# Fileset

[MDR-On_the_PF_composites.pdf](https://mdr.nims.go.jp/filesets/678a5e4b-807b-4e3a-9a4e-475fea2f67fd/download)

## Creator

A. Riss, F. Garmroudi, M. Parzer, A. Pustogow, [T. Mori](https://orcid.org/0000-0003-2682-1846), E. Bauer

## Rights

© 2024 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Thermoelectric power factor of composites](https://mdr.nims.go.jp/datasets/011b9363-6002-45f1-a645-67d389f334b5)

## Fulltext

On the thermoelectric power factor of compositesA. Riss,1, ∗ F. Garmroudi,1 M. Parzer,1 A. Pustogow,1 T. Mori,2, 3 and E. Bauer11Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria2International Center for Materials Nanoarchitectonics (WPI-MANA),National Institute for Materials Science, Tsukuba 305-0044, Japan3University of Tsukuba, Tsukuba 305-8577, JapanTo improve the performance of thermoelectric (TE) materials, a highly effective and widely im-plemented approach is to create multi-phase composites. These composites are designed to impedephononic heat transport, which accounts for the majority of thermal conductivity in conventional TEsemiconductors. In 1999, Bergman and Fel reported that also the electronic properties, specificallythe power factor, can be significantly enhanced in two-phase composites consisting of a highly-conducting, simple metal and a high-performance thermoelectric arranged in an optimal manner,sparking great experimental interest. In this work, we challenge the theoretical results of Bergmanet al. and the conclusions drawn by them by using a simple and comprehensive model. We showthat, while the improvement of the power factor is indeed extraordinary, the results lead to a mis-leading interpretation of the overall TE performance of the material. As a result, we argue thatthe power factor is not a suitable metric for evaluating multi-phase materials and composites andthat the figure of merit zT should be used instead. Finally, we demonstrate that, nonetheless, thebest TE composite always consists of a highly conductive metal and a high-performance thermoelec-tric in a serial configuration. This study presents an unintuitive yet auspicious approach to designhigh-performance TE composites with a large volume fraction of the metal component.INTRODUCTIONIn times of the steadily increasing energy consumptionand prices, there is an increasing demand to use energymore efficiently. One promising solution are thermoelec-tric (TE) materials, which can convert waste heat to elec-trical energy by making use of the Seebeck effect. Theefficiency of such a material is determined by the dimen-sionless figure of merit zT = (S2σ/λ)T , which is com-posed of the Seebeck coefficient S (voltage per tempera-ture gradient), the electrical conductivity σ and the ther-mal conductivity λ. Single-phase bulk compounds havebeen intensively studied over the past decades, result-ing in very efficient state-of-the-art materials like Bi2Te3[1, 2], PbTe [3–5], SiGe [6, 7], SnSe [8–10], Skutterudites[11–13] or Half-Heusler alloys [14–16] with large figuresof merit. Driven by the requirement to decouple thermaland electrical transport in TE materials, more sophisti-cated strategies have been employed such as the synthesisof nano-wires [17, 18], thin films [19, 20] as well as nano-structured materials and multi-phase composites [21–24].Apart from intrinsic property changes, such as a reduc-tion of the lattice thermal conductivity from increasedphonon scattering at the nano-, micro- and mesoscaledefects and interfaces, a fundamental question arises formulti-phase composites: How and to what extent do theTE properties of the individual materials contribute to-wards the overall properties measured for the composite?In the 1990s Bergman et al. theoretically showedthat a”high-performance thermoelectric“ and a”benignmetal“, i.e. a metal with high electrical and thermal