Materials Transactions, Vol. 46, No. 12 (2005) pp. 2690 to 2693
Special Issue on Growth of Ecomaterials as a Key to Eco-Society II
#2005 The Japan Institute of Metals
Carrier-Concentration-Dependent Transport
and Thermoelectric Properties of PbTe Doped with Sb2 Te3
Pinwen Zhu1;2; * , Yoshio Imai1 , Yukihiro Isoda1 , Yoshikazi Shinohara1 ,
Xiaopeng Jia2 and Guangtian Zou2
1
2
Eco-material Research Center, National Institute for Materials Science, Tsukuba 305-0047, Japan
National Lab of Superhard Materials, Jilin University, Changchun 130012, P. R. China
The conversion of heat to electricity by thermoelectric (TE) devices may play a key role in the future for energy production and utilization.
Lead telluride (PbTe) is one of the best TE materials used for TE generator in the medium temperature. In this report, the transport and TE
properties of PbTe doped with antimony telluride (Sb2 Te3 ), which has been used to optimize the carrier concentration for improved TE
performance, have been studied. The scattering factor is estimated from the temperature-dependent Hall mobility and the results indicate that the
scattering mechanism is changed from an ionized impurity scattering to the interaction between an acoustical and an optical phonon scattering as
carrier concentration decreases and the temperature increases. The thermal conductivities for all the samples exhibit linearly dependence with
reciprocal temperature and the slope increases with the carrier concentration increasing. The effective maximum power Pmax for PbTe samples
increases with an increase of carrier concentration when the temperature gradient is over 400 K and is comparable to the functional gradient
materials with the same carrier concentration. This result indicates that high TE performance has been achieved in PbTe with Sb2 Te3 as dopants.
(Received June 20, 2005; Accepted October 3, 2005; Published December 15, 2005)
Keywords: Lead telluride, Antimony telluride, thermoelectric properties, thermal conductivity
1.
Introduction
Solid-state thermoelectric (TE) devices are generally made
from heavily doped semiconductors and can be used both as
generators that directly convert heat to electricity from a heat
source and refrigeration devices that use electricity to pump
heat from cold side to hot side without any moving parts or
bulk fluids. Lead telluride (PbTe) is one of the best TE
materials used for TE generator in a temperature ranging
between 400 and 800 K.1) Recently, PbTe has been focused as
a constituent material for power supply units using the
exhausted heat of gas combustion in incinerators and other
industrial furnace.2) There are many reports on the purpose of
improving TE performance of PbTe.
The performance of a TE material is usually expressed by
the figure-of-merit, Z, represented by Z ¼ 2 =, where is
the Seebeck coefficient, is the electrical conductivity and is the thermal conductivity.1) It is evident that the high
performance of TE materials can be obtained by maximizing
the Seebeck coefficient and electrical conductivity, while
simultaneously minimizing the thermal conductivity. The
total thermal conductivity depends on two parameters, one
from the carriers e , and the other one from the lattice thermal
vibrations (phonon), ph , (i.e. ¼ e þ ph , where e is
proportional to the carrier concentration.) However, there are
some arguments on how the temperature and carrier
concentration affect the lattice thermal conductivity.
In general, iodine or PbI2 are the ordinary dopants for PbTe
to optimize the carrier concentration. But the lattice thermal
conductivities of PbTe with these dopants are too high to
restrain its application. And thus there are many methods
used to reduce the lattice thermal conductivity of PbTe, such
as those made by hot-pressing or spark plasma sintering
(SPS) technique.3) Although there are many successful
examples to reduce the thermal conductivity in Pb1x Snx Te,
*Corresponding
author, E-mail: [email protected]
a product of PbTe alloyed with SnTe, and (Bi1x Sbx )2 Te3
solutions,4) only few experimental data exist on Pb–SbTe
system. On the other hand, since PbTe is similar to BiTe and
there are many reports on BiTe–SbTe, one could expect that
PbTe–SbTe would also be a good TE material. In our
previous result, high TE performance of PbTe at room
temperature is obtained with Sb2 Te3 as sources of dopants.5)
In this work, the temperature-dependent transport and TE
properties of PbTe doped with Sb2 Te3 have been studied. The
result indicates that the PbTe samples doped with Sb2 Te3
exhibit low thermal conductivity also at high temperature and
high effective maximum power is achieved.
2.
