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Thermoelectric characterization of Bi2Te2.55Se0.45 solid solution crystal
PII: SOO22-3697(97)00119-4
Pergamon
THERMOELECTRIC
1. Phys. Chcm Solids Vd 59. No. I, pp. 13-20. 1998 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved COZZ-3697/98 $19.00 + 0.00
Q
CHARACTERIZATION OF Bi2Te2.55Se0.45 SOLID SOLUTION CRYSTAL
C. LAHALLE-GRAVIER*,
B. LENOIR, H. SCHERRER and S. SCHERRER
Laboratoire de Mktallurgie Physique et de Sciences des Mat&iaux, Ecole des Mines de Nancy, Part de Saulupt, 54000 Nancy, France (Received 6 January 1997; accepted 4 March 1997)
Abstract-The transport properties of BizTez.ssSe0.4Ssolid solution have been measured and described as functions of carrier concentration and temperature. Samples were prepared using an annealing saturation technique within a temperature range of 550-590°C. The figure of merit is determined as a function of temperature using the Harman method. The Hall coefficient and electrical resistivity are also measured from the temperature of liquid nitrogen to room temperature. This work demonstrates that this solid solution is an extrinsic semiconductor which can be described by a band parabolic model with one carrier type. The results indicate that the effective mass varies with temperature and that the acoustic phonon scattering mechanism is the predominant carrier scattering mechanism responsible for the electron diffusion. 0 1997 Elsevier Science Ltd. All rights reserved. Keywords: A. semiconductors, A. chalcogenide, D. transport properties, D. electrical conductivity, D. thermal conductivity
1. INTRODUCTION The study of the Bi2Te2,5$eo.4S solid solution was carried out because we thought that it would be an extrinsic semiconductor material and we wanted to identify the behaviour of the figure of merit at low temperature (200K). The characterization of this material has been done through electrical and thermal measurements. Hall coefficient, electrical resistivity and Hall mobility were measured at temperatures varying from liquid nitrogen to room temperature. Measurements of thermoelectric properties of samples were carried out as functions of temperature and of carrier concentration. Sample preparation and equipment used for measurements have been described previously [l-4].
2. EXPERIMENTAL PROCEDURE 2.1. Sample preparation The travelling heater method (THM) is applied for growing Bi2Te2.5SSe0.45 solid solution ingots. As described in a previous paper [1], the control of the crystal growth is critical and requires the knowledge of the ternary phase diagram. This process is a solvent zone transfer through a source ingot in a quartz ampoule sealed under vacuum. By this method, single crystals are obtained with cleavage planes parallel to the growth axis, i.e. perpendicular to the c-axis. Samples in the form of discs (1.5 mm in diameter and 3 mm thick) were cut perpendicular to the growth axis. Cleaved
samples were produced using a razor blade. Those samples were saturated in a quartz ampoule sealed under vacuum over a temperature range of 550-590°C. In this technique of saturation previously described in Ref. [1], the samples acquire the composition of the solidus line.
3. SAMPLES CHARACTERIZATION The determination of the figure of merit Zas a function of temperature is carried out following the Harman method [5, 61. Coupled with electrical resistivity p and Seebeck coefficient (Ymeasurements, the figure of merit measurement allows the calculation of the thermal conductivity h(z = a?(ph)). Hall effect measurements are carried out on cleaved saturated samples. The magnetic field is perpendicular to the cleavage planes and the electrical current is parallel to these planes. The Hall coefficient was determined, for each sample, between 100 and 300K. Electrical resistivity was also measured and described as a function of temperature applying the Van der Pauw technique.
4. RESULTS 4.1. Thermoelectric temperature
properties
at room
Fig. 1 displays room temperature values of the Seebeck coefficient (Y” as a function of carrier concentration. It appears that the absolute value decreases from 250 &V K-’ to about 170 PV K-’ when the carrier
*Author to whom correspondence should be addressed.
13
C. LAHALLE-GRAVIER
4
6
8
10
et al.
12
14
16
Catrler concentration ( lOL9cm? Fig. 1. Seebeck coefficient
as a
concentration increases from 4 X 1019crne3 to 15 X lOI cmw3, as expected from classical behavior. Electrical resistivity p l1 as a function of carrier concentration is plotted in Fig. 2, and it decreases from 17 to 7 $l m-’ as the carrier concentration increases. The behavior of the thermal conductivity vs carrier concentration is displayed in Fig. 3. The values of XL1along the cleavage planes are found to vary between 1.4 and 1.8 W m-’ K-l. Calculated figure of merit values Z” are. shown in Fig. 4. A maximum of 2.6 X 10m3K-’ is reached for the BizTe&e0.45 solid solution for a carrier concentration value equal to 7 X lOI cme3. It should be noticed that the figure of merit values are higher than 2.1 X 10T3 K-’ over the carrier concentration interval.
