- Email: [email protected]
Super thermoelectric power of one-dimensional TlInSe2
Thin Solid Films 499 (2006) 275 – 278 www.elsevier.com/locate/tsf
Super thermoelectric power of one-dimensional TlInSe2 Nazim Mamedov a, Kazuki Wakita a, Atsushi Ashida a, Toshiyuki Matsui b,*, Kenji Morii b a
b
Department of Physics and Electronics, Osaka Prefecture University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan Department of Metallurgy and Materials Science, Osaka Prefecture University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan Available online 15 August 2005
Abstract Seebeck coefficient of the structurally one-dimensional material, TlInSe2, known as a p-type conductor, has been measured in the temperature range 70 -C to 500 -C in vacuum by using four probe techniques. At temperatures above 200 -C this coefficient is found to be negative. With temperature down to below 200 -C, the coefficient is becoming positive and huge to a cutting-edge value of 107 AV/-C. The obtained results are discussed in terms of an incommensurate superlattice phase, which might have taken place in TlInSe2 at temperatures below 200 -C, and led to the above unique thermoelectric properties of this material. It is expected that thermoelectric devices based on TlInSe2 will have superior parameters. D 2005 Elsevier B.V. All rights reserved. Keywords: Thermoelectric power; Seebeck coefficient; One dimensional material; Incommensurate superlattice
1. Introduction In the past four decades thermoelectric performance of the materials and structures has attracted large interest and huge efforts have been made to rise dimensionless figure of merits (ZT = S 2T/qv, S-thermoelectric power or Seebeck coefficient, q—electric resistivity, v—thermal conductivity, and T—temperature) above 1. Very good thermoelectric performance has been reported for Bi –Te based superlattice thin films (ZT ¨ 2.4) [1] and layered cobalt oxide, Ca3Co4O9 (ZT ¨ 2.7) [2]. So far, a quantum-well approach [3,4] and a heavyfermion scenario [5], which were suggested to put off the restrains imposed by the frames of standard one-electron picture of electronic spectrum, have been considered as most interesting and resourceful for thermoelectric device application. Meanwhile, utilization of a highly degenerate incommensurate (I) superlattice (SL) phase, which is supposed to have a multi-gaped electronic spectrum [6] with giant sensitivity to temperature and electrical field gradients, is also worthy of attention.
* Corresponding author. E-mail address: [email protected] (T. Matsui). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.07.203
Novel ternary thallium compounds such as one and two dimensional (1D and 2D) TlMeX2 (Me = Ga, In; X = S, Se), which have enough high melting point (> 810 -C [7]) to consider their device application, have attracted our interest, because we believe that, apart from the low-dimensionality factor [3,4], a considerable increase of thermopower in these materials is also possible at the expense of I-phase that was already verified by extended X-ray examination on 1DTlGaTe2 in a wide range of temperatures [9 –11]. The first data on thermoelectric power of TlMeX2 appeared in 1969 in a work by Guseinov et al. [12] who reported the relatively high positive Seebeck coefficient (¨ 800 AV/-C) for 1D-TlInSe2, 1D-TlInTe2 and 2D-TlInS2 at temperatures above 100 -C. However, no works on the issue have appeared since then. Moreover, the angle resolved photoemission data obtained for 1D-TlGaTe2 have displayed a very strong temperature dependent shift of Fermi level at temperatures below 100 -C, thus suggesting large Seebeck coefficient also at these temperatures [10]. Besides, the negative differential resistance (NDR) with a clear trend of strengthening with decreasing the temperature in the region below 100 -C has been reported for 1DTlInSe2 and 1D-TlInTe2 [13]. For the above reasons, and with a thought that modern technique of thermoelectric measurements may be some-
276
N. Mamedov et al. / Thin Solid Films 499 (2006) 275 – 278
what advantageous over the one used 35 years ago, we have decided to return to the thermoelectric properties of TlMeX2. In this work we report the first observation of the unusual temperature behavior and giant values of thermopower of 1D-TlInSe2, which was readily available, and for which band structure calculations were recently performed [14].