Experimental
The compounds of PbTe and Sb2 Te3 using the elements of
6 N (99.9999% in purity) lead, tellurium and antimony as
sources, were synthesized in evacuated quartz tubes at their
respective melting points for 1 h in a stirring furnace,
respectively. After that, they were mixed with the corresponding stoichiometric ratio and then sealed in an evacuated
quartz tube. The quartz tubes containing the mixtures were
then placed in a stirring furnace and melted at 1250 K for 1 h
followed by cooling with the rate of 98 K/h. The collected
ingots were cut and polished on the surface for the measurement of TE properties.
X-Ray powder diffraction (XRD) measurements with CuK radiation were performed on an X-ray diffractometer
(JDX-3500). The measurement for TE properties, including
electrical resistivity, Seebeck coefficient and thermal conductivity, at room temperature were previously described in
detail.5) The dependences of the electrical resistivity and the
Hall coefficient were obtained using the five-probe method
with a constant magnetic field in the range 0.5 T and an
electrical current 10 mA by a five-probe technique.6) The
carrier concentration was calculated from the Hall coefficient, assuming a single carrier model as a Hall scattering
Carrier-Concentration-Dependent Transport and Thermoelectric Properties of PbTe Doped with Sb2 Te3
2691
Table 1 TE properties of PbTe at room temperature.
Sample
No.
1
2
3
4
Amount of
Sb2 Te3
Seebeck
coefficient
Electrical
resistivity
Carrier
concentration
Hall
mobility
TE power
(Mol%)
/mV K1
/mm
n/m3
H /cm2 V1 s1
2 /WK2 m1
0.55
123:7
11.9
4:19 1024
10:8 102
1:29 103
25
2
2:49 103
2
2:21 103
2
1:57 103
0.8
111:3
0.93
1.02
Fig. 1
104:3
71:3
4.98
4.92
3.23
Powder XRD patterns.
factor of unity. The thermal conductivity was measured by
the laser flash method on a thermal constant analyzer
(Shinku-riko TC-7000). The ingots were cut with a sample
size 4 4 15 mm and polished on the surface for the
effective maximum power (Pmax ) measurement. The details
of setup for the measurement were described in detail
in elsewhere.6) The thermo-electromotive force E0 and
internal resistance Rint for the samples were simultaneously
measured during the Pmax measurement. The samples were
heated with the rate 100 K/h at top end and cooled by ice
water at the bottom side. The Pmax was calculated from the
equation Pmax ¼ E0 2 =4abe , where abe is the mean internal
resistivity.6)
3.
Results and Discussions
The results of X-ray powder diffraction patterns, shown in
Fig. 1, confirm that all the (PbTe)100x (Sb2 Te3 )x samples
with 0:55 6 x 6 1:02 are NaCl-structure and the diffraction
peaks corresponding to the ternary compounds of PbSbx Tey
and Sb2 Te3 are not found. The ternary compounds
Pb2 Sb6 Te11 , PbSb2 Te4 and PbSb4 Te7 can only be formed
at x > 30 under the temperature 860 K according to the phase
diagram of PbTe–Sb2 Te3 .7) Note that, in this study, the mole
percents of Sb2 Te3 do not exceed 1.05 and the cooling rate is
98 K/h. Under these conditions, the ternary compounds
should not be formed. Based on this result, the samples
studied here are single phase PbTe and Sb2 Te3 is the source
of dopant for PbTe.
The TE properties for PbTe doped with different contents
of Sb2 Te3 , which were obtained in our study at room
1:03 10
25
1:16 10
25
2:15 10
Fig. 2
11:7 10
10:9 10
8:98 10
Temperature dependences of the electrical resistivities for PbTe.
temperature, are shown in Table 1. Ingots with the composition Sb2 Te3 of 0.55 mol% show an electrical resistivity of
11:9 106 m and the Seebeck coefficient of 123 mV/K
at room temperature, resulting in a power factor of 12.9 mW/
cmK2 . This value is consistent with that of other candidate
materials like AgPb10 SbTe12 , which has a power factor of
12.3 mW/cmK2 .8) A further enhancement in the power factor
is observed when the contents of Sb2 Te3 increase, with a
room-temperature value of 24.9 mW/cmK2 . This value is
much larger than that of Ag1x Pb10 Sb(Bi)Te12 with a roomtemperature value of 17.0 mW/cmK2 , which is reported the
best TE materials at high temperature so far, This enhancement is achieved mainly through a decrease in resistivity to
4:98 106 m without a noticeable loss in the Seebeck
coefficient. The high TE performance may be expected if the
thermal conductivity for PbTe doped with Sb2 Te3 is
consistent with that of AgPb10 SbTe12 .
