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Low frequency Raman scattering spectra of (GeS2)1−χ(Sb2S3)χ amorphous semiconductors
JOURNAL OF
ELSEVIER
Journal of Non-CrystallineSolids 211 (1997) 89-94
Low frequency Raman scattering spectra of(GeS2) l_X(Sb2S 3) x amorphous semiconductors T. Asami a, K. Matsuishi a, S. Onari a,*, T. Arai b a Institute of Applied Physics, UniversiO, of Tsukuba, Tsukuba 305, Japan b School of Science andEngineering, lshinomaki Senshu Unicersitv Ishinomaki 986, Japan
Received 21 December 1995;revised 11 September 1996
Abstract
Low frequency Raman scattering spectra of amorphous (GeS2) I_X(sb2S3)x system (0 _
1. I n t r o d u c t i o n
Investigation of the local and intermediate range structure of amorphous semiconductors is important for understanding their specific physical properties. The structural correlation range is a characteristic structural measure of disordered solids and would be important information for understanding medium range order of amorphous materials. Raman scattering, as well as electron, X-ray and neutron diffraction measurements, are useful methods to obtain the information on the medium range order. The medium range order in chalcogenide glasses has been ob-
* Corresponding author. Tel.: + 81-298 535 330; fax: + 81-298 535 205.
served by diffraction measurements (for example Refs. [1-4]). Recently, Elliott has proposed a unified model to explain the experimental data of the Raman scattering and diffraction measurements of the glasses and the amorphous materials [5,6]. However, his idea seems to be still controversial. To discuss the medium range order it is necessary to consider the observations, which are based on different experimental methods. There have not been any reports about medium range order of (GeS2) l_x(Sb2S3)x system by Raman scattering measurements. It has been suggested that Raman scattering in the low frequency or acoustic region provides information on the structural correlation range [7-9]. A Raman scattering peak appearing in the region 10-50 cm -1 has often been called the 'boson peak'; the
0022-3093/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0022-3093(96)00630-8
90
T. Asami et a L / Journal of Non -Cr?;stalline Solids 21 l (1997) 89-94
origin of this scattering peak is controversial. Shuker and Gammon suggested that the reduced Raman scattering spectrum was proportional to the product of the vibrational density of states and the Fourier transform of the spatial correlation function [7]. Martin and Brenig proposed a model of light scattering from Debye-like acoustic modes in disordered solids [8]. This model was first applied to bulk glasses by Nemanich [9] and it has been used to study various glasses and amorphous materials, for example superionic glasses [10], oxide glasses [11] and various optical glasses [12]. For crystalline GeS 2, two typical modifications are known: a high temperature phase (denoted as a-GeS 2) and a low temperature phase (denoted as fl-GeS2). The structures of c~-GeS2 and fl-GeS 2 correspond to a two dimensional and a three dimensional form, respectively. It has been suggested that the network structure of amorphous GeS 2 is layered rather than three dimensional [13,14]. Stibnite crystal, Sb2S 3, has a complex ribbon-like structure. The structure consists of two infinite ribbons (Sb486) n along the c-axis, which are very weakly bonded in the b direction (the shortest interatomic distance between the ribbons in b direction is about 1.5 times larger than that in the ribbon), and only slightly more strongly bonded in the a direction [15]. Each Sb atom has two non-equivalent positions. In one position Sb forms a pyramid with three S atoms, but in the other, Sb is bonded with five S atoms. In the amorphous state, Sb2S 3 is reported to have the pyramidal structure (SbS3/2) similar to AszS 3 [16]. It is of great interest to investigate the amorphous structure (especially medium range order) of a mixture of two materials which have different kinds of crystal structures. In this paper we report results of low frequency Raman scattering measurements on the amorphous (GeS2)l_x(Sb2S3)x system. The structural correlation range is obtained by applying the Martin and Brenig model and it decreases continuously with increase in Sb2S 3 content in the system.
