Letter
pubs.acs.org/NanoLett
Effect of Silicon and Sodium on Thermoelectric Properties of
Thallium-Doped Lead Telluride-Based Materials
Qinyong Zhang,†,‡ Hengzhi Wang,‡ Qian Zhang,‡ Weishu Liu,‡ Bo Yu,‡ Hui Wang,‡ Dezhi Wang,‡
George Ni,§ Gang Chen,§ and Zhifeng Ren*,‡
†
School of Material Science and Engineering, Xihua University, Chengdu, Sichuan 610039, P. R. China
Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, United States
§
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
‡
ABSTRACT: Thallium (Tl)-doped lead telluride
(Tl0.02Pb0.98Te) thermoelectric materials fabricated by ball
milling and hot pressing have decent thermoelectric properties
but weak mechanical strength. Addition of silicon (Si)
nanoparticles strengthened the mechanical property by
reducing the grain size and defect density but resulted in
low electrical conductivity that was not desired for any
thermoelectric materials. Fortunately, doping of sodium (Na)
into the Si added Tl0.02Pb0.98Te brings back the high electrical
conductivity and yields higher figure-of-merit ZT values of ∼1.7 at 770 K. The ZT improvement by Si addition and Na doping in
Tl0.02Pb0.98Te sample is the direct result of concurrent electron and phonon engineering by improving the power factor and
lowering the thermal conductivity, respectively.
KEYWORDS: Thermoelectric materials, lead telluride, mechanical strength, silicon, sodium
degraded significantly to ∼0.9 at 660 K by PbI2 doping.18 In
our previous work on Tl0.02Pb0.98Te by ball milling plus hot
pressing,11 the sample softens above 673 K as well. We report
here, by addition of a smaller amount of Si and doping of Na,
very strong samples of p-type Tl0.02Pb0.98TeSi0.02Na0.02 can be
obtained through ball milling plus hot pressing, with peak ZT of
∼1.7 at 770 K.
Si (99.99%, Alfa Aesar) chunk was first loaded into a ball mill
jar with stainless steel balls and ball milled in a high energy ball
mill SPEX 8000D (SPEX SamplePrep) for 30 h into Si
nanopowder. Then, the obtained Si nanopowder, element Tl
(granules, 99.999%, Alfa Aesar), Pb (granules, 99.99%, Alfa
Aesar), Te (chunks, 99.999%, EZMetals Corp.), and Na2Te
(powder, 99.99%, CERAC Inc.) were weighed according to the
stiochiometry of Tl0.02Pb0.98TeSixNay (x = 0 or 0.02, while y =
0, 0.015, 0.02, and 0.025) and loaded into ball mill jar with balls
for mechanical alloying by SPEX 8000D. The alloyed
nanopowders were then compacted into dense bulk disks of
12.7 mm in diameter in a graphite die through direct current
(dc)-induced hot pressing. An argon gas-filled glovebox was
used in materials handling process to minimize contaminations.
A laser flash system (NETZSCH LFA-457) and a DSC
system (NETZSCH DSC 200-F3) were used to measure the
thermal diffusivity and the specific heat of the disk samples,
respectively. Thermal conductivity was then calculated as the
T
hermoelectric (TE) materials and devices have demonstrated great potentials in solid state cooling and
conversion of heat to electricity.1,2 For TE device, higher
efficiency comes from TE materials’ higher dimensionless
figure-of-merit (ZT), ZT = (S2σ/κ)T, where S and σ are
Seebeck coefficient and electrical conductivity, respectively, κ is
the thermal conductivity (κ = κL + κe), the sum of electron
thermal conductivity κe and lattice thermal conductivity κL, and
T is the absolute temperature. In the past a few years, most
progress has been made on enhancing ZT to above 1 through
decreasing κL via phonon scattering by nanostructures,3−5 while
some advance also been achieved through power factor (S2σ)
improvement.6−9 Our previous work showed that ball milling
plus hot pressing is a simple and scalable method to fabricate
nanostructures with high performance bulk TE materials.10,11
As one of the most studied intermediate temperature TE
materials system, lead telluride (PbTe)-based materials retain
the highest ZT that has ever been obtained in bulk TE
materials. For example, by band engineering,12 resonant states
doping,13 nanostructuring,14 endotaxial precipitating,15 and
quantum nanodots,16 peak ZTs of ∼1.5−1.8 have been reached
in p- and n-type, which shows good potentials in moderate
temperature applications and attract much attention. Most
recently, through combining the effects of resonant doping by
Tl and alloy scattering by S partial substitution of Te, peak ZT
of 1.6 at 700 K was achieved in the Na0.01Tl0.02Pb0.97Te0.92S0.08
sample with higher average ZT.17
However, materials based on PbTe suffer from weak
mechanical strength. With an 8 at. % Si addition in PbTe,
the sample was significantly strengthened, but the ZT was also
© 2012 American Chemical Society
Received: January 18, 2012
Revised: March 17, 2012
Published: April 11, 2012
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product of the thermal diffusivity, specific heat, and volumetric
density that was determined by the Archimedes’ method. A
four-point probe system (ULVAC ZEM-3) was used to
measure the Seebeck coefficient and electrical conductivity of
the bar samples with dimensions of about 2 × 2 × 12 mm3. Hall
measurements were carried out on a Lakeshore system (Hall
Effect System7712A) for thin disk samples of around 0.5 mm in
thickness. The structures of the as-pressed samples were
characterized by X-ray diffraction (XRD Bruker-AXS, G8
GAADS) using Cu radiation (Kα: 1.54 Å), field emission
scanning electron microscopy (SEM, JEOL-6340F), and
transmission electron microscopy (TEM, JEOL-2010F).