4
6
8
function of carrier concentration.
4.2. Anisotropy of thermoelectric properties at room temperature The large size of the monocrystals obtained by THM allows us to characterize the thermoelectric properties of massive samples in a parallel direction to the c-axis, indexed 33. The anisotropy is characterized by the ratio between the cr-, X-, p- and Z-values, respectively, measured in a direction parallel and perpendicular to the cleavage planes. The results are summarized in Table 1. We note that the Seebeck coefficient is quite isotropic. Thermal conductivity values corresponding to the parallel direction to the cleavage planes are higher by about a factor of 2 than those measured in the perpendicular direction. We can also see the very strong anisotropy of the electrical resisitivity increasing with the
10
12
14
Carrier concentration (lOI cm”) Fig. 2.
Elect&al resistlvity as a function of carder concentration.
16
Characterization of BizTe;l,S$3e~..u solid solution crystal
15
1.80 -g
1.75 1.70
$ 3,
1.65
;h .::
.2
J a g
1.60 1.55
:!z
1so
g
1.45 1.40 4
6
8 10 12 Carrier concentration (1 019 cme3)
14
16
Fig. 3. Thermal conductivity as a function of carrier concentration.
concentration. These results imply a nonnegligible anisotropy for the figure of merit. These results are in good agreement with the work of Carle et al. [7].
carrier
4.3. Thermoelectric 300K
properties
between 100 and
Experimental values of the figure of merit 2” values
are plotted against temperature for different carrier concentration in Fig. 5. We can see that the figure of merit is maximum at room temperature independent of carrier concentration, as expected. Moreover, the figure of merit values increase when carrier concentration decreases independently of the temperature. On the side of low temperatures, the different curves appear to be linear and
2.7 2.6 _” 2
2.5
*= B 2.4 % $j 2.3 .h r& 2.2 2.1 4
6
8
10
12
14
16
Carrier concentration ( lOr9 cm”) Fig. 4. Figure of merit as a function of carrier concentration. Table 1. Anisotropy of themwelectric properties Annealing
Carrier
temperature
concentration (lOI cm-‘)
CC)
550
15.5
1.1
2.5
5.1
2.5
570
12.3
585
6.8
1.1 1
2.4 2.4
4.5 1.4
2.2 1.4
(*)I 1: perpendicularto the c-axis. 33: parallel to the c-axis.
C. LAHALLE-GRAVIERet al.
16
2.6 1
I.A--
/
v-
/A
l.ooF1
”
”
”
”
”
”
”
”
”
”
- 12.3
‘I
”
50
0
-50
-100
-150
-6.2
loo
Temperature (“C) Fig. 5. Figure-of merit as a function of temperaturefor several carrier concentrations.
parallel. We notice that for the upper curve, values higher than 2 X 10e3 K-’ can be obtained at -100°C. The Seebeck coefficient as a function of temperature is presented in Fig. 6. We note that the relation is roughly linear. We deal with this point in our discussion. Calculated thermal conductivity vs temperature is displayed in Fig. 7. We can see that the influence of the electronic contribution, at low temperature, is more important when the carrier concentration is high. The values of the electrical resistivity obtained during the Harman experiment and the values presented in Fig. 9 obtained by the van der Paw technique are the same. Hall coefficient p t23measurement results are presented in Fig. 8. It is important to note that the Hall coefficient is roughly constant in the temperature range from 100 to
3OOK, that is to say this solid solution is extrinsic up to room temperature. Results of resistivity p” measurements are shown in Fig. 9. The Hall mobility is calculated using p = (p ‘23/(p’I)). The behavior of the Hall mobility as a function of temperature is displayed in Fig. 10. 5. DISCUSSION The entire analysis is based on a parabolic band structure,
in the case of an extrinsic semiconductor. If the relaxation time of the scattering mechanism is a power function of the energy, the Hall mobility and the electrical resistivity can be expressed as a function of the absolute temperature T as p = poT-’ and u = o,J-I’ where p0 and u. are two constants and x and x’ are two exponents which depend
I
Carrier concentration 1o’p cm.’ . ..__ 587
-140
-o---570 - t - 550 585
-160 A. -180 -200 -220 I I
I
”
-150
”
I
”
-100
”
I
-50
”
r
“I”
0
’
I ”
50
“I 100
Temperature (“C) Fig. 6. Seebeck coefficient as a function of temperature for several carrier concentrations.