The Raman scattering measurement was performed with the normal back scattering configuration. The 647.1 nm line of a krypton ion laser was used as a light source. A double-grating monochromator (Jobin Yvon U1000) was used as a spectrometer. A photon counting system was used with a photomultiplier (RCA C31034) and a multichannel analyzer (Canberra Series 40). The polarization dependence was measured with a Glan-Taylor prism polarizer in the HH and HV geometries. Here, HH and HV represent the parallel and perpendicular configurations of the incident and scattered light, respectively. The scattering spectra were obtained in the wave number region from - 1 0 0 to 100 cm -~ . The intense central peak in this region was weakened by about 10 -6 times by neutral density filters. Temperature dependence of the Raman scattering spectra was measured by using a continuous flow liquid helium cryostat (Oxford CF-1204), and the temperature was varied from liquid helium temperature to room temperature with the aid of a temperature controller.
'
'
'
'
I
'
'
•
•
I
•
'
'
'
I
•
'
•
'
(GeSa)l.x(SbaSa)x HV 647.1nm exc. Room Temp. X= 0
Z c
rr-
o c
2. Experimental procedure
The samples were prepared by melt quenching a mixture of the elements Ge, Sb and S of purity 6N. They were melted at 950°C for 48 h in an evacuated ampoule and the ampule was quenched in air.
-100
-50
0
50
100
RAMAN SHIFT [cm"1] Fig. 1. Compositional dependences of the low frequency Raman
scattering spectra(HV).
T. Asami et al. / Journal of Non-Co,stalline Solids 211 (1997) 89-94
The sphere-resonance method [17] was used for the measurement of the sound velocity. The samples were shaped to a sphere for the sake of easy identification of the sphere-resonance mode. The diameter of the spheres was about 6 mm. A spherical sample was carefully placed between the two piezo-electric transducers of lead zirconium titanate (PZT) by using a micrometer head. The measured frequency range was from 100 to 500 kHz.
3. Results
The compositional dependence of the low frequency Raman scattering spectra for (GeS2)~_ x (Sb2S3) x system is shown in Fig. 1 for HV configuration. Both Stokes and anti-Stokes components of the spectra are obtained. Depolarization ratio IHV/IHH is about 0.5 and is nearly constant in this frequency range. The characteristic feature, 'the boson peak', is observed near 20 cm-~ at X = 0. It shifts to higher frequencies with an increase of the Sb2S 3 content.
91
cal constant by the disordered structure was assumed to be a Gaussian distribution as follows:
(AP(r) .AP(r+r')> =exp(-lr'12/4~r2),
(2)
where A p is the fluctuation of the elasto-optical constant and 2 o- represents the structural correlation range. Debye-like acoustic phonons are adopted for the vibrational density of states and the disorder of the glass structure is assumed to contribute to the photon-phonon coupling. The Raman coupling constants for HV and HH scattering are CHv(O9 ) = Ao92{3gt(~o) + 2g1(o9)},
(3a)
Cnn (to) = ao92{3gt(o9) + (15V + ~)g,( w)}, (3b) with (4a)
{(2__)2}
g l ( w ) = exp -
vl
(4b)
4. Discussion
We employed the Martin and Brenig (M-B) model [8] for the boson peak in chalcogenide glass to obtain the structural correlation range. The intensity of the Stokes Raman scattering in glasses can be presented in the form [7]:
1(o9) = ~'_,ChGh(o9) b
-
,
where A is a constant, c is the speed of light and vl, v t are longitudinal and transverse sound velocities. V is determined from the experimentally obtained depolarization by the relation: IHv (to) p(,,.,)
-
_
_
(l)
O)
where Gb(w) is the vibrational density of states; n(oJ) is the Bose factor; and C h is the light-phonon coupling constant. For the anti-Stokes component n ( w ) + 1 is replaced by n(~o). The M - B model includes effects due to both electrical and mechanical disorder. The electrical disorder is represented by the fluctuations due to the elasto-optic inhomogeneity of the glass and the mechanical disorder is described by the correlation function for the irregular local strain field of the vibrational mode. The correlation function of the fluctuations of the elasto-opti-
=
+ 2 / 3 + gt(
og)/g,(to)
(5)
V is a measure of the relative mean-square spatial fluctuations of the photoelastic constant 8C2/C 2 and elastic constant h by the relation
sc? + xc? V= 8C2t + AC2 .