con-ductivity, combined in a favourable spatial configuration,can boost the power factor PF = S2σ but not the figureof merit zT [25, 26], which restricts the potential of com-posites to a high power factor, when neglecting intrinsicproperty changes such as interface effects.In this work, we elucidate the ongoing physics and con-clude from a simplified model why the power factor isseemingly enhanced in such a system, in agreement withthe calculations by Bergman and Fel [26]. Continuingthe analysis of our results, we will show that the powerfactor enhancement is misinterpreted in these cases anddistorts the performance of such composite materials. Ul-timately, it can be shown by simple arguments that thepower factor is not a good quantity and performance in-dicator when measuring a material consisting of at leasttwo phases. This will hopefully shine a new light on theresearch of composites and rise the awareness of the am-bivalent properties. Lastly, we highlight that, againstcommon intuition, a two-phase heterostructure consist-ing of a thermoelectric with high zT and a perfect metalwith high electrical and thermal conductivity is nonethe-less the optimal thermoelectric composite.THERMOELECTRIC PROPERTIES OF ASERIAL THERMOELECTRIC-METALCOMPOSITEBergman et al. calculated the overall thermoelectricproperties of thermoelectric-metal composites for severaldifferent spatial configurations. They found that thepower factor can be improved through either alternat-ing serial slabs or a spherical structure where the metalis coated by the thermoelectric material. The latter is of-ten a good approximation to more realistic structures, asstated by the authors. In this study, we will focus on the2Thermoelectric materialSte, ρte, λteMetalSm, ρm, λmAlte lmTH TI TCa)b)te mFigure 1: a) Schematic sketch of a serial connection of athermoelectric material with the length lte and a metalwith the length lm. Both materials have individualSeebeck coefficients S, electrical resistivities ρ andthermal conductivities λ. The hot temperature at theend of the thermoelectric material, the temperature atthe interface and the cold temperature at the end of themetal are denoted as TH, TI and TC, respectively. b)Sketch of the microstructure for a fictious thermoelectriccomposite material with a serial slab configuration.slab configuration since it is simpler to model and pro-vides more understanding about the origin of the changesin the performance.Figure 1a illustrates the model used to calculate theproperties. It is similar to the one used by Bergman et al.,but with only one interface instead of alternating slabs.When ignoring interface effects, as done in both studies,these two models are equivalent. Figure 1b provides arealistic example for the application of the model in atwo-phase composite material.Power factorFor a better understanding, we will first calculate thetotal power factor of a serial connection of a thermoelec-tric material and an ideal metal with ρm → 0 and there-fore λm → ∞. From the benignity of the metal followsthat the temperature at the interface TI = TC and thewhole temperature drops along the thermoelectric mate-rial. This leads to the thermovoltage UU = Ste (TH − TC) = Ste ∆T . (1)The total Seebeck coefficient St is calculated as St =U/∆T , soSt = Ste . (2)The total resistance is only comprised of the resistance ofthe thermoelectric material due to the ideal conductivityof the metal. Thus, when calculating the resistivity, oneobtainsρt = RteAlte + lm= ρteltelte + lm= ρte δte , (3)with the volume fraction of the thermoelectric materialδte.While the Seebeck coefficient is not affected by themetal, the resistivity decreases due to δte < 1, resultingin an increase of the total power factor:PFt =S2tρt=S2teρte δte= PFte1δte. (4)When examining a more realistic scenario with finiteconductivities, the temperature differences across thethermoelectric material and the metal, ∆Tte = TH − TIand ∆Tm = TI− Tm, can be calculated from the thermalconductance Ci = λiA/li of both materials:∆Tte =CmCte + Cm∆T =lteλmlmλte + lteλm∆T , (5)∆Tm =CteCte + Cm∆T =lmλtelmλte + lteλm∆T . (6)Unlike the previous case, the measured thermovoltagenow has contributions from both the thermoelectric andthe metal and isU = Ste ∆Tte + Sm ∆Tm=Ste lteλm + Sm lmλtelmλte + lteλm∆T .