Assessment of Ultra-Thin SiO2 Film Thickness
Measurement Precision by Ellipsometry
D. Chandler-Horowitz, N.V. Nguyen, and J.R. Ehrstein
Semiconductor Electronics Division
National Institute of Standards and Technology
Gaithersburg, MD 20899-8121
Abstract. The ellipsometric film thickness measurement precision for equivalent oxide thickness as prescribed by the
International Technology Roadmap for Semiconductors is quite high. Although short-term precision on a single ellipsometric
instrument can be quite high, deviations of measured film thickness from instrument-to-instrument and from lab-to-lab for
short-term and long-term periods of time need to be addressed. Since the derived film thickness is dependent on many factors,
each one has to be dealt with in turn. These factors include: ellipsometric instrument precision and accuracy, consistency of
film/substrate modeling, optical constants, regression analysis, and film surface contamination. Recommendations for
standard models and optical constants are given along with the need to ensure high ellipsometric instrument precision and
accuracy and controlled film surfaces and environmental conditions. In this study ultra-thin refers to oxide films starting at 10
nm and being as thin as the native oxide.
INTRODUCTION
In the short-term (measurements taken over less than a
few hour time period) a single research-grade
ellipsometric instrument can predict a film thickness
with the precision as set forth by the International
Technology Roadmap for Semiconductors. However, in
every other instance, including measurements on
different ellipsometers, measurements do suffer greatly
from non-repeatability, poor precision, and drift. In the
simplest case deviations in the predicted film thickness
can always occur when processing identical
ellipsometric data with different optical models
describing the film/substrate system, when different
values of optical index data are used, and when the
thickness is determined by a regression on the various
forms of ellipsometric data (i.e. A and \|/ or a and P).
The above factors can be standardized, and when done
so, only two other factors exist.
These are the
ellipsometer instrumental sensivity and accuracy and the
state of the film surface with respect to contamination.
Although the following work is based on observations of
silicon dioxide films, the results can be carried over to
other thin dielectric films.
Considerable work has been done in the past and is
continuing in the present in terms of improving
ellipsometric instrumental precision and accuracy and in
keeping the film/substrate "clean". What is not so
standard practice is the measurement procedure in
determining thin film thickness to a high degree of
precision. Here measurement sensitivity and modeling
become very important issues.
For the purpose of
comparing measurements from different instruments and
laboratories we are considering precision on a long term
basis where the measurement is repeatable from day-today, week-to-week, and from lab-to-lab. So standard
modeling procedures are necessary to insure, not so
much a degree of accuracy, but a high degree of
consistency and therefore precision
Any discussion of accuracy here will essentially be
model dependent. In general all film substrate models,
to be physically accurate, should contain an interlayer
region. These interlayer properties directly affect the
film thickness accuracy no matter how great the
precision may be. In addition, the film is assumed to be
uniform and has no surface roughness.
For thick films (>50 nm) both the film thickness and
the film index of refraction can be measured with
ellipsometry (1). But now in the thinner oxide film
thickness regime of less than 10 nm, a similar precise
determination of both refractive index and thickness is
nearly impossible because of parameter correlation (2,3).
In order to regain the precision, one needs to
predetermine and fix the value for the film refractive
index. The past methods of using thicker firms to
determine this index in a multiple sample film thickness
regression will most likely not succeed since the
processing parameters cannot be held constant for such
long durations of oxide growth and may be different. So
at the very least, for the very thin films, one has the
problem of determining both the best model and accurate
values of the refractive indices of the component
materials that parameterize the model.
In what follows we present a sampling of some of our
ellipsometric measurements of thin SiO2 films. First the
following topics will be considered: the ellipsometer
sensitivity and precision, the optical constants of the
materials, modeling of the film/substrate structure and
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
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326
film thickness determination, and the environmental
factors. The present goal as stated in the International
Technology Roadmap for Semiconductors (4) is to
achieve a EOT (effective oxide thickness) measurement
precision of 3a less than 0.005 nm.