(6)
This model is applied for the r a n g e (277"Co9//Pl.t)O" < 1. In the Raman spectra this range corresponds to the lower frequency side of the boson peak.
92
T. Asami et al./ Journal of Non-C~stalline Solids 211 (1997) 89-94
The M - B model deals with depolarization of the low frequency light scattering. As shown in the Eqs. (3a) and (3b), the same structural correlation range, 20", should be obtained from both HH and HV spectra. The HV and HH spectra are fitted by using Eqs. (3a) and (3b), respectively. Results of the M - B model fitting for HV configurations are shown in Fig. 2. The sound velocities estimated from the sphere resonance method for (GeS 2)1 - x(Sb2 S3)x are 2700 m / s for v I and 1500 m / s for ~t. Neither v l nor vt changes appreciably with the Sb2S 3 content. The structural correlation ranges (2 0") thus obtained for HH and HV spectra are plotted versus X in Fig. 3. 20- decreases with an increase of Sb2S 3 content. As expected from the M - B model, structural correlation ranges (2 0-) obtained from both HV and HH spectra are in agreement with each other within experimental errors for each composition. Thus, we have obtained the information by Raman scattering that the medium range order is modified by the Sb2S 3 content in this system.
r,-
~d
4-
s > -1-
0
10
20
30
40
50
RAMAN SHIFT [ cm 1 ]
Fig. 2. Compositionaldependences of the low frequency Raman scattering spectra (HV) and the M-B model.
i
i
(GeSa)l.x(SbaSa)x
E e-
UJ
I
0.8 •
(.9
:HV
o:HH
Z
rr Z
O 0.7
II tti
W rr nO
o
0.6
,,_1 ,< n" I--
o n- 0.5 I,.-
0.0
I
i
i
0.2
0.4
0.6
~
I
0.8
i
1.0
MOLECULAR FRACTION X
Fig. 3. The structural correlation range (2~r) for (GeS2)I_x(Sb, S3)x system deduced by M-B model fitting calculated from Eq. (3a).
Fig. 2 shows that the above model fits the lower frequency side of the boson peak quite well; whereas the spectrum deviates from the theory below ~ 5 cm -1. This deviation is due to temperature dependent excess light scattering [ 18-20]. The temperature dependences of the low frequency Raman scattering spectra for X = 0.5 are shown in Fig. 4. The intensity of the boson peak is changed with the temperature change. The temperature dependence of the intensity of boson peak can be well explained with the Bose factor. For the same reason the anti-Stokes Raman intensity at lower temperature becomes weaker than the Stokes one. Theodrakopoulos and J~ickel have proposed a model to describe the excess light scattering ( T - J model [20]). They interpreted it by applying the idea of a two level system, in terms of relaxation processes arising from thermally activated transitions between two metastable states which form a double well potential system. The hopping between the two possible configurations contributes to the inelastic scattering of light, since the dielectric susceptibility of a defect is different in its two configurations by an
T. Asami et al. / Journal of Non-CD'stalline Solids 211 (1997) 89-94
The experimental spectral contribution due to the excess light scattering was estimated by subtracting the contribution of boson peak, i.e. the intensity calculated using Eq. (3a). The excess light scattering spectra are fitted to the curve calculated from Eq. (9) using best fit values of ~- and C. Examples of the fits are shown in Fig. 5(a), (b) for temperatures, T > 10, K. For three samples X = 0.1, 0.5 and 0.9, logarithmic plots of the transition rate, l / r , versus 1/kT
293K ~" t-
200K
>I--
lOOK
Z LU I-Z
50K
--
40K
Z < <( rr
93
30K 24K 20K 16K 12K
e-
~2 ,-'-,
-30
-20
-10
0
10
20
293K 200K
30 +
100K
R A M A N SHIFT [ cm 1 ] Fig. 4. Temperature dependences of the low frequency Raman scattering spectra for X = 0.5.
amount, A c~. They obtained for the excess light scattering
=
50K
s
40K
~.