(7)This leads toSt =Ste lteλm + Sm lmλtelmλte + lteλm. (8)The total Seebeck coefficient can be written using amaterial-related quantity ελ, following the notation ofour previous work about the thermoelectric properties ofa film-substrate setup [27]:St =Ste + ελSm1 + ελwith ελ =CteCm=lmλtelteλm. (9)Depending on the ratio between the individual thermalconductances, the total Seebeck coefficient lies betweenthose of the thermoelectric material and the metal.The finite conductivity further leads to a contributionof the metal to the total electrical resistivity. The mea-sured resistance of the setup isRt = Rte +Rm = ρtelteA+ ρmlmA(10)3and thus the electrical resistivity becomesρt = RtAl= ρte(δte +ρmρte(1− δte)), (11)which is a linear function depending on the volume frac-tion of the thermoelectric material. By introducing an-other quantity,εσ =RmRte=lteρmlmρte, (12)Equation 11 can be further simplified toρt = ρteδte(1 + εσ) . (13)Combining Equation 9 and Equation 11 leads to thetotal power factor of the system:PFt =S2tρt=(Ste + ελSm1 + ελ)21ρte(δte + ρmρte(1− δte)) . (14)The total power factor can also be written in terms ofthe individual power factors and the volume fraction ofthe thermoelectric material:PFt(δte) =(√PFte + ελ(δte)√ρmρtesgn(SmSte)√PFm)2δte (1 + ελ(δte))2(1 + εσ(δte))(15)with the δte-dependent notation of the material-relatedquantitiesεϕ(δte) =ϕteϕm(1δte− 1)∣∣∣∣ϕ=λ,σ. (16)A comparison between Equation 15 and the results ofBergman et al. can be observed in the SupplementalMaterial for three selected systems calculated by the au-thors. The remarkable agreement between the modelsvalidates our assumptions and underscores the informa-tive value of the results presented here.The presence of a local maximum in PFt depends onwhether the decrease in thermovoltage caused by themetal is overcompensated by the increase in electricalconductivity. The consequences of an enhanced powerfactor will be discussed later.Figure of meritNext, we will calculate the figure of merit zT , startingfrom an ideal metal.The total thermal conductance Ct can be calculated,in accordance to the electrical conductance, as1Ct=1Cte=lteλteA:=lte + lmλtA(17)and thusλt = λte1δte. (18)The thermal conductivity increases with decreasing vol-ume fraction of the thermoelectric material, similar tothe electrical conductivity (see Equation 3). CombiningEquation 18 and Equation 4 yields the total figure ofmeritzTt =PFtλtT =PFteλteT = zTte . (19)The total thermal conductivity is modified, when thethermal conductivity of the metal is no longer infinite. Itthen becomes1Ct=1Cte+1Cm=lteλteA+lmλmA=lte + lmλtA(20)λt =λteδte (1 + ελ). (21)From that a convenient relation of the total figure ofmerit can by derived:zTt =PFtλtT=(√zTte +√ελεσ sgn(SmSte)√zTm)2(1 + ελ) (1 + εσ).(22)As as example we calculated the thermoelectric powerfactor PFt and the figure of merit zTt for a compositeconsisting of a high-performance thermoelectric material,SnSe, mixed with elemental Ag as well as another ther-moelectric material, PbTe (see Figure 2). The figure ofmerit in composites differs from the power factor in thatthere is never a local maximum when forming a compos-ite, i.e. zTt of the composite always ranges between thevalues obtained for the pristine materials. A striking fea-ture in Figure 2 is that in case of a thermoelectric-metalcomposite the figure of merit remains nearly constanteven at very low volume