c b
a Se 2. Experimental details and other relevant information
In Fig. 2. Fragments of 1D-crystalline structure of TlInSe2. Dashed lines show direction of chains.
ature range 70 -C to 500 -C. Silver paste was used for contacts and carbide tangsten line for wiring. The contacts proved to be ohmic. The data on electrical resistivities of TlInSe2 at ambient conditions were already reported to be q II = 99.6 V cm and q – = 24.9 103 V cm, where q II and q –are the resistivities parallel and perpendicular to the c-axis, respectively [16]. Our samples generally matched the above electrical description, but the values of resistivities turned out to be higher (by order of magnitude). All the measurements were made on a number of samples and were reproducible to a good extent.
3. Results and discussion In Fig. 3 we show the temperature dependence of Seebeck coefficient of TlInSe2 for temperatures above 150 -C. A striking feature of this dependence is the change of the sign of this coefficient at temperatures around 200 -C. 1000
Thermoelectric power ( µ V/K)
The ingot of TlInSe2 we have got was obtained by Bridgmen-Stockbarger method used previously [12]. The ingot was cleaved and the samples suitable for thermoelectric measurements were then sorted out. Fig. 1 demonstrates these samples. To an extent given by our standard X-ray examination at room temperature, all the samples looked like single crystals of TlInSe2 with the space group, D 18 4h , reported previously for this material by Muller et al. [7]. However, more extended studies would have been necessary to say whether the room temperature phase of TlInSe2 we examined was already incommensurately distorted. A fresh example is TlGaTe2 for which only extended X-ray examination supported by calorimetric measurements disclosed the presence of I-modulation [11]. 1D crystal structure of TlInSe2 is shown in Fig. 2. The structure can be formally described as a set of the 1 (In3+Se2 chains extended along the crystallographic 2 ) c-axis and connected with each other through monovalent Tl1+ ions. At the same time, NMR studies [15] have shown that, in fact, neither Tl nor In is acquiring the just-specified charge and that above picture of underlying chemistry is corresponding more to a 1D metallic rather than semiconducting state. Nevertheless, above formal description is commonly adopted, probably because of the fact that all 1DTlMeX2 compounds become metals under quite moderate pressures [16] and, hence, eventually match this description. Seebeck coefficient and dc-resistivities were measured by four-probe technique [17,18] in vacuum in the temper-
Tl
500
0
-500 100
200
300
400
500
Temperature (°C)
Fig. 1. Samples of TlInSe2 used for thermoelectric measurements.
Fig. 3. Seebeck coefficient of TlInSe2 as a function of temperature between 150 -C and 500 -C.
N. Mamedov et al. / Thin Solid Films 499 (2006) 275 – 278
Above 200 -C the coefficient is negative with a relatively large absolute value of 500 AV/-C at the minimum at around 270 -C. But, below 200 -C, the coefficient already acquires positive values and shows a tendency to increase more upon lowering temperature, and to eventually reach a level of 107 AV/-C as shown in Fig. 4. For a non-degenerate semiconductor like in our case, and without allowance for electron – phonon interaction, the conventional expression for Seebeck coefficient can be written as a sum S ¼ Sp
q q þ Sn qp qn
ð1Þ
of hole (p) and electron (n) constituents [19]. As follows from (1), in principle, under the condition that electron mobility is higher than hole mobility, the change of the sign of the thermopower (Seebeck coefficient) of a p-conductor is possible in the intrinsic region where hole and electron concentrations are equal. The electrons are lighter than holes in 1D-TlInSe2 [14] and might have been more mobile. However, so far above scenario has not been verified even for well-known Si and Ge. Besides, if such a scenario were realistic the Hall coefficient of TlInSe2 would have also changed sign and this change should have been observed already in the impurity region of the electrical conduction at temperatures below 200 -C. At least to an extent given by available data [12], the Hall coefficient of TlInSe2 remains positive in a wide range of temperatures and impurity concentrations, dropping down to very small values above 200 -C though. Recently Kobayashi and Terasaki [20] have proposed a spin-entropy backflow mechanism to explain negative values of thermoelectric power in the perovskite Mn-oxides, (CaMn3x Cux Mnx O12), which is a p-type material. However, such approach implies that electric conduction is realized through a double-exchange mechanism [21] that is difficult to apply to TlInSe2 in which both conduction and valence band states are, for the most part, p-orbital states of 108
