Towards high efficiency segmented thermoelectric unicouples

Towards high efficiency segmentedthermoelectric unicouples

Pham Hoang Ngan*,1, Dennis Valbjørn Christensen1, Gerald Jeffrey Snyder2, Le Thanh Hung1,Søren Linderoth1, Ngo Van Nong1, and Nini Pryds1

1 Department of Energy Conversion and Storage, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark2Material Science, California Institute of Technology, Pasadena, CA 91125, USA

Received 19 July 2013, revised 3 October 2013, accepted 16 October 2013Published online 22 November 2013

Keywords segmented thermoelectric generators, segmented thermoelectric unicouples

* Corresponding author: e-mail [email protected], Phone: þ45 467 758 00, Fax: þ45 467 758 58

Segmentation of thermoelectric (TE) materials is a widely usedsolution to improve the efficiency of thermoelectric generatorsover a wide working temperature range. However, theimprovement can only be obtained with appropriate materialselections. In this work, we provide an overview of thetheoretical efficiency of the best performing unicouplesdesigned from segmenting the state-of-the-art TE materials.The efficiencies are evaluated using a 1D numerical modelwhich includes all thermoelectric effects, heat conduction,

Joule effects and temperature dependent material properties,but neglects contact resistance and heat losses. The calculationsare performed for a fixed cold side temperature of 300K anddifferent hot side temperatures of 700, 900, and 1100K. Weconfirm that without taking into account the compatibility of TEmaterials, segmentation can even decrease the total efficiency.Choosing the TE materials carefully, one is, however, rewardedby a significant improvement in the total efficiency.

� 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction A large amount of thermal energyassociated with many industrial and fuel combustionprocesses is available as waste heat. Waste heat recoveryprovides an opportunity to significantly improve the overallenergy efficiency of many industrial processes. Oneapproach for recovering energy from the system is togenerate electrical power through thermoelectric (TE)conversion using thermoelectric materials. Studies onthermoelectric materials have been flourishing recently,resulting in a large variety of materials with figure of meritzT¼a2T/rk (with a, k, and r being the Seebeck coefficient,thermal conductivity and electrical resistivity, respectively)exceeding 1, such as bismuth tellurides [1–3], skutteru-dites [4–6], Zinlt phases [7–12], lead tellurides [13–15],silicon germanium [16, 17], zinc antimony [18], copperselenide [19], Cu–Se derivatives [20–23], (AgSbTe)0.15(GeTe)0.85 (TAGS) [24], AgPbmSbTe2þm (LAST) [25],lanthanum telluride [26], and CuGaTe2 [27]. Together withthe development of high performance TE materials, TEdevice fabrication is also a growing area [28]. To achievehigh thermal-to-electrical energy conversion efficiencies, itis desirable to operate thermoelectric generator devices overlarge temperature spans and to maximize the thermoelectric

performance of the materials. However, no single thermo-electric material possesses a high performance over largetemperature intervals. Therefore, it is necessary to combinedifferent materials, which operate optimally in differenttemperature ranges. This can be achieved by, e.g. cascadedor segmented generators where the p- and n-type legs areformed from different materials joined in series [29–32].

A cascaded system consists of different stages with eachstage comprised of p- and n-type legs made from singlep- and n-type TE materials. The stages have their ownindependent electrical circuit. As a consequence, theoptimum load resistance for each stage can be achievedindividually, however, with the cost of both needing to doseveral load resistance optimizations and suffering fromextra heat losses through the additional wires connectingeach stage. In a segmented system, each p- and n-type leg issubdivided into segments made from different materials.Unlike cascaded systems, segmented systems use only asingle electrical circuit, but here a high figure of merit z is notthe only prime importance. Selecting compatible materialsfor combination is also a critical issue for the optimalperformance. An example of an ineffective segmentation isthe combination of TAGS with SiGe which – despite a high

Phys. Status Solidi A 211, No. 1, 9–17 (2014) / DOI 10.1002/pssa.201330155

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figure of merit of each material - results in a decrease of theoverall efficiency (9.89%) when segmented as compared to anon-segmented leg of TAGS (10.45%) subjected to the sametemperature span. Despite the importance of the materialcompatibility and that the necessary theoretical frameworkhas already been developed [1, 33, 34], so far the com-patibility factors of only these materials have been reported:TAGS, p- and n-type PbTe, SnTe, CeFe4Sb12, CoSb3,La2Te3, p- andn-type SiGe [35]. In this work, we broaden thematerials of consideration, show how to select materials forhigh performing segmented systems and evaluate how efficientthe best segmented TE elements and unicouples are expectedto be. The evaluation of efficiency was carried out using a 1Dnumerical method and the materials used in this study arestate-of-the-art TE materials reported in the literature.

