Lead telluride alloy thermoelectrics

Lead telluride alloy thermoelectrics The opportunity to use solid-state thermoelectrics for waste heat recovery has reinvigorated the field of thermoelectrics in tackling the challenges of energy sustainability. While thermoelectric generators have decades of proven reliability in space, from the 1960s to the present, terrestrial uses have so far been limited to niche applications on Earth because of a relatively low material efficiency. Lead telluride alloys were some of the first materials investigated and commercialized for generators but their full potential for thermoelectrics has only recently been revealed to be far greater than commonly believed. By reviewing some of the past and present successes of PbTe as a thermoelectric material we identify the issues for achieving maximum performance and successful band structure engineering strategies for further improvements that can be applied to other thermoelectric materials systems. Aaron D. LaLonde, Yanzhong Pei, Heng Wang, and G. Jeffrey Snyder* California Institute of Technology, Materials Science, 1200 East California Boulevard, Pasadena CA 91125, USA *E-mail: [email protected] The basic concept of thermoelectric power generation is rather

decay, the possibility of renewable sources of heat such as energy

simple; when a temperature difference exists across a material

harvesting from body heat2 or waste heat recovery from industry

a proportional voltage is generated between opposing ends

or automobiles has renewed interest in thermoelectrics to target

of the material, which can be connected to a load to provide

energy sustainability3.

electrical power (Fig.

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1a1).

Because the charge carriers are directly

A thermoelectric material’s potential to convert heat into electricity

driven by the flow of heat through the material, thermoelectric

is quantified by the thermoelectric figure of merit, zT. To date, the

generators have a distinct advantage over other heat engines by

widely believed peak zT for single phase PbTe-based material, which

operating without moving parts, thus providing a device that is

has been successfully used for several NASA space missions since the

robust and requires no maintenance. While the heat in a typical

1960s, has been ~0.8. Recent studies including precise compositional

generator is provided by burning a fuel, or through radioactive

control and modern characterization have revealed that maximum zT

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Lead telluride alloy thermoelectrics

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(b)

(c)

Fig. 1 Thermoelectric materials and electric power generators. (a) Schematic of a thermoelectric device consisting of both n- and p-type thermoelectric materials1. (b) President Eisenhower (far left) in the Oval Office of the White House being presented the “world’s first atomic battery” by officials from the Atomic Energy Commission. The radioisotope powered thermoelectric generator (left most object on the desk) is powering a fan next to it9. Image courtesy of the US Department of Energy. (c) A depiction of the Mars Science Lab rover Curiosity showing the thermoelectric power source (right end of the rover) containing PbTe-based materials11. Image courtesy of NASA.

values of ~1.4 are, in fact, intrinsic to this material for both n- and

United States was presented with the “world’s first atomic battery”

p-type materials. Further enhancement of the figure of merit has

in the oval office of the White House7,8 (Fig. 1b9). This radioisotope

been achieved in alloys where zT reaches a value approaching ~1.8

thermoelectric generator (RTG) contained simple alloys of PbTe for

for homogeneous PbTe-PbSe materials. These recent findings from

both the n- and p-type elements. NASA used this design for its first

PbTe-based alloys have shed new light on this classic thermoelectric

RTG powered spacecraft, the Transit 4A, and modified designs and

material and provide encouragement for the further development of

materials based on PbTe in the Apollo missions and the 1975 launch

thermoelectric technologies on Earth.

of the Viking 2 mission to Mars10. With the advent of the Voyager

Many types of PbTe and related compounds, alloys, and composites

missions, NASA switched to Si-Ge alloys which were of more interest

have been studied as thermoelectrics for many years. There are several

to the scientific community following the 1960s. Although the

comprehensive reviews of the older results that can be found in

excitment of the Space Race has subsided, there is new enthusiasm in

reference 4, while recent developments in PbTe based nanostructured

NASA’s forthcoming mission; the Mars Science Laboratory (MSL), which

composites are described in references 5 and 6. The focus of this review

will probe the possibility of life on Mars. Although it has been nearly

is to highlight the potential of PbTe utilizing only small concentrations

35 years, NASA will return to PbTe based alloys as the thermoelectric

of dopants (assuming the bands remain rigid) or alloying that produces

material of choice to provide power to the most sophisticated Mars

only minor perturbations to tune the band structure.

rover to date10 (Fig. 1c11). The early promotion of PbTe in thermoelectric generators was

