Measurement of Gate-Oxide Film Thicknesses by X-ray
Photoelectron Spectroscopy
C. J. Powell* and A. Jablonskif
^Surface and Micro analysis Science Division, National Institute of Standards and Technology,
Gaithersburg, MD 20899-8370, USA
i'Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52,
01-224 Warsaw, Poland
Abstract. X-Ray Photoelectron Spectroscopy (XPS) is being used to an increasing extent for the characterization of new
gate-oxide materials, particularly for the determination of film composition, uniformity, and thickness. A key parameter
for film-thickness measurements by XPS is the effective attenuation length (EAL) for a particular material, photoelectron
energy, and measurement configuration. Due to the effects of elastic scattering on signal-electron trajectories, the EAL
generally differs from the corresponding electron inelastic mean free path (IMFP) and is a function of film thickness and
electron emission angle. We present calculations of EALs for four proposed gate-oxide materials: zirconium dioxide,
hafnium dioxide, zirconium silicate, and hafnium silicate. These EALs were obtained from the NIST Electron EffectiveAttenuation-Length Database that uses an analytical expression derived from solution of the Boltzmann equation within
the transport approximation. The EALs were computed for the relevant photoelectron lines excited by Al characteristic x
rays and for a range of film thicknesses and emission angles of practical relevance. The EALs were compared with the
corresponding IMFPs to determine the magnitudes of the correction for elastic-scattering effects in each gate-oxide
material. For common measurement conditions, this correction varied between 12 % and 20 %.
INTRODUCTION
While silicon dioxide and, more recently, silicon
oxynitrides have been used as gate-dielectric materials
in semiconductor devices, other materials will be used
in the future as "high-K" dielectrics [1-3]. These
materials, with higher dielectric constants than that of
SiO2, will have larger physical thicknesses in order that
the equivalent oxide thickness (corresponding to a SiC>2
dielectric) can be reduced. For devices produced
between 2003 and 2007, the equivalent oxide thickness
will be between 0.6 nm and 1.6 nm for highperformance logic and between 1 nm and 1.6 nm for
low-operating-power logic [1]. These thicknesses need
to be measured with an uncertainty (3a) of ± 4 % [1].
Many techniques have been used for the measurement
of gate-dielectric thicknesses. Even for the relatively
favorable case of measuring the thickness of SiO2 films,
results from different methods can disagree by more
than a factor of two when the thickness is less than
about 2.5 nm [4-6]. These disagreements are due in part
to different assumptions in the models for the various
techniques (e.g., compositional and structural variations
at the silicon-silicon dioxide interface, film uniformity,
topography, and surface contamination when
measurements are made in the atmosphere) [4-6].
Thickness measurements with high-K gate dielectrics
will be more complex because of the likely presence of
both this dielectric and SiO2.
X-ray photoelectron Spectroscopy (XPS) is frequently
used for thickness measurements of thin (< 10 nm)
overlayers including gate dielectrics [4-6]. The
thickness measurement depends on the value of the
effective attenuation length (EAL) for the relevant
photoelectron energy in the overlayer material [7], The
EAL differs from the corresponding electron inelastic
mean free path (IMFP) because of the effects of elasticelectron scattering during the transport of the signal
photoelectrons from their point of generation to the
specimen surface [7]. In general, the IMFP can exceed
the EAL (for the same material and electron energy) by
up to ~ 40 % for common measurement conditions [8].
CP683, Characterization and Metrology for VLSI Technology: 2003 International Conference,
edited by D. G. Seiler, A. C. Diebold, T. J. Shaffner, R. McDonald, S. Zollner, R. P. Khosla, and E. M. Secula
© 2003 American Institute of Physics 0-7354-0152-7/03/$20.00
321
We present calculated EALs for photoelectrons in
four proposed gate-dielectric materials: zirconium
dioxide, hafnium dioxide, zirconium silicate, and
hafnium silicate. The EAL results are relevant to socalled angle-resolved XPS experiments (i.e.,
measurements of XPS intensities as the specimen was
We have defined the "practical" EAL, L, applicable
to measurements of overlayer-film thicknesses from
changes of the XPS signal intensities from the substrate
as [7,8]:
L = —————-—————
(1)
cosa(ln/o -In//)
tilted) with a fixed angle (\p= 54°) between the x-ray
source and the analyzer axis. This angle is often used
on commercial XPS instruments. Experimentally,
overlayer thicknesses can be determined from
measurements of substrate XPS intensities at a fixed
emission angle (i.e., from comparisons of intensities
measured before and after the film was deposited) or
from analyses of intensities at several emission angles.