From the temperature dependence of electrical resistivity
of PbTe doped with Sb2 Te3 over a wide temperature ranging
from 80 to 800 K (shown in Fig. 2), the resistivity increases
with rising temperature, which is consistent with a typical
degenerate semiconductor. This result indicates that the
dopants Sb2 Te3 have the same characteristic as other dopants
for PbTe. Furthermore, the intrinsic temperature for PbTe
doped with Sb2 Te3 increases with an increase of carrier
concentration. This result indicates that the optimum temperature corresponding to the sample with high-carrier concentration should be raised.
The Hall mobility, H , is calculated from the electrical
conductivity and Hall data. Frequently, the Hall mobility can
be approximated by the formula H ¼ H0 T1:5þr .9) The
2692
P. Zhu et al.
Fig. 3 Hall mobilities of PbTe Vs Temperature.
values of the scattering factor (r) are corresponding to
different carrier scattering mechanism, where r ¼ 0:0, 1:0
and 3.0 are corresponding to the scattering by the acoustical
phonon, the interaction between acoustical and optical
phonon, and ionized impurity scattering, respectively.
Figure 3 shows the temperature dependence of H for PbTe
with different carrier concentrations. The values of r are
estimated from the slope of the H T curve. Hall mobility
shows exponentially decreasing mobility as temperature
increasing. The values of r for PbTe below 200 K change
from 0.33 to 0.58 as the carrier concentration increases.
Above 400 K, the values of r for all samples are nearly
tending to about 1. These results indicate that the carrier
scattering mechanism for PbTe doped with Sb2 Te3 , which is
the same characteristic as that doped with other dopants,
gradually changes from an ionized impurity scattering to the
interaction between an acoustical and an optical phonon
scattering as the temperature increasing. Compared to iodinedoped, the values in r of Sb2 Te3 -doped are appreciably larger
with the same carrier concentration. This result may be due to
the characteristic of Sb2 Te3 as dopant.
The thermal conductivity () is calculated from the data of
thermal diffusivity (), which is measured in this study, and
heat capacity (Cp ), which is from in literature,10) with the
formula ¼ Cp ,11) where is the density. Figure 4 shows
the temperature-dependent thermal conductivity of PbTe
doped with different Sb2 Te3 content. Although the values of
thermal conductivity for PbTe doped with Sb2 Te3 increase
with carrier concentration, the values of thermal conductivities obtained in this study are much smaller than those doped
with other dopants with the same carrier concentration. For
example, the values in for the sample doped with 1.02
mol% Sb2 Te3 (carrier concentration 2:15 1025 m3 ) is 1.7
W/Km at 500 K. Orihashi12) reported that the thermal
conductivity of PbTe doped with PbI2 (carrier concentration
2:15 1025 m3 ) is high to 2.7 W/Km at 500 K. Furthermore, the values in decrease with an increase of temperature and are nearly proportion to reciprocal temperature
which is shown in the top right corner of Fig. 4. This result is
consistent with Wood’s theory1) in which the thermal
conductivity at high temperature is mainly governed by the
Fig. 4
Variation of thermal conductivities of PbTe with temperature.
temperature dependence of the mean-free path decreased as
reciprocal temperature. The slope of T 1 plot increases
with an increase of carrier concentration. This result may be
due to an increase of anharmonic coupling between phonons
causing their mutual scattering with increasing carrier
concentration. The result of thermal conductivities obtained
in this study is abnormal in bulk PbTe samples. The further
analyses are shown as follows which may give a tentative
explanation.
As is mentioned above, the total thermal conductivity
¼ carrier þ ph . Here carrier is expressed by the Wiedemann–Franz law, carrier ¼ LT, with L being the Lorenz
number and T being the absolute temperature scale. Orihashi12) reported that the values of Lorenz number monotonously decrease with temperature increasing and depends on
the scattering parameter r. However, there are some arguments on the temperature dependence of L. The values of L
calculated from the different theories at high temperature are
different. However, at room temperature, the Lorenz number
for PbTe, L ¼ 2:45 108 WK2 is generally accepted to
estimate carrier .12) Based on the calculated results at room
temperature, the thermal conductivity of PbTe doped with
Sb2 Te3 is mainly from the contribution of thermal lattice
vibrations as the carrier concentration is lower than 1025 m3 .
However, the values of carrier dramatically increase with
carrier concentration when carrier concentration is larger
than 1025 m3 . In this case, the thermal conductivity is
mainly from the contribution of carrier and the lattice thermal
conductivity keeps constant, 1 W/Km, which is the lowest
value in bulk PbTe samples and much smaller than that PbTe
doped with other dopants prepared by SPS (2:0 W/Km),3)
with an increase of carrier concentration. The very small
lattice thermal conductivity obtained in this study should be
attributed to the phonons scattered by the impurity atoms.
