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High thermoelectric performance at low temperature of p-Bi1.8Sb0.2Te3.0 grown by the gradient freeze method from Te-rich melt
Journal of Alloys and Compounds 368 (2004) 44–50
High thermoelectric performance at low temperature of p-Bi1.8Sb0.2 Te3.0 grown by the gradient freeze method from Te-rich melt Ngo Thu Huong a,1 , Yusuke Setou a , Go Nakamoto a , Makio Kurisu a,∗ , Takeshi Kajihara b , Hiroyuki Mizukami b , Seijiro Sano b a
Japan Advanced Institute of Science and Technology, 1-1 Asahidai Tatsunokuchi, Ishikawa 923-1292, Japan b Research Center, Komatsu Ltd., Hiratsuka 254-8467, Japan Received 21 July 2003; received in revised form 20 August 2003; accepted 20 August 2003
Abstract The structural and low-temperature thermoelectric properties were investigated in the temperature range from 4.2 to 300 K of Bi1.8 Sb0.2 Te3.0 grown by the gradient freeze method from Te-rich melt of Bi1.8 Sb0.2 Te3.0+δ . The composition profile was determined by electron probe microanalysis (EPMA) measurement to be homogeneous in the center part of the single crystalline ingots. An excess of Te is segregated at the top of the ingots. A high thermoelectric performance was achieved at low temperature in the p-type samples. The largest value of the Seebeck coefficient α of >500 V K−1 was obtained at 200 K for δ = 0.259 to give ZT = 1.1. The optimum carrier concentration was determined to be n = 1.6 × 1019 cm−3 for the highest thermoelectric performance. © 2003 Elsevier B.V. All rights reserved. Keywords: Semiconductors; Crystal growth; X-ray diffraction; Electronic transport; Thermoelectricity
1. Introduction Solid solutions formed in the Bi2 Te3 –Sb2 Te3 binary system are known to be effective thermoelectric materials for room temperature applications such as Peltier refrigerations and thermoelectric generations [1]. For the lower temperature use of these materials, a large reduction in the thermoelectric efficiency is encountered when the temperature is lowered down to 100–200 K. The reason for this is that these materials do not possess a high enough magnitude of the figure of merit Z at such low temperature and the thermoelectric efficiency is usually proportional to the temperature. Thus, many efforts have been made to optimize the low-temperature carrier concentration by doping Te and Se. It is well known that these solutions exhibit p-type conduction because there exist BiTe and SbTe anti-site defects in the crystals. These anti-site defects may explain that Bi2 Te3 –Sb2 Te3 solutions are non-stoichiometric toward Bi ∗
Corresponding author. Tel.: +81-761-51-1541; fax: +81-761-51-1545. E-mail address: [email protected] (M. Kurisu). 1 On leave from Faculty of Physics, Hanoi University of Science, Hanoi, Vietnam. 0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.08.066
and Sb [2,3]. In this sense, an introduction of an excess Te is an indispensable method to control the carrier concentration in this class of materials. Champness et al. have indicated that the n-type alloy with the nominal composition of Bi1.33 Sb0.67 Te3.13 prepared by the horizontal zone melting method has the maximum Z at 240 K [4]. Quite recently, Kutasov et al. have demonstrated very high Z at temperatures below 200 K for the n-type Bi2−x Sbx Te3 samples enriched in Te or doped with TeI4 [5]. The maximum Z value as large as 3.7 × 10−3 K−1 was obtained at 200 K. In the present paper, we have examined the structural and thermoelectric properties at low temperature of p-type as well as n-type Bi1.80 Sb0.20 Te3.0 single crystals which were grown from Te-rich melt by the gradient freeze method. The XRD, EPMA, Seebeck coefficient, electrical resistivity, Hall coefficient and thermal conductivity have been measured and the power factor and the figure of merit have been evaluated.
2. Experimental The single crystals of Bi1.8 Sb0.2 Te3.0 compounds were prepared by the gradient freeze method from the telluriumrich melt with liquidus compositions of Bi1.8 Sb0.2 Te3.0+δ
N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
where δ = 0.0, 0.10, 0.20, 0.259, 0.276, 0.30 and 0.40. High purity (99.9999%) Bi, Sb and Te granules were sealed into 10 cm long and 0.8 cm inner diameter quartz ampoules with a conical bottom under 10−5 Torr, melted at 610 ◦ C for 12 h in an electric furnace and furnace cooled. This melting process was done three times to ensure thorough mixing. The crystals were then grown in a vertical gradient freeze furnace with a growth rate of 1.25 mm h−1 and a temperature gradient of 40 K cm−1 at the liquid-solid interface. After furnace cooling, 500 ◦ C in 14 h, the ingots were cleaved and single crystals of 35 mm length were cut by spark erosion from the central portion of the ingots. The structural characterization was done by metallurgical observation, X-ray diffraction (XRD) and electron probe microanalysis (EPMA). The XRD measurement was performed on the cleavage planes of the ingots as well as on the powder samples by using a Rigaku RINT 2000 with a Cu Kα radiation. The parameters for these crystal structures have been refined by the Rietveld profile fitting program RIETAN-2000 [6]. The EPMA measurement was carried out by a JEOL JXA-8621 system. The Seebeck coefficient was measured by the seesaw heating method over a temperature range from 4.2 to 300 K. A temperature difference of 0.05 K was generated across the rectangular samples which were spark-cut from the single crystals with the long axis of rectangular bars parallel to the cleavage plane. The typical dimensions were 2.0 mm × 2.0 mm × 15 mm. The electrical resistivity measurements were followed on the same samples by the conventional dc four-probe method. The Hall coefficient was measured on the samples polished to thin plate with 0.5 mm thickness to which the magnetic field was applied perpendicularly up to 0.8 T over a temperature range from 77 to 300 K. All the electrical contacts between the samples and
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gold wire probes with 50 m o.d. were made by DOTITE (type D-550) silver paste. The thermal conductivity along the cleavage plane was measured on the rectangular samples with 4.0 mm × 4.0 mm × 2.0 mm by a Quantum Design PPMS system in the temperature range from 5 to 300 K.
