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Determination of optical and microstructural parameters of ceria films
Tae-Sik Oh, Yury S. Tokpanov, Yong Hao, WooChul Jung, and Sossina M. Haile
Citation: J. Appl. Phys. 112, 103535 (2012); doi: 10.1063/1.4766928
View online: http://dx.doi.org/10.1063/1.4766928
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v112/i10
Published by the American Institute of Physics.
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Determination of optical and microstructural parameters of ceria films
Tae-Sik Oh,
1,
a)
Yury S. Tokpanov,
2
Yong Hao,
1,
b)
WooChul Jung,
1
and Sossina M. Haile
1
1
Materials Science, California Institute of Technology, Pasadena, California 91125, USA
2
Moscow Institute of Physics and Technology, Moscow, Russia
(Received 30 March 2012; accepted 24 October 2012; published online 30 November 2012)
Light-matter interactions are of tremendous importance in a wide range of fields from solar energy
conversion to photonics. Here the optical dispersion behavior of undoped and 20 mol. % Sm doped
ceria thin films, both dense and porous, were evaluated by UV-Vis optical transmission
measurements, with the objective of determining both intrinsic and microstructural properties of
the films. Films, ranging from 14 to 2300 nm in thickness, were grown on single crystal YSZ(100)
and MgO(100) using pulsed laser deposition (both dense and porous films) and chemical vapor
deposition (porous films only). The transmittance spectra were analyzed using an in-house
developed methodology combining full spectrum fitting and envelope treatment. The index of
refraction of ceria was found to fall between 2.65 at a wavelength of 400 nm and 2.25 at 800 nm,
typical of literature values, and was relatively unchanged by doping. Reliable determination of film
thickness, porosity, and roughness was possible for films with thickness ranging from 500 to
2500 nm. Physically meaningful microstructural parameters were extracted even for films so thin
as to show no interference fringes at all.
V
C
2012 American Institute of Physics
.
[
http://dx.doi.org/10.1063/1.4766928
]
I. INTRODUCTION
Light-matter interactions are of tremendous importance
in a wide range of fields from solar energy conversion
to photonics. The complex refractive index [
n
(
k
)
¼
n
(
k
)

i
k
(
k
)] is the fundamental optical constant that governs
these interactions and its accurate determination is of prime
importance. In any optical measurement, the response from
the sample depends not only on its inherent optical properties
but also on its microstructure. Thus, optical transmittance
through a thin film depends on features such as thickness,
roughness, and porosity in addition to
n
. This interdepend-
ence conversely implies that, with a knowledge of the com-
plex refractive index, transmittance measurements can be
employed to determine the microstructural characteristics.
Amongst available tools for film microstructural characteri-
zation, the UV-VIS transmittance method is particularly
attractive because it is quick and non-destructive and can
probe a large area of sample. It can also be used for rela-
tively thick films that are unsuitable for x-ray based techni-
ques such as x-ray reflectivity (XRR) or Laue oscillation.
The essence of a transmission measurement is simply to
determine the fraction of light that is transmitted through the
sample of interest over a given wavelength range. Transmis-
sion through a film on a substrate deviates from 1 not only
because of absorption (non-zero imaginary component of the
complex index) but also because reflection at interfaces
creates interference fringes. Analysis by the widely used
envelope method
1
of the maximal and minimal transmittance
values associated with these fringes and the wavelength sepa-
ration between them enables one to determine both
n
(
k
) and
thickness. However, as the thickness of the film decreases,
the number of interference fringes in a given wavelength
range decreases, increasing the uncertainty in the derived
parameters, and the method becomes inapplicable.
In this work, we explore the properties of ceria films that
can be extracted from transmittance measurements using a
combination of data analysis approaches. For compositions
for which the index of refraction is first fully characterized
using dense, smooth, thick films, we show that it is possible to
accurately obtain film thickness and porosity from films with
arbitrary features. The optical properties of undoped and Sm-
doped ceria measured and reported here are interpreted in
terms of the electronic band structure. The microstructural
properties of films obtained from different deposition techni-
ques are discussed in terms of the film growth characteristics.
II. EXPERIMENTAL METHODS
A. Sample preparation
Ceria films were grown by both pulsed laser deposition
(PLD) and chemical vapor deposition (CVD). PLD was
carried out using a Neocera deposition system equipped with
a coherent 102 KrF 248 nm excimer laser, operated at a
power density of about 2 J/cm
2
and deposition frequency of
20 Hz. Targets of either undoped or 20 mol. % Sm doped
(Sm
0.2
Ce
0.8
O
1.9-
d
or 20SDC) were fabricated in-house using
commercial powders (undoped: Sigma Aldrich 202975,
99.995% pure; 20% doped: Fuel Cell Materials, 20SDC-HP,
trace metal impurity