The history of PbTe During the Cold War and the Space Race of the middle part of the

made by Soviet physicist A. F. Ioffe, reportedly as early as 192812, 20th

century it was with a sense of pride that President Eisenhower of the

and numerous thorough investigations were performed at the Semiconductor Institute in Leningrad. While the Soviets initiated the

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Lead telluride alloy thermoelectrics

lead telluride research, the 3M Corporation was actively pursuing

At the time of the initial interest in PbTe the measurement of the

similar work in the United States. Scientific reports on these materials

electrical resistivity and the Seebeck coefficient could be performed

started appearing in the literature in the early 1950s and 1960s from

accurately in research laboratories throughout the world. On the

both the United States and the Soviet Union12-15, during which time

other hand, the measurement of the thermal conductivity at high

a vast amount of experimental data was gathered on PbTe and similar

temperatures was known to be a very difficult measurement to

alloys for thermoelectric applications.

perform accurately16. It is likely that as a result of this difficulty, Fritts at 3M used a more confidently measured room temperature

Evolution of high temperature thermal conductivity measurements

thermal conductivity value, in combination with the resistivity and

The experimental data that are most frequently acquired to

interest for PbTe thermoelectric materials15. The room temperature

Seebeck measurements, to estimate κ and zT at the temperatures of

characterize the performance of a thermoelectric material are

κL value was treated as a constant (Fig. 2) and combined with the

the Seebeck coefficient (S), the electrical resistivity (ρ), and the

reliable electrical resistivity measurements at various temperatures

total thermal conductivity (κ). These three properties, along with

to determine κE and thus determine a value of κ without actual

temperature (T), constitute the dimensionless thermoelectric figure

measurements of the high temperature thermal conductivity.

of merit,

zT = (S2T)/(ρκ).

The thermal conductivity of a material is

Fritts himself knew that this approach would result in a significant

given by κ = κE + κL, where κE is the electronic component and κL

overestimate of κ and therefore lead to underestimated values

is the lattice component. The electronic component is related to the

of zT. By the time an acceptable high temperature measurement

electrical resistivity and is calculated by the Wiedemann-Franz law,

method, the flash diffusivity technique, became available in the

κE = LT/ρ, where L is the Lorenz number. The lattice component can be

USA in the early 1960s16, the focus of thermoelectric research in

estimated by subtracting the electronic component, calculated using

the United States had shifted away from PbTe. The research in the

the measured electrical resistivity, from the measured total thermal

Soviet Union continued to pursue the understanding of the physics

conductivity.

of PbTe, however, the work did not utilize the newly available flash diffusivity technique17-21. These initial results for the high temperature thermal properties of PbTe, which were more recently used for thermal conductivity calculations22, give values for κ that are up to ~30 % higher than those measured today using the flash diffusivity technique. Despite extensive research comparing results to PbTe, the underestimated figure of merit values by Fritts have subsisted within the field until it was revealed very recently that optimally doped PbTe is, in fact, almost two times better than commonly believed23,24. By using the now commonplace flash thermal diffusivity measurement technique the thermal conductivity of a material can be accurately determined if the specific heat capacity and density are known. Because the largest source of error with this method is the measurement of specific heat capacity, published values measured by drop-calorimetry are likely to be the most accurate. The recent findings shown in Fig. 3 reveal that, in fact, the zT value of the historic n-type PbTe material is ~1.4 for several sample compositions over a temperature range of 150 degrees (700 – 850 K)24. The electronic transport properties (ρ and S) were found to be in excellent agreement with numerous previously reported studies on the same compositions, allowing the increase in zT to be almost entirely attributed to the difference in thermal conductivity determined for the material. These

Fig. 2 Comparison of the thermal conductivity recently reported for PbTe, determined by laser flash diffusivity measurement, and thermal conductivity data reported by Fritts in 1960. The Fritts data is from n-type 0.055 % PbI2 and p-type 1 % Na15. The recently reported data is from n-type PbTe1-xIx (x = 0.0012)24 and p-type NaxPb1-xTe (x=0.01)23. Also shown is the constant κL for both n- and p-type PbTe at high temperatures; a value that Fritts assumed.