3. Results and discussion 3.1. Structural characterization Large single crystals were obtained with their basal planes parallel to the growth direction. The cleavage planes were examined by the XRD to be of single nature. The powder samples taken from the bottom, center and top portions of the ingots were examined by the XRD. The results for the center parts are shown in Fig. 1. The bottom parts showed almost the same patterns. All the diffraction peaks of the samples are indexed by assuming ¯ A satisa rhombohedral structure of the space group R3m. factory agreement is found between observed and calculated intensities with a factor of goodness fit S ranging between 1.84 and 1.99. However, the XRD patterns indicate segregation of tellurium metal in the top part of the samples where eutectic solidification takes place. This is supported by the metallurgical observation and the EPMA results which will be shown later. The lattice constants are listed in Table 1 and displayed in Fig. 2 against the excess Te content δ. A relatively large deviation from a linear dependence is found for a and c at δ = 0.276. However, the variations of the lattice constants are too small, a/a = −3 × 10−4 and
c/c = 6.2 × 10−3 at δ = 0.40, to conclude that excess Te is incorporated to form the crystal.
Fig. 1. The powder XRD patterns of Bi1.8 Sb0.2 Te3.0 compounds grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
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N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Table 1 The lattice constants refined by the Rietveld profile fitting of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ δ
a (Å)
c (Å)
0.0 0.10 0.20 0.259 0.276 0.30 0.40
4.3691 4.3691 4.3693 4.3693 4.3679 4.3697 4.3690
30.472 30.477 30.478 30.478 30.482 30.478 30.474
Fig. 3 shows the distribution of the composition along the growth direction z. It is seen that the sample with δ = 0.0 is homogeneous and possesses the composition Bi1.8 Sb0.2 Te3.0 up to z = 22 mm. Above z = 22 mm, there exists some deviation in the composition from Bi1.8 Sb0.2 Te3.0 , reflecting the eutectic solidification at the top part of the ingot. The sample with δ = 0.20 is also homogeneous up to 20 mm. Whereas in the sample with δ = 0.40, a larger scattering of the composition can be found. This may suggest that the formation of an appreciable amount of Te metal and Sb–Te alloys takes place not only at the end of the ingot growth but also throughout the entire growth process of the ingot. Our careful data acquisition repeated several times confirmed that there exist Te metal precipitations with cross sections smaller than the electron beam size of 10 m diameter. Fig. 4 shows the composition profile along the growth direction. Each point represents the average composition from 20 different points around z = 15 mm. The determined compositions of the ingots are also listed in Table 2. It is found that excess Te as much as δ = 0.40 in the liquid of Bi1.8 Sb0.2 Te3.0+δ is not totally incorporated to form the
Fig. 2. The lattice constants of Bi1.8 Sb0.2 Te3.0 compounds grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
crystal. It should, however, be noted that the relative concentration of Te is increased appreciably against (Bi + Sb) and the relative Bi volume is also increased against Sb with increasing δ. 3.2. Seebeck coefficient The temperature dependence of the Seebeck coefficient α along the cleavage plane is shown in Fig. 5. The sign of α is positive for 0.0 ≤ δ ≤ 0.276 and becomes negative for δ ≥0.276. Two rectangular samples were cut from the center portions of the same ingot grown from the liquidus composition δ = 0.276. They exhibit different types of conduction,
Fig. 3. Atomic composition profile of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ for (a) δ = 0.0, (b) δ = 0.20 and (c) δ = 0.40.