Thermoelectric power ( µ V/K)
107 106 105
277
Se [14]. At the same time, some intervention of Tl1+ and In3+ is possible [15] and we do not rule out completely the mechanism [20] for TlInSe2. However, we consider the influence of the incommensurability as a decisive factor for this material. In non-crystalline solids, such as, for example, amorphous As2Se3, the sign of the Hall coefficient was reported to be negative even if Seebeck coefficients acquired positive values [22 – 24]. The reason for this is not completely clear but resemblance with our case is evident if we recall that theoretically the electronic spectrum of I-phase of a crystalline material [6] is very close to that of amorphous solids. NDR with S-type current–voltage characteristics reported for TlInSe2 by Hanias et al. [13] can also be viewed as one of the sequences of ISL formation. Finally, the strong electron – phonon interaction expected in ISL might lead to very high values of Seebeck coefficient, such as ¨ 10 V/-C in our rough estimates. More comprehensive studies are necessary to say more about exact mechanism responsible for large thermopower of 1D-TlInSe2. But, engagement of ISL looks plausible.
4. Conclusions We have carried out thermoelectric measurements of 1D-TlInSe2 in the temperature range 70 -C to 500 -C. For the first time to our knowledge we have shown that Seebeck coefficient of at least the samples at our disposal is changing sign at around 200 -C and becoming negative above this temperature. Down to below 200 -C and into the region where TlInSe2 might have been incommensurately distorted, a clear trend in Seebeck coefficient with temperature to hit the plank above 107 AV/-C has been observed. By considering the relevant parameters of TlInSe2, one might expect that dimensionless figure of merits (ZT) for thermoelectric performance of this material could hit the plank above 3. We have already applied for a patent (Japan Patent No. 197416). By this short letter we have informed the scientific community about unique thermoelectric properties of TlInSe2. We hope that the informed results would inspire the wide-range studies of 1D-TlMeX2, which are currently argent.
104 103
Acknowledgments
2
10
101 100
100
200
300 400 Temperature (°C)
500
Fig. 4. Seebeck coefficient of TlInSe2 as a function of temperature between 70 -C and 150 -C.
Special thanks are due to Prof. H. Naito for his interest, help and support, and to Dr. Y. Shim for technical assistance. This work was supported in part by Ministry of Education, Culture, Sports, Science and Technology of Japan under the Grant-in-Aid for Scientific Research (C), 15510106.
278
N. Mamedov et al. / Thin Solid Films 499 (2006) 275 – 278
References [1] A. Venkatasubramanian, E. Sivola, T. Colpitts, Nature 413 (2001) 597. [2] R. Funahashi, I. Matsubara, S. Sodeoka, H. Ikuta, T. Takeichi, U. Mizutani, Jpn. J. Appl. Phys. 39 (2000) 1254. [3] L.D. Hicks, M.S. Dresselhaus, PRB 47 (1993) 16631. [4] L.D. Hicks, T.C. Harman, X. Sun, M.S. Dresselhaus, PRB 53 (1996) R10493. [5] T. Motohashi, R. Ueda, E. Naujalis, T. Tojo, I. Terasaki, T. Atake, M. Karppinen, H. Yamauchi, PRB 67 (2003) 064406. [6] J.B. Sokoloff, Phys. Rev., B 25 (1982) 5901. [7] D. Muller, G. Eulenberger, H. Hahn, J. Anorg. Allg. Chem. 398 (1973) 207. [9] N.T. Mamedov, A.M. Panich, Phys. Status Solidi, A Appl. Res. 117 (1990) K15. [10] K. Okazaki, K. Tanaka, J. Matsuno, A. Fujimori, L.F. Mattheiss, S. Iida, E. Kerimova, N. Mamedov, PRB 64 (2001) 045210. [11] V.A. Aliev, M.A. Aldzhanov, S.N. Aliev, JETP Lett. 45 (1987) 534. [12] G.D. Guseinov, E. Mooser, E.M. Kerimova, R.S. Gamidov, I.V. Alekseev, M.Z. Ismailov, Phys. Status Solidi 34 (1969) 33. [13] M. Hanias, A.N. Anagnostopoulos, K. Kambas, J. Spyridelis, Phys. Rev., B 43 (1991) 4135. [14] N. Mamedov, K. Wakita, S. Akita, Y. Nakayama, Jpn. J. Appl. Phys. 44 (2005) 709.
