Status and Prospects For VUV Ellipsometry
(Applied to High K and Low K Materials)
N.V. Edwards
Advanced Products Research and Development Laboratory, Semiconductor Products Sector, Motorola Inc.
Abstract. The recent commercialization of Vacuum Ultraviolet spectroscopic ellipsometry (VUV SE) instruments
means that it is now possible to routinely perform SE measurements at wavelengths below 190 nm. This new capability
has obvious implications for lithographic work but also for the characterization of other materials of importance to the Si
industry. These are materials that are nominally transparent at long wavelengths but that possess unique absorption
signatures in the VUV, such as newly emerging high-k gate materials (e.g. Al2O3, HfO2, ZrO2, Y2O3) and low k
materials (porous SiO2, organo-silicate glasses), as well as more familiar dielectrics (e.g. SiOxNy, Si3N4, SiOF, and
TEOS). We provide a review of recent progress and a critical assessment of the capabilities of VUV SE with respect to
a selected examples of these materials, with special emphasis on low k and high k materials. These capabilities include
increased access to unique VUV spectral features as a means of tuning process parameters and increased ability to
determine the thickness of thin films grown on Si. We also address the initial challenges that had to be overcome in
order to develop optical constants at short wavelengths and to enable this sort of materials characterization.
nominally transparent dielectrics and in terms of
increased sensitivity for measuring thin films. We will
conclude with a critical assessment of measurement
capability for high and low k dielectric materials. For
high k materials, we will assess the ability of the
technique to simultaneously determine optical
constants and film thickness for the very thin films
required by increasingly shrinking device dimensions.
The sensitivity of ellipsometric fitting routines to the
presence of interface layers is a necessary part of this
discussion, and the ability to measure band gaps of
new gate materials when good values for optical
constants are obtained will be discussed as well. For
low k materials, a special emphasis will be given to
issues concerning the ability to measure porosity and
electron density, in the context of the complicating
presence of low index inclusions. Further, we hope to
elucidate the origins of the issues, as the limitations
that we encounter are less a consequence of working in
a new spectral region but are rather more endemic to
SE measurements and data analysis routines in
general.
INTRODUCTION
Scope of Work
With the economic impetus provided by
157nm lithographic applications, Vacuum Ultraviolet
Spectroscopic Ellipsometry (VUV SE) has made a
recent
transition
from a
synchrotron-based
characterization technique more suitable for basic
research to a workhorse for industrial problem solving.
For this to occur, significant challenges associated
with instrumentation and data analysis had to be
solved. The work presented here is not simply a
general review of progress toward this transition;
rather, it will also be a critical assessment of the
capabilities of the technique with respect to key
microelectronic applications. In other words, in the
context of advanced gates and interconnects, what can
be measured and what cannot? During the course of
answering these questions, a good portion of the
evolution of the technique will be discussed by default.
Toward this end we will provide a quick
introduction to ellipsometry, followed by a discussion
of the initial challenges faced by those first using the
technique in an industrial setting.
We will
demonstrate the advantages of VUV SE with respect
to increased access to unique spectral features for
Introduction to Ellipsometry
We are perhaps most familiar with
ellipsometry in its incarnation as an in-line metrology
CP683, Characterization and Metrology for ULSI 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
723
k
2
1 
ε  1+
2 
(2νεσ )2 
1
=
2
2
ε1
Real(Dielectric Constant),
HfO2
2.0
3.0
1.5
2.5
1.0
2.0
0.5
1.5
0
2
4
6
8
Photon Energy (eV)
Index of refraction ’n’
2.8
(b)
0.60
Al2O3
n
k
2.4
2.0
1.6
0
0.0
10
0.40
0.20
300
600
900
1200
Wavelength (nm)
1500
0
1800
‘K’
(2νεσ )2 
2.5
ε1
ε2
Extinction Coefficient
1 
ε  1+
2 
1
=
3.5
ε2
n
2
(a)
4.0
Imag(Dielectric Constant),
tool, where index of refraction n and sample thickness
d are delivered at 633nm. Ellipsometry is far more
versatile than this single application, however. It can
be operated in static or dynamic mode, at single
wavelengths or over wide spectral ranges.
Traditionally, spectroscopic ellipsometry (SE) has
been performed from 1770 to approximately 190 nm,
and in static mode, it is heavily used for material
diagnostics, e.g., determination of band gap, alloy
composition, porosity and strain.1,2 Measurements in
dynamic mode range from such diverse applications as
the control or monitoring of semiconductor thin film
growth, etching processes and deposition of proteins
on semiconductor surfaces. See Refs. 1 and 2 for a an
excellent introduction to SE capabilities and system
configurations.
SE is an optical characterization technique
that is used to determine the complex reflectance ratio
ρ = rp rs-1 where rp and rs are the complex reflectances
of light polarized parallel (p) and perpendicular (s) to
the plane of incidence, respectively. From ρ, optical
constants are determined. These are the quantities
required by device designers, crystal growers, and
manufacturing engineers: index of refraction n,
extinction coefficient k, and dielectric function ε.
These are related to one another by the following:
FIGURE 1. Optical functions in the spectral range
associated with traditional spectroscopic ellipsometry. (a)
Real (ε1) and imaginary (ε2) parts of the dielectric function
for a monoclinic hafnia film. (b) Real (n) and imaginary
parts (extinction coefficient k) of the index of refraction for a
c-plane oriented Al2O3 (ordinary component).
polycrystalline and structurally inhomogeneous
materials.2 With SE, film thicknesses can be
determined, properties of buried interfaces and
surfaces can be studied, and measurements can be
performed in any transparent ambient. Until recently,
however, none of this could be done in an industrial
setting at wavelengths below 190nm—which marks
the beginning of the spectral range commonly referred
to as the “Vacuum Ultraviolet.”3

+ 1


− 1

where ν and σ are conductivity of the material and the
frequency of the impinging plane wave of radiation,
respectively. It should be pointed out that n and ε are
complex quantities, where n = n + ik and ε = ε1 + iε2.
When optical functions (i.e. optical constants given as
a function of energy or wavelength) are reported, it is
customary to give both the real and imaginary part of ε
or n, as shown in Fig. 1 (a) and (b), respectively. For
in-line metrology tools, values at 633nm (or ~2 eV)
are typically given. Here the extinction coefficient k is
0 for the majority of materials measured with these
instruments, given that most common dielectrics and
wide bandgap materials are transparent at this
wavelength.
Consistent with the classic definition of ε
from freshman physics (where ε is related to the dipole
moment per unit volume), the sensitivity of SE to the
presence of long range order on the scale of ~10 Å to
100 Å means that the technique is a non-destructive
means of measuring the density of amorphous,
The Industrial Need for Measurements in the VUV
Regardless
of
system
configuration,
ellipsometry had been traditionally performed in air
and with quartz optical elements, both of which are
absorbing at spectral wavelengths below 190 nm. The
exception was the Ultra-High Vacuum SE system at
the BESSY I synchrotron in Berlin, which had
provided a means for researchers to relate newlymeasured optical features in the VUV with the
electronic bandstructure of novel wide bandgap
materials.4 Routine, high throughput determination of
short wavelength optical constants for materials of
interest to the Si industry, e.g., photoresists, ARC
layers, high-k gate materials, photomasks, passivation
layers, or interlayer dielectrics—either at accuracies
demanded by manufacturing and production
environments or with the large, widely varying sample
sets needed to properly tune process parameters—had
724
associated with microscopic polarization phenomena
into the macroscopic sample properties of interest: thin
film thicknesses, optical constants, compositions,
porosities, etc. In other words, we cannot use
ellipsometry to directly measure much of the
information of interest to industrial customers. An
‘optical model’ is needed to bridge the gap. This
model is an ideal mathematical representation of the
sample that allows us to calculate its polarization state
change in terms of physical properties like thickness,
refractive index, and composition. For each sample, ρ
is calculated to match the experimental data, using
multilayer mathematical models that contain
parameters, such as layer thickness or composition,
which are independent of the parameters varied in the
measurements. Model parameters and their confidence
limits are then obtained by linear regression analysis
with the commercial software packages that
accompany ellipsometric instruments.3 A cartoon of
this process is given in Fig. 2. Here, a general
representation of an ellipsometer is given in the top
portion of the figure, with χi and χf representing the
initial and final polarization states, respectively. ρ can
also be determined from χ: ρ = rp rs-1 as well as ρ =
χi/ χf. How ε is calculated from ρ is more
complicated, however. A brief explanation of this
process will also explain why there were initial
challenges associated with obtaining optical constants
in the VUV.
