Structural domains and electronic contributions in amorphous chalcogenides

Article abstract of DOI:10.1016/j.jpcs.2007.02.007

The optical dielectric response of As_x Se_{1 - x} and As_x S_{1 - x} binary glass films is studied in the frame of a model based on the distinct electronic contribution of the different building blocks occurring in glasses.

Full text of DOI:10.1016/j.jpcs.2007.02.007

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Journal of Physics and Chemistry of Solids 68 (2007) 987–992
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Structural domains and electronic contributions in
amorphous chalcogenides
Ã
´
J.M. Gonzalez-Leal , J.A. Angel, E. Marquez, R. Jimenez-Garay
´ ´ ´
´ ´ ´
Departamento de Fısica de la Materia Condensada, Facultad de Ciencias, Universidad de Cadiz, 11510 Puerto Real (Cadiz), Spain
Abstract
The optical dielectric response of AsxSe1ꢀx and AsxS1ꢀx binary glass films is studied in the frame of a model based on the distinct
electronic contribution of the different building blocks occurring in glasses.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: A. Glasses; A. Amorphous semiconductors; A. Chalcogenide glasses; D. Optical properties
1. Introduction
vapour deposition technique (PECVD). The results re-
ported here are also relevant for their bulk counterparts, as
the PECVD technique lacks of material formation hyster-
esis, as it is assumed for the bulk glasses, and also, to some
extent, for their thermally evaporated counterparts,
although such film samples could be affected by in-vapour
formed clusters. The dispersion of the refractive index of
the films has been determined from their optical transmis-
sion spectra, using a refined envelope method, which
provides accuracies in the calculation of the refractive
index better than 1%, in the near infrared-visible spectral
region, depending on the optical quality of the thin-film
samples [7]. The spectral behaviour of the refractive index
at large optical wavelengths is governed by the photonic
interaction with the collective electronic shell stemming
from molecular structural arrangements. So, the analysis of
this particular spectral region should throw light about the
type of clusters present in the chalcogenide alloy, provided
that they supply different number of electrons to their
corresponding external electronic shells.
Different models can be found to analyse the dispersion
of the refractive index of optical materials. The spectral
range of interest for the electronic features to be high-
lighted is properly covered by a simple, but well-supported
model, based in a single-oscillator, as that proposed by
Wemple and DiDomenico (WD) [8–11]. Particularly,
the model pays special attention to the definition of the
dispersion parameter, which gives an account of the
efficiency of the low-energy photon interaction, and it is
In general, the different building blocks occurring in a
polymer-type material should also contribute differently to
the electronic characteristics of it, and they could be
observed at some wavelength scale. This premise is
followed in the present work, whose results support a
segregated-phase view of glass materials.
To date, a number of models have been proposed to
explain the structural arrangement in the amorphous
chalcogenide materials, which range from stochastic
models, as the continuous-random-network model, to
non-stochastic ones, as the discrete polycrystalline model,
and the question follows being controversial [1–6]. How-
ever, from the monitoring of the thermal characteristics of
some chalcogenide alloys, it has been recently reported that
different structural regimes take place at different compo-
sitions, which push to leave the stochastic models and think
of non-linearities occurring at the material formation stage
[4]. Such a non-linear behaviour observed in the composi-
tional dependence of Tg, has moved the structural view of
the chalcogenides glasses to a scenario played by a mixture
of crystalline phases, occurring differently at different
composition ratios.
The present work has been performed on AsxS1ꢀx and
AsxSe1ꢀx films prepared by the plasma-enhanced chemical
Ã
Corresponding author. Tel.: +34 956016569; fax: +34 956016288.
E-mail address: juanmaria.gonzalez@uca.es (J.M. Gonzalez-Leal).
´
0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2007.02.007