[15] S. Abdullayeva, N. Mamedov, Turk. J. Phys. 17 (1993) 568. [16] M.K. Rabinal, S.S.K. Titus, S. Asokan, E.S.R. Gopal, M.O. Godzaev, N.T. Mamedov, Phys. Status Solidi, B Basic Res. 178 (1993) 403. [17] M. Masuda, H. Mabuchi, H. Tsuda, T. Matsui, K. Morii, Mat. Sci. Forum 389 – 393 (2002) 763. [18] T. Matsui, J. Furukawa, K. Tsukamoto, H. Tsuda, K. Morii, J. Alloys Compd. 391 (2005) 284. [19] K. Seeger, Semiconductor Physics, Springer-Verlag, 1973, p. 118. [20] W. Kobayashi, I. Terasaki, Proc. TEC2002, Tokyo, 2002, pp. 96 – 97. [21] Y. Tokura, A. Urushibara, Y. Morimoto, T. Arima, A. Asamitsu, G. Kido, N. Furukawa, J. Phys. Soc. Jpn. 63 (1994) 3931. [22] R.E. Drews, R. Zallen, R.C. Keezer, Bull. Am. Phys. Soc. 13 (1968) 454. [23] J.T. Admond, Br. J. Appl. Phys. 17 (1966) 979. [24] J. Struke, J. Non-Cryst. Solids 4 (1970) 1.
Further reading [1] J.A.A. Ketelaar, W.H. Hart, M. Moerel, D. Polder, Z. Cryst. 101 (1939) 396.
Super thermoelectric power of one-dimensional TlInSe2 Nazim Mamedov a, Kazuki Wakita a, Atsushi Ashida a, Toshiyuki Matsui b,*, Kenji Morii b a
b
Department of Physics and Electronics, Osaka Prefecture University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan Department of Metallurgy and Materials Science, Osaka Prefecture University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan Available online 15 August 2005
Abstract Seebeck coefficient of the structurally one-dimensional material, TlInSe2, known as a p-type conductor, has been measured in the temperature range 70 -C to 500 -C in vacuum by using four probe techniques. At temperatures above 200 -C this coefficient is found to be negative. With temperature down to below 200 -C, the coefficient is becoming positive and huge to a cutting-edge value of 107 AV/-C. The obtained results are discussed in terms of an incommensurate superlattice phase, which might have taken place in TlInSe2 at temperatures below 200 -C, and led to the above unique thermoelectric properties of this material. It is expected that thermoelectric devices based on TlInSe2 will have superior parameters. D 2005 Elsevier B.V. All rights reserved. Keywords: Thermoelectric power; Seebeck coefficient; One dimensional material; Incommensurate superlattice
1. Introduction In the past four decades thermoelectric performance of the materials and structures has attracted large interest and huge efforts have been made to rise dimensionless figure of merits (ZT = S 2T/qv, S-thermoelectric power or Seebeck coefficient, q—electric resistivity, v—thermal conductivity, and T—temperature) above 1. Very good thermoelectric performance has been reported for Bi –Te based superlattice thin films (ZT ¨ 2.4) [1] and layered cobalt oxide, Ca3Co4O9 (ZT ¨ 2.7) [2]. So far, a quantum-well approach [3,4] and a heavyfermion scenario [5], which were suggested to put off the restrains imposed by the frames of standard one-electron picture of electronic spectrum, have been considered as most interesting and resourceful for thermoelectric device application. Meanwhile, utilization of a highly degenerate incommensurate (I) superlattice (SL) phase, which is supposed to have a multi-gaped electronic spectrum [6] with giant sensitivity to temperature and electrical field gradients, is also worthy of attention.