not been achieved due to a lack of instrumentation
feasible for use in an industrial setting. 3
Entrance
Optics
χi
ϕ
Sample
Detector
Exit
Optics
χf
χ→ρ→ε
131 to 1770 nm
Experimental Data
80
300
ExpΨ-E 65°
Exp∆-E 65°
60
200
Ψ in degrees
∆ in degrees
40
100
20
0
0
0
2
4
6
8
Photon Energy (eV)
-100
10
Model
Sample Properties:
d, n, k, ε
composition
roughness
bandgap
porosity
FIGURE 2. Schematic diagram of ellipsometer (top) and
the ellipsometric modeling process (bottom).
The need for short wavelength optical
constants by those designing optical elements for 157
nm lithography provided the economic motivation for
commercial development of such instrumentation.
Optical constants at 157nm are required for the design
of photoresists and pellicles, but also for simulations
that optimize (either minimizing or maximizing)
reflectivity for the design of ARCs and other mask
components for increased inspection contrast at
multiple wavelengths.5 The recent introduction of
commercial VUV SE instruments means that it is now
possible to routinely perform spectroscopic
ellipsometry measurements at wavelengths below 190
nm. The development of enclosed, nitrogen-purged
systems and the use of deuterium lamp sources and
MgF2 optical elements have extended the measurement
range of combined IR/ VIS/ VUV systems to span
from as low as 131 nm to as high as 1770 nm, with
relatively fast data acquisition times on the order of
several hours.3 This, however, did not guarantee that
accurate optical constants and materials diagnostics
readily followed from such measurements as a matter
of course.
3-phase model:
ambient εa
overlayer εo
d↕
a)
substrate εs
overlayer εo
b)
ε
substrate εs
=
ε
s
+
4 π id
λ
n a ε s (ε
} <ε>
}
Source
εs
)( − )
−
s ε o ε o ε a ε s −
sin
ε
ε o (ε s − ε a )
 a

2ϕ 


INITIAL CHALLENGES
FIGURE 3. (a) Schematic diagram of the pseudodielectric
function. (b) On left, what model assumes (mathematically
sharp interfaces). On right, what is encountered in reality
(interface layers, contamination, surface roughness). The
expression for the pseudodilectric function in the three-phase
model is given below.
Introduction to SE Data Analysis
Advances in instrumentation aside, reducing
data to determine optical constants in the VUV at the
throughputs and accuracies demanded in industrial
settings was initially very difficult. This had less to do
with challenges specific to the VUV and more to do
with the inherent nature of SE. The general challenge
of ellipsometry is to convert measured quantities
In the case of multilayer samples, either an
accurate mathematical description of the optical
dispersion of each layer must be generated or optical
constants must be known for each layer before a good
725
model can be constructed. 6 We will see that this refers
to intentionally deposited layers as well as
unintentional layers, such as interface layers, surface
roughness and contamination. This follows from the
basic definitions of ε. In the two–phase model2 (where
the two phases are defined as the substrate and
ambient), we can write an expression for the dielectric
function of the substrate in terms of the experimental
parameters χi, χf and the angle of incidence φ:
1− ρ 
ε s = sin ϕ + sin ϕ tan ϕ  1 + ρ 
2
2
εs is the foundation for the entire ellipsometric
modeling process. In an industrial characterization
laboratory, where most materials submitted for
analysis are multilayer samples consisting of materials
grown on Si substrates, the lack of optical constants
for Si in the VUV presented a major stumbling block
that had to be removed before analysis of the materials
of interest could proceed.
Since the optical properties of Si at lower
spectral energies are well understood, it was possible
to follow the example of previous workers to obtain
VUV optical constants. After the work of Herzinger, et
al.,7 a thermal oxide series was generated on Si,
consisting of nine samples, ranging in nominal oxide
thickness from 20 Å to 2200 Å. VUV SE
measurements were performed from 131 nm to 1770
nm at angles of incidence ranging from 40° to 75°. The
resulting optical constants for Si are shown in Fig. 4
and agree well with the prior work performed at lower
energies.8, 9, 10 The inset is a magnification of the VUV
region, where a new critical point was discovered. It
likely corresponds to a direct, band-to-band transition
between the X1V-X1C valence and conduction bands,
respectively. 11
2
2
In ellipsometric terms, the mechanism for
accounting for other layers is via the three-phase
model.2 This consists of a simple substrate/ overlayer/
ambient system where mathematically sharp interfaces
are assumed, as shown in Fig. 3a. Reality often
consists of that shown in Fig. 3b: interface layers,
oxides, roughness and other non-idealities. The full
expression for the three phase model is given in Fig. 3,
where the three phases are analyzed as two, resulting
in the combination of εo and εs into the pseudodilectric
function <ε>. The pseudodilectric function is a
weighted average of the heterostructure layers
penetrated by the measurement, which of course is a
function of wavelength. Hence, in the modeling
process, interface layers become more important for
long wavelength measurements and surface roughness
becomes more important for short wavelength
measurements. Since penetration depths of most
semiconductors are on the order of several hundred
Ångstroms in the VUV,2 this can seriously complicate
the measurement of thin films, as we will see in the
upcoming discussion. At any rate, we introduce the
concept of the three-phase model to show how
overlayers are accounted for in calculations of the
dielectric function and in doing so, to emphasize that
models must account for all heterostructure layers
present—whether intentional or unintentional-–or risk
the introduction of large uncertainties into the
determination of optical constants. Indeed, if the
model does not accurately describe all of the layers
present in the sample, then the interpretation of the
data is seriously compromised—even if the data
themselves are of the highest quality.3
pseudodielectric function
2.8
Si
50
2.3
New Critical Point:
X1v-X1C transition
30
1.8
7.2
ε1
10
7.7
8.2
ε2
Motorola11
-10
Aspnes8
Herzinger7
Jellison9
Yasuda10
-30
0
2
4
6
8
10
energy in eV
FIGURE 4. VUV optical constants for Si (black curve)
shown in the context of prior work at lower spectral
energies. The inset shows a magnification of the VUV
spectral region where a new transition corresponding to a
direct, band-to-band transition between the X1V-X1C valence
and conduction bands was discovered. (Originally
commissioned by Semiconductor Fabtech and printed in
Edition 18, 2003.)
These optical constants were obtained with:
(1) the Gaussian-Broadened Polynomial Superposition
(GBPS) parametric dispersion model of Herzinger and
Johs 12 to represent the optical dispersion of the Si
layer; (2) a Tauc-Lorentz model13 (which is typically
used to describe the optical dispersion of amorphous
materials) to represent a Si-SiO2 interface layer; and
(3) a Tauc-Lorentz model to represent the SiO2 layer.