ELLIPSOMETER SENSITIVITY AND
PRECISION
The instrumental precision and accuracy is determined
by the precision and accuracy of the measured
ellipsometric parameters, A and \|/, and the accuracy of
the angle of incidence, <|). The ellipsometric parameters
for the rotating analyzer-type instrument used in this
study are derived from the raw values of the Fourier
components, a' and |3', and the calibration offsets of the
respective polarizer and analyzer, P0 and AO, and signal
attenuation constant n. By working with an appropriate
model for the oxide film, one can predict the maximum
sensitivity of the measurement to film thickness and
accordingly adjust the angle of incidence and polarizer
setting, P, to a predetermined optimum value. For thin
oxide films (<10 nm) it is known that at a wavelength of
0.6328 nm an angle of incidence of approximately 75 °,
rather than the traditional 70 °, and a polarizer setting of
near 10 ° is needed.
For example, for the case of a 2 nm oxide film the
ellipsometric phase change with film thickness, dA/dt
and A, as a function of the angle of incidence, are plotted
in Figure 1 (5,6). The higher the value of dA/dt, the
greater the measurable change in A for a given change in
film thickness, thus greater film thickness sensitivity at
certain angles of incidence. These values can be almost
two orders of magnitude greater than the corresponding
changes in \|/, but are zero at the principal angle of
incidence (-75.5 °).
The precision and repeatability of the calibration
constants are important. From the definitions of A and \j/
with respect to a, (3, and P and the transformation of the
correct values of a and P from raw a' and P' data (7) one
observes the following generality:
Neglecting the
inaccuracy in a' and p', the uncertainty in A and \\r can
be similar in magnitude to the uncertainties in AO, PO,
and r| (5A0, 5P0 in degrees, 5rj in radians). Table 1
summarizes some of these values for the ellipsometer
used here to observe the environmental changes in film
thickness. From the table, the random uncertainties in A
and \j/ are dominated by the standard deviations in a and
p, and can be as high as approximately 0.025 °. The rest
of the values are given as reference values to be used for
any instrumental comparisons. These conditions are a
requirement so that in the following procedures the film
thickness precision will be high enough to meet the
roadmap conditions,
180
160
140
120
100
e
<
70
72
74
76
78
Angle of Incidence ft
OPTICAL CONSTANTS
Figure 1. Sensitivity plot of changes in A to changes in
thickness of a 2 nm oxide film at 632.8 nm.
One needs to have predetermined accurate values for
the optical constants of the silicon substrate and
reasonable values for the oxide film. The imaginary
part of the refractive index of silicon, k, is given as the
value determined by Geist, 0.01564 (see Table 2, ref 4).
One value for the real part, n, is given as 3.875 by a
simultaneous fit to three different oxide thicknesses (1).
These values are not far from the values of others. The
bulk value for the refractive index of silicon dioxide is
1.4571 (Table 2, ref 6). However, earlier measurements
on SRMs found the value to be higher, approximately
1.461, due in part to the compressive stress formed in the
oxide being thermally grown on silicon, which has a
higher expansion coefficient. In addition, the index also
can vary with the growth temperature and annealing
temperature, but it is most always larger than the bulk
material. This uncertainty in oxide refractive index will
directly influence the final value for the oxide thickness.
Table 1
Instrumental Uncertainties for Ellipsometer
Uncertainty in Angle of Incidence : ± 0.004 °
Uncertainty in Polarizer Angle:
± 0.002 °
Standard deviation in a' and (3':
± 0.0005
Calibration of Single Wavelength (HeNe) Rotating Analyzer
Ellipsometer
Wafer: 25 nm thick oxide film
Angle of Incidence: 74 °
Results of drift and precision of measurement:
+After warmup of 1 Yt hours for rotating analyzer and HeNe
laser
^Continuous run of calibration with 180 points spanning up to 4
Yz hour
+Analyzer offset AO 111.1718 ±0.0007°
^Polarizer offset P0
-1.4020 ± 0.0003 °
+Attenuation constant T| 1.01166 ± 0.00001
327
instruments and give a thickness value comparable to
one that may be measured by alternative means such as
with electrical measurements or other physical means.
The problem is similar to that of extracting an accurate
line width from an edge with a certain amount of slope.
How much of the interlayer should be included in the
film thickness that is reported? Again we recommend
reporting an additional half of the interlayer going
towards the final reported film thickness.