fractions of the thermoelectricmaterial due to the exceptional electrical and thermalconductivity of the metal. This can be explained by thefact that in a serial configuration most of the temperaturedifference occurs across the thermoelectric material, pre-serving the thermovoltage, while the balance between in-creased electrical and thermal conductivity maintains zT .Deviation from ideal conduction in the metal is the onlyfactor that decreases the overall zTt (see Equation 19).40 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 001234zT t� t e z T t P F tS n S e  -  A gS n S e  -  P b T e11 01 0 0PFt [mW/mK2 ]Figure 2: Total figure of merit zTt (solid lines) andpower factor (dashed lines) of a serial connection ofpolycrystalline SnSe and Ag (red line) and PbTe(orange line) in dependence of the volume fraction δte ofSnSe, calculated from Equation 15 and Equation 22.The values of all materials’ properties were taken fromliterature [4, 10, 28–30].In contrast to that, for a thermoelectric-thermoelectriccomposite both PFt and zTt show a more linear behavioras a function of the volume fraction, revealing the inferi-ority of such systems compared to single thermoelectricmaterials.COMPARISON BETWEEN POWER FACTORAND POWER OUTPUTTo further elucidate the meaning of the power factorof composites, we will compare PFt, zTt and the poweroutput for the three different systems comprised of thearchetypical thermoelectric material Bi2Te3 and elemen-tal Al, as depicted in Figure 3a. These include a purethermoelectric (I), a thermoelectric-metal composite (II)as well as the thermoelectric with reduced length (III).The maximum possible power output for a given giventemperature difference is [32]Pmaxt =PFtA∆T 24l. (23)The total power factor, figure of merit and power out-put are shown in Figure 3b.The Bi2Te3-Al composite (II) outperforms pure Bi2Te3(I) in terms of power factor and power output. Incorpo-rating metal components into the thermoelectric materialimproves the power generated by reducing the total resis-tance while the Seebeck coefficient S is almost unaffected,thereby seemingly decoupling S and σ, two transport                                              a)b)Figure 3: a) Sketch of the three systems compared inthe text with respect to their thermoelectricperformance. I: (I-doped) Bi2Te3, II: Bi2Te3-Alcomposite with δte = 0.1, III: Bi2Te3 with reducedlength similar to system II. b) Power factor, figure ofmerit and maximum power output for all three systems.The power output was calculated using l = 1 cm,A = 1 mm2, T = 300 K and ∆T = 100 K. For the sakeof simplicity, all thermoelectric properties were taken at300 K [2, 28, 29, 31].properties which are usually difficult to enhance simulta-neously [33]. However, a comparison between systems IIand III shows that when comparing both systems at thesame volume fraction of the active TE component, thepower output is higher without the metal despite the factthat the metal-composite has a seemingly much higherpower factor. Thus, the enhancement of the power fac-tor as described by Bergman and Fel and also the presentstudy merely results from a favourable yet nonsensicalcomparison of two materials with different volume frac-tions of the active TE component. We emphasize thatthis illustrates that the power factor is no longer a valid5indicator for TE device performance in composite ma-terials. Since a large PF neither indicates a higher zTnor a higher power output in such composites, the powerfactor becomes a meaningless parameter for evaluatingmaterials. Only in fixed-length setups, if power outputis more critical than efficiency, the use of composites cansignificantly increase power output by reducing the vol-ume fraction of the thermoelectric material and loweringthe resistance.Another potential application for thermoelectric mate-rials with high power factors