30K
--=
24K 20K 16K
Ie(O~) CX(Aa)2{n(o~) + l}f dVP(E)
~(E) x I
12K
+ co2r(E) 2 '
where E is an activation energy and P(E) is a distribution of activation energies. The distribution of relaxation times, r ( E ) , is expressed by the Arrhenius formula
r(E)
' = 'r o' e x p ( - E / k T ) ,
(8)
where r 0 is a constant and k is the Boltzmann constant• The polarization ratio, Ie,HV/Ic,Hn, is frequency independent. For a narrow distribution of barrier heights between the two states, Eq. (7) is represented by a simplified expression with one activation energy and one relaxation time O)T
le(w) = C { n ( o J ) + 1} ~1 + ' co2r where C is a constant.
5
(7)
(9)
10
R A M A N SHIFT [ cm "1 ]
._= r"
I
(b)
I
l
I
(GeS2)l.x(Sb2S3)x( X=0.5 )
I
.
~
e-,,
x = 1.3 ps +
c
% ' ~ ~ , / ' •\
Re~:l,_u_ced=_Raman scattering
"
---
~''i
5
moael
-
• ~ -.
~-''''i
/-d
- - M-B model .... T-J m o d e l + M-B m o d e l
•..,
.......
10
I .......
15
k .......
20
L .......
25
30
RAMAN SHIFT [ cm "1 ] Fig. 5. (a) Reduced Raman scattering spectrum of X = 0.5 at T = 200 K and the best fitting curve calculated from Eqs. (3a) and (9). (b) The spectral contribution of the excess light scattering and the best fitting curve calculated from Eq. (9) for X = 0.5.
94
T. Asami et al. / Journal of Non-Crystalline Solids 211 (1997) 89-94 I
I
I
ing by applying the Theodrakopoulos and J~ickel model. They do not show compositional dependences.
(GeS2) 1.x(Sb2S3)x 1012
7
• X=0.1
•
'o
•
• •
|
X=0.5 X=0.9
References !
1011 0
I 200
_...
I 400
|
I 600
_,
800
1000
1 / kT ( e V "1 )
Fig. 6. The logarithmic plots of the hopping rate 1/~- versus
1/~r. are shown in Fig. 6. The transition rate, 1/~-, versus l/kT dose not show compositional dependence. These results suggest that this relaxation process is composition independent and is not influenced by the change in the network structure and the medium range ordering. The plots of In(1 /~') versus 1/kT do not indicate linear dependence and this suggests that the distribution of activation energy is not narrow.
5. Conclusion
Low frequency Raman scattering spectra of amorphous (GeS2) l_x(Sb2S3)x system (0 < X < 0.9) were measured and the structural correlation range (2 o-) was obtained by applying the Martin and Brenig model. The value of 2 o- in this amorphous system decreases slightly with increasing Sb2S 3 content. The relaxation rates for atomic rearrangement between metastable states were estimated from the temperature dependences of the excess light scatter-
[1] A. Fischer-Colbrie and P.H. Fuoss, J. Non-Cryst. Solids 126 (1990) 1. [2] L. (~ervinka, O. Smotlacha, J. Bergerovfi and L. Tich~, J. Non-Cryst. Solids 137-138 (1991) 123. [3] L. (~ervinka and J. BergerovL J. Non-Cryst. Solids 150 (1992) 132. [4] E. Vateva and E. Savova, J. Non-Cryst. Solids 192-193 (1995) 145. [5] S.R. Elliott, Nature 354 (1991) 445. [6] S.R. Elliott, Europhys. Lett. 19 (1992) 201. [7] R. Shuker and R.W. Gammon, Phys. Rev. Lett. 25 (1970) 222. [8] A.J. Martin and W. Brenig, Phys. Status Solidi (b) 64 (1974) 163. [9] R.J. Nemanich, Phys. Rev. B 16 (1977) 1655. [10] G. Carini, M. Cutroni, A. Fontana, G. Mariotto and F. Rocca, Phys. Rev. B 29 (1984) 3567. [11] J. LoroAdsch, M. Couzi, J. Pelous, R. Vacher and A. Levasseur, J. Non-Cryst. Solids 69 (1984) 1. [12] D. Heiman, R.W. Hellwarth and D.S. Hamilton, J. Non-Cryst. Solids 34 (1979) 63. [13] R.J. Nemanich, S.A. Solin and G. Lucovsky, Solid State Commun. 21 (1977) 273. [14] P.M. Bridenbaugh, G.P. Espinoza, J.E. Griffiths, J.C. Phillips and J.P. Remeika, Phys. Rev. B 20 (1979) 4140. [15] J. Petzelt and J. Grigas, Ferroelectrics 5 (1973) 59. [16] T. Asami, S. Onari and T. Arai, Jpn. J. Appl. Phys. 32 (Suppl. 32-3) (1993) 784. [17] E. Schreiher, O.L. Anderson and N. Soga, Elastic Constants and Their Measurements (McGraw-Hill, New York, 1973). [18] G. Winterling, Phys. Rev. B 12 (1975) 2432. [19] G. Winterling and T. Arai, Phys. Non-Cryst. Solids (1977) 580. [20] N. Theodorakopoulos and J. J~ickel, Phys. Rev. B 14 (1976) 2637.
ELSEVIER
Journal of Non-CrystallineSolids 211 (1997) 89-94
