic electron scattering were neglible and that each
film was homogeneous in structure and composition. The
intensity Iox of the Si 2p component from an oxide
layer of thickness d covered by a contamination layer of
thickness t is
ox
Iox D C1 nox ox ox
ox cos exp[ t/con cos /]
ð f1
exp[ d/.ox
ox cos /]g
.1/
where C1 is a constant determined mainly by the photon
flux, nox is the density of Si atoms in the oxide, ox is
the Si 2p photoionization cross-section in the oxide, ox
ox is
the EAL for Si 2p photoelectrons generated in the oxide
and passing through the oxide, ox
con is the EAL for these
electrons passing through the contamination layer and is the average photoelectron emission angle, respectively.
The intensity of the Si 2p elemental component from
the substrate is similarly
sub
Isub D C2 nsub sub sub
sub cos exp[ t/.con cos /]
ð exp[ d/.sub
ox cos /]
Copyright  2000 John Wiley & Sons, Ltd.
.2/
331
where C2 D C1 for measurements from the same spectrum, nsub is the density of Si atoms in the substrate, sub
is the Si 2p photoionization cross-section in the substrate,
sub
sub is the EAL of Si 2p photoelectrons generated in the
substrate and travelling in the substrate, sub
con is the EAL of
these electrons in the contamination layer and sub
ox is the
EAL of these electrons in the oxide. In Eqns (1) and (2),
ox and sub should, strictly speaking, be replaced by the
differential photoionization cross-section d/d. In our
experiments, however, all of the measurements were carried out with the same geometrical condition and with
the same settings for the electron energy analyser, such
as pass energy. As a result, the photoionization crosssection term cancels in the ratios of Eqns (5)–(7) below.
In this work, all of the oxide films for the EAL experiments (samples C, D and E) were prepared by etching
as described above and then stored under the same conditions until the XPS experiments were performed. These
films should then have similar contamination layers. No
sputtering was performed on these thin oxides, to avoid
film thickness and roughness changes.
Similarly, the Si 2p intensities Iox,1 from the reference
SiO2 (sample A with an oxide thickness of 100 nm) and
Isub,1 from the reference Si (sample F) are
Iox,1 D C3 nox ox ox
ox cos .3/
Isub,1 D C4 nsub sub sub
sub cos .4/
and
where C3 and C4 are constants determined mainly by the
photon flux and sub
sub is the EAL for photoelectrons from
the substrate. In our experiments, C3 D C4 because measurements of Iox,1 and Isub,1 were performed sequentially
while monitoring the SR ring current and the monochromatized x-ray intensity and because there were no changes
in other SR parameters. As noted above, samples A and
F were lightly sputtered before the XPS experiments.
The difference in photoelectron kinetic energies for the
Si0 and Si4C components is only ¾4 eV. Because the EALs
for these components are not significantly different for
ox
photoelectron energies ½140 eV, sub
ox ¾ ox and will be
sub
denoted by ox and ox
¾
.
We
then
obtain
con
con
nsub sub sub
Isub
sub exp[ d/.ox cos /]
D Rd .h, /
D
ox
ox
ox
I
n ox f1 exp[ d/ox cos /]g
.5/
and
Isub,1
nsub sub sub
sub
D
D R1 .h, /
.6/
Iox,1
nox ox ox
The EAL in SiO2 is then obtained from
ox .E/ D
1
d
Ð
cos lnf[R1 .h, //Rd .h, /] C 1g
.7/
and the measured intensity ratios Rd .h, / and R1 .h, /
from Eqns (5) and (6). Equation (7) was developed previously by Carim and Hochella10 and used by them and
Lu et al.11
RESULTS AND DISCUSSION
Table 1 shows thicknesses of the oxide films measured
by different methods for each sample used in the present
Surf. Interface Anal. 29, 330–335 (2000)
332
M. SUZUKI ET AL.
Table 1. Summary of measurements of oxide thicknesses for each sample
Sample
A
B
C
D
E
F
Etching
time (s)
0
22
33
36
Nominal
thicknessa
(nm)
Thickness from
ellipsometry
(nm)
100
11.3e
5
2
1
<1g
Thickness from
AES depth
profileb (nm)
11.4 š 0.5f
3.9 š 0.4
1.2
1.2
Thickness from
SIMS depth
profilec (nm)
Thickness from
EAL datad
(nm)
3.8
1.3
0.8
1.6
1.1
a
Obtained from an assumed constant etching rate of 0.283 nm s 1 .
Obtained with a sputtering rate of 0.12 nm min 1 .
c
Obtained with a sputtering rate of 0.32 nm min 1 .
d
Obtained from comparison of EAL data for samples D and E with EAL data for sample C.
e
Also confirmed with stylus profilometry.
f
Obtained from a comparison with NIST Si/SiO2 standard reference material.
g
Oxide layer formed in a solution of H2 SO4 and H2 O2 .
b
study. We measured the oxide thickness for sample C from
comparisons of AES and SIMS depth profiles with similar
depth profiles for sample B with the 11.3 nm oxide layer.