160 ppm wt.). To minimize the influ-
ence of the limited size of the laser plume on the uniformity
of the films, the substrates were arranged at the center of the
sample stage and rotated at a constant angular speed. The
a)
Present address: Department of Chemical and Biomolecular Engineering,
University of Pennsylvania, Philadelphia, Pennsylvania 19014-6315, USA.
b)
Present address: Laboratory of Energy Systems and Renewable Energy
Institute of Engineering Thermophysics, Chinese Academy of Sciences 11
Beisihuanxi Rd, Beijing, 100190, People’s Republic of China.
0021-8979/2012/112(10)/103535/10/$30.00
V
C
2012 American Institute of Physics
112
, 103535-1
JOURNAL OF APPLIED PHYSICS
112
, 103535 (2012)
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substrate was maintained a temperature of 600–650

C
during deposition, and a cooling rate of 10

C/min was used
prevent the films from cracking due to thermal expansion
mismatch. Porosity in the deposited ceria film was varied by
varying the background pressure of oxygen (5 mTorr for
dense films, 100 mTorr for porous films
2
). Regardless
of eventual film porosity, typical PLD growth rate was
20 nm min

1
. Film growth by CVD was carried out using an
in-house constructed vertical cold-wall reactor, and composi-
tions were limited to undoped ceria. The cerium precursor,
Ce(tmhd)
4
(Strem, CAS: 18960-54-8, 99.9% cation purity),
was used without further purification. The precursor was
evaporated at a temperature of 190

C. The total system pres-
sure during deposition was varied within a range of 1–3 Torr
and the substrate temperature held at between 450 and
500

C. The oxygen to argon flow ratio was kept at 1:2. The
typical deposition rate was 15 to 20 nm min

1
.
Films were grown on 8 mol. % Y
2
O
3
-doped ZrO
2
[YSZ(100)] and MgO(100) single-crystal substrates (MTI
Corporation), polished on both sides and with dimensions
1cm

1cm

0.5 mm. The root mean square (rms) surface
roughness of the as-received substrates, as measured in-house
by atomic force microscopy (AFM), was below 0.5 nm and
the peak-to-valley roughness below 3.5 nm. It is noted that
n
YSZ
>
n
ceria
>
n
MgO
and thus this choice of substrates enables
assessment of the applicability of the optical analysis methods
to arbitrary substrate-film combinations.
B. Measurements
Optical transmittance was measured using an Ocean
optics HR2000CG-UV-NIR high-resolution, miniature, fiber-
optic spectrometer, with a data collection range of 200 to
800 nm (beyond 800 nm the data were too noisy to be useful)
and a 0.47 nm data point interval. The raw spectra for the
wavelength range 400 to 800 nm were each converted to 500
equally spaced data points for analysis. No smoothing of any
sort was applied. In all cases, when the sample was physically
inverted such that the incident photons interacted with sub-
strate first, there was essentially no change in transmittance
trace. Transmittance spectra from blank substrates were also
measured over the same wavelength range in order to obtain
the substrate index of refraction as required for the analysis.
AFM roughness measurements were performed using a
Park Systems XE-70 in non-contact mode. Occasional large
particulates that formed on the PLD surface were avoided
for the roughness measurement. These particulates were
found to have negligible impact on measured transmittance
spectra. Plane leveling and subsequent rms roughness esti-
mation were carried out using the
GWYDDION
2.25 software
package. Film morphology was observed using a ZEISS
1550VP field emission scanning electron microscope (SEM).
Examination of fractured cross-sections of films provided an
external and independent measure of film thickness. X-ray
reflection curves to probe film roughness and density were
collected using a Rigaku Smartlab diffractometer with 0.01

steps in two-theta up to 5

and data analyzed using the
X’Pert Reflectivity software package. X-ray rocking curves
were collected using an X’pert pro MRD system from Pana-
lytical. A scanning white light interferometer (SWLI), Zygo
NewView 600, was used to obtain surface topography
maps for very thin films (
<
50 nm). The field of view was
140
l
m