Through ball milling and hot pressing, dense
Tl0.02Pb0.98TeSixNay samples (∼97% relative to theoretical
density) with different values of x and y were prepared, and
all were crystallized in rock salt structure evidenced by X-ray
diffraction patterns, shown in Figure 1a. Within the detection
limit of XRD, there is no impurity found.
One interesting phenomena is that after 770 K measurements of Seebeck coefficient and resistivity in ZEM-3 the bar
samples without Si bend like a bow, shown in Figure 1b, which
clearly shows the weak mechanical strength at that temperature.
In our previous TEM work on PbTe-based materials, we found
high density of defects, such as Pb-depleted disks,19 after high
energy ball milling and hot pressing. The bending of the sample
without Si may be due to the high residual stress and strain in
the sample made by high energy ball milling process, which will
be detailed later.
For mechanical strengthening, Si was added in the materials,
inspired by its effects in the PbTe:I material to overcome
brittleness.18 With sufficient Si addition, the sample is strong
enough to experience high temperature measuring, as shown in
the photograph of Figure 1c. However, the electrical
conductivity was degraded significantly. To bring back the
electrical conductivity, we added Na to further dope the Si
added Tl0.02Pb0.98Te samples, as suggested by Singh’s
calculation20 and evidenced by Pei’s experimental results21
that heavy doping would help to improve thermoelectric
properties of PbTe. Recent work by Wang et al. on reducing
the thermal conductivity using TlSbTe 2 addition in
Tl0.02Pb0.98Te also found the decrease of electrical conductivity,
resulting in a lower ZT than the pure Tl0.02Pb0.98Te sample.22
To understand the effects of the addition of Si and doping of
Na in Tl0.02Pb0.98Te samples, extensive microscopy study was
conducted by SEM, TEM, and HRTEM. The main results are
shown in Figure 2. Analyzed by the linear intercept particle
method23 from the SEM image of Tl0.02Pb0.98Te sample
(without Si and Na) shown in Figure 2a, the average grain
size of this sample is ∼7 μm, much bigger than the ball milled
starting nanopowder with particle size less than 50 nm, clearly
indicating significant grain growth happened during hot
pressing as shown in our previous work.11 It is interesting to
note that after a 2 at. % Si addition the grain size dramatically
decreased to ∼200 nm, shown in Figure 2b. Although the
mechanism of refinement by Si addition is not clear now, this
dramatic decrease in grain size, certainly causes much stronger
phonon scattering than that without Si addition, and leads to
the reduction of lattice thermal conductivity. Like our previous
results on PbTe,19 there are Pb-depleted disks, and the strain
caused by it, shown in Figure 2d,f. These features with
dimensions of a few nanometers will also contribute to the
lattice thermal conductivity reduction. By doping Na, the grains
grow to an average of ∼500 nm, shown in Figure 2c.