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J.M. Gonzalez-Leal et al. / Journal of Physics and Chemistry of Solids 68 (2007) 987–992
988
fairly well described by a simple relationship, which
depends on the effective number of valence electrons at
molecular scale.
The present paper reports evidences about the structural
heterogeneities occurring in amorphous chalcogenides
from the monitoring of their low-frequency optical di-
electric response and the analysis of the refractive-index
dispersion.
will be discussed in terms of a single-oscillator model,
following the parametrization suggested by WD [8–11],
according to which the dielectric response of a solid (no
matter its covalent or ionic character, or its crystalline or
amorphous nature), at low optical frequencies (far from
resonance), is given by the following equation:
F
EoEd
E2o ꢀ ð_oÞ
n2 ꢀ 1 ¼
¼
,
2
(1)
2
E2o ꢀ ð_oÞ
where _o is the photon energy, the parameters Eo and Ed
stand for the oscillator resonance energy and oscillator
dispersion energy, respectively, and
2. Experimental
As above advanced, the AsxSe1ꢀx and AsxS1ꢀx glass
alloy films were prepared by the PECVD technique onto
glass substrates, from the corresponding hydrides AsH3,
SH2 and SeH2. Gas volume ratios and rf powers used for
the film-sample preparation are all listed in Table 1. Film
thicknesses span from 1 to 5 mm. Films were non-uniform
in thickness, as first evidenced by simple optical inspection
of the interference fringes on the sample surfaces, and also
by the contrast reduction between the interference extrema
appearing in their optical-transmission spectra (Fizeau
fringes). The spectra were measured at normal incidence,
over the 400–2200 nm spectral range, by a dispersive
spectrophotometer (Perkin Elmer, model Lambda-19). As
previously mentioned, a refined envelope method was used
to determine the refractive-index dispersion of the film
samples—values of the refractive index, n, were calculated
with accuracies about 1% [7].
2
X
o1
F ¼ _2o2p
f k
(2)
ok2
k
is the overall oscillator strength, which is related to the
electric-dipole oscillator strength, f k, associated with
transitions at frequency ok, the plasma frequency,
1=2
opð¼ ð4p nee2=mÞ Þ, and the first (strong) resonance
oscillator frequency, o1, ne being the effective electron
density, and e and m are the charge and mass of the
electron, respectively.
WD performed a relevant physicalization of the disper-
sion energy from a study covering more than 100 different
solids, including different structural and electronic scenar-
ios, by doing a relevant comparison of their corresponding
Ed experimental values. They concluded that such a
parameter is related with the formal valency of the anion,
Za, the effective cation coordination number, Nc, and the
total number of valence electrons per anion (cores
excluded), Ne. Such a relationship being embodied as
follows:
3. Preliminary theoretical considerations
As advanced in the introduction, the dispersion of the
refractive index of the PECVD As–Se and As–S glass alloys
Ed ¼ b Za NcNe,
(3)
where b is an energy constant expressing, as stated by WD,
the covalent or ionic character of the solid, through the
typical values 0.37 and 0.26 eV, respectively. The discussion
followed by the authors dealt with the linear behaviour of
Ed, and, as a complementary conclusion, the model points
towards an understanding of refractive-index behaviour
Table 1
Values of the experimental parameters used in the preparation of the
AsxSe1ꢀx and AsxS1ꢀx glass alloy films by the PECVD technique
Chemical
composition
AsH3/H2X volume ratio rf power (W) at
13.56 MHz
Pressure
(mbar)
(X ¼ Se, S)
Se
0/100
1/25
1/7
60
60
60
60
60
60
60
30
30
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
laying in a localized molecular theory of optical transition.
P
As10Se90
As21Se79
As27Se73
As31Se69
As37Se63
As40Se60
As44Se56
As56Se44
Linearity in Ed leans on the sum rule k f k ¼ 1, and, in
turn, in the consideration of the optical dielectric response
of a solid as a linear combination of the electronic
contributions of the distinct building blocks occurring in
1/2
1/2
2/1
2/1
the solids, which is mathematically expressed as
1/19
1/19
X
Ed ¼
wiEðdiÞ,
(4)
i
As20S80
As23S77
As25S75
As34S66
As36S64
As41S59
As43S57
As51S49
As60S40
As86S14
1/99
1/99
1/99
1/19
1/19
1/19
1/19
1/11
1/8
15
15
15
15
15
15
15
15
15
15
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
where EðdiÞ reflects the contribution to the overall dispersion
energy of the ith structural building block, existing in the
material with weight wi.
Fig. 1 illustrates different molecular units occurring in
arsenic-based chalcogenide glass alloys. The number of
valence electrons that each atom contributes with to its
bonds is also indicated in Fig. 1, as a two-term sum
reflecting the electronic contribution of each atom to a
1/4