105
l
m for all cases.
III. ANALYTICAL METHODS
Analytical expressions for the
optical transmission through
a system comprised of a thin film exposed to air and deposited
on a substrate with zero absorptio
n (i.e., a transparent substrate)
and a transmittance of no less than

0.5havebeenderivedin
the literature. In the wavelength range of interest (400 to
800 nm) MgO and YSZ have negligible extinction coefficient,
k
, and these expressions are applicable. We consider first the
case of an ideally flat, smooth and dense film on a substrate of
(arbitrary) finite thickness with the following characteristics:
n
susbtrate
¼
s

i
k
s
¼
s
(
k
),
n
film
¼
n

i
k
¼
n
(
k
)

i
k
(
k
),
d
¼
film thickness.
The wave-length dependent transmittance,
T
, for this system
is
1
,
3
T
¼
Fx
G

Hx
þ
Kx
2
;
(1)
where
x
¼
exp
ð
a
d
Þ
;
(1a)
a
¼
absorption coefficient
¼
4
p
k
=
k
;
(1b)
F
¼
16
s
ð
n
2
þ
k
2
Þ
;
(1c)
G
¼½ð
n
þ
1
Þ
2
þ
k
2
½ð
n
þ
1
Þð
n
þ
s
2
Þþ
k
2

;
(1d)
H
¼½ð
n
2

1
þ
k
2
Þð
n
2

s
2
þ
k
2
Þ
2
k
2
ð
s
2
þ
1
Þ
2 cos
/

k
½
2
ð
n
2

s
2
þ
k
2
Þþð
s
2
þ
1
Þð
n
2

1
þ
k
2
Þ
2 sin
/
;
(1e)
K
¼½ð
n

1
Þ
2
þ
k
2
½ð
n

1
Þð
n

s
2
Þþ
k
2

;
(1f)
and
u
¼
the phase
ð
in wavelength space
Þ
of the
interference fringes
¼
4
p
nd
=
k
:
(1g)
Expression
(1)
describes an oscillating spectrum over-
lain on a transmittance that shows an overall increase with
k
,
where the spacing between maxima and minima is given by
u
. The value of
T
at any given wavelength thus depends on
three parameters, the real component of the index at that
wavelength, the imaginary component (at that wavelength),
and the film thickness; accordingly, the problem, at a single
wavelength, is underdetermined. Swanepoel circumvented
this challenge by introducing the envelope method. The
approach treats the overall characteristics of the transmit-
tance function, rather than transmittance values at individual
wavelengths, and takes advantage of the fact that the differ-
ence in transmittance at maxima and minima, interpolated to
103535-2 Oh
etal.
J. Appl. Phys.
112
, 103535 (2012)
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a given wavelength, depends only on
n
(and is independent of
both
d
and
k
). The transmittance values at the maxima define
the upper envelope,
T
U
, and those at the minima, the lower en-
velope,
T
L
. Because
T
U
and
T
L
can be interpolated to arbitrary
values of
k
, the envelope method allows the index of refrac-
tion to be directly computed at any given
k
,solongas
T
U
(
k
)
and
T
L
(
k
) are appropriately established. With
n
(
k
)known,the
spacing between maxima and minima is then used to compute
d
. Finally, the extinction coefficient is determined after evalu-
ating the absorbance from the separate expression
4
x
¼f
P
þ½
P
2
þ
2
QT
a
ð
1