Characterizationof BizTez.uSea.usolid solution crystal
17
Thermal conductivity as a function of the temperature 3.5 L’I
2.5
-
2.0
-
I I,
I I I I (I
I,,
,,,
I I,,
I I’]
1.5 -
1.0 t1 -150
”
”
”
-100
”
’ I ”
I ”
I ”
-50 0 Temperature (“C)
1’
I ’ J
50
100
Fig. 7. Thermal conductivity as a function of temperature for several carrier concentrations.
on the scattering mechanism. Experimental values of x and X’ are reported in Table 2 for several carrier concentrations of the BizTez.s$ea.4s solid solution. We can see that x and x’ values are the same: that is to say that the carrier concentration is constant in the temperature range studied. x and x’ values decrease as the carrier concentration increases [7-l l] and are below 1.5, the theoretical value in the case of the acoustic phonon scattering mechanism. Deviations from this law can be explained if we take into account the scattering by ionized impurities as an additional mechanism. This scattering mechanism is possible in our material because deviations from stochiometry come from an excess of tellurium.
Nevertheless, we admit in the following that the scattering mechanism is mainly due to acoustical phonons. In this case and if the semiconductor is a nondegenerate extrinsic one in which the carrier concentration and the effective mass are constant in the involved temperature range, the Seebeek coefficient can be expressed by Q = 2 (3k/(2e))ln T 2 C where k is Boltzmann’s constant, e the electron charge and C a constant. So the curves which give the Seebeck coefficient as a function of In T have to be straight with a slope equal to + 129 PV K-l. Experimentally, according to the results presented in Fig. 6, we found values ranging
concentration -m-~-~-Am)_-q--we_-.-.-.-.-_-,-__~-_-._.-.-*.-.-
-150
-100
-50
0
Temperature (“C) Fig. 8. Hall coefficientas a function of temperature..
50
C. LAHALLE-GRAVIRRer al.
Carrier concentration lOI cm.3
15.. -t14. - -W- - 12. 10. - 0 - 9.0 e- 6.7 - . + - - 6.2 ---r---4.5 -
-100
-50
50
0
Temperature (“C) Fig. 9. Electrical resisitivity as a function of temperature, using the Van Der Pauw method.
from -80 to -105 WVK-i for carrier concentrations between 6.3 X 1OL9cm-3 and 15.5 X lOI cme3. The difference between theory and experiment can be explained first by effective mass m* variation with temperature. This variation can be deduced from the evolution of the electrical conductivity C with temperature: u=m
*5l2T
-312
If m* = T”: dln u dln=-j-ZS
3
5
According to Fig. 11, -0.14 5 s 5 -0.07. In this case, the theoretical slope of the curves a(ln2’) is between - 117 and - 123 FV K-’ for the same carrier concentration. The degeneracy of the electron gas can explain the
Carrier concentration lOI cm.3
15.5 14.3 - - v - - 12.3 10.7 - l - -9.0 +- 6.7 -. + - 6.2 -A. - 4.5 -
-200
-150
-100
-50
0
50
Temperature (“Cl Fig. 10. Hall mobility as a function of temperature.
Table 2. Values of the x exponent Annealing temperature. (T, “C) Carrier concentration (lOI cm“) X XI
550
560
570
575
580
585
587
590
15.5
14
12.3
1.1
9
6.8
6.2
4.5
1.08 1.10
1.15 1.15
1.18 1.20
1.20 1.20
1.25 1.25
1.28 1.27
1.28 1.28
1.31 1.30
Characterizationof Bi2Te&eo.4s solid solution crystal
19
I 0.5
‘E!
b t
Carrier concentration lOI cm.3 15.5 14.3 - -v - - 12.3 10.7 - l - -9.0 ----(I- - 6.7 - -+. -6.2 -A. - - 4.5
0.3
0.1
0.08 0.06 70
200
80 90 100
300
Temperature (K) Fig. 11. Electrical conductivity as function of temperature.