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results have revealed the inherent properties of PbTe and provide new motivation to continue research and development of this highly functional thermoelectric material. The low thermal conductivity intrinsic to PbTe may be due to many factors. In the Umklapp dominated phonon scattering regime above 300 K, this can be traced to the low speed of sound due to

Lead telluride alloy thermoelectrics

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(b)

Fig. 3 Overview of zT values for materials reviewed here and those in reference 1, including the n- and p-type values for PbTe reported by Fritts in 1960 for (a) p-type and (b) n-type thermoelectric materials. The n-type PbTe1-xIx (x = 0.0012) and p-type NaxPb1-xTe (x = 0.01)23,24 are shown to have significantly higher zT values than previously believed. Additionally, it can be seen that p-type PbSe (carrier concentration 3 × 1019 by Na doping43) is a very promising alternative to PbTe and that Na doped alloys of PbTe1-xSex (x = 0.15)50 show extraordinary performance.

the harmonic lattice vibrations and the relatively high anharmonicity,

position of the bands is found to be temperature dependent so that

which is quantified by the Grüneisen parameter. Low speed of sound is

the importance of the Σ band to the transport properties increases

generally found in materials with soft bonds from large, heavy atoms,

with temperature12,29,35-37. As the contribution from each band

which also correlates with a high coordination number and Grüneisen

is dependent on both carrier concentration and temperature, it is

parameter. The large Grüneisen parameter may also be due to unusual

intuitive that there will be optimized values that will result in the best

structural features relating to the near ferroelectric instability in PbTe

thermoelectric performance. Correspondingly, it is possible to “tune”

and related materials25-28.

carrier concentration (and the band structure as described below) for higher zT at the desired temperature.

Maximizing PbTe performance via doping optimization

not exist), as well as for the coexistence of both bands as a function

A similar oversight in thermal characterization also exists for

of carrier concentration is shown in Fig. 4b, where it is clear that the

p-type PbTe doped with sodium, significantly contributing to an

performance of the individual bands is optimized in different regions.

underestimated zT value23. The value found recently is nearly double

The early material development performed by Fritts for NASA is

the value of Fritts that is commonly reported, showing p-type

now known to have been too lightly doped15,23,38. It can be seen

PbTe with a maximum zT value of 0.7, (Fig. 3). However, in this

quantitatively in Fig. 4b that at 750 K the carrier concentration in

The zT for each individual band (as if the other valence band did

case, the accurately measured thermal conductivity is only partially

Fritts’ (and similar material from the USA38,39) is only about half of

responsible for the large discrepancy in the figure of merit. Additionally

the optimally required amount for maximizing zT. It can also be seen

contributing to the larger zT value is an improvement of the electronic

in Fig. 4b that if the transport properties were to be the result of the

transport properties, which are attributed to two-band conduction

Σ band alone (no L band) that the zT would have a maximum value of

behavior in heavily doped p-type PbTe. The two-band model has been proposed because of significant deviations of the transport data compared to that expected from a single band

model12,29-34.

only 1.1. However, when the Σ band is supplemented by the light mass carriers of the L band, a maximum zT of ~1.4 can be realized at 750 K (Fig. 3b) as long as it is properly doped (~2 × 1020 cm-3).

As schematically shown in (Fig. 4a), at

lower carrier concentrations the transport properties are dominated

High performance PbTe analogs

by a light mass band (with extrema at the L point of Brillouin zone)

Early studies, particularly from the 1950s to the 1970s have

and as the carrier density increases a heavy effective mass band

surveyed many IV-VI compounds (such as PbTe, PbSe, GeTe, etc.) for

(with extrema along the Σ line of the Brillouin zone) plays a more

thermoelectric applications4, which have similar atomic and electronic

significant role contributing to the carrier transport. Additionally, the

structures. PbTe was considered the best candidate and thus is the

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Lead telluride alloy thermoelectrics

(a)

(b)

Fig. 4 (a) Schematic of energy bands in PbTe and how the bands move as temperature increases. The shaded areas schematically represent the hole population of each band. The orange line indicates the movement of the L band as temperature increases. (b) The calculated zT value as a function of carrier concentration for p-PbTe comparing the result of transport from the L or Σ band alone (as if the other band did not exist). It is seen that when the interaction between the two bands is modeled, "Σ + L", the result is a significant increase of peak zT, which can only be realized at carrier concentrations twice that reported by Fritts.