R
2
R
3
Þ
1
=
2
g
=
Q
;
(2)
R
1
¼½ð
1

n
Þ
=
ð
1
þ
n
Þ
2
;
(2a)
R
2
¼½ð
n

s
Þ
=
ð
n
þ
s
Þ
2
;
(2b)
R
3
¼½ð
s

1
Þ
=
ð
s
þ
1
Þ
2
;
(2c)
P
¼ð
R
1

1
Þð
R
2

1
Þð
R
3

1
Þ
;
(2d)
Q
¼
2
T
a
ð
R
1
R
2
þ
R
1
R
3

2
R
1
R
2
R
3
Þ
;
(2e)
T
a
¼
ffiffiffiffiffiffiffiffiffiffiffi
T
U
T
L
p
:
(2f)
The ultimate effectiveness relies on accurate positioning of
the envelope values and identification of the order number
of each interference fringe.
Alternatively, if one has knowledge of the functional
forms of
n
(
k
)and
k
(
k
), then one could adjust the parameters of
those functions so as to fit a spectrum, calculated according to
Eq.
(1)
,tothemeasuredspectrum.Suchanapproachwould
utilize the full set {
T
i
} to determine a limited set of parameters,
eliminating the situation of an underdetermined problem. The
behavior of
n
(
k
) for transparent materials has been treated and
is discussed in greater detail below. The behavior of
k
(
k
)can
ideally be obtained from
n
(
k
) utilizing the Kramers-Kronig
relation. Because the wavelength range of the measurement is
finite, however, the treatment is not entirely straightforward.
Bhattacharya
et al.
applied such an envelope-free approach to
the study of films of Zn
1

x
Mg
x
O with good success, but could
do so only upon dividing the spectra into arbitrary regions.
5
In the present work, we employed a strategy that com-
bines aspects of full spectrum fitting and envelope treatment
and is free of arbitrary definitions of absorption regions. The
index of refraction,
n
(
k
), is assumed to behave according to
the Sellmeier equation,
1
n
2

1
¼
A
k
2
þ
B
;
(3)
an expression that has been found to accurately represent the
behaviors of a large number of transparent materials.
6
As the
dispersion characteristics arise from the interaction of light
with the bonding electrons, the
A
and
B
constants suitably
parameterize the behavior for subsequent analysis, as described
in detail below. For those measur
ements in which the objective
is to determine optical propertie
s rather than microstructural
features, starting estimates of A and B are employed to provide
initial estimates of
n
through Eq.
(3)
and of
k
through Eq.
(2)
,
where the latter relies on determination of the envelope values
T
U
(
k
)and
T
L
(
k
). Full spectrum fitting is performed by comput-
ing and minimizing the error,
v
2
,definedas
v
2
¼
X
N
1
1
r
i
2
ð
T
calc
i

T
meas
i
Þ
2
;
(4)
where
T
is that given in Eq.
(1)
,
N
is the number of points in
the calculation (
¼
500), and
r
i
is the experimental uncer-
tainty in each transmittance point. The latter is taken to be
0.01 over the entire wavelength range of interest based on
the transmittance measured from an empty cell (
T
¼
1). The
analysis is limited to the wavelength regime in which
T

0.5, corresponding to
k

400 nm. For the types of films
discussed to this point (smooth, dense, and flat), refined pa-
rameters are the material properties,
A
and
B
. Refinement of
the thickness,
d
, can also be introduced at this stage.
We now consider two microstructural modifications—
roughness and porosity—of relevance to films obtained under
typical experimental growth co
nditions. As recognized by Swa-
nepoel,
7
roughness on the film surface has the effect of
“softening” the interference fri
nges in the transmittance spec-
trum such that
T
U
and
T
L
approach each other, but without mod-
ification to the wavelength dependence of the position of the
extrema. Treatment of the probl
em requires a physical model of
the manner in which the thickness varies. Here, each film is con-
sidered to display a mean thickness and a Gaussian distribution
of thicknesses about this mean. Numerical implementation is
achieved by dividing the film into 5000 equal-footprint vertical
columns with heights reflecting the Gaussian distribution. The
transmittance is then computed a
ssuming a spatial average over
the transmittances through each column,
T
j
,givenby
T
¼
1
5000
X
5000
j
¼
1
T
j
ð
d
j
Þ
;
(5)
where the 5000
d
j
values are distributed about
d
with stand-
ard deviation
r
. This standard deviation corresponds to the
root-mean-square roughness and ideally matches the value
measured directly by AFM.
Porosity in the film has the effect of lowering the effec-
tive index of refraction by rendering it an average, in some
way, of the bulk properties of the film material (
>
1) and of
air (