N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Fig. 4. The composition of Bi, Sb and Te in the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
indicating that the thermoelectric properties are highly dependent on the electronic structures of the samples. The α values for p-type compounds grown from δ = 0.0, 0.20 and 0.259 are larger, about 300 V K−1 , than those ever reported at room temperature [1,5]. Our n-type samples have room temperature α values between −280 and −220 V K−1 . The most remarkable results are that α takes the largest value at 200 K for the n-type as well as p-type samples. The samples prepared from δ = 0.259 and 0.30 possess >500 and −370 V K−1 at 200 K, respectively. Smaller α values of 220–260 V K−1 at higher temperature around 280 K were reported in the n-type Bi1.8 Sb0.2 Te3.0 [5]. The α values are plotted against the logarithm of temperature for all the samples in Fig. 6. A logarithmic temperature dependence is found for α between 50 and 200 K where the slope is between 170 and 290 V K−1 for the p-type and −160 and −95 V K−1 for the n-type. The p-type samples have larger slope than expected, 129 V K−1 , for the non-degenerate extrinsic semiconductors. The low-temperature behavior below 50 K is due to the increasing degeneracy of the carrier. The decrease in α at high temperature may be ascribed to the fact that the samples are in a region of intrinsic conduction or a mixed one.
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Fig. 5. The temperature dependence of the Seebeck coefficient α of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
3.3. Electrical resistivity The temperature dependence of the electrical resistivity ρ is shown in Fig. 7. The resistivity at room temperature is increased with δ, taking the largest value at δ = 0.276(p) for the samples exhibiting p-type conduction, whereas for the n-type samples it is decreased. Similar dependence of the room temperature resistivity on the excess Te composition was found in Sb-free Bi2 Te3+δ compounds [7].
Table 2 The composition profile of the crystal along the crystal growth direction grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ δ
Composition
0.0 0.10 0.20 0.259 0.276
(Bi0.900 Sb0.100 )2.0 Te2.986 (Bi0.902 Sb0.098 )2.0 Te2.989 (Bi0.905 Sb0.095 )2.0 Te2.994 (Bi0.906 Sb0.094 )2.0 Te2.994 (Bi0.906 Sb0.094 )2.0 Te2.994
Fig. 6. The Seebeck coefficient α as a function of the logarithm of the temperature T of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
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N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Fig. 7. The resistivity ρ as a function of the temperature T of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
The thermal variation of the resistivity is highly dependent on δ. In Fig. 8, the logarithm of the resistivity is plotted against the logarithm of the temperature for all the samples measured. The resistivity for the sample with δ = 0.0 follows a T 1.97 law over the temperature range from 120 to 300 K. Below 120 K the variation in ρ is smaller, implying an increasing degeneracy. The sample prepared from δ = 0.10 exhibits a T 1.80 dependence down to 170 K, below which a shoulder appears with further decreasing tempera-
Fig. 9. The temperature dependence of the carrier concentration n of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
ture. For the samples with δ = 0.20, 0.276 and 0.30, their peculiar variation of the resistivity should be noted. Their resistivity forms a peak above 100 K and shows a decrease with increasing temperature, indicating that the conduction is intrinsic above 200 K. The sample with δ = 0.40 exhibits T 1.49 behavior in the wider temperature range from 80 to 300 K. 3.4. Hall coefficient Fig. 9 shows the temperature dependence of the carrier concentration n for the selected samples. The sign of Hall coefficient was confirmed to be positive for δ = 0.0, 0.10 and 0.20 and negative for δ = 0.30 and 0.40, which is consistent with the thermopower. It is found that the carrier concentration n at 300 K is decreased with δ, (3–0.8)×1019 cm−3 . It is also interesting to note that the p-type samples show a larger temperature dependence of n than the n-type. The n for δ = 0.0 is increased largely as the temperature is lowered. One can calculate the apparent Hall mobility µ using the data of the electrical resistivity. Fig. 10 gives the logarithm of µ versus the logarithm of the temperature. Below 200 K, all the samples follow the power law of µ ∝ T −r , where r = 1.30, 1.66, 1.41 and 0.66 for δ = 0.0, 0.20, 0.30 and 0.40, respectively. Thus, we may conclude that acoustic phonon scattering is dominant in the temperature range from 77 to 200 K for the samples prepared from δ ≤0.30. The larger exponents at high temperature may be attributed to intrinsic conduction. 3.5. Thermal conductivity
Fig. 8. The logarithm of the resistivity ρ as a function of the logarithm of the temperature T of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
Fig. 11 shows the temperature dependence of the thermal conductivity κ(T). A maximum in κ is found at 23, 25,
N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Fig. 10. The temperature dependence of the carrier mobility µ of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