Low frequency Raman scattering spectra of(GeS2) l_X(Sb2S 3) x amorphous semiconductors T. Asami a, K. Matsuishi a, S. Onari a,*, T. Arai b a Institute of Applied Physics, UniversiO, of Tsukuba, Tsukuba 305, Japan b School of Science andEngineering, lshinomaki Senshu Unicersitv Ishinomaki 986, Japan
Received 21 December 1995;revised 11 September 1996
Abstract
Low frequency Raman scattering spectra of amorphous (GeS2) I_X(sb2S3)x system (0 _
1. I n t r o d u c t i o n
Investigation of the local and intermediate range structure of amorphous semiconductors is important for understanding their specific physical properties. The structural correlation range is a characteristic structural measure of disordered solids and would be important information for understanding medium range order of amorphous materials. Raman scattering, as well as electron, X-ray and neutron diffraction measurements, are useful methods to obtain the information on the medium range order. The medium range order in chalcogenide glasses has been ob-
* Corresponding author. Tel.: + 81-298 535 330; fax: + 81-298 535 205.
served by diffraction measurements (for example Refs. [1-4]). Recently, Elliott has proposed a unified model to explain the experimental data of the Raman scattering and diffraction measurements of the glasses and the amorphous materials [5,6]. However, his idea seems to be still controversial. To discuss the medium range order it is necessary to consider the observations, which are based on different experimental methods. There have not been any reports about medium range order of (GeS2) l_x(Sb2S3)x system by Raman scattering measurements. It has been suggested that Raman scattering in the low frequency or acoustic region provides information on the structural correlation range [7-9]. A Raman scattering peak appearing in the region 10-50 cm -1 has often been called the 'boson peak'; the
0022-3093/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0022-3093(96)00630-8
90
T. Asami et a L / Journal of Non -Cr?;stalline Solids 21 l (1997) 89-94
origin of this scattering peak is controversial. Shuker and Gammon suggested that the reduced Raman scattering spectrum was proportional to the product of the vibrational density of states and the Fourier transform of the spatial correlation function [7]. Martin and Brenig proposed a model of light scattering from Debye-like acoustic modes in disordered solids [8]. This model was first applied to bulk glasses by Nemanich [9] and it has been used to study various glasses and amorphous materials, for example superionic glasses [10], oxide glasses [11] and various optical glasses [12]. For crystalline GeS 2, two typical modifications are known: a high temperature phase (denoted as a-GeS 2) and a low temperature phase (denoted as fl-GeS2). The structures of c~-GeS2 and fl-GeS 2 correspond to a two dimensional and a three dimensional form, respectively. It has been suggested that the network structure of amorphous GeS 2 is layered rather than three dimensional [13,14]. Stibnite crystal, Sb2S 3, has a complex ribbon-like structure. The structure consists of two infinite ribbons (Sb486) n along the c-axis, which are very weakly bonded in the b direction (the shortest interatomic distance between the ribbons in b direction is about 1.5 times larger than that in the ribbon), and only slightly more strongly bonded in the a direction [15]. Each Sb atom has two non-equivalent positions. In one position Sb forms a pyramid with three S atoms, but in the other, Sb is bonded with five S atoms. In the amorphous state, Sb2S 3 is reported to have the pyramidal structure (SbS3/2) similar to AszS 3 [16]. It is of great interest to investigate the amorphous structure (especially medium range order) of a mixture of two materials which have different kinds of crystal structures. In this paper we report results of low frequency Raman scattering measurements on the amorphous (GeS2)l_x(Sb2S3)x system. The structural correlation range is obtained by applying the Martin and Brenig model and it decreases continuously with increase in Sb2S 3 content in the system.