most studied of the lead salts4,12,13,41. As a result of the growing

partially responsible for the high zT observed. The low lattice thermal

expense of Te there is a renewed interest in materials that do not

conductivity can be attributed to the larger Grüneisen parameter12

contain Te. Among the alternate materials is PbSe, which had been

corresponding to the stronger anharmonic nature of the lattice

thought to have much lower performance compared with PbTe12,20

vibrations25.

due to its lower band gap (actually, only at low temperatures) and

High zT is well known in p-type AgSbTe2 and TAGS (GeTe alloy

the general trend that isostructural compounds composed of lighter

with 15 % AgSbTe2)25,40 and is likely due to the structure, which is

elements have higher κL. However, recent theoretical work and

similar to PbTe, along with the same reasons that make PbTe and PbSe

experimental results have reported that this material may in fact

good thermoelectric materials, although additional factors (e.g., due to

outperform PbTe at high temperatures42, 43.

alloying) are also present.

When PbSe is made p-type by doping with Na it is found that the electronic transport properties can be explained by the same

Band structure engineering by alloying

type of complex band structure as that found in Na-doped PbTe43

Incorporating additional elements into PbTe opens new opportunities

and this leads to substantial zT (Fig. 3). The maximum zT achieved

for tuning the electronic transport properties through band

in samples with hole concentrations of 3 × 1019 cm-3 is near 1.

structure engineering as well as providing a route to κL reductions.

However, a significant contribution from the presence of the heavy

The reduction of lattice thermal conductivity by alloying (such as

hole band and a resulting peak zT > 1.2 is realized in samples having

PbTe1-xSex) due to the scattering of phonons by point defects is

hole concentrations even greater than 1 × 1020 cm-3. In heavily doped

well known and was promoted by A. F. Ioffe well before 195713.

(1 × 1020 cm-3) PbSe samples the large band gap at high temperatures

The substitution of Te with Se reduces κL by ~35 % at 300 K for

inhibits thermally activated minority carriers that degrade charge

x = 0.15, but greater amounts of Se present in the material result in

carrier transport, the bipolar effect, and consequently the zT of these

a detrimental net effect due to the simultaneous reduction of the

samples does not appear to be approaching a maximum value at

carrier mobility caused by scattering of carriers by the additional

850 K.

Se atoms.

While the increase in Seebeck accounts considerably for the zT

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Concurrent to the rather simple effects on κL due to the addition

values observed, the thermal conductivity of PbSe is much lower than

of Se in PbTe, a more complicated impact on the electronic band

expected as compared to PbTe, which has a larger molar mass, and is

structure is also observed, which provides an additional avenue for

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Lead telluride alloy thermoelectrics

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developing high performance thermoelectric materials based on band

proposed to improve thermoelectric performance at low temperature

structure engineering.

by a different means53.

It is straightforward to show that if it can be assumed that carrier

Band convergence by alloying has a distinct advantage over

concentration can be tuned to optimize zT, this optimized zT value

nanowires or superlattices because the high symmetry (e.g., cubic in

depends on the thermoelectric quality factor, B, determined by the

PbTe), and therefore high inherent NV, for each band is maintained

lattice thermal conductivity, κL, and the electronic band structure44-47.

while low dimensional structures break this symmetry. In addition, small concentrations of alloying elements can be used to enable fine,

3/

2 μN M*b –– B ∝ ——v—— κL

(1)

Here, μ is the carrier mobility, κL is the lattice thermal conductivity, and mb

* is

the density-of-states effective mass of a single carrier

precise adjustments in the band energies.

Potential for future band structure engineering

pocket. While μ decreases rapidly with mb*, it is clear that large

The effectiveness of alloying to induce band convergence has only

valley degeneracy (NV) is good for thermoelectric materials. Valley

begun to be fully appreciated in PbTe and a few other systems54,55.

degeneracy arises when multiple bands have the same energy (are

The quality factor can be further developed to encourage other

degenerate) at the band extrema (orbital degeneracy), or when there

strategies for band structure engineering, or even the search for entirely

are multiple degenerate carrier pockets in the Brillouin zone due to the

new thermoelectric materials. Since virtually all good thermoelectric

symmetry of the crystal. High symmetry crystals can have very high

materials have carrier mobility limited by acoustic phonon scattering,

valley degeneracy when the band extrema are located at low symmetry

the deformation potential theory15,56 can be used to show that

points in the Brillouin

zone48.