26 and 30 K for δ = 0.0, 0.10, 0.20 and 0.40, respectively. The lattice thermal conductivity κL (T) is analyzed assuming Matthiesen’s rule to be applicable to the following contributions to the thermal conduction in the samples: the electronic thermal conductivity and the lattice contributions from the electron and phonon scattering and the Umklapp process. We have calculated κL (T) using the Wiedemann–Franz law with the Lorentz number fixed and show it in Fig. 12. The fitting was made for κL (T) assuming the following
49
Fig. 12. The temperature dependence of the inverse of the lattice thermal conductivity κL of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
relation: 1 A = 2 + BT + C, κL (T) T where the first term describes the electron–phonon scattering and the second one gives the Umklapp process. It is seen that the fitting is very good in the whole temperature range except above 200 K where the ambipolar diffusion is dominant in the intrinsic region. The temperature at which κ(T) forms a minimum is increasing with δ from 250 K (δ = 0.0) to above 300 K (δ = 0.40). Similar behavior was reported by others [4,5,8–10]. Champness et al. have noted that the minima and the rise at higher temperature are most marked in the near intrinsic samples of Bi2−x Sbx Te3.13 [4]. The deduced parameters are listed in Table 3. The parameters A and B show decreasing tendency with δ. The B is compared with the reported values of 0.51 × 10−1 W−1 cm [8] and 3.14 × 10−1 W−1 cm [10] for Bi2 Te3 . Any satisfactory interpretation is not given for the parameter C. 3.6. Thermoelectric performance Fig. 13 shows the temperature dependence of the power factor (PF) α2 ρ−1 for all the samples. The most promiTable 3 The parameters in 1/κL (T) = A/T 2 + BT + C giving the temperature dependence of the lattice thermal conductivity of Bi1.8 Sb0.2 Te3.0 grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ
Fig. 11. The temperature dependence of the thermal conductivity κ of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
δ
A (W−1 K3 cm)
B (W−1 cm)
C (W−1 K cm)
0.0 0.10 0.20 0.40
2.98 × 103 1.63 × 103 2.24 × 103 1.92 × 103
4.56 × 10−1 2.15 × 10−1 2.26 × 10−1 1.52 × 10−1
2.39 × 101 1.28 × 101 2.33 × 101 2.16 × 101
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N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
moelectric performance is achieved in the p-type sample at δ = 0.259 above which the p-type to n-type conduction transition takes place. With increasing δ, the carrier concentration n is decreased but the mobility µ is increased through the series, i.e. µ is a decreasing function of n as reported in the Bi2 Te3 compounds [7]. The highest Z is obtained in the p-type materials at n = 1.6 × 1019 cm−3 .
4. Conclusion The structural and thermoelectric properties of Bi1.8 Sb0.2 Te3.0 grown by the GF method from Te-rich melt Bi1.8 Sb0.2 Te3.0+δ were investigated. The following results were obtained:
Fig. 13. The temperature dependence of the power factor (PF) of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
nent feature is that the largest PF of 100 W K−2 cm−1 is achieved for the sample with δ = 0.259 at 200 K. For the n-type samples, a comparable magnitude was not obtained with that reported by the Kutasov et al. Only half the magnitude of PF was obtained for the sample at δ = 0.30 at 200 K. The temperature dependence of the figure of merit Z is shown in Fig. 14. The Z for δ = 0.259 was calculated using κ(T) of δ = 0.20 and is plotted. It is found that the largest value of Z = 5.8 × 10−3 K−1 is achieved for δ = 0.259 at 200 K corresponding to ZT = 1.1. The optimum condition for the high thermoelectric performance is discussed. The highest ther-
(1) The composition was determined by the EPMA measurement to be homogeneous in the center part of the single crystalline ingots. An excess of Te is segregated at the top of the ingots. (2) A high thermoelectric performance was achieved at low temperature in the p-type samples. The largest value of α, >500 V K−1 , was obtained at 200 K for δ = 0.259 to give ZT = 1.1. (3) The optimum carrier concentration was determined to be n = 1.6 × 1019 cm−3 for the highest thermoelectric performance in the p-type Bi1.8 Sb0.2 Te3.0 . (4) The transport properties are well explained by assuming a non-degenerate extrinsic semiconductor. Acknowledgements We wish to thank Mr. O. Notoya of JAIST for his help in the EPMA measurement. Our acknowledgements are extended to Dr. Vladimir K. Zaitsev of the Ioffe Institute for the fruitful discussions during his stay in JAIST and to Dr. H. Kaibe of the Komatsu Research Center for his valuable suggestions for the transport properties of our samples. References
Fig. 14. The temperature dependence of the figure of merit Z of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
[1] H. Scherrer, S. Scherrer, in: D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC Press, New York, 1995, p. 211. [2] N.Kh. Abrikosov, V.F. Bankina, L.A. Kolomoets, N.V. Dzhaliashvili, Neorg. Mater. 13 (1975) 827. [3] N.Kh. Abrikosov, L.V. Poretskaya, Neorg. Mater. 19 (1983) 388. [4] C.H. Champness, P.T. Chiang, P. Parekh, Can. J. Phys. 43 (1965) 653. [5] V.A. Kutasov, L.N. Luk’yanova, P.P. Konstantinov, Semiconductors 34 (2000) 376. [6] F. Izumi, T. Ikeda, Mater. Sci. Forum 321–324 (2000) 198. [7] J.P. Fleurial, L. Gailliard, R. Triboulet, H. Scherrer, S. Scherrer, J. Phys. Chem. Solids 49 (1988) 1237. [8] C.B. Satterthwaite, R.W. Ure Jr., Phys. Rev. 108 (1957) 1164. [9] L.R. Testardi, J.N. Bierly Jr., F.J. Donahoe, J. Phys. Chem. Solids 23 (1962) 1209. [10] H. Kaibe, Y. Tanaka, M. Sakata, I. Nishida, J. Phys. Chem. Solids 50 (1989) 945.