The Need for VUV Optical Constants for Si
The complexity of building ellipsometric data
analysis models that represent the multiplicity of
layers present in actual samples also strongly
emphasizes the importance of understanding the
optical dispersion of the substrate layer. Knowledge of
726
samples and a common fit was performed. In Fig. 6 a
and b we show the results of the common fit for the
thinnest and thickest sample, respectively, to illustrate
the validity of the assumption that the optical constants
for Si and SiO2 are largely the same across the sample
set. (Fits for samples of intermediate thickness are
shown later in the discussion, in the context of
increased sensitivity to film thickness for the
measurement of thin films.) While it is reasonable to
grant that the interface layer may vary for samples of
different thickness, grown by under slightly different
deposition conditions, we did not have sensitivity to
this degree of variation in the samples. Indeed, an
interface layer of 7 Å was initially assumed for all of
the samples, but this coupled thickness was eventually
released in the fitting and a coupled thickness value of
9.4 was obtained. Further details will be discussed
elsewhere, as this work is still in progress.
The mathematical formalism for these is described
further in Refs. 12 and 13, but most are part of the
standard recipes included in commercial ellipsometric
data analysis software (or can be readily programmed).
In this case, a multi-sample analysis was performed.
This type of analysis is predicated on the assumption
that the optical constants for the materials are the same
in each sample, independent of thickness. The data
analysis is performed simultaneously for all samples,
with the optical constants of each material coupled in
all models for all of the samples. Thus it is possible to
reduce strong correlations that often occur between fit
parameters.12
SiO2: Tauc-Lorentz oscillator
Amp= 40.024, En= 10.643, C= 0.72608, Eg= 7.5258
Pole 1: Pos= 13.167, Mag= 94.386
Pole 2: Pos= 0.135, Mag= 0.0127
E1 offset= 1.263
Interface Layer: Tauc-Lorentz oscillator
Amp= 158.67, En= 10.643, C= 0.72608, Eg= 7.5258
Interface Layer
Pole 1: Pos= 13.167, Mag= 94.386
Pole 2: Pos= 0.135, Mag= 0.0127
Si: Parameterized Semiconductor Layer
2.00
FIGURE 5. Additional details concerning fit parameter for
data ellipsometric models for analysis of Si and SiO2 VUV
SE data.
(a)
Data: ε1, blue
ε2, green
Model: red
Thinnest Sample:
SiO2
Int. Layer 9.4 Å
100
(b)
Si Substrate
Ψ in degrees
Int. Layer 9.4 Å
200
60
100
40
1.80
0.040
1.70
0.030
1.60
0.020
1.50
0.010
2
4
6
Photon Energy (eV)
8
0
300
600
900
1200
Wavelength (nm)
1500
0.000
1800
Since SiO2 is also an important material for
the microelectronics industry—and as it is a byproduct of the analysis used to obtain Si optical
constants—these optical constants are shown in Fig. 7.
Note the absorption edge near 160 nm; this edge
cannot be seen with traditional IR/ VIS/ UV
ellipsometry. 3
0
20
0
0
∆ in degrees
2189.3 Å
300
80
Thickest Sample:
0.050
FIGURE 7. VUV optical constants for SiO2: index of
refraction n (solid) and extinction coefficient k (dashed).
(Originally commissioned by Semiconductor Fabtech and
printed in Edition 18, 2003.)
Si Substrate
SiO2
1.90
1.40
7.5 Å
0.060
n
k
SiO2
Extinction Coefficient k
Index of refraction n
E1 offset= 1.5705
-100
10
FIGURE 6. Sample fits for thin (a) and thick (b) SiO2
samples grown on Si substrates. The fit was a by-product of
a multisample analysis that involved the simultaneous fitting
of nine thermal oxide samples of various thickness.
ADVANTAGES AND APPLICATIONS
OF VUV SE
Additional information about fit parameters is
given in Fig. 5. Here the parameter values for the
Tauc-Lorentz oscillators used for the interface and
SiO2 layers are shown. All parameters in the interface
layer of a given sample were coupled to the
corresponding parameter in the SiO2 layer of the same
sample, with the exception of the Amplitude and E1
offset. (This was done in order to allow the index of
the interface layer to vary.) As well, all of the
parameters were subsequently coupled for the nine
With the optical constants of the substrate and
its oxide determined, it became possible for us to
analyze a wide variety of materials grown on Si
substrates. These materials span a wide range of
industrial applications—in addition to the obvious
lithographic work for which the VUV technique is so
well suited. We have selected a few examples
designed to illustrate the capabilities of VUV SE
compared to standard IR/ VIS/ UV systems. Since our
own system is a combined IR/ VIS/ VUV system,
727
constants to distinguish between nominally similar
organo-silicate glasses in order to correlate optical and
mechanical properties for interlayer dielectric
applications; 14 to correlate optical and electrical
properties for SiNx films for MIM capacitor
applications15; and for the development of novel ARC
layers to enable the inspection of reticles for 157nm
and EUV lithography.5 An example from the latter
application is given in Fig. 8. Here the extinction
coefficient k vs. wavelength is plotted for a selection
of SiOxNy films of different compositions (as
determined by Rutherford Backscattering16) deposited
on Si. At wavelengths above ~200 nm, all of the
samples are transparent. Accordingly, k = 0.17 In the
VUV, the optical properties of the films are all very
different and composition dependent (the red labels
provide a summary of the RBS results). Not
surprisingly, films without nitrogen have optical
properties similar to SiO2. As the oxygen and nitrogen
concentration increases, optical structure is introduced
into the extinction coefficient lineshape. The greater
extinction coefficient seen for these films reflects the
fact that the these films are more absorbing, as
absorption coefficient α is related to the extinction
coefficient k by the expression k = (λ/ 4π) • α.17
Clearly one must be careful to select the appropriate
nitrogen and oxygen composition of SiOxNy films if
they are to be used for 157nm or other lithographic
applications.3
spanning a spectral range of 131 nm to 1770 nm, we
obviously view the two systems as complementary.
The addition of the VUV capability, however, has
some distinct advantages.
Extinction Coefficient k
0.5
SiOx Ny
0.4
0.3
Equal Parts Si, N, O
0.2
Si: mid 30%
O: high 40%
N: high teens
0.1
No Nitrogen
0
100
150
200
250
300
Wavelength (nm)
FIGURE 8. Extinction coefficients in the VUV for a series
of SiOxNy films of varying compositions. Compositional
information (as determined by RBS) is given by the red
labels. Note the large differences seen in the VUV between
the films. At longer wavelengths, the films are transparent
and indistinguishable. (Originally commissioned by
Semiconductor Fabtech and printed in Edition 18, 2003.)
Increased Access to Unique Spectral Features
Many of the materials used in Si processing
are nominally transparent at long wavelengths:
SiOxNy, organo-silicate glasses, Si3N4, SiOF, and
TEOS are familiar examples. Additionally, many of
the new high-k gate materials under consideration by
the semiconductor industry—e.g., Al2O3, HfO2, ZrO2,
Y2O3 –are wide bandgap materials and can be included
in this category as well. This is quite convenient for inline optical metrology, as it allows for the use of
relatively simple mathematical formalisms to build
optical models and recipes for use at 633nm. However,
this also means that it can be very hard to distinguish
between films of the same material grown under
slightly different conditions, based on what can often
be very small changes of index of refraction at and
near 633nm. For these materials, gaining access to the
absorption behavior in the VUV gives us a foothold
for additional materials diagnostics; ie. we now have a
way to distinguish between films that otherwise appear
very similar when measured with a standard IR/ VIS/
UV system or in-line metrology tool. 3
We have found this newly available access to
VUV absorption behavior useful for tuning process
parameters to address mechanical, electrical and
optical performance issues of blanket depositions of
many materials used throughout the CMOS process.