2 Calculation model The efficiency of segmentedand non-segmented TE elements is calculated using the 1Dmodel described in details by Snyder [1]. This method takesinto account all thermoelectric effects (the Peltier, Seebeck,and Thomson effect), heat conduction, Joule heating and thetemperature dependence of the resistivity r(T), thermalconductivity k(T) and Seebeck coefficient a(T). Using thesematerial properties together with the hot (Th) and cold (Tc)side temperatures and the expected heat flux from the heatsource, a large number of properties can be calculated for asingle leg, unicouple or module. These properties include theefficiency, the output power, the optimal load resistance andthe optimal geometry (cross sectional area ratio of p- andn-TE legs and length of the legs).

Here, we use the 1D model to evaluate the efficiency ofsegmented and non-segmented TE elements under theoptimal conditions, i.e. we disregard heat losses, thermal andelectrical contact resistances and only report the efficiencyfor the optimal geometry and load resistance. Thecalculations can therefore be regarded as an upper limitfor the actual efficiency obtainable in experiments. Underthese optimal conditions, the efficiency solely depends onthe hot and cold side temperatures and the selected TEmaterials; the expected flux from the heat source needs not tobe specified. The 1D model seeks to define and use intrinsicvariables that are independent on the system size. Ratherthan using the electrical current (I) as a fundamental variable,the reduced current density u¼ J/k5T is defined as the ratiobetween the current density (J) and the heat flux byconduction. The reduced current density is both independenton the length and cross-sectional area of the leg, and thusmerely a function of the material parameters and thetemperature along the leg. When u is defined at a single point– e.g. at the hot side, u(T¼Th) – the value of u at anytemperature along the leg is fixed by the differential equation

dudT

¼ u2TdadT

þ u3rk; ð1Þ

with an approximate recursive solution given elsewhere [1].Note that the properties in the model (such as u) has a direct

reference to the temperature along the leg rather than aspatial coordinate x, conversion to the spatial coordinate canbe made by calculating the temperature profile T(x). Thedifferential equation is valid for both non-segmented andsegmented legs if – for the latter – the material properties arechanged from one material to another at a certain interfacetemperature (Ti) where the segments meet.

From the reduced current densities evaluated at the coldand hot side temperatures, uc¼ u(T¼Tc) and uh¼ u(T¼Th),the efficiency of a segmented or non-segmented single legcan be found as

hleg ¼ 1� acTc þ 1uc

ahTh þ 1uh

: ð2Þ

The value of uh is a free parameter varied in the model toget the highest efficiency. In practice, uh is varied bychanging the load resistance. When an n-type leg and a p-type leg are connected electrically in series and thermally inparallel to form a unicouple, the efficiency is calculated by

hunicouple ¼ 1�ap;cTc þ 1

up;c� an;cTc � 1

un;c

ap;hTh þ 1up;h

� an;hTh � 1un;h

; ð3Þ

where the subscripts n and p denote the n- and p-type legs.Numerically, both up,h and un,h are optimized simultaneous-ly. Since up,h and un,h are mutually dependent by currentconservation Ip¼Ap Jp¼AnJn¼ In (with Ap and An being thecross-sectional areas of p- and n-type legs), this is done inpractice by optimizing both the load resistance and the arearatio Ap/An (see Ref. [1]).