High thermoelectric performance at low temperature of p-Bi1.8Sb0.2 Te3.0 grown by the gradient freeze method from Te-rich melt Ngo Thu Huong a,1 , Yusuke Setou a , Go Nakamoto a , Makio Kurisu a,∗ , Takeshi Kajihara b , Hiroyuki Mizukami b , Seijiro Sano b a
Japan Advanced Institute of Science and Technology, 1-1 Asahidai Tatsunokuchi, Ishikawa 923-1292, Japan b Research Center, Komatsu Ltd., Hiratsuka 254-8467, Japan Received 21 July 2003; received in revised form 20 August 2003; accepted 20 August 2003
Abstract The structural and low-temperature thermoelectric properties were investigated in the temperature range from 4.2 to 300 K of Bi1.8 Sb0.2 Te3.0 grown by the gradient freeze method from Te-rich melt of Bi1.8 Sb0.2 Te3.0+δ . The composition profile was determined by electron probe microanalysis (EPMA) measurement to be homogeneous in the center part of the single crystalline ingots. An excess of Te is segregated at the top of the ingots. A high thermoelectric performance was achieved at low temperature in the p-type samples. The largest value of the Seebeck coefficient α of >500 V K−1 was obtained at 200 K for δ = 0.259 to give ZT = 1.1. The optimum carrier concentration was determined to be n = 1.6 × 1019 cm−3 for the highest thermoelectric performance. © 2003 Elsevier B.V. All rights reserved. Keywords: Semiconductors; Crystal growth; X-ray diffraction; Electronic transport; Thermoelectricity
1. Introduction Solid solutions formed in the Bi2 Te3 –Sb2 Te3 binary system are known to be effective thermoelectric materials for room temperature applications such as Peltier refrigerations and thermoelectric generations [1]. For the lower temperature use of these materials, a large reduction in the thermoelectric efficiency is encountered when the temperature is lowered down to 100–200 K. The reason for this is that these materials do not possess a high enough magnitude of the figure of merit Z at such low temperature and the thermoelectric efficiency is usually proportional to the temperature. Thus, many efforts have been made to optimize the low-temperature carrier concentration by doping Te and Se. It is well known that these solutions exhibit p-type conduction because there exist BiTe and SbTe anti-site defects in the crystals. These anti-site defects may explain that Bi2 Te3 –Sb2 Te3 solutions are non-stoichiometric toward Bi ∗
Corresponding author. Tel.: +81-761-51-1541; fax: +81-761-51-1545. E-mail address: [email protected] (M. Kurisu). 1 On leave from Faculty of Physics, Hanoi University of Science, Hanoi, Vietnam. 0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.08.066
and Sb [2,3]. In this sense, an introduction of an excess Te is an indispensable method to control the carrier concentration in this class of materials. Champness et al. have indicated that the n-type alloy with the nominal composition of Bi1.33 Sb0.67 Te3.13 prepared by the horizontal zone melting method has the maximum Z at 240 K [4]. Quite recently, Kutasov et al. have demonstrated very high Z at temperatures below 200 K for the n-type Bi2−x Sbx Te3 samples enriched in Te or doped with TeI4 [5]. The maximum Z value as large as 3.7 × 10−3 K−1 was obtained at 200 K. In the present paper, we have examined the structural and thermoelectric properties at low temperature of p-type as well as n-type Bi1.80 Sb0.20 Te3.0 single crystals which were grown from Te-rich melt by the gradient freeze method. The XRD, EPMA, Seebeck coefficient, electrical resistivity, Hall coefficient and thermal conductivity have been measured and the power factor and the figure of merit have been evaluated.
2. Experimental The single crystals of Bi1.8 Sb0.2 Te3.0 compounds were prepared by the gradient freeze method from the telluriumrich melt with liquidus compositions of Bi1.8 Sb0.2 Te3.0+δ
N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
where δ = 0.0, 0.10, 0.20, 0.259, 0.276, 0.30 and 0.40. High purity (99.9999%) Bi, Sb and Te granules were sealed into 10 cm long and 0.8 cm inner diameter quartz ampoules with a conical bottom under 10−5 Torr, melted at 610 ◦ C for 12 h in an electric furnace and furnace cooled. This melting process was done three times to ensure thorough mixing. The crystals were then grown in a vertical gradient freeze furnace with a growth rate of 1.25 mm h−1 and a temperature gradient of 40 K cm−1 at the liquid-solid interface. After furnace cooling, 500 ◦ C in 14 h, the ingots were cleaved and single crystals of 35 mm length were cut by spark erosion from the central portion of the ingots. The structural characterization was done by metallurgical observation, X-ray diffraction (XRD) and electron probe microanalysis (EPMA). The XRD measurement was performed on the cleavage planes of the ingots as well as on the powder samples by using a Rigaku RINT 2000 with a Cu Kα radiation. The parameters for these crystal structures have been refined by the Rietveld profile fitting program RIETAN-2000 [6]. The EPMA measurement was carried out by a JEOL JXA-8621 system. The Seebeck coefficient was measured by the seesaw heating method over a temperature range from 4.2 to 300 K. A temperature difference of 0.05 K was generated across the rectangular samples which were spark-cut from the single crystals with the long axis of rectangular bars parallel to the cleavage plane. The typical dimensions were 2.0 mm × 2.0 mm × 15 mm. The electrical resistivity measurements were followed on the same samples by the conventional dc four-probe method. The Hall coefficient was measured on the samples polished to thin plate with 0.5 mm thickness to which the magnetic field was applied perpendicularly up to 0.8 T over a temperature range from 77 to 300 K. All the electrical contacts between the samples and
45
gold wire probes with 50 m o.d. were made by DOTITE (type D-550) silver paste. The thermal conductivity along the cleavage plane was measured on the rectangular samples with 4.0 mm × 4.0 mm × 2.0 mm by a Quantum Design PPMS system in the temperature range from 5 to 300 K.