Indeed, VUV SE has been used to determine optical
10
HfO2

8
ε1
6
monoclinic
4
amorphous
2
0
0
2
4
6
8
10
8

6
ε2
amorphous
4
monoclinic
2
0
0
2
4
6
8
10
Energy in eV
FIGURE 9. The real and imaginary part of the dielectric
function ε = ε1 +ε2 are plotted vs. energy for an as-deposited
HfO2 film (blue curve) and for two HfO2 films that have
been annealed post-growth (black and yellow curve). In the
VUV, large differences between the annealed and as-grown
films emerge. At lower energies, the films are transparent
and indistinguishable. (Originally commissioned by
Semiconductor Fabtech and printed in Edition 18, 2003.)
728
We observe similar behavior for HfO2,
potentially of interest for high-k gate applications.
Optical constants for three HfO2 films are shown in
Fig. 9.18 The real and imaginary parts of the dielectric
function ε = ε1 + i ε2 are plotted vs. energy for an asdeposited film (blue curve) and for two films that have
been annealed post-growth (black and yellow curve).
Just below 6 eV (above ~200nm) the material is
transparent, deducible from the fact that ε2= 0
(analogous to k=0).17 Note that the differences in ε1 are
very small in this region, which makes it difficult to
distinguish between the films by optical means. In the
VUV, large differences between the annealed and asgrown films emerge: the as-grown film lacks the
optical structure apparent for the other films, important
because these features are related to direct band-toband electronic transitions identifiable in HfO2 band
structure. X-ray diffraction analysis19 indicated that
the as-grown film was in fact amorphous while the
annealed films were of the monoclinic phase, meaning
that the relative lack of optical structure in the one
case can be accounted for by differences in electronic
structure expected for an amorphous vs. crystalline
film. Thus we have a means to differentiate between
HfO2 films grown under different conditions and for
interpreting the electronic structure of the different
phases of HfO2 that often emerge with different
growth conditions in these films.20
100
Model Fit
Data 65°
Data 70°
Data 75°
185 Å Al2O3
80
Ψ in degrees
Si Substrate
60
40
20
0
0
2
4
6
Photon Energy (eV)
8
10
FIGURE 10. Ellipsometric data (green dotted lines) and
model fit (red solid line) for a 185 Å thick Al2O3 film, at
three angles of incidence. The spectra for this relatively thin
film are dominated by a single interference oscillation near
6.7 eV, highlighted with the red arrow. The location of this
oscillation in the VUV illustrates the extra capability that the
instrument provides for measuring thin films on absorbing
substrates. (Originally commissioned by Semiconductor
Fabtech and printed in Edition 18, 2003.)
with the red arrow. The location of this oscillation in
the VUV illustrates the extra capability that the
instrument provides with respect to measuring thin
films on absorbing substrates. If a film is sufficiently
thick to build up one cycle of interference, we can
exploit the classic conditions for thin-film interference
to determine optical thickness of the sample, assuming
that the film is transparent. In the three-phase model,
the phase θ is given by 2k0⊥d, where wavevector
k=2π/λ.6 For one cycle of interference (i.e. one
interference oscillation), the phase change ∆θ is given
by 2π = ∆θ = (4πnd/ hc) ∆E, where E is spectral
energy, h is Planck’s constant, and c is the speed of
light. Since ∆E = -(hc/ λ2) ∆λ, we can substitute the
latter equation into the former and determine that
λ2 /∆λ = -2nd. Note that for a thin film, the quantity
defining the spectral width ∆λ of the interference
oscillation will be relatively large, as thick films
produce more oscillations in the same spectral energy
range than a thin film. Therefore, neglecting optical
dispersion and angle of incidence effects, we observe
that for small values of film thickness d,
interference—or that which enables us to determine
the optical thickness of the film— will occur for small
values of λ. We demonstrate in Fig. 11, which
features ellipsometric data (data shown in green;
model fit in red) vs. energy for a series of increasingly
thick SiO2 films grown on Si. For the thinnest film
(95Å shown in Fig. 6a), the interference oscillation is
located just outside of our spectral range; only the low
energy edge is visible near 9 eV (cf. red arrow). This
film is too thin to determine n and d independently;
here we used a multi-sample analysis approach to
Increased Sensitivity to Film Thickness
Accompanying the increased access to the
VUV spectral range is an increased ability to
determine film thickness for thin films deposited or
adsorbed on substrates. The more rigorous arguments
justifying this premise are based on the solution of the
Fresnel reflectance expressions for a three-phase
model (i.e. ambient/ film/ substrate)21 for the optical
thickness (nd) of the sample in terms of the
ellipsometric parameter ρ and angle of incidence φ.
From this analysis, the concept of a thickness period
Dφ is developed, where shorter wavelengths will move
through one complete period for smaller values of film
thickness, since the thickness period is directly
proportional to spectral wavelength. The reader is
referred to Refs. 22 and 23 for a more complete
treatment.
This principle can also be demonstrated
empirically. In Fig. 10 we show ellipsometric data
(green dotted lines) and model fit (red solid line) for a
185 Å thick Al2O3 film, a material of interest for highk gate applications. The ellipsometric angle Ψ is
plotted vs. energy at three angles of incidence. The
spectra for this relatively thin film are dominated by a
single interference oscillation near 6.7 eV, highlighted
729
one of the monoclinic hafnia films18 discussed
previously. When optical constants are obtained for a
material, it is possible to use them in conjunction with
the Si substrate optical constants to simulate
ellipsometric data. This was done to simulate the
equivalent data for a “series” of films deposited on Si,
all of varying thickness but with the same optical
constants. We do so in order to determine a projected
range for the minimum thickness required to determine
n and d independently for the hafnia film, as per our
earlier discussion. The results of the simulation are
shown in Fig. 12. Here ellipsometric angles (Ψ) were
simulated (assuming a Si substrate) to create a series
of curves analogous to the data series in Fig. 11. In this
case, the interference oscillation of interest arises near
6.5 eV for a 50 Å film deposited on Si. In other words,
for simulated thicknesses less than 50 Å one cycle of
interference has not yet been completed. Since
projected thicknesses for hafnia gates are in the 40 to
50 Å range, for this particular hafnia film we are
unable to determine n and d independently (or could
barely do so in the best case). This casts doubt on the
ability of VUV SE to measure the thickness of thin
hafnia gate material unless the optical constants are
previously determined.
reduce correlations between fit parameters. We are,
however, able to de-correlate d and n for a SiO2 145 Å
film on Si. In Fig. 11b, for a 145 Å film the entire
interference oscillation is contained within our spectral
range, exhibiting a maximum at 9eV. The 500 Å film
(11c) is sufficiently thick so as to generate two
interference oscillations. The first oscillation is now
located near 5 eV, well within the measurement range
of standard IR/ VIS/ UV systems. The extended
spectral range of VUV instruments therefore provide
an increased ability to determine the thickness of thin
films grown on Si. 3
(a)
Ψin degrees
80
95 Å SiO2
60
*
Si Substrate
Model Fit
Data 40°
45°
50°
55°
60°
65°
70°
75°
40
(b)
Ψin degrees
20
0
80
145 Å SiO2
60
Si Substrate
40
20
60
50
500 Å SiO2
40
20
0
0
*All model fits include a 9.4 Å interface layer
2
HfO2
40
Si Substrate
Psi
(c)
Ψin degrees
0
80
4
6
8
Photon Energy (eV)
10 Ang
20 Ang
30
30 Ang
20
40 Ang
50 Ang
10
60 Ang
0
10
0
2
4
6
energy in eV
FIGURE 11. Ellipsometric data (data shown in green;
model fit in red) vs. energy for a series of increasingly thick
SiO2 films grown on Si: (a) 95 Å; (b) 145 Å ; (c) 500 Å .