difference between experiment and the model. The effect of this degenerescence induces a linear relation between the Seebeck coefficient and the temperature [ 121. This is exactly what we found on Fig. 6. As known, the dimensionless figure of merit ZT is given by the relation [ 131:
with X, the lattice thermal conductivity, B a constant term, A = p(rn*/r~$‘~ and mo the electron mass. From our results, we obtain ZT s T”. According to Fig. 12, which shows the evolution of the parameter A with temperature, for a sample with a carrier concentration equal to 6.2 X 10 I9cm-3, d In A/d
-2.2 -2.4
-2.6
-3.2
In T = 1.3.So the thermal conductivity h, varies with the temperature according to T-O.‘. This law is compared with X,(T) = T-’ in the bismuth telluride compound. We can see that the lattice thermal conductivity has a lesser dependence with temperature in the case of the solid solution. This result explains that, in the case of Bi2Te&e0,4r solid solution, the figure of merit decreases more slowly when the temperature decreases. Finally, the evolution of the thermal conductivity as a function of electrical conductivity is shown in Fig. 13. The oscillations are due to the Lorentz number variations [14]. By this curve, the lattice thermal conductivity value can be estimated. We found it equal to 1.1 W m-’ K- ‘. It is possible to calculate this value
C. LAHALLE-GRAVJER et al.
20
1.00~“““““““““““““” 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Electrical Conductivity (clQ-‘.rn-‘) Fig. 13. Thermal conductivity as a function of electrical conductivity. using
the figure of merit results: z=
thermal conductivity is estimated to be equal to 1.l W m-r K-‘. The figure of merit values comprised between 2 and 2.6 X lo-’ K- ’ for temperature range varying between 100 and 300K. REFERENCES
with
Lahalle-Gravier,C., Scherrer,H. and Schemx, S., J. Phys. k2&12 (kt)“F&)[$-q]’ &?I($= eh3 &r”’ g2(d
k2’D
=
(kT)3’2F0($T
;; Chem. Solids, 1996,57 (ll), 1713-1717.
Caillat, T., Carle, M., Pierrat, P., Scherrer, H. and Scherrer, S., J. Phys. Chem. Solids, 1992.53 (a), 1121-1129. 3. Goudot, A., Schlicklin, P.M. and Stockholm, J.G., Proceedings of the 5th International Conference on Thermoelectric. Energy Conversion, Arlington, 1984.
eR3 4~”
Carle, M., Caillat, T., Lahalle-Gravier, C., Scherrer. H. and x
I
[z-4(z)2]
:: Scherrer, S., J. Phys. C/tern. Solids, 1995,56 (2) 211-215. Harman, T. C., J. Appl. I’hys., 1958,29, 1373.
where h is Plank’s constant, fi = h/Z*, Fi the Fermi integrals, and q the reduced Fermi level. We found the same result.
6. CONCLUSION An analysis of all results obtained allows us to put forward some ideas about the transport properties of the Bi2Te2,s5Se0.~ssolid solution. This material is an extrinsic semidegenerated semiconductor. The scattering mechanism is mainly due to acoustical phonons, but a small influence of ionized impurities is possible. The band structure appears to be similar to the BirTe3 structure, but the effective mass varies with temperature. The lattice
6. Lenoir, B. These JNPL, Nancy, France. I. Carle, M., Pierrat, P., LahaJle-Gravier, C., Scherrer, H. and Scherrer, S., J. Phys. Chem. Solids, 1995,56 (2). 201-209.
8. Kutasov, V.A., Svechnikova, T.E., Chizhevskaya, S.N., Fiz. 9. 10. 11. 12. 13. 14.
Tverd. Tell (Leningrad) 1987,29,3008-3011; Sov. Phys. Solid State. 1987,10, 1724-1730. Abrikosov, N. Kh., Svechnikova, T. E. and Chizhevskaya, S., Izv.Akad nauk. SSSR, Neorg. Mater., 1978,14(1),43-45. Abrikosov, N. Kh., Kutasov, V. A., Luk’yanova, L.N., Svechnikova. T. E. and Chizhevskaya, S. N., Izv. Akad. Nauk. SSSR, Neorg. Mater., 1980.16, 1394. Kutasov, V. A. and Luk’yanova, L. N., Sov. fhys. Solid State, 1978, 20 (lo), 1767-1769. Goldsmid, H.J., Thermoelectric Rejridgeration. Temple, London, 1966. Chasmar, R. P. and Stratton, R. J., J. Electr. Contr., 1959.7 (1) 52-72. Kolomoets, N. V., Fiz. Tverd. Tela (Leningrad), 1966, 8, 999.