Our EAL calculations were made for photoelectron
excitation by characteristic Al Koc x rays.
We find that elastic-scattering effects cause a
systematic difference of up to about 20 % between
EAL and IMFP values in the four gate dielectrics for
photoelectron emission angles (with respect to the
surface normal) of less than 50°. At larger emission
angles, the systematic difference can be appreciably
larger.
where a is the electron emission angle with respect to
the surface normal, and /Q and // are the substrate
intensities before and after deposition of an overlayer
film of thickness t. We can similarly define a practical
EAL for measurements of overlayer-film thicknesses
from changes of the XPS signal intensities from the
overlayer material (here the high-K dielectric) as:
(2)
where /£ and // are the overlayer-film intensities for
a film of infinite thickness and for a thickness t,
respectively.
Two material parameters are needed for the EAL
calculation: (a) the inelastic mean free path (IMFP)
which is inversely proportional to the total cross section
for inelastic scattering, and (b) the transport mean free
path (TMFP) which is inversely proportional to the
transport cross section that is a measure of the strength
of large-angle elastic scattering. Table 1 shows IMFPs
and TMFPs for the high-K materials and the relevant
photoelectron lines [18] and energies [19]. The IMFPs
were obtained from the IMFP predictive equation TPP2M of Tanuma et al [20]. The EAL calculation also
requires values of the photoionization asymmetry
parameter for each line [21].
EAL CALCULATIONS
The EALs for each gate-dielectric material were
obtained from the NIST Electron EffectiveAttenuation-Length Database [9]. These EALs were
computed from an algorithm based on solution of the
kinetic Boltzmann equation within the transport
approximation [10,11]. This algorithm accounts for
elastic scattering along photoelectron trajectories in the
solid. An assessment of the accuracy of this algorithm
has been published recently [12]. We have also
published similar EAL calculations for SiO2 on Si [1315].
Our calculational algorithm is based on the implicit
assumption that the inelastic- and elastic-scattering
properties of the overlayer film are similar to those of
the substrate. This assumption is valid for an overlayer
of SiO2 on a Si substrate [15] but less valid for the
high-K dielectrics on Si (or on an intermediate layer of
SiO2) considered here. Nevertheless, Monte Carlo
simulations indicate that the substrate has a relatively
minor effect on the EAL for the overlayer [16,17]. We
therefore believe it reasonable to compute EALs for the
high-K dielectrics that are relevant to the attenuation of
Si 2p photoelectrons from the Si (and possibly also
SiO2) of the substrate by the dielectric and to the
increase of the photoelectron signal from the dielectric
material with increasing thickness of this material.
Table 1. Values of the inelastic mean free path (IMFP) and
transport mean free path (TMFP) for the EAL calculations
for the listed materials, photoelectron lines, and electron
energies.
Material
Line Energy (eV) IMFP (nm) TMFP (nm)
(a) Photoelectrons from the substrate
ZrO2
Si2p
1385
2.532
9.836
ZrSiO4
Si2p
1385
2.757
12.89
Hf02
Si2p
1385
2.173
6.286
HfSiO4
Si2p
1385
2.355
8.894
(b) Photoelectrons from
ZrO2
Zr3d 5/2
ZrSiO4
Zr3d 5/2
HfO2
Hf4d 5/2
HfSiO4
Hf4d 5/2
322
the high-K dielectric
1304
2.417
1304
2.631
1273
2.038
1273
2.207
9.077
11.84
5.736
8.047
RESULTS
Si 2p (AI Ka)
ZrO
We consider first attenuation of Si 2p photoelectrons
from the Si substrate and possibly an intermediate layer
of SiO2 through overlayers of high-K dielectrics of
variable thickness. As an example, Fig. 1 shows EAL
results for an overlayer of ZrO2. The solid lines show
plots of the ratio of L from Eq. (1) to the IMFP, AJ, as a
function of ZrO2 thickness for selected values of a; for
clarity, similar plots for values of a between 10° and
40° are not shown. The short-dashed lines in Fig. 1
represent loci of L/Ai values corresponding to
attenuation of the substrate Si 2p intensity to 1 % and
10 % of the value for an uncovered substrate. The
regions of Fig. 1 to the left of these lines indicate the
combinations of film thickness and emission angle for
which practical XPS measurements are most likely to
be made.