These measurements yielded oxide thicknesses of 3.9 and
3.8 nm, respectively. However, AES depth profiling could
not distinguish any difference between the thicknesses
of the oxide layers on samples D and E; these oxide
thicknesses, however, should be regarded only as rough
estimates because there were no clear plateaus in the
depth profiles. Although SIMS depth profiling gave oxide
thicknesses for samples D and E that were qualitatively
consistent with the nominal thicknesses, the changes in
Figure 1. Typical Si 2p photoemission spectra for Si and for Si with SiO2 layers of nominally 1.1, 1.6 and 100 nm thickness. These
spectra were measured for the indicated x-ray energies and for the indicated emission angles. The spectra have been normalized to
have the same maximum intensities. The peaks at binding energies of ¾99 eV and ¾103 eV correspond to the elemental .Si0 / and
oxide .Si4C / components.
Surf. Interface Anal. 29, 330–335 (2000)
Copyright  2000 John Wiley & Sons, Ltd.
EFFECTIVE ATTENUATION LENGTH IN SiO2 . I
the concentration profiles of silicon and oxygen were not
sharp enough for the derived thicknesses to be useful
(i.e. of sufficient accuracy) for the EAL measurements.
Because the uncertainties of thickness measurements from
SIMS depth profiles are considered to be larger than those
for AES depth profiles, we adopted 3.9 nm as the actual
oxide thickness for sample C.
Figure 1 shows typical raw Si 2p spectra for Si and
for three thicknesses of SiO2 on Si. These spectra were
measured for x-ray energies between 458 and 505 eV
and for photoelectron emission angles of 0° and 55° . As
expected, the Si0 component becomes weaker as the oxide
thickness increases and as the emission angle increases.
In this work, we use spectra for D 0° to minimize the
333
effects of roughness and surface electronic excitations;6
the results for D 55° are presented and discussed in
the companion paper.12 The Si 2p doublet structure is not
as clear for the specimen without an oxide as for the
specimens with oxide layers because of the degradation
of surface crystallography caused by ion sputtering.
The spectra were fitted with Gaussian–Lorentzian functions and a Shirley background, and peak areas were found
for the Si elemental and oxide components. The Si0 peak
was fitted with two components (2p1/2 and 2p3/2 with a
1 : 2 intensity ratio) and the Si4C peak was fitted as a single peak. Weak intensity was found between the Si0 and
Si4C peaks, and this has been attributed to intermediate
SiC , Si2C , and Si3C oxides at the Si/SiO2 interface.13,14 We
Figure 2. Perspective tapping-mode AFM images (scan area: 1 µm ð 1 µm) for specimens with oxide thicknesses of 1.1 nm (a) and
1.6 nm (b).
Copyright  2000 John Wiley & Sons, Ltd.
Surf. Interface Anal. 29, 330–335 (2000)
334
M. SUZUKI ET AL.
have ignored this weak intensity in our EAL determination; if this intensity was added to the Si4C intensity, the
resulting EALs would change by <5%. The uncertainty in
the measured intensity ratios Rd .h, / and R1 .h, / due
to counting statistics, finite energy resolution and the fitting procedure varied between š1% at the lowest photon
energies to š5% at the highest energies.
Figure 2 shows tapping-mode AFM images for samples D and E. The average roughnesses of these surfaces
were 0.47 and 0.53 nm, respectively. These roughnesses
are essentially the same as those found in similar measurements of ‘atomically flat’ Si in the atmosphere.15 The
chemical process used to produce the oxide layers therefore does not create or increase the roughness of the oxide
surfaces.
Figure 3 shows EALs determined from Eqn (7) as
a function of photoelectron energy for sample C with
the 3.9 nm oxide. Because the oxide thicknesses for
samples D and E could not be determined with sufficient
reliability from the AES and SIMS depth profiles, we
determined these thicknesses by adjusting d in Eqn (7) so
that the resulting EALs were in general agreement with
the EALs for sample C. This procedure yielded oxide
thicknesses of 1.6 and 1.1 nm for samples D and E,
respectively. The differences between these thicknesses
and the nominal thicknesses derived from the etching
times are believed to be acceptably small because the
wet-etching process was controlled manually.
Figure 3 shows EALs reported by other authors at
various photoelectron energies.9,16 – 18 Most of these measurements were made with Mg and Al K˛ x-rays for
which the photoelectron energies are 1153 and 1383 eV,
Figure 3. Effective attenuation lengths in SiO2 as a function of
photoelectron energy for specimens with oxide thicknesses of
1.1 nm (squares), 1.6 nm (circles) and 3.9 nm (triangles). The
symbols E, F, L, Y and H show EAL values reported in Refs 15, 16,
10, 17 and 12, respectively. The thin solid line (TPP) shows IMFPs
calculated from experimental optical data by Tanuma et al.5 and
the thick solid line shows these IMFPs multipled by 0.63. The
thick dashed line shows values calculated from the CS2 formula
proposed in Ref. 2. In TPP and CS2 calculations, we adopted a
density of 2190 kg m 3 for vitreous SiO2 . The CS2 values differ
from the corresponding curve shown in Fig. 15 of Ref. 2, which
was supposed to be calculated using a density of ¾2700 kg m 3
corresponding to a material like quartz.