Compared to other dopants, the impurity atoms and ions
provided by Sb2 Te3 have larger atomic number, which have a
more strong scattering effect on the phonons.
For TE materials as generator, the values of effective
maximum power (Pmax ) with fixed temperature gradient can
directly show the TE properties of this material. The
temperature-gradient dependences of Pmax for PbTe doped
Carrier-Concentration-Dependent Transport and Thermoelectric Properties of PbTe Doped with Sb2 Te3
2693
indicates that PbTe doped with Sb2 Te3 exhibits high TE
properties at not only room temperature but also high
temperature. A further enhancement in Pmax may be expected
in the samples of continuous carrier concentration FGM with
Sb2 Te3 as dopants.
4.
Fig. 5 Power effective maximum of PbTe.
with Sb2 Te3 are shown in Fig. 5. It can be seen that the Pmax
for the sample doped with 0.55 mol% Sb2 Te3 is only 50 W/m
when the temperature gradient is up to 400 K. Although the
figure of merit in this sample is 5:4 104 K1 which is
higher than those doped with PbI2 at room temperature, the
Pmax is not as high as expected. This result of small value in
Pmax may be resulted from the low carrier concentration
(4:2 1024 m3 ). When the temperature gradient is lower
than 350 K, the values in Pmax for the sample doped with
0.8 mol% Sb2 Te3 are larger than the others which is
consistent with the figure of merit obtained at room temperature.5) The values in Pmax for the samples with the content of
Sb2 Te3 exceeded 0.8 mol% are about 90 W/m at the temperature gradient 400 K. Although the values in Pmax for the
samples doped with 1.02 mol% Sb2 Te3 is lower than that
doped with 0.8 mol% below 350 K, it is larger than the latter
when the temperature gradient is over 350 K. In another
word, the ratio of Pmax and temperature gradient increases
with an increase of carrier concentration. This result may be
due to the carrier concentrations difference in these samples.
The carrier concentration of the sample doped with
1.02 mol% Sb2 Te3 is 2:15 1025 m3 , which is two times
higher than that with 0.8 mol% (1:03 1025 m3 ). The
results are consistent with the results of temperature-dependent resistivity that the increase of carrier concentration
induces the optimum temperature of TE materials upward.
It is well known that the functional gradient materials
(FGM), in which the different carrier concentrations are
corresponding to the different optimum temperature, can
maximize the power output of the TE materials if the
temperature gradient supplied for TE materials is fixed. As a
comparison, a continuous carrier FGM, doped with PbI2 , Al
and Zr (shown in elsewhere13)), with carrier concentration
from 7 1024 to 2 1025 m3 and a junctional material with
ne of 1.1 and 2:9 1025 m3 are measured in Pmax (shown in
top left corner of Fig. 5). The values in Pmax for continuous
carrier concentration and juntional materials are about 103
and 86 W/m respectively with the temperature gradient at
400 K. The values in Pmax for the samples doped with Sb2 Te3
are comparable to the junctional material and about 90% of
the continuous carrier concentration FGM. This result
Summary
In summary, the temperature-dependent transport and TE
properties of PbTe doped with Sb2 Te3 have been studied. The
scattering factor is estimated from the temperature-dependent
Hall mobility and the results indicate that the scattering
mechanisms change from an ionized impurity scattering to
the interaction between an acoustical and an optical phonon
scattering as carrier concentration decreases and the temperature increases. The thermal conductivities for all the
samples exhibit linearly dependence with reciprocal temperature and the slope increases with an increase of carrier
concentration. The low thermal conductivities obtained in
this study may be due to the strong scattering effect on the
phonons by Sb2 Te3 which induces low lattice thermal
conductivity. The effective maximum power Pmax for PbTe
samples increases with an increase of carrier concentration
when the temperature gradient is over 400 K and is
comparable to the functional gradient materials with the
same carrier concentration. This result indicates that high TE
performance has been achieved in PbTe with Sb2 Te3 as
dopants. A further enhancement in Pmax may be expected in
the samples of continuous carrier concentration FGM with
Sb2 Te3 as sources of dopants.
Acknowledgments
This work were supported in part by the Japan Society for
the Promotion of Science (JSPS), the NSFC (No. 501710300)
and the International Cooperation Project of the Ministry of
Science and Technology of China (No. 2001CB711201).
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