Pergamon
THERMOELECTRIC
1. Phys. Chcm Solids Vd 59. No. I, pp. 13-20. 1998 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved COZZ-3697/98 $19.00 + 0.00
Q
CHARACTERIZATION OF Bi2Te2.55Se0.45 SOLID SOLUTION CRYSTAL
C. LAHALLE-GRAVIER*,
B. LENOIR, H. SCHERRER and S. SCHERRER
Laboratoire de Mktallurgie Physique et de Sciences des Mat&iaux, Ecole des Mines de Nancy, Part de Saulupt, 54000 Nancy, France (Received 6 January 1997; accepted 4 March 1997)
Abstract-The transport properties of BizTez.ssSe0.4Ssolid solution have been measured and described as functions of carrier concentration and temperature. Samples were prepared using an annealing saturation technique within a temperature range of 550-590°C. The figure of merit is determined as a function of temperature using the Harman method. The Hall coefficient and electrical resistivity are also measured from the temperature of liquid nitrogen to room temperature. This work demonstrates that this solid solution is an extrinsic semiconductor which can be described by a band parabolic model with one carrier type. The results indicate that the effective mass varies with temperature and that the acoustic phonon scattering mechanism is the predominant carrier scattering mechanism responsible for the electron diffusion. 0 1997 Elsevier Science Ltd. All rights reserved. Keywords: A. semiconductors, A. chalcogenide, D. transport properties, D. electrical conductivity, D. thermal conductivity
1. INTRODUCTION The study of the Bi2Te2,5$eo.4S solid solution was carried out because we thought that it would be an extrinsic semiconductor material and we wanted to identify the behaviour of the figure of merit at low temperature (200K). The characterization of this material has been done through electrical and thermal measurements. Hall coefficient, electrical resistivity and Hall mobility were measured at temperatures varying from liquid nitrogen to room temperature. Measurements of thermoelectric properties of samples were carried out as functions of temperature and of carrier concentration. Sample preparation and equipment used for measurements have been described previously [l-4].
2. EXPERIMENTAL PROCEDURE 2.1. Sample preparation The travelling heater method (THM) is applied for growing Bi2Te2.5SSe0.45 solid solution ingots. As described in a previous paper [1], the control of the crystal growth is critical and requires the knowledge of the ternary phase diagram. This process is a solvent zone transfer through a source ingot in a quartz ampoule sealed under vacuum. By this method, single crystals are obtained with cleavage planes parallel to the growth axis, i.e. perpendicular to the c-axis. Samples in the form of discs (1.5 mm in diameter and 3 mm thick) were cut perpendicular to the growth axis. Cleaved
samples were produced using a razor blade. Those samples were saturated in a quartz ampoule sealed under vacuum over a temperature range of 550-590°C. In this technique of saturation previously described in Ref. [1], the samples acquire the composition of the solidus line.
3. SAMPLES CHARACTERIZATION The determination of the figure of merit Zas a function of temperature is carried out following the Harman method [5, 61. Coupled with electrical resistivity p and Seebeck coefficient (Ymeasurements, the figure of merit measurement allows the calculation of the thermal conductivity h(z = a?(ph)). Hall effect measurements are carried out on cleaved saturated samples. The magnetic field is perpendicular to the cleavage planes and the electrical current is parallel to these planes. The Hall coefficient was determined, for each sample, between 100 and 300K. Electrical resistivity was also measured and described as a function of temperature applying the Van der Pauw technique.
4. RESULTS 4.1. Thermoelectric temperature
properties
at room
Fig. 1 displays room temperature values of the Seebeck coefficient (Y” as a function of carrier concentration. It appears that the absolute value decreases from 250 &V K-’ to about 170 PV K-’ when the carrier
*Author to whom correspondence should be addressed.
13
C. LAHALLE-GRAVIER
4
6
8
10
et al.
12
14
16
Catrler concentration ( lOL9cm? Fig. 1. Seebeck coefficient
as a
concentration increases from 4 X 1019crne3 to 15 X lOI cmw3, as expected from classical behavior. Electrical resistivity p l1 as a function of carrier concentration is plotted in Fig. 2, and it decreases from 17 to 7 $l m-’ as the carrier concentration increases. The behavior of the thermal conductivity vs carrier concentration is displayed in Fig. 3. The values of XL1along the cleavage planes are found to vary between 1.4 and 1.8 W m-’ K-l. Calculated figure of merit values Z” are. shown in Fig. 4. A maximum of 2.6 X 10m3K-’ is reached for the BizTe&e0.45 solid solution for a carrier concentration value equal to 7 X lOI cme3. It should be noticed that the figure of merit values are higher than 2.1 X 10T3 K-’ over the carrier concentration interval.