3. Results and discussion 3.1. Structural characterization Large single crystals were obtained with their basal planes parallel to the growth direction. The cleavage planes were examined by the XRD to be of single nature. The powder samples taken from the bottom, center and top portions of the ingots were examined by the XRD. The results for the center parts are shown in Fig. 1. The bottom parts showed almost the same patterns. All the diffraction peaks of the samples are indexed by assuming ¯ A satisa rhombohedral structure of the space group R3m. factory agreement is found between observed and calculated intensities with a factor of goodness fit S ranging between 1.84 and 1.99. However, the XRD patterns indicate segregation of tellurium metal in the top part of the samples where eutectic solidification takes place. This is supported by the metallurgical observation and the EPMA results which will be shown later. The lattice constants are listed in Table 1 and displayed in Fig. 2 against the excess Te content δ. A relatively large deviation from a linear dependence is found for a and c at δ = 0.276. However, the variations of the lattice constants are too small, a/a = −3 × 10−4 and
c/c = 6.2 × 10−3 at δ = 0.40, to conclude that excess Te is incorporated to form the crystal.
Fig. 1. The powder XRD patterns of Bi1.8 Sb0.2 Te3.0 compounds grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
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N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Table 1 The lattice constants refined by the Rietveld profile fitting of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ δ
a (Å)
c (Å)
0.0 0.10 0.20 0.259 0.276 0.30 0.40
4.3691 4.3691 4.3693 4.3693 4.3679 4.3697 4.3690
30.472 30.477 30.478 30.478 30.482 30.478 30.474
Fig. 3 shows the distribution of the composition along the growth direction z. It is seen that the sample with δ = 0.0 is homogeneous and possesses the composition Bi1.8 Sb0.2 Te3.0 up to z = 22 mm. Above z = 22 mm, there exists some deviation in the composition from Bi1.8 Sb0.2 Te3.0 , reflecting the eutectic solidification at the top part of the ingot. The sample with δ = 0.20 is also homogeneous up to 20 mm. Whereas in the sample with δ = 0.40, a larger scattering of the composition can be found. This may suggest that the formation of an appreciable amount of Te metal and Sb–Te alloys takes place not only at the end of the ingot growth but also throughout the entire growth process of the ingot. Our careful data acquisition repeated several times confirmed that there exist Te metal precipitations with cross sections smaller than the electron beam size of 10 m diameter. Fig. 4 shows the composition profile along the growth direction. Each point represents the average composition from 20 different points around z = 15 mm. The determined compositions of the ingots are also listed in Table 2. It is found that excess Te as much as δ = 0.40 in the liquid of Bi1.8 Sb0.2 Te3.0+δ is not totally incorporated to form the
Fig. 2. The lattice constants of Bi1.8 Sb0.2 Te3.0 compounds grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
crystal. It should, however, be noted that the relative concentration of Te is increased appreciably against (Bi + Sb) and the relative Bi volume is also increased against Sb with increasing δ. 3.2. Seebeck coefficient The temperature dependence of the Seebeck coefficient α along the cleavage plane is shown in Fig. 5. The sign of α is positive for 0.0 ≤ δ ≤ 0.276 and becomes negative for δ ≥0.276. Two rectangular samples were cut from the center portions of the same ingot grown from the liquidus composition δ = 0.276. They exhibit different types of conduction,
Fig. 3. Atomic composition profile of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ for (a) δ = 0.0, (b) δ = 0.20 and (c) δ = 0.40.
N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Fig. 4. The composition of Bi, Sb and Te in the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
indicating that the thermoelectric properties are highly dependent on the electronic structures of the samples. The α values for p-type compounds grown from δ = 0.0, 0.20 and 0.259 are larger, about 300 V K−1 , than those ever reported at room temperature [1,5]. Our n-type samples have room temperature α values between −280 and −220 V K−1 . The most remarkable results are that α takes the largest value at 200 K for the n-type as well as p-type samples. The samples prepared from δ = 0.259 and 0.30 possess >500 and −370 V K−1 at 200 K, respectively. Smaller α values of 220–260 V K−1 at higher temperature around 280 K were reported in the n-type Bi1.8 Sb0.2 Te3.0 [5]. The α values are plotted against the logarithm of temperature for all the samples in Fig. 6. A logarithmic temperature dependence is found for α between 50 and 200 K where the slope is between 170 and 290 V K−1 for the p-type and −160 and −95 V K−1 for the n-type. The p-type samples have larger slope than expected, 129 V K−1 , for the non-degenerate extrinsic semiconductors. The low-temperature behavior below 50 K is due to the increasing degeneracy of the carrier. The decrease in α at high temperature may be ascribed to the fact that the samples are in a region of intrinsic conduction or a mixed one.