1). Following the general approach of effective medium
theory, here, the microstructure-specific optical properties of
the porous material or two-phase composite (of the solid and
air) are replaced with those of a hypothetical dense film with
equivalent properties. Available models for the optical proper-
ties are developed for the dielectric function,
e
¼
e
1

i
e
2
,
which can be mapped to the refractive index according to
n
¼
ð
e
2
1
þ
e
2
2
Þ
1
=
2
þ
e
1
2
!
1
=
2
;
k
¼
ð
e
2
1
þ
e
2
2
Þ
1
=
2

e
1
2
!
1
=
2
:
(6)
We consider three specific forms of effective medium
theory. The first is the symmetric Bruggeman (S-BG) model
103535-3 Oh
etal.
J. Appl. Phys.
112
, 103535 (2012)
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for binary mixtures, in which t
here is no distinction between
continuous (matrix) and discontinuous (inclusion) phases; each
inclusion is in contact with other inclusions of either phase.
The result for sphere-shaped inclusions is expressed as
8
f
b
e
b

e
eff
e
eff
þ
1
3
ð
e
b

e
eff
Þ
þ
f
p
e
p

e
eff
e
eff
þ
1
3
ð
e
p

e
eff
Þ
¼
0
;
(7)
where
f
b
is the volume fraction of oxide;
f
p
is the volume
fraction of pore (total porosity) (fitting parameter,
0
f
p
0.6);
e
b
is the dielectric function of fully dense ox-
ide;
e
p
¼
1 (air)
¼
e
p
; and
e
eff
is the effective dielectric func-
tion (oxide/air composite).
Of the two roots to Eq.
(7)
, only one is physically mean-
ingful, and it reads
e
eff
¼
ð
3
f
b
e
b

e
b

e
p
þ
3
f
p
e
p
Þþ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
3
f
b
e
b

e
b

e
p
þ
3
f
p
e
p
Þ
2
þ
8
e
b
e
p
q
4
:
(8)
The second formalism is the asymmetric Bruggeman
(A-BG) model, in which it is assumed that the inclusions,
air-filled pores in our case, are always spherical and are
coated with matrix material such that they cannot touch one
another.
9
The A-BG model yields an implicit form for
e
eff
as
shown below,
e
p

e
eff
e
p

e
b
¼
1

f
p

e
eff
e
b

1
=
3
:
(9)
The solution for
e
eff
from the above is obtained using Sihvo-
la’s series expansion method. The complete form can be
found in Ref.
10
.
Looyenga and Landau-Lifshitz independently derived a
third dielectric mixing law (henceforth the LLL model) in
which the host and matrix phases are assigned dielectric
constant values of
e
eff
þ
D
e
and
e
eff
D
e
,
11
,
12
and no assump-
tions are made regarding phase distributions. The result is
given as
e
eff
¼½ð
e
p
1
=
3

e
b
1
=
3
Þ
f
p
þ
e
b
1
=
3

3
:
(10)
While there are some instances in which this expression fits
experimental data more closely than the Bruggeman expres-
sions [e.g., Ref.
13
] and the absence of microstructual
assumptions renders the approach attractive, the LLL model
fails when the permittivity of the host material differs greatly
from that of the inclusion.
It is of value to explore the sensitivity of predicted
behavior of refractive index to the choice of model. In fact,
the
n
eff
(
k
) computed for the three different models at two dif-
ferent representative porosity levels (assuming realistic
n
for
the oxide) shows that the two Bruggeman approaches yield
almost indistinguishable results (Fig.
1
). In contrast, the LLL
model implies an
n
eff
(
k
) that is quite distinct from the Brug-
geman behavior. Accordingly, analysis of porous films was
carried out using only the S-BG and LLL models.
With the physical models established, the minimization
was carried out by simply varying the fit parameters over a
wide range of values and selecting those that yielded a mini-
mum
v
2
. The statistical uncertainty in the parameters,
d
x
j
(where {
x
j
} is the set of fit variables), was estimated by eval-
uating the expression,
d
x
j
¼
@
T
@
x
j





f
x
i
6
¼
j
g
"#

1
d
T
;
(11)
with
d
T
being equivalent to the experimental uncertainty,
estimated above as 0.01 from the noise level. All calculations
were performed using in-house written MATLAB codes.
IV. OPTICAL PROPERTIES
A summary of the film-substrate systems prepared and
examined in this work are provided in Table
I
. The first set
of samples are three thick (