4
6
8
function of carrier concentration.
4.2. Anisotropy of thermoelectric properties at room temperature The large size of the monocrystals obtained by THM allows us to characterize the thermoelectric properties of massive samples in a parallel direction to the c-axis, indexed 33. The anisotropy is characterized by the ratio between the cr-, X-, p- and Z-values, respectively, measured in a direction parallel and perpendicular to the cleavage planes. The results are summarized in Table 1. We note that the Seebeck coefficient is quite isotropic. Thermal conductivity values corresponding to the parallel direction to the cleavage planes are higher by about a factor of 2 than those measured in the perpendicular direction. We can also see the very strong anisotropy of the electrical resisitivity increasing with the
10
12
14
Carrier concentration (lOI cm”) Fig. 2.
Elect&al resistlvity as a function of carder concentration.
16
Characterization of BizTe;l,S$3e~..u solid solution crystal
15
1.80 -g
1.75 1.70
$ 3,
1.65
;h .::
.2
J a g
1.60 1.55
:!z
1so
g
1.45 1.40 4
6
8 10 12 Carrier concentration (1 019 cme3)
14
16
Fig. 3. Thermal conductivity as a function of carrier concentration.
concentration. These results imply a nonnegligible anisotropy for the figure of merit. These results are in good agreement with the work of Carle et al. [7].
carrier
4.3. Thermoelectric 300K
properties
between 100 and
Experimental values of the figure of merit 2” values
are plotted against temperature for different carrier concentration in Fig. 5. We can see that the figure of merit is maximum at room temperature independent of carrier concentration, as expected. Moreover, the figure of merit values increase when carrier concentration decreases independently of the temperature. On the side of low temperatures, the different curves appear to be linear and
2.7 2.6 _” 2
2.5
*= B 2.4 % $j 2.3 .h r& 2.2 2.1 4
6
8
10
12
14
16
Carrier concentration ( lOr9 cm”) Fig. 4. Figure of merit as a function of carrier concentration. Table 1. Anisotropy of themwelectric properties Annealing
Carrier
temperature
concentration (lOI cm-‘)
CC)
550
15.5
1.1
2.5
5.1
2.5
570
12.3
585
6.8
1.1 1
2.4 2.4
4.5 1.4
2.2 1.4
(*)I 1: perpendicularto the c-axis. 33: parallel to the c-axis.
C. LAHALLE-GRAVIERet al.
16
2.6 1
I.A--
/
v-
/A
l.ooF1
”
”
”
”
”
”
”
”
”
”
- 12.3
‘I
”
50
0
-50
-100
-150
-6.2
loo
Temperature (“C) Fig. 5. Figure-of merit as a function of temperaturefor several carrier concentrations.
parallel. We notice that for the upper curve, values higher than 2 X 10e3 K-’ can be obtained at -100°C. The Seebeck coefficient as a function of temperature is presented in Fig. 6. We note that the relation is roughly linear. We deal with this point in our discussion. Calculated thermal conductivity vs temperature is displayed in Fig. 7. We can see that the influence of the electronic contribution, at low temperature, is more important when the carrier concentration is high. The values of the electrical resistivity obtained during the Harman experiment and the values presented in Fig. 9 obtained by the van der Paw technique are the same. Hall coefficient p t23measurement results are presented in Fig. 8. It is important to note that the Hall coefficient is roughly constant in the temperature range from 100 to
3OOK, that is to say this solid solution is extrinsic up to room temperature. Results of resistivity p” measurements are shown in Fig. 9. The Hall mobility is calculated using p = (p ‘23/(p’I)). The behavior of the Hall mobility as a function of temperature is displayed in Fig. 10. 5. DISCUSSION The entire analysis is based on a parabolic band structure,
in the case of an extrinsic semiconductor. If the relaxation time of the scattering mechanism is a power function of the energy, the Hall mobility and the electrical resistivity can be expressed as a function of the absolute temperature T as p = poT-’ and u = o,J-I’ where p0 and u. are two constants and x and x’ are two exponents which depend
I
Carrier concentration 1o’p cm.’ . ..__ 587
-140
-o---570 - t - 550 585
-160 A. -180 -200 -220 I I
I
”
-150
”
I
”
-100
”
I
-50
”
r
“I”
0
’
I ”
50
“I 100
Temperature (“C) Fig. 6. Seebeck coefficient as a function of temperature for several carrier concentrations.
