Ellipsometric at and below energy gap on polycrystalline calcium and strontium thiogallates

Article abstract of DOI:10.1002/pssa.200306635

The CaGa₂S₄ and SrGa₂S₄ with various grain sizes were studied over a wide range of photon energies at and below energy gap by using a spectroscopic phase modulated ellipsometer at room temperature. Complimentary, SEM and XRD techniques were applied. The pseudo-dielectric function of the samples with large grain sizes as compared to the light wavelength was found to be fairly reasonable. The energy gap for direct transitions in CaGa₂S₄ was estimated at ～4.10eV. For samples with small grain sizes (～100 nm), a splitting between principle angle and angle of minimal elliptic ratio, that could not be assigned to absorption was observed in the transient spectral range between diffraction and geometric optics.

Full text of DOI:10.1002/pssa.200306635

phys. stat. sol. (a) 198, No. 2, 478–486 (2003) / DOI 10.1002/pssa.200306635
Ellipsometric studies at and below energy gap
on polycrystalline calcium and strontium thiogallates
*
, 1
2
1
1
2
Nazim Mamedov , Hideyuki Toyota , Atsushi Yasunaka , Yonggu Shim , Ariyuki Kato ,
1
2
1
Atsushi Ashida , Seishi Iida , and Nobuyuki Yamamoto
1
Department of Physics and Electronics, Osaka Prefecture University, Gakuen-cho 1-1, Sakai,
Osaka 599-8531, Japan
Department of Electrical Engineering, Nagaoka University of Technology,
2
1603-1 Kamitomioka–machi, Nagaoka 940-2188, Japan
Received 20 June 2002, revised 25 May 2003, accepted 28 May 2003
Published online 8 August 2003
PACS 78.20.Ci, 78.40.Pg, 78.68.+m
The CaGa S and SrGa S with various grain sizes were studied over a wide range of photon energies at
2
4
2 4
and below energy gap by using a spectroscopic phase modulated ellipsometer at room temperature. Com-
plimentary, SEM and XRD techniques were applied. The pseudo-dielectric function of the samples with
large grain sizes as compared to the light wavelength was found to be fairly reasonable. The energy gap
for direct transitions in CaGa2S4 was estimated at ~4.10 eV. For samples with small grain sizes
(~100 nm), a splitting between principle angle and angle of minimal elliptic ratio, that could not be as-
signed to absorption was observed in the transient spectral range between diffraction and geometric optics.
1
Introduction
Continuing progress of growth and preparation technology of the calcium and strontium thiogallates,
CaGa S (CGS) and SrGa S (SGS) [1–3] is largely motivated by the interest in their useful phosphores-
2
4
2 4
cent properties [4]. Laser action, discovered recently in CGS at high enough concentration of some of the
rare-earth elements [5, 6], also attracts much attention. In response to a demand for lasing materials
3
+
3+
competitive with Ti :sapphire [7], Ce -doped CGS and SGS with broadband emissions centered below
480 nm may come to the fore as suitable candidates.
In view of the above applications CGS and SGS need an optical characterization especially in the
region below the energy gap. Although extinction coefficients are small (<0.001) in this region, reflec-
tion ellipsometry (RE) with typical accuracy of ~0.001 for optical constants may yet be useful especially
for polycrystalline materials that are often opaque and unreachable for transmission-type methods.
In this work performed with RE the polycrystalline samples of CGS and SGS with various grain sizes
as compared to the light wavelength were studied using fixed and variable angle-of-incidence operational
modes of a spectroscopic phase-modulated ellipsometer (SPME) in the photon energy range 1.5–4.2 eV
at room temperature.
2
Samples
2.1 Preparation and morphology
Polycrystalline CGS and SGS were prepared by solid-state reaction growth from CaS + Ga S and
2
3
SrS + Ga S binary stoichiometric mixtures for one week above 900 °C, in the form of large poly-
2
3
*
Corresponding author: e-mail: mamedov@pe.osakafu-u.ac.jp, Tel.: +81 72 25 49 268, Fax: +81 72 25 49 908
©
2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 0031-8965/03/19808-0478 $ 17.50+.50/0

