Temperature dependence of the Raman-active phonon frequencies in indium sulfide

Article abstract of DOI:10.1016/S0038-1098(99)00062-9

The temperature dependence of the Raman-active mode frequencies in indium sulfide was measured in the range from 10 to 300 K. The analysis of the temperature dependence of the A_g intralayer optical modes show that Raman frequency shift results

Full text of DOI:10.1016/S0038-1098(99)00062-9

PERGAMON
Solid State Communications 110 (1999) 231–236
Temperature dependence of the Raman-active phonon frequencies
in indium sulfide
a
b
a
N.M. Gasanlya,1, , H. Ozkan , A. Aydinli , I. Yilmaz
¨
˙
*
aPhysics Department, Middle East Technical University, 06531 Ankara, Turkey
bPhysics Department, Bilkent University, 06533 Ankara, Turkey
Received 1 August 1998; received in revised form 5 November 1998; accepted 1 December 1998 by F. Yndurain
Abstract
The temperature dependence of the Raman-active mode frequencies in indium sulfide was measured in the range from 10 to
300 K. The analysis of the temperature dependence of the Ag intralayer optical modes show that Raman frequency shift results
from the change of harmonic frequency with volume expansion and anharmonic coupling to phonons of other branches. The
pure-temperature contribution (phonon–phonon coupling) is due to three- and four-phonon processes. ᭧ 1999 Elsevier Science
Ltd. All rights reserved.
Keywords: A. Semiconductors; D. Optical properties; E. Inelastic light scattering
1. Introduction
modes of the Brillouin zone center, observed in the
Raman spectra show a decrease in frequency as pres-
sure increases. They proposed that the initial orthor-
hombic phase of InS transforms into the calomel type
(Hg2Cl2) structure under pressures of P ˆ 7 ^ 1 GPa.
Subsequent measurements of the electrical resistance
[2], Raman spectra, optical properties and lattice para-
meters [3,4] show certain anomalies between 2.5 and
5 GPa. In a previous article [5], we have reported the
variation of the Raman frequencies and the lattice
parameters of InS as a function of pressure up to 30
and 16 GPa, respectively. Anomalies in the pressure
dependence of the Raman frequencies and rather
rapid decrease of the lattice parameter b toward a
with pressure clearly indicated a phase transition
at 5.0 ^ 0.3 GPa. The continuous structural changes
of the orthorhombic low-pressure modification as
well as the high-pressure monoclinic structure were
investigated.
The layer-type semiconductors, AIIIBVI, where A is
Ga, In; B is S, Se, have attracted particular interest in
recent years due to high degree of anisotropy in their
physical properties. In indium sulfide, the In atoms
have a tetrahedral coordination (three S atoms and
one In atom), the two S atoms and one In atom
being in one layer, whereas the third S atom is in
the neighboring layer. Therefore, the crystal structure
of InS can be considered as a three-dimensional
network which is slightly different from a layered
structure of its counterparts (GaS, GaSe, InSe).
A room temperature pressure-induced structural
phase transition in InS crystal was predicted on the
basis of Raman scattering studies at various hydro-
static pressures up to 1.2 GPa [1]. Six of the nine
* Corresponding author.
The influence of anharmonic interactions on the
lattice vibrations can be experimentally studied by
1 On leave from Physics Department, Baku State University,
Baku, Azerbaijan.
0038-1098/99/$ - see front matter ᭧ 1999 Elsevier Science Ltd. All rights reserved.
PII: S0038-1098(99)00062-9

232
N.M. Gasanly et al. / Solid State Communications 110 (1999) 231–236
measuring changes of phonon frequencies with
temperature and pressure. A large number of articles
devoted to the study of the temperature dependence of
the frequency shift and the linewidth of the first-order
Raman scattering in semiconductors may be found in
the literature [6–10]. They showed that the Raman
shifts can be successfully modeled by including the
effects of thermal expansion and the phonon–phonon
coupling.
The purpose of this article is to present the results of
the temperature dependence of the optical phonon
frequencies of InS in the 10–300 K temperature
range. We report softening of the optical phonon
frequencies at the Brillouin zone center with increase
in temperature as observed in some other semiconduc-
tors. The analysis of our results indicates that the
purely anharmonic contribution to the phonon
frequency shifts is due to interactions with phonons
of other branches.
2. Experimental
Fig. 1. Atomic displacement vectors for Ag intralayer optical modes
of InS.
InS polycrystals were synthesized from particular
high-purity elements (at least 99.999%) taken in stoi-
chiometric proportions. Single crystals of InS were
grown by the modified Bridgman method. The analy-
sis of X-ray diffraction data showed that they crystal-
lize in an orthorhombic unit cell with parameters: a ˆ
0.394, b ˆ 0.444 and c ˆ 1.065 nm. Due to the fact
that one of its three In–S bonds extends into the
neighboring layers, InS crystal has no distinct clea-
vage plane. Crystals suitable for measurements were
obtained by hard cleavage perpendicular to the OX-
axis (optical c-axis). As-grown InS is a n-type semi-
conductor having an indirect band gap with an energy
of 1.90 and 2.11 eV at 300 and 10 K, respectively
[11].
determined within an accuracy of 0.2 cmϪ1. A
‘‘CT1-Cryogenics M-22’’ close-cycle helium cryostat
was used to cool the crystals from room temperature
down to 10 K. The temperature was controlled within
an accuracy of ^1 K. In order to avoid sample heating
effects, we chose a cylindrical lens to focus the inci-
dent beam on the sample. The laser power was kept
below 30 mW. No changes in the spectra were
observed when the applied power was reduced by a
factor of two.
3. Results and discussion
Unpolarized Raman scattering measurements were
performed in the back-scattering geometry in the
frequency range from 20 to 350 cmϪ1. The 632.8 nm
(hn ˆ 1.96 eV) line of a He–Ne laser and the
617.5 nm (hn ˆ 2.01 eV) line of dye laser were
used as exciting light sources. The scattered light
was analyzed using a U-1000 ‘‘Jobin Yvon’’ double
grating spectrometer and a cooled GaAs photomulti-
plier supplied with the necessary photon counting
electronics. The Raman line positions were
InS has the orthorhombic structure composed of
four molecules in a primitive unit cell and belongs
to the space group Pmnn. According to the group
theory, there should be 24 fundamental phonon modes
G ϵ 4Ag ϩ 2Au ϩ 4B1g ϩ 2B1u ϩ 2B2g
ϩ4B2u ϩ 2B3g ϩ 4B3u:
Thus, there are 12 Raman active modes in InS,