Surf. Interface Anal. 29, 330–335 (2000)
respectively. Most of these EALs are larger than those
found here. There is, however, good agreement with the
EALs of Hochella and Carim.10 One reason for the discrepancy might be an overestimation of oxide thicknesses
determined by ellipsometry.10 Nevertheless, our EAL values have an uncertainty of about š10% due mainly to
uncertainty in thickness measurement. Attenuation lengths
obtained from the Cumpson and Seah semi-empirical
formula2 are plotted as a dashed curve. This curve is
¾15% larger than our experimental values for all energies.
Figure 3 also shows a comparison of IMFPs for SiO2
from Tanuma et al.5 (thin solid line). The EALs reported
here are ¾37% less than the corresponding IMFPs, as
indicated by the thick solid curve in Fig. 3. Part of this
difference is believed to be due to the uncertainty in the
oxide layer thicknesses (¾10%) whereas the remainder
is believed to be due to the effects of elastic electron
scattering.6,10,19
The thick solid curve in Fig. 3 is a good representation
of the EAL energy dependence. In order to analyse the
EAL energy dependence in more detail, Fig. 4 shows a
Fano plot20 in which the ratio of the EAL .ox / to the
photoelectron kinetic energy E is plotted against E on
a logarithmic scale. A linear plot, as shown in Fig. 4,
indicates that the EAL energy dependence is consistent
with the Bethe equation for inelastic scattering21
E/ox D ˇE2p ln.E/
.8/
In Eqn (8), Ep is the free electron plasmon energy for
SiO2 (22 eV) and ˇ and are parameters. Figure 4 shows
that the Bethe equation provides an adequate description
of the EAL energy dependence over the 140–1100 eV
range. Values of ˇ and from the fit of Eqn (8) to the
measured values of ox /E are shown in Table 2, together
with the corresponding values from the calculated IMFPs
of Tanuma et al.5 for SiO2 and the values found from the
IMFP predictive equation3 TPP-2M for SiO2 . The close
correspondence in the values of for the calculated IMFPs
and the measured EALs indicates that the ratio of these
Figure 4. Fano plot in which ratios (symbols) of the measured
EAL .ox / to the photoelectron kinetic energy E are plotted
against E on a logarithmic scale. The solid line is a fit of Eqn (8)
to the plotted data.
Copyright  2000 John Wiley & Sons, Ltd.
EFFECTIVE ATTENUATION LENGTH IN SiO2 . I
Table 2. Comparison of values of b and g in Eqn (8) for
SiO2
ˇ(eV
Calculated IMFPs (Ref. 5)
TPP-2M equation (Ref. 3)
Measured EALs (this work)
a
1
nm 1 /
0.158
0.143
0.234 š 0.016a
(eV 1 /
0.0925
0.1291
0.0920 š 0.024a
Standard deviation from least-squares fit.
two quantities does not vary substantially with electron
energy, i.e. the elastic scattering or other corrections to
the IMFP to obtain the EAL do not depend significantly
on energy for SiO2 in the 140–1100 eV range.
CONCLUSION
335
to changes in SR intensity and to surface contamination
layers could be eliminated.
Most previous EAL measurements were made by XPS
with Mg and Al K˛ x-rays for which the photoelectron
energies are 1153 and 1383 eV, respectively. Our EAL
measurement at 1100 eV is smaller than most of the
earlier EALs for an energy of 1153 eV, although there
is good agreement with the EAL at this energy reported
by Hochella and Carim.10
We have compared the measured EALs with the IMFPs
calculated from optical data for SiO2 by Tanuma et al.5
The measured EALs are 37% smaller than the corresponding IMFPs. Part of this difference is believed to be
due to uncertainty in the oxide layer thicknesses (about
š10%) and the remainder to the effects of elastic electron scattering, which will be discussed in Part II.11 It is
believed that diffraction effects are not significant in the
EAL measurements.11
Acknowledgement
We have measured EALs for ultrathin SiO2 layers on Si
using SR for kinetic energies of 140–1100 eV. These
measurements were made from comparisons of Si0 and
Si4C peak intensities for each film thickness and from
comparisons of the Si0 and Si4C peak intensities for Si and
thick SiO2 films, respectively. In this way, artefacts due
This work was financially supported by the New Energy and Industrial
Technology Development Organization. Certain commercial instruments
are identified in this paper to specify the experimental conditions. Such
identification is not intended to imply recommendation or endorsement
by the National Institute of Standards and Technology, nor is it intended
to imply that the equipment identified is necessarily the best available
for the purpose.
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Surf. Interface Anal. 29, 330–335 (2000)
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