phys. stat. sol. (a) 198, No. 2 (2003)
479
Fig. 1 Scanning electron micrographs of CGS-S (a, c, e) and CGS-L (b, d, f): as-grown (a, b) and pol-
ished (c, d) surfaces; general view (e, f).
crystalline ingots. The samples were obtained by cutting the ingots into plane-parallel round plates with
2
thickness of ~5 mm and surface area of ~50 mm .
Hereafter, the samples with small (S) and large (L) grain size by comparison with the wavelength of
the utilized light are called CGS-S and -L or SGS-S and -L, respectively. The details on surface mor-
phology, studied by scanning electron microscopy (SEM), are shown in Fig. 1 (CGS-S and -L) and Fig. 2
(
SGS-S and -L).
Visual observations and counts on numerous surface fragments of CGS-S (Fig. 1a) and SGS-S
(
Fig. 2a) have given the average grain size, l , around ~100 nm and ~250 nm, respectively. For CGS-L
g
(
Fig. 1b) and SGS-L (Fig. 2b), l is apparently far above the long-wavelength limit (0.8 µm) of our ellip-
g
someter.
Morphological details of the polished surfaces are shown in Figs. 1c (CGS-S), 1d (CGS-L), 2c
SGS-S) and 2d (SGS-L). CGS-L (Fig.1d) and SGS-S (Fig. 2c) have perfectly smooth surfaces. CGS-S
Fig. 1c) and SGS-L (Fig. 2d) display less perfect surface morphology, which, however, seems to
(
(
be insignificant compared to the total roughness of the surfaces to be probed by a 0.5 mm diameter light

480
N. Mamedov et al.: Ellipsometric studies at and below energy gap on polycrystalline thiogallates
Fig. 2 Scanning electron micrographs of SGS-S (a, c, e) and SGS-L (b, d, f): as-grown (a, b) and pol-
ished (c, d) surfaces; general view (e, f).
beam of the ellipsometer. A macroscopic scale of this roughness is apparent from SEM images of all
samples under investigation (Figs. 1e, 1f, 2e, and 2f).
2
.2 Microstructure
The XRD patterns of CGS and CGS are shown in Fig. 3 and Fig. 4, respectively. Reference JCPDS
Joint Committee on Powder Diffraction Standards) data are also given for comparison (Figs. 3 and 4,
(
topmost curves).
The XRD patterns of CGS-S (Fig. 3a) and CGS-L (Fig. 3b) are free of any traces of a crystalline sec-
ond phase. At the same time the XRD pattern of CGS-S displays a broadened background, associated
probably with an admixture of a growing amorphous phase (Fig. 3a). This background, along with the
fact that CGS-S had the smallest grain size among the investigated samples, indicates the unfavorable
conditions for crystallization during the solid-state growth of CGS-S.
For SGS-S with at least twice as large an average grain size as CGS-S, an amorphous-like background
was not observed (Fig. 4a). Nor was it observed for large-grain second-phase-free CGS-L (Fig. 3b), nor
for large-grain SGS-L with a small, ascertained fraction of Ga S (Fig. 4b).
2
3

phys. stat. sol. (a) 198, No. 2 (2003)
481
Reference JCPDS
Reference JCPDS
SGS-S
(
(
a)
b)
CGS-S
(a)
1
00
100
50
0
5
0
0
100
CGS-L
1
00
50
0
(b)
SGS-L
?
Ga
2
S
3
2 3
Ga S
5
0
0
20
30
40
50
60
20
30
40
50
60
Diffraction Angle 2θ (degree)
Diffraction Angle 2θ (degree)
Fig. 3 XRD patterns of CGS-S a) and CGS-L b), and Fig. 4 XRD patterns of SGS-S a) and SGS-L b), and
reference JCPDS data (topmost part). reference JCPDS data (topmost part).
3
Experimental details
3.1 General remarks
The problem of adequate treatment of ellipsometric data from polycrystalline media is not settled com-
pletely. Quantitative ellipsometric examinations, mostly on polycrystalline film patterns of Si and Ge,
have been mainly related to the microscopic roughness, and the region above the energy gap [8]. Aspnes
et al. [9] suggested BEMA (Bruggeman’s effective medium approximation) as the most universal and
fairly rigorous approach to treat this kind of roughness, which is typical when grain sizes are far below
the wavelength of the light.
Even without reservations for the macroscopic roughness of the small grain samples, the average grain
size in CGS-S (l ~100 nm) and SGS-S (l ~250 nm) is not very far below the utilized wavelengths in the
g
g
range 300–800 nm.
3.2 Ellipsometric approach
For non-depolarizing materials, ellipsometric angles Ψ and ∆ are unique parameters unambiguously
related with the dielectric function. However, in the presence of scattering, in particular, multiple scatter-
ing, which is commonly responsible for depolarization, and can be very strong especially in the region
below energy gap, these angles become ambiguous and configuration dependent.
In our studies we were using both fixed and variable angle-of-incidence operational modes of SPME.
The fixed angle-of-incidence spectroscopic mode was already applied to the amorphous CGS (CGS-A)
and polycrystalline CGS-S, with details described comprehensively in [10]. The angle-dependent mode,
applied here for the first time, allowed us to determine the angles known in the reflectance theory as the
principal angle and the angle of minimum elliptic ratio [11]. After combining the data from configuration
(
II) with the ones from configuration (III), we were also able to determine the degree of polarization,
using the well-known procedure [12].