The Raman scattering measurement was performed with the normal back scattering configuration. The 647.1 nm line of a krypton ion laser was used as a light source. A double-grating monochromator (Jobin Yvon U1000) was used as a spectrometer. A photon counting system was used with a photomultiplier (RCA C31034) and a multichannel analyzer (Canberra Series 40). The polarization dependence was measured with a Glan-Taylor prism polarizer in the HH and HV geometries. Here, HH and HV represent the parallel and perpendicular configurations of the incident and scattered light, respectively. The scattering spectra were obtained in the wave number region from - 1 0 0 to 100 cm -~ . The intense central peak in this region was weakened by about 10 -6 times by neutral density filters. Temperature dependence of the Raman scattering spectra was measured by using a continuous flow liquid helium cryostat (Oxford CF-1204), and the temperature was varied from liquid helium temperature to room temperature with the aid of a temperature controller.
'
'
'
'
I
'
'
•
•
I
•
'
'
'
I
•
'
•
'
(GeSa)l.x(SbaSa)x HV 647.1nm exc. Room Temp. X= 0
Z c
rr-
o c
2. Experimental procedure
The samples were prepared by melt quenching a mixture of the elements Ge, Sb and S of purity 6N. They were melted at 950°C for 48 h in an evacuated ampoule and the ampule was quenched in air.
-100
-50
0
50
100
RAMAN SHIFT [cm"1] Fig. 1. Compositional dependences of the low frequency Raman
scattering spectra(HV).
T. Asami et al. / Journal of Non-Co,stalline Solids 211 (1997) 89-94
The sphere-resonance method [17] was used for the measurement of the sound velocity. The samples were shaped to a sphere for the sake of easy identification of the sphere-resonance mode. The diameter of the spheres was about 6 mm. A spherical sample was carefully placed between the two piezo-electric transducers of lead zirconium titanate (PZT) by using a micrometer head. The measured frequency range was from 100 to 500 kHz.
3. Results
The compositional dependence of the low frequency Raman scattering spectra for (GeS2)~_ x (Sb2S3) x system is shown in Fig. 1 for HV configuration. Both Stokes and anti-Stokes components of the spectra are obtained. Depolarization ratio IHV/IHH is about 0.5 and is nearly constant in this frequency range. The characteristic feature, 'the boson peak', is observed near 20 cm-~ at X = 0. It shifts to higher frequencies with an increase of the Sb2S 3 content.