The interference oscillation that is located just outside of the
VUV spectral range moves into view (cf. red arrow) as the
SiO2 film thickness increases. This enables the determination
of film thickness. (Originally commissioned by
Semiconductor Fabtech and printed in Edition 18, 2003.)
8
10
Projected gate thickness 40-50Å
FIGURE 12.
Three-phase model calculations of
ellipsometric data for hafnia films grown on Si substrates.
∆d= 10 Å. Note that the interference oscillation needed to
allow for the independent determination of n and d occurs at
only 50 Å.
However, one could argue that this problem should
be almost trivial to solve, after the initial research on
optical constants are performed on thicker films. After
all, this is the approach taken with in-line metrology
tools for the measurement of thin films of SiO2 on Si.
As well, a multi-sample analysis could be undertaken
to aid in this fundamental work, similar to work done
in the Si/ SiO2 system. There are two strong objections
to this line of thinking for hafnia. First, hafnia films
have been observed to change phase with thickness.19
The assumption that optical constants are the same for
films of varying thickness both invalidates the main
premise of the multisample analysis and prevents the
STATUS AND PROSPECTS
Critical Issues for High- k Materials
The previous discussion is a convenient segue
into the topic of critical issues for determining optical
constants and film thickness of new high k dielectric
materials—where very often the thickness of the films
required for gate applications are insufficiently thin to
allow for the independent determination of n and d.
We illustrate with the optical constants obtained for
730
facile application of in-line metrology tool recipes
predicated on the analysis of thicker films. Second,
because the films under consideration are relatively
thin, both the interface layer between film and
substrate and surface roughness layer becomes a
significant portion of the measured film stack in the
VUV (recall the argument that penetration depths of
most semiconductors are on the order of a few hundred
Ångstroms in the VUV). This means that obtaining
optical constants, even for relatively thick films (i.e.
on the order of several hundred Ångstroms) is
nontrivial. We illustrate by examining the fitting
procedure for the previously discussed monoclinic
hafnia film and then by demonstrating the sensitivity
of VUV optical features to growth parameters, which
further complicates the application of standardized
recipes for data analysis.
Interface Layer
Si Substrate
207 Å
2Å
1 mm
80
300
MSE= 1.6956
60
100
40
0
0
2
4
6
Photon Energy (eV)
8
2
4
6
8
10
12
14
16
Interface Layer Thickness in Ang.
FIGURE 14. Results of uniqueness fitting algorithm. This
involves fixing the fit parameter under evaluation to a range
of physically reasonable predefined values, where fits (with
other parameters not fixed) are performed at each value. The
relative Mean Squared Error is plotted vs. the fit parameter
under evaluation. Here, the minima in the curve indicates
that the optimal interface layer for the fit shown in Fig. 13 is
2 Å.
0
20
1.01
1
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0
200
∆ in degrees
Model Fit
Exp Ψ-E 65°
Exp Ψ-E 70°
Exp Ψ-E 75°
Model Fit
Exp ∆-E 65°
Exp ∆-E 70°
Exp ∆-E 75°
100
Ψ in degrees
9Å
Relative MSE
Surface Roughness
Hafnia
Lack of uniqueness in fitting of course arises
because of correlation between fit parameters that
result in “good” fits that yield multiple and
nonequivalent n and d combinations for roughly
similar Mean Squared Errors. In short, during the
course of analyzing ellipsometric data obtained on
hafnia films, we have discovered that the most relevant
question seems to be the degree of sensitivity to the
presence of both interface and surface roughness
layers. This degree of sensitivity appears to vary
according to the degree of optical structure in the
data,18 which we will see varies with growth and postgrowth processing parameters. We are currently
working to quantify the extent of this correlation.
-100
10
FIGURE 13. Ellipsometric angles Psi (green) and delta
(blue) vs. energy for a 207 Å thick monoclinic hafnia film.
Fit to the data is shown in red.
To verify the results obtained in Fig. 13, a fit
uniqueness algorithm25 was employed. This involves
fixing the fit parameter under evaluation to a range of
physically reasonable predefined values, where fits
(with other parameters not fixed) are performed at
each value. The quality of the fit is then evaluated at
each fixed parameter value in order to determine the
degree of sensitivity to the test parameter. That is, the
relative Mean Squared Error is plotted vs. the fit
parameter under evaluation. In Fig. 14, this was done
to evaluate the sensitivity to the thickness of the
interface layer for the fit shown in Fig. 13. Here we
see a distinct minima for an interface layer of 2Å, for
this particular sample. A similar minima was observed
for the surface roughness layer thickness value for this
fit as well. However, for other samples in the series,
we were not sensitive to the parameters under test, and
a flat curve was obtained for a similar plot (graphed on
a similar scale). Possible sources of this variation are
currently under investigation.
Ellipsometric angles Ψ and ∆ for a nominally
200 Å thick film are shown in Fig. 13. Data are given
in green (Ψ) and blue (∆); the fit to the data is shown
in red. This is same fit used as a basis for the
simulation in Fig. 12. The data were fit with a general
oscillator model in a commercial software
environment, with a 2 Å interface layer (a TaucLorentz oscillator model, similar to the SiO2 layer but
with different fit parameters) and a 9 Å surface
roughness layer (50 % voids in the EMA
approximation).24 Details of the fit will be given in
more detail elsewhere. We see from the Mean Squared
Error (MSE= ~1.7) and from visual inspection that the
fit is quite good; however, with these relatively thin
high k dielectric films, the challenge is not to obtain a
good fit, but rather to obtain a unique fit.
731
8
ε1
ε2
Option 1
Option 2
8
6
Second
direct
transition
6
4
x
Direct transition
4
2
0
Bandgap
Onset of
absorption due to
indirect gap.
The onset from the
model is 5.02 eV
2
2
exciton before
the bandedge
4
6
Photon Energy (eV)
0
10
8
207 Å thick
the dielectric
in green. The
given in blue;
12
8
e1
T2
Real Part of the Dielectric Function vs. Energy
10
9
8
7
6
5
4
3
2
1
0
Real Part of the Dielectric Function vs. Energy
10
e1
FIGURE 15. Optical functions for the
monoclinic hafnia film. The real part of
function is shown in red; the imaginary part
first interpretation of the observed features is
the second is shown in red.
Imag(Dielectric Constant), ε2
Real(Dielectric Constant), ε1
10
occurring near 7.5 eV (in red.)26 These features vary
with growth and/ or post-growth parameters, as seen
in Figs. 16 and 17, where with different growth and
annealing temperatures, different phases of hafnia
(most mixed phase combinations of monoclinic and
tetragonal,
according
to
X-ray
diffraction
measurements18) which results in different VUV
optical structure. Preliminary attempts to correlate this
optical structure with phase as determined by XRD are
complicated by the presence of this mixed phase
material, leading us to conclude that fundamental work
in the VUV with bulk samples is necessary before we
can understand the more complex thin film systems.
To demonstrate, we refer to VUV measurements and
analysis performed on another candidate high k
material, Al2O3.
6
4
2
0
T3
0
2
4
6
8
10
energy in eV
No anneal
Increasing
anneal temp
0
2
4
6
8
8 Imaginary Part of the Dielectric Function vs. Energy
10
7
Energy in eV
6
No anneal
5
Imaginary Part of the Dielectric Function vs. Energy
8
e2
Increasing
anneal temp
Monoclinic; all others mixed
phase (M + tetragonal) with
increasing percentage of
monoclinic phase with
increasing anneal temp
6
5
e2
4
3
7
4
3
2
1
0
0
2
4
6
8
10
Energy in eV
2
1
0
0
2
4
6
8
10
FIGURE 17. The real and imaginary part of the dielectric
function ε = ε1 +ε2 are plotted vs. energy for an as-deposited
HfO2 film (red curve) and for two HfO2 films that have been
annealed post-growth (blue, pink, and yellow curves), grown
at a different growth temperature than the films shown in
Figs. 9 and 16. . In the VUV, large differences between the
annealed and as-grown films emerge. At lower energies, the
films are transparent and indistinguishable.