47
Fig. 5. The temperature dependence of the Seebeck coefficient α of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
3.3. Electrical resistivity The temperature dependence of the electrical resistivity ρ is shown in Fig. 7. The resistivity at room temperature is increased with δ, taking the largest value at δ = 0.276(p) for the samples exhibiting p-type conduction, whereas for the n-type samples it is decreased. Similar dependence of the room temperature resistivity on the excess Te composition was found in Sb-free Bi2 Te3+δ compounds [7].
Table 2 The composition profile of the crystal along the crystal growth direction grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ δ
Composition
0.0 0.10 0.20 0.259 0.276
(Bi0.900 Sb0.100 )2.0 Te2.986 (Bi0.902 Sb0.098 )2.0 Te2.989 (Bi0.905 Sb0.095 )2.0 Te2.994 (Bi0.906 Sb0.094 )2.0 Te2.994 (Bi0.906 Sb0.094 )2.0 Te2.994
Fig. 6. The Seebeck coefficient α as a function of the logarithm of the temperature T of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
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N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Fig. 7. The resistivity ρ as a function of the temperature T of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
The thermal variation of the resistivity is highly dependent on δ. In Fig. 8, the logarithm of the resistivity is plotted against the logarithm of the temperature for all the samples measured. The resistivity for the sample with δ = 0.0 follows a T 1.97 law over the temperature range from 120 to 300 K. Below 120 K the variation in ρ is smaller, implying an increasing degeneracy. The sample prepared from δ = 0.10 exhibits a T 1.80 dependence down to 170 K, below which a shoulder appears with further decreasing tempera-
Fig. 9. The temperature dependence of the carrier concentration n of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
ture. For the samples with δ = 0.20, 0.276 and 0.30, their peculiar variation of the resistivity should be noted. Their resistivity forms a peak above 100 K and shows a decrease with increasing temperature, indicating that the conduction is intrinsic above 200 K. The sample with δ = 0.40 exhibits T 1.49 behavior in the wider temperature range from 80 to 300 K. 3.4. Hall coefficient Fig. 9 shows the temperature dependence of the carrier concentration n for the selected samples. The sign of Hall coefficient was confirmed to be positive for δ = 0.0, 0.10 and 0.20 and negative for δ = 0.30 and 0.40, which is consistent with the thermopower. It is found that the carrier concentration n at 300 K is decreased with δ, (3–0.8)×1019 cm−3 . It is also interesting to note that the p-type samples show a larger temperature dependence of n than the n-type. The n for δ = 0.0 is increased largely as the temperature is lowered. One can calculate the apparent Hall mobility µ using the data of the electrical resistivity. Fig. 10 gives the logarithm of µ versus the logarithm of the temperature. Below 200 K, all the samples follow the power law of µ ∝ T −r , where r = 1.30, 1.66, 1.41 and 0.66 for δ = 0.0, 0.20, 0.30 and 0.40, respectively. Thus, we may conclude that acoustic phonon scattering is dominant in the temperature range from 77 to 200 K for the samples prepared from δ ≤0.30. The larger exponents at high temperature may be attributed to intrinsic conduction. 3.5. Thermal conductivity
Fig. 8. The logarithm of the resistivity ρ as a function of the logarithm of the temperature T of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
Fig. 11 shows the temperature dependence of the thermal conductivity κ(T). A maximum in κ is found at 23, 25,
N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
Fig. 10. The temperature dependence of the carrier mobility µ of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
26 and 30 K for δ = 0.0, 0.10, 0.20 and 0.40, respectively. The lattice thermal conductivity κL (T) is analyzed assuming Matthiesen’s rule to be applicable to the following contributions to the thermal conduction in the samples: the electronic thermal conductivity and the lattice contributions from the electron and phonon scattering and the Umklapp process. We have calculated κL (T) using the Wiedemann–Franz law with the Lorentz number fixed and show it in Fig. 12. The fitting was made for κL (T) assuming the following
49
Fig. 12. The temperature dependence of the inverse of the lattice thermal conductivity κL of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