As the profile of the reduced current density along the leg(u(T)) is fixed by Eq. (1), it will generally differ from theoptimal reduced current density called the compatibilityfactor (s):

sðTÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ zT

p � 1aT

: ð4Þ

For the optimal case where u(T)¼ s(T) at all temper-atures, the maximum efficiency for a single leg (hu¼ s) iscalculated as

hu¼s ¼ 1� exp �Z Th

Tc

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ zT

p � 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ zT

p � 1� 1TdT

� �: ð5Þ

3 Results and discussion3.1 Compatibility factor: proof-of-concept The

features of the calculation model are described in Fig. 1,which consider an example of a segmented leg consisting ofBi0.6Sb1.4Te3, Ba8Au5.3Ge40.7, and MnSi2 that is subjectedto Tc¼ 300K and Th¼ 900K. The interface temperature is524K between Bi0.6Sb1.4Te3 and Ba8Au5.3Ge40.7 and 772Kbetween Ba8Au5.3Ge40.7 and MnSi2. Figure 1a demonstratesan example of the profiles of optimum relative currentdensity usegmented (Eq. (1)) and efficiency hleg (Eq. (2)) along

10 P. H. Ngan et al.: Towards high efficiency segmented thermoelectric unicouples

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the segmented leg. The accumulated efficiency at anytemperature T’ is found from Eq. (2) by replacing Th with T’,a with a (T¼T’) and uh with usegmented (T¼ T’). hleg buildsup along the Bi0.6Sb1.4Te3 and Ba8Au5.3Ge40.7 segments,and starts to decrease from MnSi2 part. Comparing thealmost constant relative current density with the widelyvarying compatibility factors of each segment (see Fig. 1a)reveals that each segment operates far from their individualoptimal conditions even though the whole segmented leg hasbeen optimized for efficiency. The total efficiency of theentire leg is hleg¼ 12.9%. If u were not constrained byEq. (1), its best performing value is the compatibility factor s.This would result in the efficiency hu¼s¼ 18.3%, which isthe maximum obtainable efficiency as calculated fromEq. (5) with the replacement T¼T’. The difference betweenthe actual efficiency and the maximum obtainable efficiencydiverges mainly in Bi0.6Sb1.4Te3 and MnSi2. In particular,the decrease in the overall efficiency by adding the MnSi2segment confirms the importance of choosing compatiblematerials as even replacing the incompatible MnSi2 with apassive material (thermal insulator) will result in a betterperformance. Figure 1b explains in more detail theincompatibility of the three materials. The optimum relativecurrent density for each segment – when working as a singlematerial leg – is 5.7, 4.6, and 1.2V�1 for Bi0.6Sb1.4Te3,Ba8Au5.3Ge40.7 and MnSi2, respectively. Putting them into asegmented leg, with the cold and hot end fixed at 300 and900K, the segmented leg as a whole reaches its highestefficiency at uh¼ 3.01V�1. From the profile of optimizedusegmented along the leg (Fig. 1a), this corresponds to theuh of 2.61, 2.59, and 3.01V�1 for the Bi0.6Sb1.4Te3,Ba8Au5.3Ge40.7, and MnSi2 segments, respectively(highlighted as (1), (2), and (3) in the figure). At thesereduced current densities, the efficiencies are 7.77% for theBi0.6Sb1.4Te3 segment, 6.16% for Ba8Au5.3Ge40.7 and�0.65% for MnSi2. That is, albeit the Bi0.6Sb1.4Te3 andBa8Au5.3Ge40.7 segments are not working at their optimalconditions, they both contribute to a positive efficiency,

while the MnSi2 segment consumes power in order toachieve the required current density in the segment.

3.2 Materials in consideration and their TEefficencies In order to study the possible combinationsof segmented TE couples, the state-of-the-art n- and p-typeTE materials have been considered. Thermal conductivity,Seebeck coefficient and resistivity as functions of tempera-ture were collected from the literature. Note that theseproperties are not shown here. Figure 2 shows thedimensionless figure of merit zT and the compatibilityfactors as functions of temperature for both p- and n-typematerials. It is obvious from Fig. 2a and c, that below 500Kbismuth tellurides (both n- and p-type) are hitherto the bestperforming materials. The majority of the materials such asPbTe, Zn4Sb3, TAGS, skutterudites, Cu2Se, half-Heusleralloys show high zT at a medium-high temperature range of500–1000K. LAST is also a competitive material, with areported zT of 2.2 at 800K [25]. However, this high zTmaterial so far has not yet been reproduced due to thedifficulties in controlling its microstructure [36, 37]. Toavoid a false impression, we do not include this reported datain the present calculation. At the higher temperature range(1000–1200K) the Zinlt (p-type), lanthanum telluride(n-type) and silicon germanium (p- and n-type) are the bestavailable materials (without including some possible hightemperature oxides such as ZnO:Al,Ga [38] andCa3Co4O9 [39]).