482
N. Mamedov et al.: Ellipsometric studies at and below energy gap on polycrystalline thiogallates
The pseudo-dielectric function (PDF) [13] is found from the ellipsometric data for principal angle of
incidence, i.e. the angle Φ for which the phase change ∆ equals π/2, in the especially simple form
p
2
2
2
2
2
〈
ε 〉 = n − k = tan Φ
(
1− 2 sin Φ sin Ψ
)
,
p
(1a)
r
p
p
and
2
2
〈
ε 〉 = 2nk = tan Φ sin Φ sin 4Ψ ,
(1b)
i
p
p
p
for real and imaginary parts, respectively [11].
The principal angle Φ , the angle, Φ , of the minimal elliptic ratio that corresponds to a minimum,
p
m
Ψ , of the amplitude diminution Ψ, and the Brewster angle, Φ = arctan n, are known to be equal in the
m
B
case of transparent media with a perfect surface. In all the other cases these angles will differ from one
another.
The standard case below the energy gap, as is well applicable to our samples, is a situation with n very
large compared to k (n ӷ k), and n and k both behaving smoothly and increasing with increasing photon
energy. In the region below the energy gap all the above angles are supposed to be practically the same.
The small absorption (k Ӷ 1) can lead only to a difference within several minutes, as can be shown using
Eq. (1) and expression for Φ [14] in the form
m
2
2
2
2
a − b
a − b
8
6
4
2
2
4
tan Φ +
tan Φ +
tan Φ − 4a tan Φ − 4a = 0 ,
(2)
m
m
m
m
1
− b
1− b
2
2
2
2
where a = n − k and b = n + 3k . On account of absorption the splitting between the above angles can
occur only in one way, namely, Φ – Φ > 0, Φ – Φ > 0.
p
m
m
B
4
Results and discussion
4.1 Pseudo-dielectric function
Two-phase modeling (TPM) and PDF representation would have a meaning only for non-depolarizing
samples. For depolarizing samples a layered system consisting of effective medium layers with plane
parallel interfaces can hardly be useful, as already mentioned elsewhere [15].
For the purpose of illustration of the depolarization effects in our case, in Fig. 5 we show the degree
of polarization (DP) of the light reflected by large- and small-grain samples of SGS. It is seen that DP is
a function of both photon energy and incident angle, and is different for large- and small-grain samples.
Fig. 5 Polarization degree of the light
reflected by SGS-L and SGS-S at different
angles of incidence.

phys. stat. sol. (a) 198, No. 2 (2003)
483
Fig. 6 Real and imaginary parts of pseudo-
dielectric functions of CGS-L (curves 1), CGS-A
(curves 2) and SGS-L (dashed curves 3).
Physically unrealistic values, such as DP > 1 are related with calibration artifacts in the corresponding
spectral range. Since all samples were polished with exactly the same polishing powders, the finest of
which was of ~100 nm, the observed difference in DPs of SGS-L and SGS-S could not be explained by
the existence of a surface damage layer caused by polishing. Similarly, a natural overlayer also could not
account for the observed difference.
We refer this difference to the difference in grain size that would determine the strength of multiple
scattering (MS) and depolarization, as explained below.
MS in the bulk can occur and change the state of light polarization when photon-traveling distances
become at least twice the penetration depth. In other words, we can expect depolarization when the dou-
bled value of grain size becomes smaller than the penetration depth. Indeed, SGS-S with much smaller
grain sizes is more depolarizing than SGS-L (Fig. 6). At the same time DP levels of small- and large-
grain samples are approaching each other with increasing angle of incidence. This can be explained by
an increased fraction of surface scattering, caused by the increasing of the reflection coefficient at large
angles of incidence. At 80° DPs of SGS-L and SGS-S are practically the same (Fig. 5).
The DP of CGS-S was generally smaller than that of SGS-S, which is consistent with the smaller grain
size of CGS-S. In all the other respects the DPs of CGS-S and SGS-S were similar.
Although MS is, in a sense, similar to multiple reflections, which regularly occur in transparency
regions and lead to strong depolarization observed in plane parallel samples in the form of a remarkable
and drastic decrease of DP just below the absorption edge, it is rather irregular and, in our opinion, the
transition between coherent and incoherent scattering and the corresponding depolarization may not be
so easy to observe as the transition between coherent and incoherent reflection.
As to DP of CGS-L, it was closer to unity than that of SGS-L, adding further to our confidence regard-
ing applicability of TPM to this sample. PDFs of both CGS-L and SGS-L are shown in Fig. 6. The data
for amorphous CGS-A are also given for comparison (Fig. 6, curves 3).
The imaginary part of PDF of CGS-L displays the onset of the direct transitions across the band gap at
~
4.10eV (Fig. 6, bottom part, solid curve 1, E ). The real part also shows peculiarity around the same
o
photon energy (Fig. 8, upper part, solid curve 1, E ). Besides, both real and imaginary parts of PDF are
o