Characterizationof BizTez.uSea.usolid solution crystal
17
Thermal conductivity as a function of the temperature 3.5 L’I
2.5
-
2.0
-
I I,
I I I I (I
I,,
,,,
I I,,
I I’]
1.5 -
1.0 t1 -150
”
”
”
-100
”
’ I ”
I ”
I ”
-50 0 Temperature (“C)
1’
I ’ J
50
100
Fig. 7. Thermal conductivity as a function of temperature for several carrier concentrations.
on the scattering mechanism. Experimental values of x and X’ are reported in Table 2 for several carrier concentrations of the BizTez.s$ea.4s solid solution. We can see that x and x’ values are the same: that is to say that the carrier concentration is constant in the temperature range studied. x and x’ values decrease as the carrier concentration increases [7-l l] and are below 1.5, the theoretical value in the case of the acoustic phonon scattering mechanism. Deviations from this law can be explained if we take into account the scattering by ionized impurities as an additional mechanism. This scattering mechanism is possible in our material because deviations from stochiometry come from an excess of tellurium.
Nevertheless, we admit in the following that the scattering mechanism is mainly due to acoustical phonons. In this case and if the semiconductor is a nondegenerate extrinsic one in which the carrier concentration and the effective mass are constant in the involved temperature range, the Seebeek coefficient can be expressed by Q = 2 (3k/(2e))ln T 2 C where k is Boltzmann’s constant, e the electron charge and C a constant. So the curves which give the Seebeck coefficient as a function of In T have to be straight with a slope equal to + 129 PV K-l. Experimentally, according to the results presented in Fig. 6, we found values ranging
concentration -m-~-~-Am)_-q--we_-.-.-.-.-_-,-__~-_-._.-.-*.-.-
-150
-100
-50
0
Temperature (“C) Fig. 8. Hall coefficientas a function of temperature..
50
C. LAHALLE-GRAVIRRer al.
Carrier concentration lOI cm.3
15.. -t14. - -W- - 12. 10. - 0 - 9.0 e- 6.7 - . + - - 6.2 ---r---4.5 -
-100
-50
50
0
Temperature (“C) Fig. 9. Electrical resisitivity as a function of temperature, using the Van Der Pauw method.
from -80 to -105 WVK-i for carrier concentrations between 6.3 X 1OL9cm-3 and 15.5 X lOI cme3. The difference between theory and experiment can be explained first by effective mass m* variation with temperature. This variation can be deduced from the evolution of the electrical conductivity C with temperature: u=m
*5l2T
-312
If m* = T”: dln u dln=-j-ZS
3
5
According to Fig. 11, -0.14 5 s 5 -0.07. In this case, the theoretical slope of the curves a(ln2’) is between - 117 and - 123 FV K-’ for the same carrier concentration. The degeneracy of the electron gas can explain the
Carrier concentration lOI cm.3
15.5 14.3 - - v - - 12.3 10.7 - l - -9.0 +- 6.7 -. + - 6.2 -A. - 4.5 -
-200
-150
-100
-50
0
50
Temperature (“Cl Fig. 10. Hall mobility as a function of temperature.
Table 2. Values of the x exponent Annealing temperature. (T, “C) Carrier concentration (lOI cm“) X XI
550
560
570
575
580
585
587
590
15.5
14
12.3
1.1
9
6.8
6.2
4.5
1.08 1.10
1.15 1.15
1.18 1.20
1.20 1.20
1.25 1.25
1.28 1.27
1.28 1.28
1.31 1.30
Characterizationof Bi2Te&eo.4s solid solution crystal
19
I 0.5
‘E!
b t
Carrier concentration lOI cm.3 15.5 14.3 - -v - - 12.3 10.7 - l - -9.0 ----(I- - 6.7 - -+. -6.2 -A. - - 4.5
0.3
0.1
0.08 0.06 70
200
80 90 100
300
Temperature (K) Fig. 11. Electrical conductivity as function of temperature.