91
cal constant by the disordered structure was assumed to be a Gaussian distribution as follows:
(AP(r) .AP(r+r')> =
(2)
where A p is the fluctuation of the elasto-optical constant and 2 o- represents the structural correlation range. Debye-like acoustic phonons are adopted for the vibrational density of states and the disorder of the glass structure is assumed to contribute to the photon-phonon coupling. The Raman coupling constants for HV and HH scattering are CHv(O9 ) = Ao92{3gt(~o) + 2g1(o9)},
(3a)
Cnn (to) = ao92{3gt(o9) + (15V + ~)g,( w)}, (3b) with (4a)
{(2__)2}
g l ( w ) = exp -
vl
(4b)
4. Discussion
We employed the Martin and Brenig (M-B) model [8] for the boson peak in chalcogenide glass to obtain the structural correlation range. The intensity of the Stokes Raman scattering in glasses can be presented in the form [7]:
1(o9) = ~'_,ChGh(o9) b
-
,
where A is a constant, c is the speed of light and vl, v t are longitudinal and transverse sound velocities. V is determined from the experimentally obtained depolarization by the relation: IHv (to) p(,,.,)
-
_
_
(l)
O)
where Gb(w) is the vibrational density of states; n(oJ) is the Bose factor; and C h is the light-phonon coupling constant. For the anti-Stokes component n ( w ) + 1 is replaced by n(~o). The M - B model includes effects due to both electrical and mechanical disorder. The electrical disorder is represented by the fluctuations due to the elasto-optic inhomogeneity of the glass and the mechanical disorder is described by the correlation function for the irregular local strain field of the vibrational mode. The correlation function of the fluctuations of the elasto-opti-
=
+ 2 / 3 + gt(
og)/g,(to)
(5)
V is a measure of the relative mean-square spatial fluctuations of the photoelastic constant 8C2/C 2 and elastic constant h by the relation
sc? + xc? V= 8C2t + AC2 .
(6)
This model is applied for the r a n g e (277"Co9//Pl.t)O" < 1. In the Raman spectra this range corresponds to the lower frequency side of the boson peak.
92
T. Asami et al./ Journal of Non-C~stalline Solids 211 (1997) 89-94
The M - B model deals with depolarization of the low frequency light scattering. As shown in the Eqs. (3a) and (3b), the same structural correlation range, 20", should be obtained from both HH and HV spectra. The HV and HH spectra are fitted by using Eqs. (3a) and (3b), respectively. Results of the M - B model fitting for HV configurations are shown in Fig. 2. The sound velocities estimated from the sphere resonance method for (GeS 2)1 - x(Sb2 S3)x are 2700 m / s for v I and 1500 m / s for ~t. Neither v l nor vt changes appreciably with the Sb2S 3 content. The structural correlation ranges (2 0") thus obtained for HH and HV spectra are plotted versus X in Fig. 3. 20- decreases with an increase of Sb2S 3 content. As expected from the M - B model, structural correlation ranges (2 0-) obtained from both HV and HH spectra are in agreement with each other within experimental errors for each composition. Thus, we have obtained the information by Raman scattering that the medium range order is modified by the Sb2S 3 content in this system.
r,-
~d
4-
s > -1-
0
10
20
30
40
50
RAMAN SHIFT [ cm 1 ]
Fig. 2. Compositionaldependences of the low frequency Raman scattering spectra (HV) and the M-B model.
i
i
(GeSa)l.x(SbaSa)x
E e-
UJ
I
0.8 •
(.9
:HV
o:HH
Z
rr Z
O 0.7
II tti
W rr nO
o
0.6
,,_1 ,< n" I--
o n- 0.5 I,.-
0.0
I
i
i
0.2
0.4
0.6
~
I
0.8
i
1.0
MOLECULAR FRACTION X
Fig. 3. The structural correlation range (2~r) for (GeS2)I_x(Sb, S3)x system deduced by M-B model fitting calculated from Eq. (3a).