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Fig. 1. Illustration of the valence electron counting and the determination of the cross-section parameter m, for a set of building blocks present in
AsxSe1ꢀx and AsxS1ꢀx glasses.
single bond. It is easy to confirm that the sum of the
electronic contributions around an anion would be just the
Ne-parameter suggested in the WD model, and it is
straightforward to infer, that the product NcNe could be
regarded as the total number of valence electrons around
a particular cation. However, a linear interpretation of
Eq. (3) would suggest that the effect of the anion valency
Za applies over the total number of valence electrons linked
to a cation-centred molecular unit.
and the effective electron plasma. This interaction is
eventually modulated by the b-parameter, which was
originally stated to be a two-valued constant, having units
of energy, and different values for ionic ð0:26 ꢁ 0:04 eVÞ,
and covalent ð0:37 ꢁ 0:05 eVÞ materials.
Fig. 1 illustrates the above comments concerning the
calculation of the m-parameter. It can be checked that the
chalcogen chain shown in Fig. 1(a) supplies 12 electrons
around each chalcogen atom, extended over the both sides
of its nearest neighbours, in such a way that the non-
dimensionless cross-section parameter m takes the value of
48. It can be checked that the structural scenario illustrated
in Fig. 1(b), which could be reasonably valid in the case of
chalcogen-rich binary alloys, provides a significant increase
in the m-parameter, up to a number of 64, due to the
homopolar bonds bridging the pyramidal structural units.
In the rest of the cases illustrated in Fig. 1, involving larger
As contents, values of m follow in the way they are
indicated in the figure.
Alternatively, we suggest at this point to write Eq. (3) in
the way Ed ¼ bNcðZaNeÞ, just to emphasize that the
contribution of the electron plasma to the dielectric
response intrinsically lays both in the number of valence
electrons per anion, Ne, and, let said, in how they are
polarized, or, equivalently, exposed, through the bonds
linked to these anions, which is described by the parameter
Za. Eventually, the overall effect over the optical dielectric
response of the electron plasma linked to a cation-centred
molecular unit would be evaluated by summing all the
ðZaNeÞj contributions, over the total number of anions
For the sake of clarity, the detailed calculation of the m
number for the As4X3 (X ¼ S, Se) building block shown
in Fig. 1(e), is explained here, as follows: differently to the
rest of the cases, this one involves different electronic
scenarios around the As species forming it, which has to be
considered in the valence electron counting for the
calculation of the cross-section parameter m. Taking into
P
Nc
i
around the cation, i.e.,
ðZaNeÞj. It follows from here
that if ðZaNeÞj is constant over the sum, the original
product NcZaNe proposed by WD is recovered. It is
suggested here that the linear combination m ¼
P
Nc
i
ðZaNeÞj contributes to the definition of the cross-
section for the interaction between low-energy photons,

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account the underlining linearity of Eq. (3), and, in turn,
the localized molecular approach for the optical transi-
tions, it can be probed that
m ¼ ð3 ꢂ ð2 ꢂ 28=3 þ 10=3 þ 10=3Þ þ ð2 ꢂ 28=3 þ 2 ꢂ 28=3
þ 2 ꢂ 28=3ÞÞ=4
¼ ð3 ꢂ 76=3 þ 56Þ=4 ¼ 33
for the cage-type As4Ch3 molecular cluster.
ð5Þ
A picture of the dielectric response lying in the degree of
exposure of the electronic molecular contribution, allows
speculating about the dependence of the energy-parameter
b with the bond length L. In fact, the oscillator energy Eo,
which appears in the original definition of Edð¼ F=EoÞ, as
derived from Eq. (1), has been reported to be related to the
bond length in the way Eo / Lꢀs, with s varying in the
2o so3 range [12]. In a first approximation, assuming F
independent or weakly dependent upon L, on the basis of
2
the ðo1=okÞ term in Eq. (2), the parameter b can be then
thought to depend on Ls, in such a fashion that the
following relationship would be verified:
Db
b
DL
L
¼ s
.
(6)
˚
Differences between the lengths of S–S bonds (2.06 A)
˚
[13] and Se–Se bonds (2.32 A) [14], would justify a
reduction in the value of b for amorphous sulphur. A
value for s ¼ 3 will be considered hereafter, in such a
fashion that the L3 dependence for the b-parameter could
be interpreted as related with the effective volume of the
valence-electron spatial distribution. Thus, b would de-
crease about 38% in the case of the amorphous sulphur, in
comparison with the one corresponding to the amorphous
selenium, and this could explain the large difference
between their refractive-index values.
Fig. 2. Values of the oscillator energy Eo (a) and the dispersion energy Ed
(b), as a function of As content, for both binary glass alloys. Curves are to
guide the eye.
Compositional trends of Ed in both film glassy systems
track closely those reported for the glass transition
temperature, Tg, of their corresponding bulk counterparts
[4]. Such a remarkable coincidence in the trends of these
thermal and electronic quantities can be understood if a
glass is regarded as a segregated-phase network made of
distinct building blocks, which contribute differently to the
optical dielectric response of the material depending on
their ionicity, coordination number and chemical valency,
or, intrinsically, on the metallicity and polarity, as it was
suggested by Wemple [11]. Hence, while Tg would reflect
those features related with the global connectivity of the
glass network, Ed would lift, to some extent, the ones
linked to heterogeneities occurring in the also global
electronic distribution in the network. Fig. 3 shows the
values for the oscillator-strength parameter F, which also
lifts the rigidity transitions taking place at distinct
compositional ratios.
4. Results and discussion
Values of the refractive-index factor ðn2 ꢀ 1Þꢀ1 were
2
plotted against the photon energy squared, ð_oÞ , for all
the thin-film samples studied, according to Eq. (1). In all
the cases, the experimental data departed, as expected,
from the linear trend ruled by Eq. (1), at high-photon
energies, or, equivalently, high optical frequencies, once the
optical absorption effects start playing a significant role in
the optical response. Departures are also observed at low-
photon energies, which arise from lattice contributions to
the dielectric response.
WD parameters Eo and Ed for both AsxSe1ꢀx and
AsxS1ꢀx alloy films have been determined from the
corresponding least-squares fits of their refractive-index
experimental data. Least-squares linear fits to the experi-
mental data for the AsxSe1ꢀx alloys can be found in [15].
The compositional dependences of both Eo and Ed
parameters are plotted in Fig. 2. Distinct features are
observed in both graphs evidencing the complex character
of the electronic distribution in these glass alloys.
Fig. 2(b) agrees well, in general, with the proposed
dependence of b on bond lengths. The higher values found
for Ed in the case of the As–Se glass alloys, in comparison
with the ones for the As–S alloys, are consistent with the
˚
fact that As–Se bond lengths ðꢃ2:40 AÞ are also larger than