Figure 1. (a) XRD spectra of various samples: (1) Tl0.02Pb0.98Te, (2)
T l 0 . 0 2 Pb 0 . 9 8 TeSi 0 . 0 2 , (3) Tl 0 . 0 2 Pb 0 . 9 8 TeSi 0 . 0 2 Na 0 . 0 1 5 , (4)
Tl0.02Pb0.98TeSi0.02Na0.02, and (5) Tl0.02Pb0.98TeSi0.02Na0.025, (b) Photograph of the softened sample Tl0.02Pb0.98Te after measurement up to
673 K. (c) Photograph of the strong sample Tl0.02Pb0.98TeSi0.02Na0.02
up to 770 K.
Another interesting structure character discovered by TEM
studies is that the defect density is significantly decreased by
addition of Si. Our previous report on PbTe19 showed that the
sample without Si have many Pb-depleted disks lying in the
⟨001⟩ planes (the inset of Figure 2d shows the plane
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Figure 2. (a) SEM image of sample Tl0.02Pb0.98Te, (b) SEM image of sample Tl0.02Pb0.98TeSi0.02, (c) SEM image of sample Tl0.02Pb0.98TeSi0.02Na0.02,
(d) TEM image of sample Tl0.02Pb0.98Te showing the very high density of Pb-depleted disks (the inset is the FFT of this image), (e) TEM image of
sample Tl0.02Pb0.98TeSi0.02Na0.02 with low density of Pb-depleted disk, with the inset of FFT of this image, and (f) HRTEM of sample
Tl0.02Pb0.98TeSi0.02Na0.02.
orientation) with a volume density of 9 × 1017 cm−3, diameter
of 2−5 nm, and thickness less than 0.5 nm. It is believed that
these defects cause strain and stress near the disks leading to
the sample bending at temperature higher than 673 K. It is
surprising that with Si addition and Na doping the volume
density of the Pb-depleted disks is greatly decreased, as shown
in Figure 2e,f, which is believed to be one of the main reasons
of the much higher mechanical strength in the sample with Si
addition and leads the samples to endure temperature up to
770 K without bending.
The Hall effect measurements show that the carrier
concentration and mobility of Tl0.02Pb0.98Te samples prepared
by ball milling and hot pressing are 2.8 × 1019 cm−3 and 72.7
cm2 V−1 s−1, respectively, which are different from 5.3 × 1019
cm−3 and 50 cm2 V−1 s−1 in the samples prepared by melting
method reported by Heremans,13 primarily due to the different
fabricating processes. After a 2 at. % Si addition, these values
turn into 1.9 × 1019 cm−3 and 44.4 cm2 V−1 s−1, resulting in a
much lower electrical conductivity (further discussed later).
The decreasing of carrier concentration and mobility from Si
addition is consistent with the results reported by Nemov.24 By
doping of 1.5, 2, and 2.5 at. % Na, the carrier concentration
increased to 5.7, 8.9, and 12 × 1019 cm−3, respectively, while the
mobility stayed as 42, 46, and 45.7 cm2 V−1 s−1, respectively.
The room temperature (RT) Seebeck coefficient dependence
on carrier concentration (Pisarenko plot25) of the samples is
illustrated in Figure 3a, compared with the reported Tl13 and
Na21,26−29 doped PbTe samples, as well as the recently
reported PbTeS:Tl and PbTeSe:Tl data.8 When the carrier
concentration is higher than 5 × 1019 cm−3, the deviation of the
reported Na-doped samples from the single parabolic band
(SPB) model30 (solid line in Figure 3a) clearly shows the
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which agrees well with the recent theory prediction included
resonant states effects.17
The temperature dependence of Seebeck coefficient shown
in Figure 3b clearly demonstrate that the sample of the lowest
carrier concentration, Tl0.02Pb0.98TeSi0.02, has the highest
Seebeck coefficient, which may be possibly due to the carrier
scattering from grain boundary and Si impurity. From Figure 2
and the discussions above, the Tl0.02Pb0.98TeSi0.02 sample has
the smallest grain size in the studied samples that would cause
strongest carrier scattering by grain boundaries, resulting in
higher Seebeck coefficient. This also can explain higher Seebeck
coefficient than Tl-doped PbTe/Se/S samples8 and theoretical
prediction17 in the same carrier concentration. In the range of
570−670 K, the Seebeck coefficient of this sample shows
independent relationship with temperature and begins to
decrease with temperature at above 670 K, due to the presence
of thermally excited minor carriers. In the three samples with
Na doping, the sample of moderate Na doping and carrier
concentration, 2 at. % and 8.9 × 1019 cm−3, respectively, has the
highest Seebeck coefficient in the measured temperature, which
may originate from the good alignment of Fermi level with the
energy of the Tl impurity created resonant states, that would
lead to higher Seebeck coefficient enhancement.40,41 At
temperature higher than 570 K, Seebeck coefficient stays
almost the same for samples with 1.5 and 2 at. % Na doping
primarily due to the bipolar effect, leading to lower Seebeck
coefficient than the reference data.