N.M. Gasanly et al. / Solid State Communications 110 (1999) 231–236
233
Fig. 2. (a) Raman spectrum of InS at T ˆ 10 K; (b) extended parts of Raman spectra of Ins at T ˆ 10 K (solid curves) and T ˆ 300 K (dashed
curves).
given by 4Ag ϩ 4B1g ϩ 2B2g ϩ 2B3g. The symmetry
coordinates found by Melvin projection operators
method [12] were used to obtain the displacement
vectors of atoms in all phonon modes. Fig. 1 shows
the atomic displacement vectors for Ag intralayer opti-
cal modes of InS. As seen from this figure at each Ag
mode all the indium and sulfur atoms move either
perpendicular or parallel to the layers.
Fig. 2 presents the Raman spectra of InS at 10 and
300 K. The phonon spectra of InS have been reported
previously at room temperature from Raman and
infrared measurements [5,13,14]. The present assign-
ment of the observed modes is in excellent agreement
with that of Ref. [5]. We have measured and analyzed
only the most intensive, at employed geometry, Ag
intralayer optical modes with room temperature

234
N.M. Gasanly et al. / Solid State Communications 110 (1999) 231–236
frequency values 59.5 (Ag3), 150.6 (Ag1), 222.7 (Ag4),
and 317.6 (Ag2) cmϪ1. As seen from Fig. 1, in the Ag1
and Ag2 modes the atoms vibrate in the direction of
stretching bonds, whereas the Ag3 and Ag4 modes corre-
spond to the bending vibrations of the atoms. It was
previously observed that the frequencies of Ag1 and Ag2
modes increase and those of Ag3 and Ag4 modes
decrease with pressure [1]. It was reported that the
Gru¨neisen parameters of the first two modes are posi-
tive ꢀg1 ˆ 0:7; g2 ˆ 0:2† and those of the last two are
negative ꢀg3 ˆ Ϫ1:5; g4 ˆ Ϫ0:4†. Thus, negative
Gru¨neisen parameters were observed for modes at
which the atoms move perpendicular to the OX-axis
of the crystal.
The frequency shifts of Ag modes investigated in
the temperature range 10–300 K were found to be 2.7
(Ag1), 2.5 (Ag2), 1.2 (Ag3), and 2.1 cmϪ1 (Ag4). The
experimental results (open circles) for the line posi-
tions n(T) of different Ag modes are shown in Fig. 3.
The phonon frequency shift with temperature can be
described by the following expression [7]
nꢀT† ˆ n0 ϩ D1ꢀT† ϩ D2ꢀT†;
ꢀ1†
where n0 ϩ D2ꢀ0† is the Raman shift as T approaches
0 K, D1ꢀT† represents the volume dependence of the
frequency due to the thermal expansion of the crystals
and D2ꢀT† specifies the contribution of anharmonic
coupling to phonons of other branches.
D1ꢀT† can be written as [7]:
ꢂ
ꢀ
ꢁ
ꢃ
ZT
D1ꢀT† ˆ n0 exp Ϫ3g aꢀT 0† dT 0 Ϫ 1 ;
ꢀ2†
0
Fig. 3. Temperature dependencies of the Raman frequencies in InS
(open circles). The solid curves give the theoretical fits using both
three- and four-phonon processes. The dashed curves give the theo-
retical fits using only three-phonon processes.
where aꢀT† is the coefficient of linear thermal
expansion.
The purely anharmonic contribution to the frequency
Table 1
Parameters for fitting the temperature dependence of Raman frequencies of InS crystal
Modes
n0 (cmϪ1
)
A (cmϪ1
)
B (cmϪ1
)
B/A
1.727
0.042
Ϫ0.636
0.026
n01 (cmϪ1
)
A1 (cmϪ1
)
Ag1
Ag2
Ag3
Ag4
153.4
321.0
60.9
Ϫ0.022
Ϫ0.818
0.011
Ϫ0.038
Ϫ0.034
Ϫ0.007
Ϫ0.022
153.9
321.3
61.2
Ϫ0.419
Ϫ1.129
Ϫ0.153
Ϫ1.007
225.6
Ϫ0.836
225.8