* Corresponding author. E-mail address: [email protected] (T. Matsui). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.07.203
Novel ternary thallium compounds such as one and two dimensional (1D and 2D) TlMeX2 (Me = Ga, In; X = S, Se), which have enough high melting point (> 810 -C [7]) to consider their device application, have attracted our interest, because we believe that, apart from the low-dimensionality factor [3,4], a considerable increase of thermopower in these materials is also possible at the expense of I-phase that was already verified by extended X-ray examination on 1DTlGaTe2 in a wide range of temperatures [9 –11]. The first data on thermoelectric power of TlMeX2 appeared in 1969 in a work by Guseinov et al. [12] who reported the relatively high positive Seebeck coefficient (¨ 800 AV/-C) for 1D-TlInSe2, 1D-TlInTe2 and 2D-TlInS2 at temperatures above 100 -C. However, no works on the issue have appeared since then. Moreover, the angle resolved photoemission data obtained for 1D-TlGaTe2 have displayed a very strong temperature dependent shift of Fermi level at temperatures below 100 -C, thus suggesting large Seebeck coefficient also at these temperatures [10]. Besides, the negative differential resistance (NDR) with a clear trend of strengthening with decreasing the temperature in the region below 100 -C has been reported for 1DTlInSe2 and 1D-TlInTe2 [13]. For the above reasons, and with a thought that modern technique of thermoelectric measurements may be some-
276
N. Mamedov et al. / Thin Solid Films 499 (2006) 275 – 278
what advantageous over the one used 35 years ago, we have decided to return to the thermoelectric properties of TlMeX2. In this work we report the first observation of the unusual temperature behavior and giant values of thermopower of 1D-TlInSe2, which was readily available, and for which band structure calculations were recently performed [14].
c b
a Se 2. Experimental details and other relevant information
In Fig. 2. Fragments of 1D-crystalline structure of TlInSe2. Dashed lines show direction of chains.
ature range 70 -C to 500 -C. Silver paste was used for contacts and carbide tangsten line for wiring. The contacts proved to be ohmic. The data on electrical resistivities of TlInSe2 at ambient conditions were already reported to be q II = 99.6 V cm and q – = 24.9 103 V cm, where q II and q –are the resistivities parallel and perpendicular to the c-axis, respectively [16]. Our samples generally matched the above electrical description, but the values of resistivities turned out to be higher (by order of magnitude). All the measurements were made on a number of samples and were reproducible to a good extent.
3. Results and discussion In Fig. 3 we show the temperature dependence of Seebeck coefficient of TlInSe2 for temperatures above 150 -C. A striking feature of this dependence is the change of the sign of this coefficient at temperatures around 200 -C. 1000
Thermoelectric power ( µ V/K)
The ingot of TlInSe2 we have got was obtained by Bridgmen-Stockbarger method used previously [12]. The ingot was cleaved and the samples suitable for thermoelectric measurements were then sorted out. Fig. 1 demonstrates these samples. To an extent given by our standard X-ray examination at room temperature, all the samples looked like single crystals of TlInSe2 with the space group, D 18 4h , reported previously for this material by Muller et al. [7]. However, more extended studies would have been necessary to say whether the room temperature phase of TlInSe2 we examined was already incommensurately distorted. A fresh example is TlGaTe2 for which only extended X-ray examination supported by calorimetric measurements disclosed the presence of I-modulation [11]. 1D crystal structure of TlInSe2 is shown in Fig. 2. The structure can be formally described as a set of the 1 (In3+Se2 chains extended along the crystallographic 2 ) c-axis and connected with each other through monovalent Tl1+ ions. At the same time, NMR studies [15] have shown that, in fact, neither Tl nor In is acquiring the just-specified charge and that above picture of underlying chemistry is corresponding more to a 1D metallic rather than semiconducting state. Nevertheless, above formal description is commonly adopted, probably because of the fact that all 1DTlMeX2 compounds become metals under quite moderate pressures [16] and, hence, eventually match this description. Seebeck coefficient and dc-resistivities were measured by four-probe technique [17,18] in vacuum in the temper-
Tl
500
0
-500 100
200
300
400
500
Temperature (°C)
Fig. 1. Samples of TlInSe2 used for thermoelectric measurements.