We see from Fig. 1 that L/Ai does not vary
appreciably with ZrO2 thickness for emission angles
less than about 60°, as found for SiO2 and other
materials [8,13-15]. It is then useful to calculate
average values of the ratio, Lave/Ai, which we denote
LL/A; and L]lO
corresponding to ZrO2
thicknesses for which the substrate intensity is reduced
= 54°
1.15
._
-10% to 100% substrate intensity (L10 /A.) i
1.1
-1% to 100% substrate intensity (L1 /A.) '
S*
'-a*
c
CO
d"
1
~J
^-- 0.95
- jS
0.9
0.85
0.8
20
40
60
80
Emission Angle (degrees)
FIGURE 2. Plot of L^/A; (solid line) and L\lve I ^
(short-dashed line) as a function of emission angle a for
attenuation of Si 2p photoelectrons by an overlayer of ZrO2.
The long-dashed line shows LSG/Ai where LSc was obtained
from the EAL formula of Seah and Gilmore [22].
to 1 % and 10 %, respectively, of its maximum value
(for an uncovered substrate). These average values
were calculated by averaging the L/Ai results over film
thickness for thicknesses (at 1 A increments) from zero
to the maximum values corresponding to attenuation of
the Si 2p intensities to 1 % and 10 % of its maximum
value.
Figure 2 shows plots of Llave I A,- and L1^ / A/, from
the ZrO2 data in Fig. 1, as a function of emission angle,
a. It is clear that L\lve I A, and L1^ / A,- do not vary
significantly with a for 0° <a<50°. At larger
emission angles, these ratios change more rapidly with
a, as expected from the plots in Fig. 1. We also show in
Fig. 2 the ratio LSG/Aj where LSo is an attenuation length
derived from an empirical formula proposed by Seah
and Gilmore [22] for emission angles between 0° and
58°. This LSG value is less than L^/A, and
1.2 -
0.8 -
^ave I ^i by 1-8 % and 2.7 %, respectively.
0
2
4
6
Film Thickness (nm)
FIGURE 1. Plot of ratios of the average values of the EAL,
L, from Eq. (1) to the IMFP, Ai, for attenuation of Si 2p
photoelectrons from a Si (or Si/SiO2) substrate as a function
of the thickness of a ZrO2 overlayer film for XPS with AI
Ka x rays at different emission angles a (solid lines). For
clarity, curves for 10° < a < 40° are not shown. The shortdashed lines show L/Aj values for film thicknesses and
emission angles for which the substrate Si 2p intensity was
reduced to 1% and 10% of its value for uncovered substrate.
323
Similar plots of Llave I A, and L1^ / A, as a function
of a for attenuation of Si 2p photoelectrons in HfO2 are
shown in Fig. 3. These plots (and corresponding plots
for ZrSiO4 and HfSiO4 [23]) show trends similar to
those presented in Fig. 2. Because Llave I A,- and
^ave I ^i
do
not
var
y appreciably with a for
0° < a < 50° , it is useful to calculate average values of
_i
_ i r\
these ratios, Lave / Af and Lave / A f , over this angular
range. These values, shown in Table 2(a), differ from
We consider now thickness measurements of high-K
materials from intensity changes of photoelectron
signals from overlayer films of these materials, e.g.,
through use of Eq. (2). The NIST EAL database [9]
provides EALs based on Eq. (1). That is, for the
present application, it is assumed that there is a
(fictitious) substrate of the same high-K material, and
EALs are computed for attenuation of photoelectrons
from this substrate by the overlayer film [7].
Replacement of this substrate by another (as we have
done for the previous results here) has a small effect on
the derived EALs [16,17]. Lassen et al [17] showed
that EALs from this approach can also be used to
obtain film thicknesses from changes in overlayer-film
photoelectron intensities. Their estimates of the
uncertainties of derived thicknesses (ranging from
6.2 % to 16.5 % for overlayers of C and Au on Si,
respectively) were based on analyses of photoelectron
intensities for emission angles at 10° increments
between 0° and 80°. We expect (by inspection of the
illustrative results in Fig. 1) that the uncertainties found
by Lassen et al. would have been smaller if they had
restricted the angular range in their analysis to between
0° and 50°.
Figures 4 and 5 show plots similar to Figs. 2 and 3 for
attenuation of Zr 3d5/2 and Hf 4d5/2 photoelectrons in
ZrO2 and HfO2, respectively. Values of Llave I A, and
1.3
HfO
Si2p(AIKa)
54
1.2
10
———10% to 100% substrate intensity (L
/ A )7 '
v
'
ave I /
- - - - - 1 % to 100% substrate intensity (L1 /A) /
- - Seah-Gilmore (L / A )
SQ
i
"
•
0.8
0.7
20
40
60
80
Emission Angle (degrees)
FIGURE 3. Plot of L^/A; (solid line) and L\lve I k(
(short-dashed line) as a function of emission angle a for
attenuation of Si 2p photoelectrons by an overlayer of HfO2.