The electrical conductivity and power factor are demonstrated in Figures 4a and 4b, respectively, compared with
reference data (dashed line) from Heremans.13 The 2 at. % Si
added Tl0.02Pb0.98Te sample has electrical conductivity of 18
000 S m−1 at 300 K and 9000 S m−1 at 767 K, respectively,
about half of the reference data, which is due to the low carrier
concentration and high grain boundary scattering of carriers
Figure 3. (a) RT Seebeck coefficient dependence of carrier
concentration (Pisarenko plot). The references are Jaworski,8
Heremans,13 Airapetyant,26 Pei,21 Crocker,27 Alekseeva,28 and
Androulakis.29 The solid line is calculated from single parabolic
band model (SPB) 30 where acoustic scattering is assumed
predominant and m* = 0.36m0 as that adopted by Airapetyant.26 (b)
Seebeck coefficient dependence of temperature of the studied samples;
the dashed line is reference data from Heremans.13
failure of SPB model in PbTe, where there are actually two
nonparabolic valence bands: a “light” one whose band edge lies
at ∼0.3 eV under the bottom of conduction band and another
“heavy” one whose band edge lies at ∼0.2 eV under the “light”
one, as discussed in the reported theory 20,31−33 and
experimental work.26,34−39 When the carrier concentration is
higher than 5 × 1019 cm−3, the Fermi level enters in the second
band, and the “heavy” carrier contributes to higher thermopower, which leads to the deviation from the SPB
model.21,26−29 The Tl-doped PbTe samples, with the help of
distortion of density of states (DOS) caused by resonant states
from Tl, have much higher Seebeck coefficient than that
without resonance enhancement13 at the same carrier
concentration. The research on the Tl effects was extended
to PbTexS1−x and PbTeySe1−y in recent report,8 which yielded a
peak ZT ∼ 1.6 at 700 K, due to the Seebeck enhancement of
resonant states created by Tl, illustrated also in Figure 3a. The
RT Seebeck coefficient of our Tl0.02Pb0.98TeSi0.02Nax (x = 0,
0.015, 0.02, 0.025) samples, shown in Figure 3a, confirms the
resonant states created by Tl at even higher carrier
concentration than that reported by Heremans.13 One more
interesting thing can be observed in Figure 3a is that in the Tldoped samples where resonant states exist in our study and
other reports,8,13 the Seebeck coefficients at RT decreased from
180 to 150 μV K−1 (about a 20%) when carrier concentration
increased from 2 × 1019 cm−3 to 12 × 1019 cm−3, wherease the
decrease is about 50% for the samples without resonant states,
Figure 4. Electrical conductivities (a) and power factor (b) of the
studied samples. The reference data (dashed line) is from Heremans.13
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Figure 5. Thermal diffusivity (a), Cp (b), thermal conductivity (c), and lattice thermal conductivity (d) of the studied samples, with the reference
samples of Tl0.02Pb0.98Te from Heremans,13 PbTe:Na from Pei,21 and PbTe:Si from Sootsman.18
scattering was used to estimate L,44 where the reduced Fermi
energy were deduced from the Seebeck coefficient in SPB
model.30 Despite the roughness in the estimation, the result of
L ∼ 1.52 × 10−8 V2 K−2 at ∼770 K is consistent with the
rigorous calculation based on multiband model having
considered the nonparabolicity of the band,44 quite lower
than the widely used metal values of 2.44 × 10−8 V2 K−2. Also,
the RT Lorenz number ∼1.7 × 10−8 V2 K−2 is about 11% off
the results of Kaidanov,45 who ascribed the reducing factor of
1.65 from full degenerate value to the resonant scattering by Tl
in PbTe. This method of estimation was used to recalculate the
Lorenz number of the PbTe:Si sample.18
From Figure 5d, the lattice thermal conductivity of the
studied samples is well below the reference data. The κL of
Tl0.02Pb0.98TeSi0.02Na0.02 sample at 770 K, 0.54 W m−1 K−1, is
about 27% lower than that of PbTe:Tl sample,13 and 45% lower
than that of PbTe:Na sample,21 which shows big increase of
phonon scattering by the grain boundary and the point defects,
directly from the fine Si particles. The sample without Na
doping, having smallest grain size in this study (shown in
Figure 2b), demonstrates the lowest κL, confirming the size
effects on lattice thermal conductivity reduction. It is interesting
that the κL of our 2 at. % Si added samples from RT to 580 K is
about 40%−22% lower than the PbTeSi0.08 sample fabricated by
melting and quenching method,18 which again suggests an
effective way of κL reduction by ball milling and hot pressing
method.