Energy in eV
FIGURE 16. The real and imaginary part of the dielectric
function ε = ε1 +ε2 are plotted vs. energy for an as-deposited
HfO2 film (pink curve) and for three HfO2 films that have
been annealed post-growth (yellow, dark blue, and light blue
curves), grown at a different growth temperature than the
films shown in Fig. 9. In the VUV, large differences
between the annealed and as-grown films emerge. At lower
energies, the films are transparent and indistinguishable.
In Fig. 18a, we show optical functions for bulk cplane Al2O3. There are several points to consider for
this material. First, the more stable surface of Al2O3
eliminates concerns about surface preparation, save
accounting for surface roughness. We do so both in the
optical model used to fit the data and with
complimentary AFM measurements. For this substrate,
the RMS roughness was on the order of 5Å, averaged
between substrate center and edge values. The real and
imaginary parts of the pseudodielectric function
(dotted lines) are plotted vs. photon energy. Our model
fit (solid lines) and some IR/ VIS/ UV data from Yao
and coworkers (dashed lines) are shown for
comparison.27 Their user defined Cauchy fit is an
After a reasonable fit to the data was
achieved, optical functions ε = ε1 + iε2 can be
obtained and are shown in red and green, respectively,
in Fig. 15. The larger question of the interpretation of
these data, however, is still unanswered. In the same
figure we show two possible interpretations: option 1,
which consists of an onset of absorption preceding a
direct gap near 5 eV, with two higher lying direct
transitions located near 6 and 7.5 eV, respectively (in
blue), and option 2, where the feature in ε2 near 6 eV
is interpreted as an exciton before the bandedge
732
excellent fit to the data, until roughly 6.5 eV. Of
course, it is well-known that the Cauchy model is a
(a)
benchmark for the analysis of thin Al2O3 films on Si.
We see from this and the preceding example the
necessity for a thorough analysis of bulk high k
materials before proceeding with more complex
heterostructures. 29
(b)
c-plane Al2O3 substrate
7.0
Index of refraction ’n’
<ε1>
5.0
2.8
this work: model fit
this work: data
prior art: Yao, et al.
J.Appl. Phys., 1999
2.0
1.6
3.0
4.0
0.40
0.20
0
300
600
900
1200
Wavelength (nm)
1500
0
1800
Critical Issues for Low- k Materials
‘K’
4.0
0.60
n
k
2.4
Extinction Coefficient
6.0
From extensive investigations of low k
dielectric materials in our laboratory, the following
became apparent: while ellipsometry is sensitive to
differences in relative electron density in low k films
(recall the argument made about sensitivity to long
range order made earlier), the difficulty in data
analysis for these materials lies in the fact that multiple
unknown microscopic and macroscopic material
properties contribute to the averaged ellipsometric
information. Sensitivity to these material properties is
not the issue; rather, deconvoluting multiple correlated
parameters during the data analysis process is the large
challenge for low k materials. Even with the additional
information that the VUV provides, static
ellipsometric approaches are often not equal to the
challenges posed to them by the processing engineers.
We illustrate with a discussion
involving
organosilicate glasses (OSG). These materials are
best described as C-doped silica, where it is assumed
that the incorporation of CHx species introduces
porosity into the SiO2-like matrix. This is of course
one of the preferred means of achieving materials with
dramatically lower static dielectric constants,
hopefully without sacrificing robust mechanical
properties.
In contrast to high k materials, the interlayer
dielectric thicknesses are safely within specifications
that allow for the independent determination of n and
d. Each layer is typically hundreds to thousands of
Ångstroms thick, with the thickness of the entire ILD
stack typically on the order of 1000 Å.30 This is
fortunate, as these materials often shrink during the
course of imaging by scanning electron microscope,
meaning that the ability to determine n and d
independently, by ellipsometric means, becomes
crucial. Pore size and distribution, however, is the
desired information for these materials. And while
static ellipsometric measurements are certainly
sensitive to changes in pore size and distribution, we
maintain that it is unrealistic to extract meaningful
(detailed) information about these parameters from
such measurements—especially given that a slight
adjustment of processing parameters can riddle the
film with low index inclusions. These inclusions of
course complicate the analysis further and prevent the
facile application of in- line metrology recipes
predicated on the assumption that the films are always
<ε2>
3.0
2.0
rough surface
12.5 Å
Gen. Osc. Model
1 mm
1.0
0
0
2
4
6
8
Photon Energy (eV)
10
FIGURE 18. (a) Pseudodielectric function data (dotted line)
for Al2O3, from 0.7 to 9.5 eV. Our model fit, which involves
a superposition of several oscillators is shown by the solid
line, while the Cauchy fit of previous workers is given by the
dashed line. (b) Optical constants index of refraction n
(solid line) and extinction coefficient k (dashed) obtained to
fit to the data in (a). (After Ref. 29, reprinted with
permission)
good representation of the transparent region of any
optical spectrum. In the VUV the model fails, as
expected because of the critical point located just
above 9eV. To model both the transparent and
absorbing regions, our fit was a complex superposition
of two Lorentzians, one Gaussian, a pole and an ε1
offset term. (Details will be discussed elsewhere). The
identity of this critical point can be deduced from
previous VUV reflectivity work,28 where it was
observed that there was an exciton associated with the
O 2p nonbonding M0 bandedge, located just below the
bandedge in spectral energy. Both are located at 9.2
and 9.5 eV at 325K, respectively. Our data are
consistent with this interpretation; thus it is likely that
the observed critical point is the excitonic transition
just below the Al2O3 bandedge.29
However, optical constants obtained from
VUV reflectivity are subject to a variety of errors,
such as fluctuations in source intensity and issues
surrounding Kramers-Kronig analysis that requires
knowledge about optical constants beyond the
measured spectral range. Because SE measures the
ratio of two values, the data are not subject to such
errors. Indeed, once a good fit to the ellipsometric data
is achieved, it is possible to calculate optical constants
without KK analysis. These constants are shown in
Fig. 18b, where index of refraction n and extinction
coefficient k are plotted vs. wavelength. The dramatic
onset of absorption at 155nm (ie. the onset of non-zero
k values) is associated with the excitonic critical point
that we saw in ε1 and ε2. These data (and indeed the
presence or absence of this feature) act as an excellent
733
identical to porous SiO2 (i.e. are transparent), as might
be reasonable to expect. We illustrate the capabilities
and limitations of static VUV SE measurements and
data analysis for the characterization of low k
organosilicate glasses with the following example
from an industrial production environment. (See Ref.
14 for further details concerning samples and
measurements).
During the transfer of an OSG film growth
process, we found that the films from the researchgrade reactor consistently had higher hardness.31 than
those from the higher throughput production reactor,
for nominally similar process parameters. Despite such
a large difference in mechanical properties, the films
appeared virtually identical when compared by XPS
and also by TEM cross-section.31 Accordingly,
spectroscopic ellipsometry (SE) was performed to see
if any difference that could explain between the two
sets of films could be observed that would explain the
unusual differences in mechanical properties.