See also caption to Fig. 2.
unity by between 12.3 % and 19.1 %. These differences
indicate the magnitudes of the effects of elastic
scattering of the signal electrons on film-thickness
determinations from measurements of the attenuation of
Si 2p photoelectrons in the indicated materials.
Because these elastic-scattering effects are substantial,
film thicknesses should be determined using EALs for
the relevant measurement conditions rather than
^ave ^ ^i were obtained, as described previously, for
these lines and materials and for ZrSiO4 and
—i
—10
These values as well as values of Lave and Lave are
shown in Table 2(b). We see that, due to elastic
IMFPs. Table 2(a) also shows values of Lave and Lave
which differ by only 0.2 A. These values (or similar
values obtained for the specific measurement
conditions of interest) can be used to derive film
thicknesses from Eq. (1). Alternatively, these values
be used as the "lambda parameter" to obtain film
thicknesses from analyses of a set of angle-resolved
XPS data for 0° <a< 50° [24].
1.2
ZrO
Zr3d
(Al Ka)
1.15
._
1.1
———10% to 100% substrate intensity (L10 /A) ,
ave
- - - - - 1 % to 100% substrate intensity (L^Jl)
i ,
,'
W
^
Table 2. Values Of Lave I ht , Lave / A; , Lave , and Lave
1-05
--Seah-Gilmore (L /A.)
;
cc
for the indicated materials and photoelectron lines.___
Material
Line Lave I hj Lave
(a) Photoelectrons from the substrate
ZrO2
Si2p
0.848
0.856
ZrSiO4
Si2p
0.869
0.877
HfO2
Si2p
0.809
0.818
HfSiO4
Si2p
0.844
0.853
^~ 0.95 -
Lave (nm) Lave (nm)
-"" 0.9
2.15
2.40
1.76
1.99
2.17
2.42
1.78
2.01
0.85
0.8
20
40
60
80
Emission Angle (degrees)
(b) Photoelectrons from the high-K dielectric
ZrO2
Zr3d 5/2 0.843
0.852
2.04
ZrSiO4 Zr3d 5/2 0.865
0.872
2.28
Hf02
Hf4d<5/2 0.803
0.814
1.64
HfSiO4 Hf4d V2 0.839
0.848
1.85
FIGURE 4. Plot of L^/A; (solid line) and Lave / ^
(short-dashed line) as a function of emission angle a for
attenuation of Zr 3d5/2 photoelectrons by an overlayer of
ZrO2. See also caption to Fig. 2.
2.06
2.30
1.66
1.87
324
REFERENCES
1.3
HfO
Hf4d
54
(AIKo)
1.2
———10% to 100% substrate intensity v(L10 /A)
ave
> 1.1
- - - - - 1 % to 100% substrate intensity (L1 /A.)
- - Seah-Gilmore (L /A.)
r
•'
/
0.9
o .
0.8
0.7
20
40
60
80
Emission Angle (degrees)
l
FIGURE 5. Plot of L / A
ave
(short-dashed line) as a function of emission angle a for
attenuation of Hf 4d5/2 photoelectrons by an overlayer of
HfO2. See also caption to Fig. 2.
scattering of the signal electrons,
Llave I K{
and
l}^ve I KI differ from unity by between 12.8 % and
—i
—10
19.7 %. We believe that the values of Lave and Lave
in Table 2(b) can provide useful estimates of film
thicknesses of high-K materials from Eq. (2), but Monte
Carlo simulations should be performed to validate this
approach.
SUMMARY
We have presented calculated EALs needed for
measurement of film thicknesses of four proposed highK gate dielectrics: ZrO2, HfO2, ZrSiO4, and HfSiO4.
These EALs were computed for XPS with Al Koc x rays
in a common measurement configuration.
For photoelectron emission angles between 0° and
50°, average values of the EAL may be satisfactory for
the film-thickness measurements. These average EALs
are typically between 12 % and 20 % (depending on the
material and photoelectron line) less than the
corresponding IMFPs. For larger emission angles, it
will generally be necessary to determine the film
thickness by iteration. That is, a preliminary thickness
should be obtained first from an estimated EAL, and
then this EAL should be subsequently refined for the
next estimate of film thickness.
325
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