484
N. Mamedov et al.: Ellipsometric studies at and below energy gap on polycrystalline thiogallates
Fig. 7 Angular dependencies of Ψ and ∆ of CGS-S
(curve 1), CGS-L (curves 2), SGS-S (curves 3), and
SGS-L (curves 4) at 3eV. Horizontal and vertical dashed
lines show minimal Ψ and principal angle, respectively.
less broadened for CGS-L than for CGS-A (Fig. 6, solid curves 3), which is also reasonable. As a whole,
we can conclude that PDF of CGS-L is a fairly good representation. This PDF characterizes the CGS-
phase only, since no admixture of a second phase was found in CGS-L (Sect. 2.2).
With similar arguments, we can say that PDF of SGS-L is also sufficiently reasonable (Fig. 6, dashed
curves 3). But, whether this PDF represents only SGS-phase is not clear. Apparently, the admixture of
Ga S found in SGS-L (Sect. 2.2) is an obstacle for observation of the absorption edge.
2
3
According to the obtained PDFs, absorption below the energy gap of CGS or SGS is not infinitesi-
mally small. This fact is generally consistent with observations done on single crystals [16]. In the poly-
crystalline case, however, the absorption level below the energy gap is somewhat higher. According to
our very recent studies [17], the E -structure of PDF of polycrystalline CGS-L is nothing but the edge
o
singularity of the zz-component of the dielectric function tensor of biaxial CGS.
4
.2 Principal angle and angle of minimal elliptic ratio
Angle-dependent data are given in Fig. 7 for optional photon energy of 3 eV. As indicated by horizontal
and vertical dashed lines, for all samples, both incident (Φ ) and ellipsometric (Ψ ) angles determined at
p
p
∆
= ± π / 2 are found at a minimum,Ψ , of Ψ, for which the elliptic ratio is minimal.
m
For SGS-S, CGS-L, and SGS-L a one-to-one correspondence between Φ and Ψ holds in the whole
p
m
range of the accessed photon energies. For CGS-S, however, below 2.75 eV, this correspondence does
not hold any longer and significant splitting, δΦ, between Φ and Φ , is observed. This splitting is
p
m
shown in Fig. 8.
The splitting is negative (Φ < Φ ), which, in turn, rules out the applicability of TPM because TPM
p
m
permits only absorption-induced splitting that would have been positive (section 3.2). The splitting in-
creases with decreasing photon energy at least to an observable extent (Fig. 8). This might be put in the
same line as the expected decrease of the absorption level and the corresponding increase of MS. Never-
theless, the diffraction-type effects could not be ruled out entirely since the spectral range for small grain
CGS-S (~100 nm), as well as SGS-S (~250 nm), is transient between diffraction and geometric optics.
We would note that the effective refraction index, neff = tanΦ , determined for the spectral range where
p
splitting was not observed, was significantly decreased for small-grain samples of both CGS and SGS.

phys. stat. sol. (a) 198, No. 2 (2003)
485
Fig. 8 Angular dependencies of Ψ and ∆ of
CGS-S below 3 eV. Horizontal dashed lines:
minimal and principal Ψ; Vertical dashed lines:
principal angle and angle of minimal elliptic ratio.
Differences δΦ are numbered according to the
curve numbers.
At the same time, the difference δneff between large- and small-grain samples of the same material in-
creased on increasing the wavelength from 300 nm, at which δneff was ~0.1 and ~0.2 for CGS-S and
SGS-S, respectively. In other words, moving toward the diffraction region, where the effects of dilution
of the surface microstructure by air voids are supposed to be more pronounceable, appears to have taken
place. Studies on well-prepared model systems are necessary to clarify the matter in the transient region.
5
Conclusions
Polycrystalline samples of CGS and SGS with macroscopically rough surfaces and various grain sizes,
such as from less to substantially larger than the wavelength of the utilized light, were studied at and
below the energy gap, using variable and fixed angle-of-incidence operational modes of SPME at room
temperature. SEM and XRD were used to overview surface morphology and the microstructure of the
samples.
With reservations regarding absorption level below the energy gap, PDF representations of large-grain
samples, especially CGS-L, were found to be reasonable. The energy gap for direct transitions in CGS
was estimated at ~4.10 eV. For small-grain samples, the PDF representation was more inadequate be-
cause of the depolarization and the apparently diffraction effects becoming more pronounced in the tran-
sient spectral range. A splitting between the principle angle and the angle of minimal elliptic ratio was
observed for samples with grain size of ~100 nm. The nature of this splitting would need, however, fur-
ther investigations using well-prepared model systems.
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