Fig. 2 shows that the above model fits the lower frequency side of the boson peak quite well; whereas the spectrum deviates from the theory below ~ 5 cm -1. This deviation is due to temperature dependent excess light scattering [ 18-20]. The temperature dependences of the low frequency Raman scattering spectra for X = 0.5 are shown in Fig. 4. The intensity of the boson peak is changed with the temperature change. The temperature dependence of the intensity of boson peak can be well explained with the Bose factor. For the same reason the anti-Stokes Raman intensity at lower temperature becomes weaker than the Stokes one. Theodrakopoulos and J~ickel have proposed a model to describe the excess light scattering ( T - J model [20]). They interpreted it by applying the idea of a two level system, in terms of relaxation processes arising from thermally activated transitions between two metastable states which form a double well potential system. The hopping between the two possible configurations contributes to the inelastic scattering of light, since the dielectric susceptibility of a defect is different in its two configurations by an
T. Asami et al. / Journal of Non-CD'stalline Solids 211 (1997) 89-94
The experimental spectral contribution due to the excess light scattering was estimated by subtracting the contribution of boson peak, i.e. the intensity calculated using Eq. (3a). The excess light scattering spectra are fitted to the curve calculated from Eq. (9) using best fit values of ~- and C. Examples of the fits are shown in Fig. 5(a), (b) for temperatures, T > 10, K. For three samples X = 0.1, 0.5 and 0.9, logarithmic plots of the transition rate, l / r , versus 1/kT
293K ~" t-
200K
>I--
lOOK
Z LU I-Z
50K
--
40K
Z < <( rr
93
30K 24K 20K 16K 12K
e-
~2 ,-'-,
-30
-20
-10
0
10
20
293K 200K
30 +
100K
R A M A N SHIFT [ cm 1 ] Fig. 4. Temperature dependences of the low frequency Raman scattering spectra for X = 0.5.
amount, A c~. They obtained for the excess light scattering
=
50K
s
40K
~.
30K
--=
24K 20K 16K
Ie(O~) CX(Aa)2{n(o~) + l}f dVP(E)
~(E) x I
12K
+ co2r(E) 2 '
where E is an activation energy and P(E) is a distribution of activation energies. The distribution of relaxation times, r ( E ) , is expressed by the Arrhenius formula
r(E)
' = 'r o' e x p ( - E / k T ) ,
(8)
where r 0 is a constant and k is the Boltzmann constant• The polarization ratio, Ie,HV/Ic,Hn, is frequency independent. For a narrow distribution of barrier heights between the two states, Eq. (7) is represented by a simplified expression with one activation energy and one relaxation time O)T
le(w) = C { n ( o J ) + 1} ~1 + ' co2r where C is a constant.
5
(7)
(9)
10
R A M A N SHIFT [ cm "1 ]
._= r"
I
(b)
I
l
I
(GeS2)l.x(Sb2S3)x( X=0.5 )
I
.
~
e-,,
x = 1.3 ps +
c
% ' ~ ~ , / ' •\
Re~:l,_u_ced=_Raman scattering
"
---
~''i
5
moael
-
• ~ -.
~-''''i
/-d
- - M-B model .... T-J m o d e l + M-B m o d e l
•..,
.......
10
I .......
15
k .......
20
L .......
25
30
RAMAN SHIFT [ cm "1 ] Fig. 5. (a) Reduced Raman scattering spectrum of X = 0.5 at T = 200 K and the best fitting curve calculated from Eqs. (3a) and (9). (b) The spectral contribution of the excess light scattering and the best fitting curve calculated from Eq. (9) for X = 0.5.
94
T. Asami et al. / Journal of Non-Crystalline Solids 211 (1997) 89-94 I
I
I
ing by applying the Theodrakopoulos and J~ickel model. They do not show compositional dependences.
(GeS2) 1.x(Sb2S3)x 1012
7
• X=0.1
•
'o
•
• •
|
X=0.5 X=0.9
References !
1011 0
I 200
_...
I 400
|
I 600
_,
800
1000
1 / kT ( e V "1 )
Fig. 6. The logarithmic plots of the hopping rate 1/~- versus
1/~r. are shown in Fig. 6. The transition rate, 1/~-, versus l/kT dose not show compositional dependence. These results suggest that this relaxation process is composition independent and is not influenced by the change in the network structure and the medium range ordering. The plots of In(1 /~') versus 1/kT do not indicate linear dependence and this suggests that the distribution of activation energy is not narrow.
5. Conclusion
Low frequency Raman scattering spectra of amorphous (GeS2) l_x(Sb2S3)x system (0 < X < 0.9) were measured and the structural correlation range (2 o-) was obtained by applying the Martin and Brenig model. The value of 2 o- in this amorphous system decreases slightly with increasing Sb2S 3 content. The relaxation rates for atomic rearrangement between metastable states were estimated from the temperature dependences of the excess light scatter-
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