is the so-called active Peltiercooling, which combines traditional heat conduction withthe Peltier effect to enhance cooling capabilities [34]. Inthis context, a large thermal conductivity and power fac-tor are desired to maximize the effective thermal conduc-tivity λeff:λeff =(λ +PF T 2H2∆T), (24)with the temperature of the hot side TH. Active cool-ing does indeed looks like a promising application whencomposites are compared to conventional materials (seeSupplemental Materials).However, it is important to examine the macroscopicquantity of the actual cooling power, as the high powerfactor can be misleading and give a false impression ofthe performance. A closer look at the cooling power,dQdt= λeffAl∆T =(L+S2T 2H2R∆T)∆T , (25)reveals the inferiority of composites to pure thermo-electrics. Adding a simple metal to the thermoelectricmaterial slightly decreases the thermal conductance andincreases the resistance, thus reducing the cooling power.Conversely, substituting part of the thermoelectric mate-rial with a metal increases the thermal conductance andreduces the resistance, enhancing the cooling power – butthen again, removing the entire metal further increasesthe efficiency.THE BEST COMPOSITEBefore exploring the potential applications of compos-ites, it is important to acknowledge that the formulasused to predict the thermoelectric performance are sub-ject to ideal conditions and may not accurately reflectreal-world scenarios. This is because they do not accountfor the impact of external factors such as contact resis-tances and inter-phase scattering. As a result, the actualperformance may differ from predicted values. On theother hand, more realistic, disordered composites can of-ten be approximated by spherical structures, which showthe same tendency as parallel slabs [26]. Thus, the fol-lowing statements should be valid in many cases.                                                     ThermoelectricmaterialMetalReduction of λFigure 4: Figure of merit zTt of a SnSe-Ag compositefor different reductions of lambda due to increasedscattering on the metallic structures. The reduction wascalculated from a simple δte-dependent relation,λredt = λt/[1 + aδte(1− δte)], with a chosen such thatthe reduction equals 5 %, 10 % and 20 % for δte = 0.5.As we have shown in this work, an enhancement of thethermoelectric properties due to a smart combination ofa high-performance thermoelectric and a simple metalin a serial configuration is not possible without intrinsicproperty changes of the individual materials comprisingthe composite, such as interface effects. When consider-ing the significant impact of these secondary effects onthe properties of real composite materials, and the fre-quent use of composites to improve the figure of merit, itprompts the question of which materials are best suitedfor making composites.As can be seen in Figure 2 the total figure of meritzTt stays almost constant down to a few percent of thevolume fraction of the TE material when a simple metalis used as the second material. This opens a giganticplayground to reduce the lattice thermal conductivity viaincreased boundary scattering, as sketched in Figure 4.Although the reduction of the thermal conductivity isshown for an oversimplified δte relation, it is clearly visi-ble that scattering of phonons with long mean free pathson mesoscale-sized metallic structures will have a pos-itive effect on the performance [23]. Hence, adding anon-soluble and highly conducting metal is a cheap andprofitable strategy to achieve a larger figure of merit.CONCLUSIONWe recalculated the results of Bergman et Fel [26]from a simple model while avoiding any approximations.Our results shed a new light on the origin of the ex-6treme power factor values derived for composites, whichare caused by a drastic reduction of the resistance whilethe