2
l
m), dense films of two differ-
ent compositions prepared by pulsed laser deposition and
applied to two different types of substrates. With these films
we determine the material properties to a high degree of
FIG. 1. Simulated dispersion behavior of refractive
index (real part) for different effective medium mod-
els. (a) Assumed porosity: 15%, (b) assumed porosity:
30%. The two BG models are indistinguishable in
terms of dispersion behavior.
103535-4 Oh
etal.
J. Appl. Phys.
112
, 103535 (2012)
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accuracy, evaluate their variation with stoichiometry, and
determine the influence, if any, of the substrate on the trans-
mission analysis. The second set of samples constitute three
thinner films (500–700 nm) grown under various conditions
so as to yield microstructural differences. Analysis is carried
out using fixed values of
n
(
k
) and
k
(
k
) obtained from the
evaluation of the dense films. The final set of samples are a
pair of extremely thin films for which the envelop method is
entirely unsuitable. It is shown that, despite the absence of
interference fringes, meaningful microstructural data can be
obtained.
Figure
2
shows the SEM cross-sectional and AFM
topological images of two dense ceria films (films 1 and 2,
obtained by PLD) of differing stoichiometries grown on
YSZ(100) with (SEM determined) thicknesses of 1820 and
1900 nm for dopant concentrations of 0 and 0.20, respectively.
The films have negligible porosity and the rms roughnesses are,
respectively, 2.5 and 2 nm. As described elsewhere, such PLD
films adopt an epitaxial relationship with the YSZ substrate and
are stoichiometrically identical to the target material.
2
The trans-
mittance spectra obtained for these films are shown in Figure
3
,
along with the results of two fits. Because the films are thick and
relatively smooth, the spectra show a large number of sharp in-
terference fringes in the wavel
ength range of the measurement.
Such films are amenable to treatment by a traditional envelope
method just as they are to the full spectrum fitting undertaken in
this work. Here, the inherent dispersion properties for the two
compositions were determined b
y fixing rms roughness and film
thickness at the independently, experimentally determined values
just quoted, setting porosity to zero, and performing least squares
fitting with only A and B as varied parameters. The resulting fits
are shown in red in the plots in Figure
3
(“dispersion fit”), and
the corresponding parameter values are provided in Table
II
.
The dispersion behavior implied for undoped and 20%
Sm doped ceria is summarized in Figure
4
, where Fig.
4(a)
compares the present results for undoped ceria with literature
values,
14
19
and Fig.
4(b)
compares the three films studied
here to one another. The index of refraction of undoped ceria
obtained in this study is in general agreement with the many
literature reports on this material. In all cases, the long-
wavelength index falls between 2.1 and 2.4, and an upturn
occurs around 400 nm as the photon energy approaches the
average oscillator energy. As shown in Fig.
4(b)
, despite a
difference in substrate, the results from the two undoped
ceria films are almost identical, suggesting that artifacts aris-
ing from differences in substrate are negligible. The slightly
lower index for CeO
2
on MgO (film 3) relative to that on
TABLE I. Summary of general characteristics of ceria films prepared in this
study.
Film #
Deposition
method
Composition Substrate Thickness
Film
density
1
PLD
Undoped
YSZ(100)
Thick
a
Dense
2
PLD
20SDC
YSZ(100)
Thick
a
Dense
3
PLD
Undoped
MgO(100)
Thick
a
Dense
4
CVD
Undoped
YSZ(100) Moderate
b
Porous
5
PLD
20SDC
YSZ(100) Moderate
b
Porous
6
PLD
20SDC
YSZ(100) Moderate
b
Porous
7
CVD
Undoped
MgO(100)
Thin
c
Porous
8
CVD
Undoped
YSZ(100)
Thin
c
Dense
a