N.M. Gasanly et al. / Solid State Communications 110 (1999) 231–236
235
(four-phonon processes). Here, x ˆ hcn0=2kBT and
y ˆ hcn0=3kBT.
Using the experimental values of g [1] and aꢀT†
[15], the frequency shifts for Ag modes were fitted
(solid curves in Fig. 3) by means of Eqs. (1), (2)
and (3) with n0, A and B as adjustable parameters.
The agreement between the experimental points and
the solid curves is seen to be good for all Ag modes.
The fitting parameters are presented in Table 1. The
absolute values of B/A for Ag2 and Ag4 modes are very
low, 0.042 and 0.026, respectively. This indicates that
pure-temperature dependence of the frequencies
D2ꢀT† is dominated by the three-phonon processes.
The four-phonon coupling processes (quartic interac-
tion) are less effective. This result is consistent with
the previous experiments in Si and Ge [6,7], ZnSe and
ZnTe [8], CuGaS2 [9] and AgGaS2 [10] compounds.
By contrast, relatively higher absolute values for B/A
were found for Ag1 and Ag3 modes, 1.727 and 0.636,
respectively (Table 1). Consequently, we deduce that
the contribution of four-phonon processes to the
frequency shift D2ꢀT† is important for these modes.
If we try to fit the experimental data with three-
phonon processes only, by omitting the term in Eq.
(3) with the factor B, we obtain the dashed curves in
Fig. 3 with adjustable parameters n01 and A1, also
given in Table 1. The agreement between calculated
curves and the experimental points is quite good for
Ag2 and Ag4 modes, but for Ag1 and Ag3 modes the curves
do not represent the data well, especially for the latter
mode. This further demonstrates that the four-phonon
processes are important for the Ag1 and Ag3 modes.
We have stated before that to describe the results
obtained for Ag2 and Ag4 modes, having high absolute
values of adjustable parameter A, mainly three-
phonon processes is sufficient, whereas for Ag1 and
Ag3 modes with lower values of A (almost 50 times)
both three- and four-phonon processes should be
included. These features may be related to the differ-
ences in sets of atomic displacements for these pairs
of modes. Indeed, as seen from Fig. 1, in the Ag2 and
Ag4 modes the restoring forces are due to the In–In and
In–S bonds, whereas in the Ag1 and Ag3 modes primar-
ily the In–In bonds are involved.
Fig. 4. Experimental Raman frequency shifts as a function of
temperature (triangles). Open and solid circles are the thermal-
expansion and the purely anharmonic contributions to the line shifts,
respectively.
shift can be modeled as [6]:
ꢂ
ꢃ
2
D2ꢀT† ˆ A 1 ϩ
ex Ϫ 1
ꢂ
ꢃ
3
3
ϩ B 1 ϩ
ϩ
;
ꢀ3†
ey Ϫ 1
ꢀey Ϫ 1†
2
We have also calculated the thermal-expansion
contribution to the line shift ‰D1ꢀT†Š for Ag modes
by using the experimental values of g and aꢀT† and
obtained the value of the adjusted parameter n0. The
where the first term corresponds to the coupling of
the optical phonon to two identical phonons
(three-phonon processes) and the second term corre-
sponds to the coupling to three identical phonons

236
N.M. Gasanly et al. / Solid State Communications 110 (1999) 231–236
variations of D1ꢀT† are given in Fig. 4 for all Ag
modes, together with the experimental frequency
shifts. The pure-temperature effect on the frequency
shift ‰D2ꢀT†Š, obtained from the difference between
the experimental results and the thermal expansion
contribution D1ꢀT† are also plotted in Fig. 4 (solid
circles). An interesting feature of these plots is that
for Ag3 and Ag4 modes, having negative Gru¨neisen
parameters, the pure-temperature contribution D2ꢀT†
dominates the pure-volume contribution D1ꢀT† for the
entire temperature range studied. But for Ag1 and Ag2
modes, having positive Gru¨neisen parameters, D2ꢀT†
prevails D1ꢀT† only at relatively high-temperature
ranges 150–300 K and 100–300 K, respectively.
The analysis of the temperature dependence of the
Ag symmetrical optical modes in InS crystal shows
that the Raman frequency shift is well described by
considering the thermal-expansion and pure-tempera-
ture (phonon–phonon coupling) contributions. The
cubic (three-phonon) and quartic (four-phonon)
anharmonicities responsible for the pure-temperature
contributions to the Ag mode frequency shift were
determined. We have shown that the term correspond-
ing to quartic processes should be included in the
frequency shift expression D2ꢀT† for Ag1 and Ag3
modes.
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