Fig. 3. Seebeck coefficient of TlInSe2 as a function of temperature between 150 -C and 500 -C.
N. Mamedov et al. / Thin Solid Films 499 (2006) 275 – 278
Above 200 -C the coefficient is negative with a relatively large absolute value of 500 AV/-C at the minimum at around 270 -C. But, below 200 -C, the coefficient already acquires positive values and shows a tendency to increase more upon lowering temperature, and to eventually reach a level of 107 AV/-C as shown in Fig. 4. For a non-degenerate semiconductor like in our case, and without allowance for electron – phonon interaction, the conventional expression for Seebeck coefficient can be written as a sum S ¼ Sp
q q þ Sn qp qn
ð1Þ
of hole (p) and electron (n) constituents [19]. As follows from (1), in principle, under the condition that electron mobility is higher than hole mobility, the change of the sign of the thermopower (Seebeck coefficient) of a p-conductor is possible in the intrinsic region where hole and electron concentrations are equal. The electrons are lighter than holes in 1D-TlInSe2 [14] and might have been more mobile. However, so far above scenario has not been verified even for well-known Si and Ge. Besides, if such a scenario were realistic the Hall coefficient of TlInSe2 would have also changed sign and this change should have been observed already in the impurity region of the electrical conduction at temperatures below 200 -C. At least to an extent given by available data [12], the Hall coefficient of TlInSe2 remains positive in a wide range of temperatures and impurity concentrations, dropping down to very small values above 200 -C though. Recently Kobayashi and Terasaki [20] have proposed a spin-entropy backflow mechanism to explain negative values of thermoelectric power in the perovskite Mn-oxides, (CaMn3x Cux Mnx O12), which is a p-type material. However, such approach implies that electric conduction is realized through a double-exchange mechanism [21] that is difficult to apply to TlInSe2 in which both conduction and valence band states are, for the most part, p-orbital states of 108
Thermoelectric power ( µ V/K)
107 106 105
277
Se [14]. At the same time, some intervention of Tl1+ and In3+ is possible [15] and we do not rule out completely the mechanism [20] for TlInSe2. However, we consider the influence of the incommensurability as a decisive factor for this material. In non-crystalline solids, such as, for example, amorphous As2Se3, the sign of the Hall coefficient was reported to be negative even if Seebeck coefficients acquired positive values [22 – 24]. The reason for this is not completely clear but resemblance with our case is evident if we recall that theoretically the electronic spectrum of I-phase of a crystalline material [6] is very close to that of amorphous solids. NDR with S-type current–voltage characteristics reported for TlInSe2 by Hanias et al. [13] can also be viewed as one of the sequences of ISL formation. Finally, the strong electron – phonon interaction expected in ISL might lead to very high values of Seebeck coefficient, such as ¨ 10 V/-C in our rough estimates. More comprehensive studies are necessary to say more about exact mechanism responsible for large thermopower of 1D-TlInSe2. But, engagement of ISL looks plausible.
4. Conclusions We have carried out thermoelectric measurements of 1D-TlInSe2 in the temperature range 70 -C to 500 -C. For the first time to our knowledge we have shown that Seebeck coefficient of at least the samples at our disposal is changing sign at around 200 -C and becoming negative above this temperature. Down to below 200 -C and into the region where TlInSe2 might have been incommensurately distorted, a clear trend in Seebeck coefficient with temperature to hit the plank above 107 AV/-C has been observed. By considering the relevant parameters of TlInSe2, one might expect that dimensionless figure of merits (ZT) for thermoelectric performance of this material could hit the plank above 3. We have already applied for a patent (Japan Patent No. 197416). By this short letter we have informed the scientific community about unique thermoelectric properties of TlInSe2. We hope that the informed results would inspire the wide-range studies of 1D-TlMeX2, which are currently argent.