Most of the collected materials are compatible with eachother over a large temperature range. Both p-type and n-typebismuth tellurides, however, are not compatible with theother materials at the low temperature region (300–400K)but become more compatible at higher temperatures(Fig. 2b–d).

The optimized efficiencies of the collected materials atdifferent Th¼ 700, 900, and 1100K and Tc at 300K werecalculated using Eq. (2), and the result is presented inTable 1. p- and n-type bismuth tellurides have efficiencies of

Figure 1 (a) Relative current density and accumulated efficiency versus temperature between cold side and hot side for a typical p-typesegmented leg, which is a combination of Bi0.6Sb1.4Te3, Ba8Au5.3Ge40.7, and MnSi2. (b) Efficiency of the segmented leg in thetemperature range 300–900K and of each single segment subjected to the appropriate temperature difference (e.g. 300–524K forBi0.6Sb1.4Te3) as a function of the relative current density at the hot side.

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9.9% (300–525K) and 8.3% (300–580K), respectively. At700K, although PbTe–SrTe and PbTe have comparable zTvalues, the efficiency of PbTe (11.1%) over the workingtemperature range of 300–700K wins that of PbTe–SrTe(9.5%). This is due to the fact that over the entire temperaturerange of 300–700K, the average zT of PbTe (zT ¼ 1.18) ishigher than that of PbTe-SrTe (zT ¼ 0.97). However, PbTe–SrTe has been reported to stand higher temperatures, andachieves the highest efficiency of 15.3% among all theselected materials at the working temperature range of 300–900K. For the n-type materials in this temperature range, thehalf-Heusler alloy (Ti0.5(Zr0.5Hf0.5)0.5NiSn0.998Sb0.002 [40])shows the highest efficiency, 13.8%. Zinlt, SiGe,Si0.78Ge0.22, and La3Te4 can be used at high temperatureof 1100K, where the Carnot efficiency is significantlyincreased, but their calculated efficiency values are justwithin 10–11% resulting from their good performance onlyat high temperatures (>800K). Therefore, if it is not the caseof segmentation one should use, e.g. PbTe–SrTe joined withan insulator to bring down the hot side temperature, andreducing the capital cost of the TE devices.

3.3 Segmented legs Figure 3 demonstrates theefficiencies of non-segmented p- and n-type legs and legswith 2- or 3 segments with different hot side temperatures atTh¼ 700, 900, and 1100K. The listed TE materials given inFig. 2 were paired with the bismuth tellurides to formsegmented TE legs. For 3-segment legs, only the ones withhighest efficiencies are plotted. The gain in efficiencyobtained by segmentation is also illustrated. In general,segmentation of most p-type materials gives a higherefficiency boost than n-type materials. Among n-legs,segmented n-Clathrate leg with hot side at 700K gives asignificant improvement in efficiency of more than 50%compared to the non-segmented n-Clathrate one. PbTe-I,n-HH (half-Heusler), and n-Skutt. (Skutterudite) with theirhigh zT are the three most efficient n-TE legs withefficiencies above 10% at 700K (12% for segmentedn-HH leg at 900K). Among p-type segmented legs,Mo3Sb5.4Te1.6 exhibits the highest increment in efficiency,i.e. from 2.1 to 9.6%. Strikingly, segmentation of PbSrTewith Bi0.6Sb1.4Te3 provides an outstanding efficiency ofover 19%. Yet, a better improved efficiency can also be

Figure 2 zT and compatibility factor s of the collected state-of-the-art p- (a and b) and n- (c and d) types thermoelectric materials. For eachmaterial, the reference is shown in Table 1.



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Figure 3 Efficiency of p- and n-segmented and non-segmented TE legs p2, p3, n2, n3: second and third p- and n-type materials added tomake segmented legs. (Note: for 3-segment legs, “single leg efficiency” is the efficiency of the whole segmented leg.) Abbreviations:p-HH: Hf0.5Zr0.5CoSb0.8Sn0.2; p-Clathrate: Ba8Au5.3Ge40.7; p-Skutt.: NdFe3,5Co0,5Sb12; PbSrTe: PbTe-SrTe; TAGS: (AgSbTe)0.15(GeTe)0.85;p-Zinlt: Yb14Mn0.2Al0.8Sb11; n-HH: Ti0.5(Zr0.5Hf0.5)0.5NiSn0.998Sb0.002; n-Clathrate: Ba8Ga16Ge30; n-Skutt.: Ba0.08La0.05Yb0.04Co4Sb12.