1.455
1.445
3.0E-05
a)
b)
2.5E-05
wfr13
wfr14
wfr17
2.0E-05
k
k
n
1.435
1.425
wfr18
1.5E-05
wfr19
1.0E-05
1.415
wfr20
wfr21
5.0E-06
1.405
SiO2
0.0E+00
500
700
900
1100
350
400
450
500
550
Wavelength in nm
FIGURE 20. OSG optical properties, data: in (a) index of
refraction n vs. wavelength; in (b), extinction coefficient k
vs. wavelength. Wafer 13, the representative sample from
the research-grade reactor has a higher index of refraction
(and thus lower relative porosity) than the production-grade
samples. It also has a lower absorption edge (i.e. defined
here as the onset of non-zero ‘k’ values) than the other
samples, it is transparent to higher energies than the other
films. (After Ref. 14, reprinted with permission)
curve). The index of refraction scales as we would
expect between the two extremes, with n decreasing
with decreasing electron density/ increasing porosity.
Extinction coefficients were also simulated from 138
to 1771nm (or 0.7 to 9.0 eV). The extinction
coefficient for dense as well as porous (all ∆p values)
SiO2 was zero. Recall that an extinction coefficient
value of zero means that the material is transparent;
i.e. that there was no absorption expected for SiO2 in
this spectral range, whether porous or dense.
Experimentally-derived values of n and k for
the OSG films are given in Fig. 20 (a) and (b),
respectively. It is immediately apparent that Wfr13
(squares), the representative research-grade sample
with higher hardness, has different optical properties
from both the production-grade samples (Wfrs. 14-21)
and from SiO2 (dotted line). First, it has a higher index
of refraction and lower onset of absorption (defined
for our purposes as the onset of non-zero k values)
than its production-grade counterparts. Compared to
SiO2, we see in (a) that n for relatively more dense
SiO2 is greater than for all of the OSG films (e.g.
nSiO2=1.45 at 900nm). The introduction of voids with
index n =1 into this matrix will decrease n, with nmatrix
approaching nair as the void fraction increases, as we
observed in Fig. 19. Thus n values of these OSG films
are by comparison lower, ranging approximately
between ~1.41 and 1.42 at 900nm. Accordingly, we
can argue that Wfr13 with its high hardness and
notably higher index of refraction is also more
electronically dense than the other OSG films and is
significantly less dense than SiO2. Unexpectedly, from
the non-zero k values in (b), it is evident that the OSG
films, unlike porous or dense SiO2, experience some
FIGURE 19. Results of an effective medium approximation
(EMA) calculation, simulating the effect of porosity on the
index of refraction of SiO2. Porosity is introduced at an
increment of ∆p=10%. Top curve: the index of SiO2 (0%
porosity); bottom: air (100% porosity). As the porosity of the
material increases, the index of refraction decreases. (After
Ref. 14, reprinted with permission)
We have argued that ellipsometry is sensitive
to electron density and thus to local structural
arrangement; therefore, differences in crystal structure,
interface and surface properties, stoichiometry and
relative porosity, if present, should manifest
themselves in the optical data. 8,32 To investigate, we
first simulated the effect of voids/ low index inclusions
on the SiO2 index of refraction, shown in Fig. 19. Here
pores of increasing void fraction (in increments of
∆p=10%) were introduced into a SiO2 matrix via an
effective medium approximation (EMA) calculation.24
The index of refraction n as a function of wavelength
was calculated for each case, ranging from 0%
porosity (pure SiO2 ; top curve) to100% (air: bottom
734
After a thorough characterization of the
materials in the VUV, it is possible to provide some
degree of absorption in the spectral range under
consideration. Here too Wfr 13 can be distinguished
from its production-grade counterparts with its onset
value. This is also indirect evidence for the presence of
a combination of voids and other low index inclusions
in all of the films, the identity and amount of which
cannot be strictly verified by the available
ellipsometric data.
Model Fit
Exp E 65°
60
Relative Porosity
40
← Sellmeier →
20
10
520
520
480
480
440
H(GPa)
2.05
1.378
1.254
1.240
1.29
1.47
1.33
Stdev
0.20
0.085
0.091
0.089
0.13
0.30
0.15
Research
440
Production
400
10
0
0
9
9
8
8
7
7
6
6
Porosity
Porosity(%)
(%)
wfr
w13
w14
w17
w18
w19
w20
w21
1
1
1.2
1.2
1.4
1.6
1.8
2
1.4 Hardness
1.6
1.8
(GPa)2
Hardness (GPa)
2
4
6
Photon Energy (eV)
8
10
60
5
5
400
← Cauchy /
Urbach→
80
Ψ in degrees
560
Absorption (nm)
Tauc-Lorentz
Ψ in degrees
Absorption Onset (nm)
560
Tauc-Lorentz + 2 Gaussians
80
2.2
40
Tauc-Lorentz Model
b
20
2.2
0
0
FIGURE 21. Ellipsometrically-obtained relative porosities
and absorption onsets plotted vs. mechanical hardness for the
two sets of samples. Mechanical hardness data is given in the
inset table. The difference between the optical and
mechanical properties of production-grade samples vs. the
representative research-grade sample is readily apparent.
(After Ref. 14, reprinted with permission)
2
4
6
Photon Energy (eV)
8
10
FIGURE 22. (a) Ellipsometric angle Ψ data (dashed line)
vs. photon energy for Wfr 13 for a 65º angle of incidence.
The optical model (solid line) that best fit the data was
comprised of a Tauc-Lorentz and two Gaussian oscillators.
The dashed vertical lines denote the spectral range of
viability for other kinds of optical models. (b) The same
ellipsometric data with a fit extrapolated into the VUV. Here
we see that the single Tauc-Lorentz oscillator that fits so
well at low energies cannot fit the data well above 6 eV.
(After Ref. 14, reprinted with permission)
Nonetheless, though these measurements
cannot definitively yield pore size and distribution
information—since ellipsometry is sensitive to net
electron density only—they can serve as a very
effective in-line diagnostic for processes yielding films
with undesired electron densities. This is important
because such properties should affect the mechanical
behavior of a film (and presumably the static dielectric
constant as well). This premise is supported in Fig. 21,
where ellipsometrically-obtained relative porosities
and absorption onsets for the films are plotted vs.
mechanical hardness (see Ref. X for more detail).
Though, again, we cannot determine pore size and
distribution with the VUV SE data, these results
indicate that ellipsometry is sufficiently sensitive to
the differences in the local structure of the films
conclude that the technique—even at longer
wavelengths—has promise for the characterization of
OSG films. If this degree of sensitivity at long
wavelengths is possible, then in-line metrology is
promising to identify potentially mechanically
compromised materials.
insight into challenges associated with the analysis of
SE data of OSG films. In particular, we warn of
complications that can arise during the course of the
development of data reduction recipes because of the
large difference that can exist between the onset of
absorption and the onset of opacity for these materials.
Lest the distinction between these onsets appear
trivial, we reiterate that the correct choice of optical
model applied over the correct spectral range is the
means by which sample properties like thickness,
relative porosity, n and k are extracted. We illustrate
with an example: in Fig. 22(a) we have plotted the
ellipsometric angle Ψ vs. photon energy at one angle
of incidence for Wfr13. Below around 7eV, the data
(dotted line) completely consist of interference
oscillations, which is typical for transparent films
grown on absorbing substrates. Above this energy is
the onset of opacity, where the oscillations cease and
735
eV, where there clearly is none (cf. Fig 22b). In
summary, then, it is important to note that for OSG
films, the onset of absorption can be very different
from the onset of opacity, because of the potential
presence of low-index inclusions. For these particular
films complementary Raman analysis indicated that
amorphous Si clusters were present. In fact, it was
possible to correlate the absorption edges obtained by
SE and the a-Si cluster concentration, as shown in Fig.
the film is completely absorbing. The model
calculation (solid line) used to best fit the data was
Absorption Edge (eV)
3.2
3
23.33
2.8
In short, for process transfer or the
evaluation of new growth recipes, it is worthwhile to
first evaluate the film over the broadest possible
spectral range and to critically assess the confidence
limits of model parameters to determine the suitability
of the optical model. Moreover, blind application of
standard oxide in-line metrology recipes applied to
these materials, based on the assumption that they are
merely porous SiO2, will result in spurious values for
film thickness and electron density—and the link to
mechanical behavior could be lost or distorted. In this
way, though VUV SE does not have the capability to
yield the desired pore size and distribution for low k
films, we can see that it is very useful for the
fundamental studies necessary for the development of
in-line metrology recipes for these materials.