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ꢀ1
˚
Qꢃ1:7 A
in the XRD-diffraction patterns of these
particular samples (see Fig. 4 in [15]), and the feature
appearing at a scattering frequency of ꢃ240 cmꢀ1 in their
Raman spectra, as reported in [4], which are in agreement
with the ones observed in amorphous arsenic samples
[17–20]. The occurrence of the g-As phases embedded in the
glass network below the stoichiometric composition,
x ¼ 40 at%, is thought to be smaller in the AsxS1ꢀx alloys,
on the basis of the trend observed for Ed in Fig. 2(b), where
no similar point of inflection, stressing a rigidity transition,
is seen. Complementary evidences supporting this state-
ment stem from both the XRD and Raman features
characteristics of amorphous As, which are observed only
at large values of x (above 40 at%) in the AsxS1ꢀx alloys.
As already mentioned, a structural conformation having
a significant amount of cage-type building blocks would
reduce the cross-section of the electronic cloud around the
cations, which explains the decrease observed in Ed above
x ꢄ 40 at%. A similar trend has been reported for the
glass-transition temperature of both the AsxSe1ꢀx and
AsxS1ꢀx glass alloys, which has been interpreted as a probe
of phase segregation in chalcogenides glasses, on the basis
of the Raman features observed in the spectra of the
samples in the 40 at% t x t60 at% compositional range.
Finally arsenic sulphide alloy films with As contents of
ꢃ60 at% and ꢃ86 at% were also prepared by the PECVD
technique. Their optical parameters are consistent with the
expected trends pointing to the values for amorphous
arsenic: refractive index ꢄ 4 and optical gap ꢄ 1:2 eV [18].
According to the present model, it seems clear that the
large increase of Ed above x ¼ 60 at% arises from the also
large electronic contribution of the more and more
emerging g-As domains. In addition, as already discussed,
the value of b would increase up to ꢃ0:46 eV for these As-
rich binary alloys, as homopolar As–As bond length is
larger than the rest of relevant bonds in the material. Both
effects would explain the large positive slope found in Ed,
at large x-values, in both glassy systems.
Fig. 3. Values of the oscillator strength parameter F as a function of As
content for both binary glass alloys. Curves are to guide the eye.
˚
the corresponding to the As–S bonds ðꢃ2:24 AÞ [16]. In
both glassy systems it is observed a monotonous increase in
the oscillator dispersion energy when increasing the As
concentration.
Data plotted in Fig. 2, for both Eo and Ed, suggest a
higher influence of the As atoms in sulphur-based alloys
than in the selenium-based ones. The rapid increase of Ed
with arsenic content at low x values can be explained in
both cases by the large photon interaction cross-section of
the building block illustrated in Fig. 1(b), which provide a
large m-number. Taking into account the m-values
indicated in Fig. 1, the slight increase found in the
compositional dependence of the Ed-parameter, in the
range 20 at%t x t30 at%, could be interpreted as a
consequence of the formation of corner-sharing pyramidal
units, as illustrated in the case (c) in Fig. 1, leading to a
reduction in the electric-dipole coupling efficiency with the
light probe. In a similar fashion that the trends reported for
Tg in the case of the AsxSe1ꢀx glass alloys, a point of
inflection is noticed in the Ed trend around the 30 at% of
As, which could be ascribed to the rigidity transition from
a floppy structural scenario to the so-called intermediate
structural region (see Fig. 2(b)).
Larger values of Ed start building up in the 30 at%
t x t 40 at% region, which cannot be explained in terms
of the appearance of the cage-type clusters shown in Fig. 1,
as they supply m-numbers smaller than 56, and, therefore,
they interact less efficiently with the low-frequency light
radiation. Nevertheless, these clusters plausibly explain the
decrease found in the Ed-values above 40 at%. It is
therefore thought that the trend observed in Ed in the
range 30 at% t x t 40 at% could be due to the presence
of As orthorhombic phases (g-As) [17–19], as illustrated in
Fig. 1(f). This speculation is supported by both, the feature
appearing at a value of the modulus of the scattering vector
5. Concluding remarks
Evidences about structural heterogeneities occurring in
amorphous chalcogenides have been reported from the
monitoring of their low-frequency optical dielectric re-
sponse and the analysis of the refractive-index dispersion,
of both AsxSe1ꢀx and AsxS1ꢀx glass film alloys, deposited
by the PECVD technique. A molecular interpretation of
the oscillator dispersion energy, Ed, introduced by WD for
the analysis of the refractive-index dispersion has been
described, and it has supported the discussion of the optical
dielectric response of the glass samples. Discussion has
been performed in the frame of the rigidity transitions
evidenced by calorimetric measurements, and links with the
molecular electronic contribution have been identified,
which suggest that the parameterization presented here
could be an useful complementary analytical tool for the
study of self-organization in optical glasses.