Table 1 Calculated efficiencies of collected TE materials working as non-segmented TE leg at 700, 900, and 1100K. Missing datacorresponds to temperature where the TE material properties are not reported due to material instability or limitations of the measurementequipment.

materials efficiency (%)

Th¼ 700K Th¼ 900K Th¼ 1100K

p-typeBi0.6Sb1.4Te3 [3] – – –

NdFe3.5Co0.5Sb12 [5] 8.9 – –

Hf0.5Zr0.5CoSb0.8Sn0.2 [41] 5.8 8.9Yb14Mn0.2Al0.8Sb11 (Zinlt) [7] 4.5 7.6 10.8Zn4Sb3 [18] 10.4 – –

Cu2Se [19] 6.2 9.8 –

PbTe [13] 11.1 – –

PbTe-SrTe [14] 9.5 15.3 –

MoSb5.4Te1.6 [42] 2.1 4.2 –

YbCd1.6Zn0.4Sb2 [43] 8.3 – –

EuZn2Sb2 [44] 8.1 – –

SiGe [16] 5 7.8 10.4(AgSbTe)0.15(GeTe)0.85 [25] 10.2 – –

Ba8Au5.3Ge40.7 [45] 10 – –

MnSi2 [46] 4.5 6.7 –

n-typeBi2Te3 [4] – – –

Ba0.08La0.05Yb0.04Co4Sb12 [5] 11.1 – –

Ti0.5(Zr0.5Hf0.5)0.5NiSn0.998Sb0.002 [40] 7.7 13.8 –

CoSb3a 6.2 9.6 –

PbTe1�xIx (x¼ 0.0012) [15] 10.1 – –

Si0.78Ge0.22 [17] 5.8 9.5 –

Ba8Ga16Ge30 [47] 3.6 6.7 –

Mg2SiSn [46] 9.4 – –

La3Te4 [26] 4.3 7.2 10.0

aMaterial data is provided by Gerald Jeffrey Snyder, California Institute of Technology, USA.



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Table 2 Efficiency of unicouples at Th¼ 700 (blue), 900 (green), and 1100K (red) made by legs of different p-type legs (rows) and n-typelegs (columns). The legs are made by two segments (Table 2a, upper part) or three segments (Table 2b, lower part) with the segment at thecold side being fixed to be bismuth telluride. The red highlights mark the highest efficiencies.

↓

→

n-Sk

utt.

n-C

lath

rate

CoS

b 3

La3T

e 4

PbTe

SiG

e

n- H

H

Mg 2

SiSn

p-Clathrate 12.7 11.7 11.2 10.8 13.4 11.6 12 12.2

Cu2Se 10.6 10.1 9.4 9.7 11.6 10 10.4 10.6 13.0 12 10.3 11.7 11.7 EuZn2Sb2 12.0 11.1 10.6 10.2 12.7 11 11.4 11.6

p-HH 11.1 9.8 9.8 8.8 11.3 9.8 10.3 10.5 11.7 12.2 9.4 11.9

MoSb5.4Te1.6 10.8 9.2 9.4 8.1 10.8 9.3 9.8 10 10.6 11.5 8.2 11

MnSi2 9.9 9.3 8.9 8.8 10.6 9.2 9.7 9.9 10.7 10.7 10.2 9.6 10.8

PbTe 12.8 11.7 11.2 10.7 13.3 11.6 12 12.3

PbTe-SrTe 12.3 11.6 10.9 10.8 13.1 11.4 11.7 12 15.2 14 13.5 14.8

SiGe 11 9.9 9.7 9.0

11.4 9.9

9.8 10.6 11.7 11.8 9.7 11.9 11 14.2

p-Skutt.

12.8

11.0 11.1 9.6 12.8 11 11.5 11.7

TAGS 13.0 11.8 11.4 10.6 13.5 11.7 12.1 12.3

YbCd0.6Zn0.4Sb2 12.2 11.2 10.7 10.4 12.9 11.1 11.5 11.8

Zinlt 9.8 9.5 8.7 9.3

10.9 9.4

9.8 10 10.9 9.2 11.1 10.6 13.5 12.5

Zn4Sb3 11.9 11.4 10.5 10.9 13 11.2 11.5 11.8

Th = 700 K Th = 900 K Th = 1100 K

↓

↓ → n-Sk

utt.+

SiG

e

n-Sk

utt.