2
l
m.
b
500–1000 nm.
c
<
50 nm.
TABLE II. Dispersion relation fit parameters and indirect band gap energies
obtained for dense PLD films on YSZ(100). Statistical errors (
<
0.1%) are
too small to reflect the true uncertainty and values are simply reported to
three significant digits.
Film
A
(/nm
2
)
B
(unitless)
E
g
indirect
(/eV)
Eq.
(12)
#1, ceria
18200
0.272
3.23
#2, 20SDC
18600
0.287
3.15
FIG. 2. Microstructural images of dense PLD
films on YSZ (100): (a) SEM cross-sectional
and (b) AFM topological images of undoped
ceria (Film #1); and (c, d) analogous images for
20SDC (Film #2).
103535-5 Oh
etal.
J. Appl. Phys.
112
, 103535 (2012)
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YSZ (film 1) may be due to lattice mismatch in the former
case, which can, in turn, generate defects that lower material
density. The index of refraction of the Sm-doped film is
slightly lower still than either of the two doped films, but the
impact of doping is small. Turning to the literature, only one
prior study of the optical properties of Sm-doped ceria, which
specifically focuses on the 15% Sm composition, could be
found.
20
Those authors reported that the doped composition
had a slightly higher index than the undoped (in contrast to
the present work), but for both doped and undoped composi-
tions the reported index was unusually low, below 2 over
400–800 nm. The low index of refraction suggests that poros-
ity in the sol-gel derived films of that study, though not
reported, was non-negligible, and thus trends with composi-
tion cannot be established from those results. The present
study, comparing films 1 and 2 (both with 100% density),
suggests a lowering of
n
by 0.03 at all wavelengths upon
introduction of 20% Sm. Because Sm
3
þ
ion has a higher
dielectric polarizability than Ce
4
þ
, an increase in
n
could be
expected.
21
On the other hand, because the fluorite lattice
expands upon doping, the opposite would be expected. The
competition between these two characteristics prevents a
straightforward prediction. The experimental results suggest
the latter effect is slightly more significant.
The dispersion behavior can be interpreted in terms of
the electronic properties of the solid. Specifically, the optical
band gap,
E
g
, is related to the absorption coefficient (Eq.
(1)
)
according to the expression,
14
,
19
,
23
a
E
ph
E
ph

E
g
Þ
g
;
(12)
where
E
ph
is the photon energy (given by
E
ph
¼
hc
/
k
, where
h
is Planck’s constant and
c
is the speed of light) and
g
is a
constant of value 0.5 for a direct transition and 2 for an indi-
rect one. This expression was used here only for the determi-
nation of the indirect band gap (
E
g
indirect
), which is smaller
than

3.5 eV in ceria, because extinction coefficient values
computed in the range below

350 nm displayed too much
scatter for analysis of the higher energy, direct band gap. An
alternative method for interpretation of the dispersion behav-
ior to obtain the direct band gap as suggested by Wemple
and DiDomenico
22
was also found to be unsuitable. Thus,
only the indirect band gap is reported, Table
II
.
V. MICROSTRUCTURAL PROPERTIES
A. Model validation using dense films
With the index of the ceria compositions well character-
ized, an initial validation of the fitting procedure was carried
out using the data from the three dense films. The varied pa-
rameters were density, roughness, and film thickness. In this
case, because both
k
and
n
are taken as known input parame-
ters, there is no need to make use of the envelop method for
any of the calculations, and only minimization of
v
2
in
Eq.
(4)
was implemented. Table
III
summarizes the fitting
results, and the computed
T
values for this case are shown in
Figure
3
as the blue curves (“structure fit”). The parameters
obtained from the fitting are in good agreement with the in-
dependently measured values, providing a validation of the
procedures.
B. Properties of arbitrary typical films
Films 4–6 are representative of typical deposition condi-
tions. Film 4 is a CVD-derived film of undoped ceria (growth
temperature: 500

C; deposition pressure: 1 Torr); films 5
FIG. 3. Transmittance measurement and analy-
sis for dense PLD films (a) undoped ceria (Film
#1); (b) 20SDC (Film #2), of comparable thick-
nesses. Dispersion fits obtained upon varying A,
B parameters in the Sellmeier dispersion rela-
tion, Eq.
(3)
, with thickness and roughness fixed.
Structure fits obtained upon varying porosity,
thickness, and roughness, with known dispersion
relationship from dispersion fits.
FIG. 4. Derived dispersion behavior of PLD
grown films: (a) undoped ceria (Film #1)
compared to literature results;
14
19
(b) sub-
strate and dopant effects. Deposition on
MgO(100) (Film #3) leads to a slight
decrease in
n
relative to deposition on
YSZ(100) (Film #1), likely due to poorer
crystallographic registry between film and
substrate creating a slightly lower density.
Sm doping leads to a marginal decrease in
n
by 2%–3% over the wavelength range of in-
terest, indicating minimal impact on the elec-
tronic characteristics.
103535-6 Oh
etal.
J. Appl. Phys.
112
, 103535 (2012)
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