thermovoltage only changes moderately. We furtherelucidated the misleading meaning of the power factorin such multi-phase systems by comparing measurablemacroscopic quantities such as the power output to purethermoelectric materials. We strongly advise using therobust and error-resistant figure of merit zT when com-paring the performance of composite systems to single-phase thermoelectric materials. Lastly, we showed that,in theory, the best thermoelectric composite consists of ahigh-zT thermoelectric and a simple metal with maximalthermal and electrical conductivity.ACKNOWLEDGEMENTSFinancial support for the research in this paper wasgranted by the Japan Science and Technology Agency(JST) programs MIRAI, JPMJMI19A1.∗ alexander.riss@tuwien.ac.at[1] L. Yang, Z.-G. Chen, M. Hong, G. Han, and J. Zou,Enhanced thermoelectric performance of nanostructuredbi2te3 through significant phonon scattering, ACS ap-plied materials & interfaces 7, 23694 (2015).[2] I. T. Witting, T. C. Chasapis, F. Ricci, M. Peters, N. A.Heinz, G. Hautier, and G. J. Snyder, The thermoelec-tric properties of bismuth telluride, Advanced ElectronicMaterials 5, 1800904 (2019).[3] J. P. Heremans, V. Jovovic, E. S. Toberer, A. Sara-mat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka,and G. J. Snyder, Enhancement of thermoelectric effi-ciency in pbte by distortion of the electronic density ofstates, Science 321, 554 (2008).[4] Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, and G. J.Snyder, Convergence of electronic bands for high perfor-mance bulk thermoelectrics, Nature 473, 66 (2011).[5] Y. Pei, A. LaLonde, S. Iwanaga, and G. J. Snyder, Highthermoelectric figure of merit in heavy hole dominatedpbte, Energy & Environmental Science 4, 2085 (2011).[6] G. Joshi, H. Lee, Y. Lan, X. Wang, G. Zhu, D. Wang,R. W. Gould, D. C. Cuff, M. Y. Tang, M. S. Dresselhaus,et al., Enhanced thermoelectric figure-of-merit in nanos-tructured p-type silicon germanium bulk alloys, Nano let-ters 8, 4670 (2008).[7] X. Wang, H. Lee, Y. Lan, G. Zhu, G. Joshi, D. Wang,J. Yang, A. Muto, M. Tang, J. Klatsky, et al., Enhancedthermoelectric figure of merit in nanostructured n-typesilicon germanium bulk alloy, Applied Physics Letters 93,193121 (2008).[8] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher,C. Wolverton, V. P. Dravid, and M. G. Kanatzidis, Ul-tralow thermal conductivity and high thermoelectric fig-ure of merit in snse crystals, nature 508, 373 (2014).[9] L.-D. Zhao, C. Chang, G. Tan, and M. G. Kanatzidis,Snse: a remarkable new thermoelectric material, Energy& Environmental Science 9, 3044 (2016).[10] C. Zhou, Y. K. Lee, Y. Yu, S. Byun, Z.-Z. Luo, H. Lee,B. Ge, Y.-L. Lee, X. Chen, J. Y. Lee, et al., Polycrys-talline snse with a thermoelectric figure of merit greaterthan the single crystal, Nature materials 20, 1378 (2021).[11] C. Uher, Skutterudites: Prospective novel thermo-electrics, in Semiconductors and semimetals, Vol. 69 (El-sevier, 2001) pp. 139–253.[12] X. Shi, J. Yang, J. R. Salvador, M. Chi, J. Y. Cho,H. Wang, S. Bai, J. Yang, W. Zhang, and L. Chen,Multiple-filled skutterudites: high thermoelectric figureof merit through separately optimizing electrical andthermal transports, Journal of the American ChemicalSociety 133, 7837 (2011).[13] G. Rogl, A. Grytsiv, K. Yubuta, S. Puchegger, E. Bauer,C. Raju, R. Mallik, and P. Rogl, In-doped multifilled n-type skutterudites with zt= 1.8, Acta Materialia 95, 201(2015).[14] C. Fu, T. Zhu, Y. Liu, H. Xie, and X. Zhao, Band en-gineering of high performance p-type fenbsb based half-heusler thermoelectric materials for figure of merit zt¿ 1,Energy & Environmental Science 8, 216 (2015).[15] C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao, andT. Zhu, Realizing high figure of merit in heavy-band p-type half-heusler thermoelectric materials, Nature com-munications 6, 8144 (2015).