+ C

oSb 3

n-Sk

utt.

+ La

3Te 4

PbTe

+ S

iGe

PbTe

+ C

oSb 3

PbTe

+ La

3Te 4

n-C

lath

rate

+ L

a 3Te

4

n-C

lath

rate

+ S

iGe

n- H

H +

La 3

Te4

n- H

H +

SiG

e

p-Clathrate + Cu2Se 13.6 13.4 13.4 14.9 14.5 14.8 13.2 13.2 13.5 13.7

p-Clathrate + PbTe-SrTe 15.8 15.7 15.6 16.6 16.5 13.7 15 15 15.2 15.6

PbTe-SrTe + Zinlt

16 15.9

11.9 16.8 16.7

16.6 15.2 15.2 15.4 15.8 16.5 14.1 17.7 17.4 16.6 16.6 16.9 16.9

PbTe-SrTe + SiGe

16 15.9

15.7 16.8 16.7

16.6 15.2 15.2 15.4 15.8 17.6 18.2 18.2 16.7 16.2 16.9 16.9 17.7

Cu2Se + SiGe 12

11.8 11.2 13.6

13.0 13.7 12 12 12.2 12.3

14.6 14.7 15.6 15.3 14.3 14.4 14.9 14.9

Cu2Se+ Zinlt 12

11.8 11.9 13.6

13.0 13.7 12 12 12.2 12.3

13.5 14.2 14.9 15.5 14.1 13.8 14.6 14

p-HH + Zinlt 11.7

13.8 11.7 13.3

13.7 12.7 11.7 11.7 12.6 13.1

14.1 13.1 15.5 13.4 13.1 14.1 14.1 15.3

p-HH + SiGe 11.7

13.7 11.7 13.2

13.7 12.6 11.7 11.7 12.5 13.1

13.9 12.6 15.3 12.7 12.6 13.9 13.7 15.3



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obtained by segmentation of three materials of, e.g.Bi0.6Sb1.4Te3 [2] with Ba8Au5.3Ge40.7 [47] and PbSrTe[13]. Remarkably, an efficiency value of over 20% can beobtained for the segmented leg of Bi0.6Sb1.4Te3/PbSrTe withZinlt [45] or SiGe [15] for applications at temperature rangeof 300–1100K, whereas the segmentation of Zinlt or SiGewith Bi0.6Sb1.4Te3 only results in an efficiency of �15%.

3.4 Segmented unicouples The p- and n-typesegmented TE legs were then paired together to make TEunicouples whose efficiencies are calculated by using Eq. (3)and the maximum values are presented in Table 2. The legswere chosen in correspondence with their workingtemperature ranges (300–700, 900, or 1100K). At hot sidetemperatures of 900 and 1100K, besides 2-segment TE legs,only 3-segmented TE legs with the highest efficiencies wereconsidered for unicouples. At Thot¼ 700K, with the samen-leg, the unicouples with Bi0.6Sb1.4Te3þTAGS p-legs givethe highest efficiencies. Similarly, unicouples with Bi2Te3þ PbTe n-segmented legs give the best performance amongthe segmented n-legs. The unicouple paired from segmentedBi0.6Sb1.4Te3þTAGS and Bi2Te3þPbTe legs has theefficiency of 13.5%, which is the top value computed in 300–

700K range. For the same temperature range, the unicouplewith non-segmented p-TAGS leg and n-PbTe leg gives anefficiency of 10.2% (not shown in Table 2), which can beimproved by about 30% by the segmentation of them withBi0.6Sb1.4Te3 and Bi2Te3 to form segmented legs. Increasingthe hot side temperature up to 900K, for most cases,although segmentations of two materials can enhance theperformance of the unicouple, the improvement is generallysmall. One example is: 2-segment unicouple of p-legBi0.6Sb1.4Te3þPbSrTe and n-leg Bi2Te3þ n-Clathratepossesses 15.2% efficiency, while the most efficient3-segment unicouple of (p-leg Bi0.6Sb1.4Te3þ p-Clathrateþ PbSrTe and n-leg Bi2Te3þPbTeþ SiGe) gives 16.8%,that is, only a small enhancement. Increasing the hot sidetemperature up to 1100K, designing unicouples with3-material segments becomes more feasible. For example,the efficiency of 3-segmented unicouple comprised of p-legBi0.6Sb1.4Te3þPbSrTeþ SiGe and n-leg Bi2Te3þ PbTeþSiGe reaches 18.2%, implying an improvement of 28% ascompared to 2-segment unicouple (14.2%) of p-legBi0.6Sb1.4Te3þSiGe and n-leg Bi2Te3þSiGe. The3-segment unicouple with the highest calculated efficiencyis found by segmenting Bi0.6Sb1.4Te3þPbSrTeþSiGe as