relation: 1 A = 2 + BT + C, κL (T) T where the first term describes the electron–phonon scattering and the second one gives the Umklapp process. It is seen that the fitting is very good in the whole temperature range except above 200 K where the ambipolar diffusion is dominant in the intrinsic region. The temperature at which κ(T) forms a minimum is increasing with δ from 250 K (δ = 0.0) to above 300 K (δ = 0.40). Similar behavior was reported by others [4,5,8–10]. Champness et al. have noted that the minima and the rise at higher temperature are most marked in the near intrinsic samples of Bi2−x Sbx Te3.13 [4]. The deduced parameters are listed in Table 3. The parameters A and B show decreasing tendency with δ. The B is compared with the reported values of 0.51 × 10−1 W−1 cm [8] and 3.14 × 10−1 W−1 cm [10] for Bi2 Te3 . Any satisfactory interpretation is not given for the parameter C. 3.6. Thermoelectric performance Fig. 13 shows the temperature dependence of the power factor (PF) α2 ρ−1 for all the samples. The most promiTable 3 The parameters in 1/κL (T) = A/T 2 + BT + C giving the temperature dependence of the lattice thermal conductivity of Bi1.8 Sb0.2 Te3.0 grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ
Fig. 11. The temperature dependence of the thermal conductivity κ of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
δ
A (W−1 K3 cm)
B (W−1 cm)
C (W−1 K cm)
0.0 0.10 0.20 0.40
2.98 × 103 1.63 × 103 2.24 × 103 1.92 × 103
4.56 × 10−1 2.15 × 10−1 2.26 × 10−1 1.52 × 10−1
2.39 × 101 1.28 × 101 2.33 × 101 2.16 × 101
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N. Thu Huong et al. / Journal of Alloys and Compounds 368 (2004) 44–50
moelectric performance is achieved in the p-type sample at δ = 0.259 above which the p-type to n-type conduction transition takes place. With increasing δ, the carrier concentration n is decreased but the mobility µ is increased through the series, i.e. µ is a decreasing function of n as reported in the Bi2 Te3 compounds [7]. The highest Z is obtained in the p-type materials at n = 1.6 × 1019 cm−3 .
4. Conclusion The structural and thermoelectric properties of Bi1.8 Sb0.2 Te3.0 grown by the GF method from Te-rich melt Bi1.8 Sb0.2 Te3.0+δ were investigated. The following results were obtained:
Fig. 13. The temperature dependence of the power factor (PF) of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
nent feature is that the largest PF of 100 W K−2 cm−1 is achieved for the sample with δ = 0.259 at 200 K. For the n-type samples, a comparable magnitude was not obtained with that reported by the Kutasov et al. Only half the magnitude of PF was obtained for the sample at δ = 0.30 at 200 K. The temperature dependence of the figure of merit Z is shown in Fig. 14. The Z for δ = 0.259 was calculated using κ(T) of δ = 0.20 and is plotted. It is found that the largest value of Z = 5.8 × 10−3 K−1 is achieved for δ = 0.259 at 200 K corresponding to ZT = 1.1. The optimum condition for the high thermoelectric performance is discussed. The highest ther-
(1) The composition was determined by the EPMA measurement to be homogeneous in the center part of the single crystalline ingots. An excess of Te is segregated at the top of the ingots. (2) A high thermoelectric performance was achieved at low temperature in the p-type samples. The largest value of α, >500 V K−1 , was obtained at 200 K for δ = 0.259 to give ZT = 1.1. (3) The optimum carrier concentration was determined to be n = 1.6 × 1019 cm−3 for the highest thermoelectric performance in the p-type Bi1.8 Sb0.2 Te3.0 . (4) The transport properties are well explained by assuming a non-degenerate extrinsic semiconductor. Acknowledgements We wish to thank Mr. O. Notoya of JAIST for his help in the EPMA measurement. Our acknowledgements are extended to Dr. Vladimir K. Zaitsev of the Ioffe Institute for the fruitful discussions during his stay in JAIST and to Dr. H. Kaibe of the Komatsu Research Center for his valuable suggestions for the transport properties of our samples. References
Fig. 14. The temperature dependence of the figure of merit Z of the crystals grown by the GF method from the tellurium-rich melt of Bi1.8 Sb0.2 Te3.0+δ .
[1] H. Scherrer, S. Scherrer, in: D.M. Rowe (Ed.), CRC Handbook of Thermoelectrics, CRC Press, New York, 1995, p. 211. [2] N.Kh. Abrikosov, V.F. Bankina, L.A. Kolomoets, N.V. Dzhaliashvili, Neorg. Mater. 13 (1975) 827. [3] N.Kh. Abrikosov, L.V. Poretskaya, Neorg. Mater. 19 (1983) 388. [4] C.H. Champness, P.T. Chiang, P. Parekh, Can. J. Phys. 43 (1965) 653. [5] V.A. Kutasov, L.N. Luk’yanova, P.P. Konstantinov, Semiconductors 34 (2000) 376. [6] F. Izumi, T. Ikeda, Mater. Sci. Forum 321–324 (2000) 198. [7] J.P. Fleurial, L. Gailliard, R. Triboulet, H. Scherrer, S. Scherrer, J. Phys. Chem. Solids 49 (1988) 1237. [8] C.B. Satterthwaite, R.W. Ure Jr., Phys. Rev. 108 (1957) 1164. [9] L.R. Testardi, J.N. Bierly Jr., F.J. Donahoe, J. Phys. Chem. Solids 23 (1962) 1209. [10] H. Kaibe, Y. Tanaka, M. Sakata, I. Nishida, J. Phys. Chem. Solids 50 (1989) 945.