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Acknowledgements
[4] D.G. Georgiev, P. Boolchand, K.A. Jackson, Philos. Mag. 83 (2003)
2941.
[5] M. Micoulaut, J.C. Phillips, Phys. Rev. B 67 (2003) 104204.
This work has been partly supported by the MCYT
(Spain) and FEDER (EU), under FIS2005-01409 research
project, and Marie Curie European Reintegration Grant of
the Sixth Framework Programme, under contract MERG-
CT-2004-507791. The authors acknowledge Dr. A.M.
Bernal-Oliva and Dr. M. Vlcek for their contribution to
the experimental part.
[6] M.A. Popescu, J. Ovonic Res. 1 (2005) 7.
´
[7] J.M. Gonzalez-Leal, R. Prieto-Alcon, J.A. Angel, D.A. Minkov,
´ ´
E. Marquez, Appl. Opt. 41 (2002) 7300.
´
[8] S.H. Wemple, M. DiDomenico Jr., Phys. Rev. Lett. 23 (1969) 1156.
[9] S.H. Wemple, M. DiDomenico Jr., Phys. Rev. B 3 (1971) 1338.
[10] S.H. Wemple, Phys. Rev. B 7 (1973) 3767.
[11] S.H. Wemple, J. Chem. Phys. 67 (1977) 2151.
[12] H. Chen, W.Z. Shen, Eur. Phys. J. B 43 (2005) 503.
[13] F. Tuinstra, Acta Cryst. 20 (1966) 341.
[14] Y.H. Zhao, K. Lu, T. Liu, Phys. Rev. B 59 (1999) 11117.
References
[15] J.M. Gonzalez-Leal, J.A. Angel, P. Krecmer, E. Marquez,
´ ´
R. Jimenez-Garay, Phys. Rev. B 74 (2006) 205204.
´
[1] S.R. Elliott, Physics of Amorphous Materials, second ed., Longman,
London, 1990.
[16] P. Goldstein, A. Paton, Acta Cryst. B 30 (1974) 915.
[17] J.S. Lannin, Phys. Rev. B 15 (1977) 3863.
[2] J.C. Phillips, C.A. Beevers, S.E.B. Gould, Phys. Rev. B 21 (1980)
5724.
[3] M.V. Thorpe, J. Non-Cryst. Solids 57 (1983) 355.
[18] G.N. Greaves, S.R. Elliott, E.A. Davis, Adv. Phys. 28 (1979) 49.
[19] M. Popescu, Chalcogenide Lett. 2 (2005) 45.
[20] Y. Zhu, Y. Qian, Mater. Sci. Eng. B 47 (1997) 184.