Because of the quite low lattice thermal conductivity by
greatly increased grain boundary scattering of phonons, the Si
added Na doped samples have much lower total thermal
conductivity, shown in Figure 5c, leading to ZTs higher than
the reference data shown in Figure 6. We achieved peak ZT
value ∼1.7 at 770 K in samples Tl0.02Pb0.98TeSi0.02Na0.02, close
to the most recently reported 1.8 in samples PbSeTe:Na12 and
PbTe:Sr,Na.15
In summary, Si was found to have dramatically increased the
mechanical strength of samples Tl0.02Pb0.98TeSi0.02 made by ball
milling and hot pressing due to probably the dramatically
decreased defect density of Pb-depleted disks and much smaller
grains of ∼200 nm, but also much lower electrical conductivity
caused by Si nanoparticles. To make up the loss of electrical
conductivity by Si, Na as an effective p-type dopant in PbX (X
= Te, Se, and S)12,15,21,42,43 was doped into Tl0.02Pb0.98TeSi0.02
samples. The results indicate that, first, the electrical
conductivity is greatly improved and is even higher than the
reference data when enough Na is used. Second, higher
concentration of Na leads to higher electrical conductivity. The
2 at. % Na-doped Tl0.02Pb0.98TeSi0.02 sample has electrical
conductivity of 18 000 S m−1 at 770 K, a little bit higher than
that of reference data. This improvement of electrical
conductivity is due to the increased carrier concentration by
Na doping.
The power factors of the measured samples, calculated from
S2σ, are shown in Figure 4b. It can be seen that the
Tl0.02Pb0.98TeSi0.02 sample has the lowest power factor due to
the lowest electrical conductivity, but Na doping increased the
power factors significantly. The power factors are even higher
than the reference data at temperatures lower than 525 K
though lower than the reference data at temperatures higher
than 525 K. The highest power factor at 770 K, 16.3 μW
cm−1 K−2, of Tl0.02Pb0.98TeSi0.02Na0.02 sample is about ∼13%
lower than that of the reference sample.13
The total thermal conductivity was calculated using κ =
ρDCp, where ρ is the volumetric density, D the diffusivity
(Figure 5a), and Cp the specific heat (Figure 5b). In calculating
κ, the Cp values of 2 at. % Na-doped sample were used for all
Na-doped samples in a conservative way. The total (Figure 5c)
and lattice thermal conductivity (Figure 5d) of our studied
samples are plotted together with the Si added PbTe samples,18
the only data we can find in the literature of Si added PbTe, as
reference as well as that of samples PbTe:Na21 and PbTe:Tl.13
The lattice thermal conductivity is calculated by subtracting the
electronic contribution from the total thermal conductivity (κL
= κ − κe = κ − LσT, where L is the Lorenz number). Because
the difficulty of accurate determination of Lorenz number due
to the complex band structure and nonparabolicity of the light
hole band, especially when presented with Tl created resonant
states which has strong impact on the carrier transport, an
assumption of one parabolic band, predominant acoustic
scattering of phonons, and elastic mechanism of carriers
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Figure 6. Dimensionless figure-of-merit (ZT) dependence of temperature of the studied samples.
for lower ZTs. However, a small amount of Na doping for
samples Tl0.02Pb0.98TeSi0.02Na0.02 brings back the high electrical
conductivity while keeping the enhanced Seebeck coefficient by
Tl created resonant states and also produces low thermal
conductivity, with the lowest lattice thermal conductivity of
∼0.54 W m−1 K−1 at 770 K. The highest ZT value reaches ∼1.7
at 770 K in mechanically strong samples
Tl0.02Pb0.98TeSi0.02Na0.02 involving resonant doping, nanograins,
and high carrier concentration.
■
■
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
This work is funded by the “Solid State Solar-Thermal Energy
Conversion Center (S3TEC)”, an Energy Frontier Research
Center funded by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Science, under Award DESC0001299/DE-FG02-09ER46577 (G.C. and Z.F.R.).
■
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