Secondly, in the case of very thin films (<10 nm), as
mentioned previously, the correlation between film
thickness and film refractive index is high. Therefore it
is very necessary to fix the film refractive index to an
appropriate value to get a physically meaningful
thickness. By fixing the film index, calculated values for
the film thickness are very precise.
Now, when only one parameter is being determined
by ellipsometry, namely the film thickness, the method
of regression becomes increasingly important. The
calculation is overdetermined since ellipsometry yields
two measurement parameters and only only one
independent thickness value is to be predicted.
Therefore the regression should always be consistent in
the way it is setup.
Any optical properties of the interlayer will be
approximated, because of its thinness, as an EMA
(Effective Medium Approximation) of a volume fraction
of both silicon substrate and thermal oxide.
These optical constant values are recommended
values and the consistent use of them will insure
consistent lab- to-lab film thickness measurement
results.
Table 2
Silicon
OPTICAL CONSTANTS
@ 632.8 nm
n
k
3.8706(1)
3.8739(2)
0.01564(4)
3.875 ±0.003 (3)
Silicon Dioxide Film:
(1)
(2)
(3)
(4)
(5)
(6)
1.4571 (6)
1.461 (3 &5)
Jellison, Opt. Mat. 1,41 (1992)
Woollam, JAP 83, 3323 (1998)
NIST SP 260-109 (1988) ±0.003 uncertainty
Geist, J. Res. NIST 95, 549 (1990)
Taft, J. Electr. Soc. 125 (6), 968 (June, 1978)
showing index vs. growth temp
Mallitson, L, J. Opt. Soc.55, 1205 (1965)
ENVIRONMENTAL FACTORS
MODELING AND FILM THICKNESS
DETERMINATION
There are two main points to be concerned with here.
First, it has been shown that a small (<1 nm) interface
region exists between the oxide film and the silicon
substrate (8,9). When measuring ellipsometrically an
appropriate multiple sample set of various oxide film
thicknesses, both accurate single wavelength data and
accurate spectroscopic data show that a model
containing an interlayer gives a better fit to the
experimentally observed data than the use of the simple
ambient-film-substrate model.
Because of parameter
correlation and the use of bulk material databases,
spectroscopic ellipsometric measurements on a single
wafer give a precise, wavelength-averaged value for film
thickness using a simple film/substrate model. Here the
film refractive index uses a densified value for the
thermally grown oxide since it is in a state of
compression. The same independence of an interlayer,
because of correlation, occurs for single wavelength
measurements on a single wafer.
However, we
recommend the use of an interlayer at all times.
However, an additional problem is presented with the
use of the interlayer model. What one wants to report
usually is only the oxide film thickness, regardless of
whether an interlayer is present.
This would allow
comparisons between different thickness measuring
328
Environmental factors can affect both the instrument
and the sample surface. Mechanical vibrations, air
currents, and air-borne particles (dust) all can add noise
to the light detector output of the ellipsometer. But these
can be reduced to acceptable levels below that of the
effects of temperature and humidity.
Spikes in
temperature or changes in temperature abnormal to the
laboratory environment can cause drift in the
ellipsometer output and must be monitored to assure
consistent results. Environmental effects to the sample
surface are subtle.
Changes in humidity and/or
contamination from storage containers or laboratory air
(hydrocarbons) are the most crucial factors influencing
the oxide thickness measurement. Long-term drift can
be associated with just the mere taking of a wafer from a
nitrogen storage environment to the laboratory air
environment.
A series of tests was performed exemplifying the film
thickness variation with surface treatments. One in
particular, using a hotplate to desorb organic
contaminants, was performed to see what magnitude of
film thickness change could be expected. In addition, a
somewhat crude but effective sample isolation chamber
was affixed to the ellipsometer's wafer vacuum chuck to
allow a source of water vapor to change the relative
humidity near the sample surface. A test was performed
by measuring as a function of time the film thickness
change as the water vapor source was taken in and out of
the chamber.
Results of Testing
Fig. 2 shows the corresponding change in \j/ with
humidity for a wafer having a 10 nm thick oxide and
exposed repeatedly to a moisture source using the above
described chamber having openings to let the incident
and reflected beams through.