The known good thermoelectric materials

such as Si1-xGex, Bi2Te3, and CoSb3 have NV of 6 or less. In p-type PbTe the valence band maxima occur at the L point in the Brillouin zone where NV is 4, while the Σ band has an exceptionally large NV of

1212,41,49,50,

which certainly contributes to its good electronic

Nv Cl –— — B ∝ T —— m*I Ξ2 κ L

(2)

where Cl is a combination of elastic constants57 that will be correlated with κL, mI* is the inertial effective mass along the conduction

properties and high zT at high carrier concentration. One can think

direction, and Ξ is the deformation potential coefficient that describes

of valley degeneracy as leading to multiple (NV) pathways for charge

the change in energy of the electronic band with elastic deformation.

carriers to participate in electronic transport without altering the

This formula suggests that low effective masses and low deformation

Seebeck coefficient (determined by the Fermi level).

should be targeted in future band structure engineering58,59. In

One way to increase NV, and therefore zT, is to converge different

addition, it is also desirable to engineer increases in band gap, as long

bands which are not required to be degenerate because of orbital

as it does not include detrimental effects to NV, mI*,or Ξ, as it enables

or Brillouin zone symmetry. Such bands are effectively converged

higher temperature operation without the influence of minority

when their band extrema are within a few kBT of each other (kB is

carriers16,45.

the Boltzmann constant). This concept formed the basis of early

Ultimately, however, band structure engineering will be used to

carrier pocket engineering attempts to increase zT in low dimensional

improve the average zT (or more precisely, device zT1) for higher

thermoelectric materials51.

overall thermoelectric efficiency rather than peak zT, which will lead to

Perhaps the most dramatic demonstration of band structure

somewhat different goals60,61.

engineering to increase NV, to date, has been in p-type PbTe1-xSex alloys where the alloying allows small, controlled manipulation of the

Summary and outlook

band energies. The relative energies of the L and Σ bands in PbTe are

Simple binary lead telluride alloy thermoelectric materials have

temperature dependent and as the temperature increases the band

demonstrated exceptional thermoelectric performances, with an

energies converge to produce a combined valley degeneracy of 16. As

optimized peak zT of ~1.4, far exceeding the values commonly reported

Se is added to PbTe the energy difference between the L and Σ bands

since 1960. Two key aspects for high performance n- and p-type PbTe

increases, raises the temperature at which the band convergence

are the use of modern thermal diffusivity measurements for thermal

occurs, and makes the convergence effect more noticeable as the peak

conductivity characterization and optimal dopant concentration.

zT approaches ~1.8 in bulk PbTe1-xSex. Alloying can also be used to introduce resonant electronic states,

The large Grüneisen parameter and high valley degeneracy in p-type materials contribute to the exceptional zT in PbTe and related IV-VI

such as Tl in PbTe52. Additional electronic states brought by the

semiconductors. These trends, understandable from the perspective

incorporation of resonant impurities to increase NV will increase

of simple semiconductor physics, can help guide other thermoelectric

thermoelectric properties in the same manner as discussed above.

material systems as well as the search for new thermoelectric

Resonant states can also introduce resonant scattering, which is

materials.

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Lead telluride alloy thermoelectrics

Additionally, the concept of band structure engineering to achieve

boundary scattering of phonons is most effective, raising the average

band convergence is demonstrated with the exceptional peak zT

zT60. However, with such strategies, it will be important to consider the

of ~1.8 in PbTe1-xSex alloys. Such a small modification of the band

effect on other parameters that determine the thermoelectric quality

structure through alloying promises to be a fruitful route to tune other

factor to ensure a net increase in the performance of the material.

band parameters as well. Alternatively, the more dramatic changes

Small improvements in sample homogeneity, fine tuning of the doping

brought about by resonant states may provide another mechanism

and alloy concentrations, microstructure and composite control, as

for increasing the number of converged bands and would expand the

well as functionally grading63 could all combine to produce a truly

possibilities for further improvements. A summary of the materials

optimized thermoelectric material.

reviewed in this paper and the corresponding zT values is shown in Fig. 3, as compared to other thermoelectric materials. While alloying has proven successful in reducing lattice thermal

Even though PbTe is one of the oldest and most studied thermoelectric materials for power generation, recent work has demonstrated several new possibilities that can be explored to ensure

conductivity, other methods such as nanostructuring6,62 should lead

a bright future for the further development and use of PbTe-based

to further improvements, particularly at low temperatures where

thermoelectric materials.

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