104 103
Acknowledgments
2
10
101 100
100
200
300 400 Temperature (°C)
500
Fig. 4. Seebeck coefficient of TlInSe2 as a function of temperature between 70 -C and 150 -C.
Special thanks are due to Prof. H. Naito for his interest, help and support, and to Dr. Y. Shim for technical assistance. This work was supported in part by Ministry of Education, Culture, Sports, Science and Technology of Japan under the Grant-in-Aid for Scientific Research (C), 15510106.
278
N. Mamedov et al. / Thin Solid Films 499 (2006) 275 – 278
References [1] A. Venkatasubramanian, E. Sivola, T. Colpitts, Nature 413 (2001) 597. [2] R. Funahashi, I. Matsubara, S. Sodeoka, H. Ikuta, T. Takeichi, U. Mizutani, Jpn. J. Appl. Phys. 39 (2000) 1254. [3] L.D. Hicks, M.S. Dresselhaus, PRB 47 (1993) 16631. [4] L.D. Hicks, T.C. Harman, X. Sun, M.S. Dresselhaus, PRB 53 (1996) R10493. [5] T. Motohashi, R. Ueda, E. Naujalis, T. Tojo, I. Terasaki, T. Atake, M. Karppinen, H. Yamauchi, PRB 67 (2003) 064406. [6] J.B. Sokoloff, Phys. Rev., B 25 (1982) 5901. [7] D. Muller, G. Eulenberger, H. Hahn, J. Anorg. Allg. Chem. 398 (1973) 207. [9] N.T. Mamedov, A.M. Panich, Phys. Status Solidi, A Appl. Res. 117 (1990) K15. [10] K. Okazaki, K. Tanaka, J. Matsuno, A. Fujimori, L.F. Mattheiss, S. Iida, E. Kerimova, N. Mamedov, PRB 64 (2001) 045210. [11] V.A. Aliev, M.A. Aldzhanov, S.N. Aliev, JETP Lett. 45 (1987) 534. [12] G.D. Guseinov, E. Mooser, E.M. Kerimova, R.S. Gamidov, I.V. Alekseev, M.Z. Ismailov, Phys. Status Solidi 34 (1969) 33. [13] M. Hanias, A.N. Anagnostopoulos, K. Kambas, J. Spyridelis, Phys. Rev., B 43 (1991) 4135. [14] N. Mamedov, K. Wakita, S. Akita, Y. Nakayama, Jpn. J. Appl. Phys. 44 (2005) 709.
[15] S. Abdullayeva, N. Mamedov, Turk. J. Phys. 17 (1993) 568. [16] M.K. Rabinal, S.S.K. Titus, S. Asokan, E.S.R. Gopal, M.O. Godzaev, N.T. Mamedov, Phys. Status Solidi, B Basic Res. 178 (1993) 403. [17] M. Masuda, H. Mabuchi, H. Tsuda, T. Matsui, K. Morii, Mat. Sci. Forum 389 – 393 (2002) 763. [18] T. Matsui, J. Furukawa, K. Tsukamoto, H. Tsuda, K. Morii, J. Alloys Compd. 391 (2005) 284. [19] K. Seeger, Semiconductor Physics, Springer-Verlag, 1973, p. 118. [20] W. Kobayashi, I. Terasaki, Proc. TEC2002, Tokyo, 2002, pp. 96 – 97. [21] Y. Tokura, A. Urushibara, Y. Morimoto, T. Arima, A. Asamitsu, G. Kido, N. Furukawa, J. Phys. Soc. Jpn. 63 (1994) 3931. [22] R.E. Drews, R. Zallen, R.C. Keezer, Bull. Am. Phys. Soc. 13 (1968) 454. [23] J.T. Admond, Br. J. Appl. Phys. 17 (1966) 979. [24] J. Struke, J. Non-Cryst. Solids 4 (1970) 1.
Further reading [1] J.A.A. Ketelaar, W.H. Hart, M. Moerel, D. Polder, Z. Cryst. 101 (1939) 396.