2.6
More a-Si
2.4
2.2
4.8
5
5.2
5.4
-1
5.6
5.8
-1
6
6.2
R(480cm )/R(800cm )
FIGURE 23. Ellipsometrically-obtained absorption edges
of the OSG films plotted vs. a-Si cluster concentration,
determined by Raman.
comprised of a Tauc-Lorentz oscillator, which is
typically used to describe the optical dispersion of
amorphous materials,13 plus two Gaussian oscillators
to fit the VUV absorption. (Further details will be
given elsewhere.) With the VUV instrument, we can
observe this edge for the very first time, and its
presence in this spectral region is an obvious clue that
the film is not structurally similar to (transparent)
SiO2. Further, the vertical dotted lines in the figure
define regions over which certain optical models are
applicable, which is necessary to delineate because of
this very small amount of absorption below the onset
of opacity. Significant errors arise when these are
applied outside of their region of applicability: e.g., the
Cauchy and Sellmeier formalism should only be
applied in the transparent region of the spectra and
thus are common in-line recipes for measuring SiO2
optical properties. Since sample thickness is usually
determined by applying one of these models in the
transparent spectral region, thicknesses can be
disastrously off-target (by as much as 1/3 in this case)
if the model is mistakenly applied in a region where
absorption is occurring (i.e. where k is actually nonzero). For this particular sample, this is at ~2.1 and 3.6
eV for the Cauchy and Sellmeier model, respectively.
On the other hand, a single Tauc-Lorentz oscillator
gives a beautiful fit for the data until just above 6 eV,
which happens to cover the spectral range of most
standard IR/ VIS/ UV instruments. While the sample
thickness obtained with this model will only be offtarget by a percent or so, for this sample, the optical
constants were distorted, since this fit mistakenly
placed a large oscillator-related structure squarely at 8
VUV SE: status and prospects….
High k
Low k
Extract n and d independently
for thickness required for
process
Extract n and d independently
for thickness required for
process
Sensitive to interface layer
and surface roughness in
‘thick’, single layer films
Sensitive to density and
surface roughness in ‘thick’,
single layer films
Sensitive to interface layer
and surface roughness for
multilayers
Sensitive to pore size and
distribution
Legend:
Requires invention/ potential showstopper
Development required
Solution known
FIGURE 24. Status and prospects for VUV SE, as applied
to the problems facing applications utilizing high k and low
k dielectrics.
CONCLUSIONS
We have shown with the previous examples
that VUV SE allows for increased access to unique
spectral features and increased sensitivity to film
thickness, meaning that the technique is of use not
only for determining optical constants at 157nm (the
obvious lithographic application) but also for
analyzing materials from other stages of the device
736
fabrication process. Given the initial problems in
reducing data to determine optical constants at the
throughputs and accuracies demanded in industrial
settings, a significant challenge for the industrial
practitioner of VUV SE has been to develop the
technique from its more esoteric origins as a research
instrument to an industrially-viable diagnostic
technique. Since most of these issues were rooted in
the absence of optical constants for Si in the VUV,
these types of problems have largely been solved.
Indeed, when applied properly, VUV SE is not only
practical for determining VUV optical constants and
material properties but also a powerful instrument for
industrial problem solving. However, other issues
remain that are endemic to the general SE data
analysis process. With respect to low k and high k
materials, capability VUV SE is powerful, but (like
any technique) not without its limits. In Fig. 24 we
summarize the preceding discussion into a table
capturing the status and prospects of the technique for
these applications.
11
N.V. Edwards, “ VUV Ellipsometry of Si, SiO2, and Lowk Organo-Silicate Glasses,” SEMATECH Metrology
Council Meeting, Austin, TX, 05 May, 2002.
12
B. Johs, J. A. Woollam, C. M. Herzinger, J. N. Hilfiker, R.
Synowicki, and C. Bungay, Proc. SPIE CR72, 29 (1999).
13
G.E. Jellison and F. A. Modine, Appl. Phys. Lett. 69, 371
(1996).
14
N. V. Edwards, J. Vella, Q. Xie, S. Zollner, D. Werho, I.
Adhihetty, R. Liu, T. E. Tiwald, C. Russell, J Vires, and K.
H. Junker. Mat. Res. Soc. Symp. Proc. 697, P4.7.1 (2002).
15
N.V. Edwards, S. Zollner, J. White, D. Gajewski,
Motorola Inc., unpublished.
16
H.G. Tompkins, R. B. Gregory, P.W. Deal, and S.M.
Smith, J. of Vac. Sci. and Technol. A 17, 391 (1999).
17
H.G. Tompkins and W.A. McGahan, Spectroscopic
Ellipsometry and Reflectometry: A User’s Guide, John Wiley
and Sons, New York, 54-61 (1999).
18
R. Liu, N.V. Edwards, R. Gregory, D. Werho, E. Duda, J.
Kulik, G. Tam, E. Irwin, X-D Wang, D. Triyoso, Motorola
Inc., unpublished.
19
R. Liu, S. Zollner, P. Fejes, R. Gregory, S. Lu, K. Reid, D.
Gilmer, B.-Y. Nguyen, J. Yu, R. Droopad, J. Curless, A.
Demkov, J. Finder, and K. Eisenbeiser, Mat. Res. Soc. Symp.
Proc. 670, K1.1 (2001).
20
J. Schaeffer, N.V. Edwards, R. Liu, D. Roan., B. Hradsky, R.
Gregory, J. Kulik, E. Duda, L. Contreras, J. Christiansen, S.
Zollner, P. Tobin, B-Y. Nguyen, R. Nieh, M. Ramon, R. Rao, R.
Hegde, R. Rai, J. Baker, S. Voight, J. Electrochem. Soc., in print.
21
D.E. Aspnes in Optical Properties of Solids: New
Developments, edited by B.O. Seraphin, North-Holland,
Amsterdam, 799 (1976).
22
J. Hilfiker in Handbook of Ellipsometry, edited by H.G.
Tompkins and E.A. Irene, Noyes Press, Park View, in print.
23
R. M. A. Azzam and N. M. Bashara, Ellipsometry and
Polarized Light, Elsevier, Amsterdam, 283-293 (1987).
24
D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
25
C.M. Herzinger, private communication.
26
A. Demkov and N.V. Edwards, Motorola, Inc.,
unpublished.
27
H. Yao and C. H. Yan, Appl. Phys. Lett. 85, 6717 (1999).
28
R.H. French, D. J. Jones, and S. Loughin, J. Am. Ceram.
Soc. 77[2], 412 (1994).
29
N. V. Edwards, O.P.A. Lindquist, L.D. Madsen, S.
Zollner, K. Jarrendahl, C. Cobet, S. Peters, N. Esser, R. Liu,
and D. E. Aspnes, Mat. Res. Soc. Symp. Proc. 697 (2002).
30
K. Junker, Motorola Inc., private communication.
31
J. Vella, Q. Xie, N.V. Edwards, J. Kulik and K. Junker,
Mat. Res. Soc. Symp. Proc. 697, 6.25 (2002).
32
D. E. Aspnes, Thin Solid Films 89, 249 (1982).
33
R. Liu and N.V. Edwards, Motorola Inc., unpublished.
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3
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6
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737