In this experiment a
relative change in humidity of 20 % gave a change in
thickness of approximately 0.1 nm. Fig. 3 also shows
the corresponding change in \\r with humidity for the
same sample for a weekend run in which the local
weather change more gradually affected the laboratory
room air. Here the thickness change was close to 0.3 nm
for a 30 % change in relative humidity.
Table 3 shows an example ellipsometric measurement
of data taken on a wafer with a native oxide that yielded
an excellent fit to the interlayer model. This was
accomplished by fixing the interlayer thickness, oxide
refractive index, and silicon extinction coefficient (real
part allowed to vary).. The MSE value (mean square
error in the fit) is very small because two parameters
were allowed to vary. Here, EMA is the effective
medium theory that was used to calculate the interlayer
refractive index.
Initial film thickness: nominal 20 A
plus 2.57 A c o n t a m i n a n t s
I °3"
e l a p s e d time ( m i n u t e s )
Figure 4. Hotplate desorption.
Table 3
]experimental data on native oxide sample:
K
(332.8
time (2 minute intervals)
(|>
74.00
\i/
3.364
A
161.37
]Model
Figure 2. Film Thickness (\|/) variation with enclosed humidity
controlled chamber
2 oxide
1 EMA si-50 %
0 si
Fig 4 shows the changes in thickness that can occur
from contamination. Here a 2 nm thick oxide was
measured before and after being put on a hotplate (300
°C for 4 min.). It was found to have initially lost
approximately 0.25 nm and then grow back about 0.04
nm in an hour. Therefore, a method used for reporting
the thickness of the uncontaminated oxide is of great
importance.
0.9988 nm
0.7 nm
1 mm
1Fit to data:
MeanSquareError=4.558e-010
nSi 3.872
kSi =0.0156
][nterlayer thickness t=0.7 nm
]Results: Oxide thickness 0.999 nm
]Fixed parameters: SiO2 n=1.461
CONCLUSIONS
Even when one has access to a high-accuracy and
precise ellipsometer, along with standardized regression
software, ellipsometric measurements will still be
subject to two factors, (1) film surface contamination,
which directly affects precision and (2) the adequacy of
the model, which does not directly affect precision.
With the use of this ellipsometric instrument, operating
at optimal sensitivity for thin film measurement, using
consistent models, reliable optical constants, and a
proper regression analysis, the precision of film
thickness measurements is still very dependent upon
being able to control and monitor film contamination.
8t~0.3nm -
Weekend Run 3/9-3/11 2002
12nm oxide. Al = 75.23 deg, Pol=7.6
500
1000
1500
time (2 minute intervals)
Figure 3. Film thickness (\\t) variation with changes in room
humidity.
329
However, with good sample film surface control the
guidelines for roadmap film thickness precision can be
met. Secondly, because of the indirect nature of the
ellipsometric measurement, it will always be true that
high measurement precision can be obtained quite easily
compared with the ability to measure the film thickness
accurately.
With that in mind the following general conclusions
can be made for making precision measurements on very
thin oxide films: First, all ellipsometric instrumentation
software for data analysis must use the same models,
optical constants and regression parameters. These
factors can be easily checked by processing simulated
data.
Secondly, the accuracy and precision of the
ellipsometer is not always known, especially if it is one
designed for production, because speed and automation
are often the design factors, and not necessarily accuracy
of ellipsometric parameters. Only instruments with
proven accuracy in ellipsometric values of A and ij/ and
the angle of incidence can be used.
Finally, reproducible film thickness measurements
depend on a "clean" surface and will vary with
contamination from water and organic vapors. The
present study and use of a hotplate to desorb
contaminants thermally, monitoring and control of room
temperature (1 °C) and relative humidity (<5 %), gives at
this time one method to begin to obtain a relatively
precise prediction of the film thickness within the
guidelines of the semiconductor roadmap.
ACKNOWLEDGEMENTS
This work was supported by the NIST Office of
Microelectronics Programs (OPM).
REFERENCES
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al., NIST SP 260-109, "Standard Reference Materials:
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Parameters A and \|/ and Derived Thickness and Refractive
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2) Easwarakhanthan, T., and Pigeat, P., "Error Propagation in
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