Figure 4 Selected segmented unicouples in working temperature ranges 300–700 (a), 900 (b), 1100K (c).



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p-leg and either segmenting Bi2Te3þPbTeþ Si0.78Ge0.22 orBi2Te3þ n-Skutt.þLa3Te4 as n-leg. Bi2Te3þCoSb3 andBi2Te3þ n-Clathrate can offer similar efficiencies forunicouples whose p-legs are the same and n-legs aresegmentations from either one of these two materials withSi0.78Ge0.22 at the uppermost hot side.

Besides the requirement of high efficiency, consider-ation on the practical aspects of material choices is inevitablewhen designing segmented unicouples. The combinationsthat give the highest efficiencies are made frommaterials thatare toxic (such as telluride and lead), expensive (gold andtelluride) or facing the issue of low supply (tellurides) [48].For this reason, other materials that are relatively inexpen-sive (e.g. half-Heusler alloys, silicides) [49] and environ-mental-friendly (e.g. silicides and oxides) [39] are becomingmore and more important despite their lower efficiencies.Figure 4 displays the most promising segmented unicoupleswith possible high efficiencies. From Fig. 4, it is clear thatthere exist many materials combinations resulting in animproved unicouple efficiency of over 10% upon the hot sidetemperature at 700, 900, and 1100K. At Th¼ 700K, theunicouple with segmented p-leg Bi0.6Sb1.4Te3þTAGS andn-leg Bi2Te3þ PbTe yields in the highest efficiency of13.5%. Unicouples built based on segmenting silicides withbismuth tellurides can achieve a calculated efficiency of10.5%. With segmented half-Heusler-based unicouples, thecalculated efficiency is 11.5%. At a hot side temperature of900K, the highest calculated efficiency, 15.3%, belongs tothe segmented unicouple from p-leg Bi0.6Sb1.4Te3þ PbSrTeþZinlt and n-leg Bi2Te3þPbTeþ Si0.78Ge0.22. Increasingthe hot side temperature to 1100K, the efficiency can reachthe highest value of 18.2% for unicouples of p-legBi0.6Sb1.4Te3þPbSrTeþ SiGe and n-leg either of Bi2Te3þ PbTeþSiGe or Bi2Te3þPbTeþLa3Te4.

4 Conclusions The efficiency of different segmentedthermoelectric single legs and unicouples comprising of one,two or three state-of-the-art materials for each leg wascalculated. At Tc¼ 300K and Th¼ 700K, the most efficientunicouple was found to be 13.5% in which the unicoupleswere n-leg Bi2Te3þPbTe and p-leg Bi0.6Sb1,4Te3þTAGS((AgSbTe)0.15(GeTe)0.85). At Tc¼ 300K and Th¼ 900K thep-leg Bi0.6Sb1,4Te3þClathrateþ PbTe-SrTe with n-legBi2Te3þ PbTeþSiGe unicouple has the highest efficiencyof 16.6%. At 1100K, the highest calculated efficiency is18.2% which belonged to p-leg Bi0.6Sb1,4Te3þClathrateþPbTe-SrTeþSiGe and n-leg of either Bi2Te3þ PbTeþSiGe or Bi2Te3þSkutteruditeþLa3Te4 unicouples. Segmen-tation can provide significant improvements in efficiency.However, segmentation may also decrease the efficiency ifincompatible materials are used.

Acknowledgements The authors acknowledge the supportfrom Copenhagen Cleantech Cluster for the research work (in theproject 48062 X-CCC) and the Programme Commisssion onEnergy and Environment (EnMi), which is part of the Danish

Council for Strategic Research (Contract No. 10-093971), forsponsoring the research of the OTE-Power Project.

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Towards high efficiency segmented thermoelectric unicouples