[16] W. G. Zeier, J. Schmitt, G. Hautier, U. Aydemir, Z. M.Gibbs, C. Felser, and G. J. Snyder, Engineering half-heusler thermoelectric materials using zintl chemistry,Nature Reviews Materials 1, 1 (2016).[17] A. L. Prieto, M. S. Sander, M. S. Martin-Gonzalez,R. Gronsky, T. Sands, and A. M. Stacy, Electrodepo-sition of ordered bi2te3 nanowire arrays, Journal of theAmerican Chemical Society 123, 7160 (2001).[18] O. Rabina, Y.-M. Lin, and M. S. Dresselhaus, Anoma-lously high thermoelectric figure of merit in bi 1- x sb xnanowires by carrier pocket alignment, Applied PhysicsLetters 79, 81 (2001).[19] R. Venkatasubramanian, E. Siivola, T. Colpitts, andB. O’quinn, Thin-film thermoelectric devices with highroom-temperature figures of merit, Nature 413, 597(2001).[20] B. Hinterleitner, I. Knapp, M. Poneder, Y. Shi,H. Müller, G. Eguchi, C. Eisenmenger-Sittner, M. Stöger-Pollach, Y. Kakefuda, N. Kawamoto, et al., Thermoelec-tric performance of a metastable thin-film heusler alloy,Nature 576, 85 (2019).[21] W. Kim, J. Zide, A. Gossard, D. Klenov, S. Stemmer,A. Shakouri, and A. Majumdar, Thermal conductivityreduction and thermoelectric figure of merit increase byembedding nanoparticles in crystalline semiconductors,Physical review letters 96, 045901 (2006).[22] Z. Xiong, X. Chen, X. Zhao, S. Bai, X. Huang, andL. Chen, Effects of nano-tio2 dispersion on the thermo-electric properties offilled-skutterudite ba0. 22co4sb12,Solid State Sciences 11, 1612 (2009).[23] K. Biswas, J. He, I. D. Blum, C.-I. Wu, T. P. Hogan,D. N. Seidman, V. P. Dravid, and M. G. Kanatzidis,High-performance bulk thermoelectrics with all-scale hi-erarchical architectures, Nature 489, 414 (2012).[24] F. Delorme, P. Diaz-Chao, E. Guilmeau, and F. Giovan-nelli, Thermoelectric properties of ca3co4o9–co3o4 com-posites, Ceramics International 41, 10038 (2015).[25] D. J. Bergman and O. Levy, Thermoelectric propertiesof a composite medium, Journal of Applied Physics 70,mailto:alexander.riss@tuwien.ac.at76821 (1991).[26] D. J. Bergman and L. G. Fel, Enhancement of thermo-electric power factor in composite thermoelectrics, Jour-nal of Applied physics 85, 8205 (1999).[27] A. Riss, M. Stöger, M. Parzer, F. Garmroudi,N. Reumann, B. Hinterleitner, T. Mori, and E. Bauer,Criteria for erroneous substrate contribution to the ther-moelectric performance of thin films, Phys. Rev. Appl.19, 054024 (2023).[28] C. Ho, M. Ackerman, K. Wu, S. Oh, and T. Havill, Ther-mal conductivity of ten selected binary alloy systems,Journal of Physical and Chemical Reference Data 7, 959(1978).[29] C. Y. Ho, M. Ackerman, K. Wu, T. Havill, R. Bogaard,R. Matula, S. Oh, and H. James, Electrical resistivity often selected binary alloy systems, Journal of physical andchemical reference data 12, 183 (1983).[30] C. Ho, R. Bogaard, T. Chi, T. Havill, and H. James,Thermoelectric power of selected metals and binary alloysystems, Thermochimica acta 218, 29 (1993).[31] R. J. Gripshover, J. B. VanZytveld, and J. Bass, Ther-mopower of pure aluminum, Physical Review 163, 598(1967).[32] J. Chen, Z. Yan, and L. Wu, The influence of thomsoneffect on the maximum power output and maximum ef-ficiency of a thermoelectric generator, Journal of appliedphysics 79, 8823 (1996).[33] G. J. Snyder and E. S. Toberer, Complex thermoelectricmaterials, Nature materials 7, 105 (2008).[34] M. Adams, M. Verosky, M. Zebarjadi, and J. Heremans,Active peltier coolers based on correlated and magnon-drag metals, Physical Review Applied 11, 054008 (2019).https://doi.org/10.1103/PhysRevApplied.19.054024https://doi.org/10.1103/PhysRevApplied.19.054024 On the thermoelectric power factor of composites Abstract Introduction Thermoelectric properties of a serial thermoelectric-metal composite Power factor Figure of merit Comparison between power factor and power output The best composite Conclusion Acknowledgements References