difference between experiment and the model. The effect of this degenerescence induces a linear relation between the Seebeck coefficient and the temperature [ 121. This is exactly what we found on Fig. 6. As known, the dimensionless figure of merit ZT is given by the relation [ 131:
with X, the lattice thermal conductivity, B a constant term, A = p(rn*/r~$‘~ and mo the electron mass. From our results, we obtain ZT s T”. According to Fig. 12, which shows the evolution of the parameter A with temperature, for a sample with a carrier concentration equal to 6.2 X 10 I9cm-3, d In A/d
-2.2 -2.4
-2.6
-3.2
In T = 1.3.So the thermal conductivity h, varies with the temperature according to T-O.‘. This law is compared with X,(T) = T-’ in the bismuth telluride compound. We can see that the lattice thermal conductivity has a lesser dependence with temperature in the case of the solid solution. This result explains that, in the case of Bi2Te&e0,4r solid solution, the figure of merit decreases more slowly when the temperature decreases. Finally, the evolution of the thermal conductivity as a function of electrical conductivity is shown in Fig. 13. The oscillations are due to the Lorentz number variations [14]. By this curve, the lattice thermal conductivity value can be estimated. We found it equal to 1.1 W m-’ K- ‘. It is possible to calculate this value
C. LAHALLE-GRAVJER et al.
20
1.00~“““““““““““““” 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Electrical Conductivity (clQ-‘.rn-‘) Fig. 13. Thermal conductivity as a function of electrical conductivity. using
the figure of merit results: z=
thermal conductivity is estimated to be equal to 1.l W m-r K-‘. The figure of merit values comprised between 2 and 2.6 X lo-’ K- ’ for temperature range varying between 100 and 300K. REFERENCES
with
Lahalle-Gravier,C., Scherrer,H. and Schemx, S., J. Phys. k2&12 (kt)“F&)[$-q]’ &?I($= eh3 &r”’ g2(d
k2’D
=
(kT)3’2F0($T
;; Chem. Solids, 1996,57 (ll), 1713-1717.
Caillat, T., Carle, M., Pierrat, P., Scherrer, H. and Scherrer, S., J. Phys. Chem. Solids, 1992.53 (a), 1121-1129. 3. Goudot, A., Schlicklin, P.M. and Stockholm, J.G., Proceedings of the 5th International Conference on Thermoelectric. Energy Conversion, Arlington, 1984.
eR3 4~”
Carle, M., Caillat, T., Lahalle-Gravier, C., Scherrer. H. and x
I
[z-4(z)2]
:: Scherrer, S., J. Phys. C/tern. Solids, 1995,56 (2) 211-215. Harman, T. C., J. Appl. I’hys., 1958,29, 1373.
where h is Plank’s constant, fi = h/Z*, Fi the Fermi integrals, and q the reduced Fermi level. We found the same result.
6. CONCLUSION An analysis of all results obtained allows us to put forward some ideas about the transport properties of the Bi2Te2,s5Se0.~ssolid solution. This material is an extrinsic semidegenerated semiconductor. The scattering mechanism is mainly due to acoustical phonons, but a small influence of ionized impurities is possible. The band structure appears to be similar to the BirTe3 structure, but the effective mass varies with temperature. The lattice
6. Lenoir, B. These JNPL, Nancy, France. I. Carle, M., Pierrat, P., LahaJle-Gravier, C., Scherrer, H. and Scherrer, S., J. Phys. Chem. Solids, 1995,56 (2). 201-209.
8. Kutasov, V.A., Svechnikova, T.E., Chizhevskaya, S.N., Fiz. 9. 10. 11. 12. 13. 14.
Tverd. Tell (Leningrad) 1987,29,3008-3011; Sov. Phys. Solid State. 1987,10, 1724-1730. Abrikosov, N. Kh., Svechnikova, T. E. and Chizhevskaya, S., Izv.Akad nauk. SSSR, Neorg. Mater., 1978,14(1),43-45. Abrikosov, N. Kh., Kutasov, V. A., Luk’yanova, L.N., Svechnikova. T. E. and Chizhevskaya, S. N., Izv. Akad. Nauk. SSSR, Neorg. Mater., 1980.16, 1394. Kutasov, V. A. and Luk’yanova, L. N., Sov. fhys. Solid State, 1978, 20 (lo), 1767-1769. Goldsmid, H.J., Thermoelectric Rejridgeration. Temple, London, 1966. Chasmar, R. P. and Stratton, R. J., J. Electr. Contr., 1959.7 (1) 52-72. Kolomoets, N. V., Fiz. Tverd. Tela (Leningrad), 1966, 8, 999.