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Conductivity-limiting bipolar thermal conductivity in semiconductors

Scientific Reports volume 5, Article number: 10136 (2015) | Download Citation


Intriguing experimental results raised the question about the fundamental mechanisms governing the electron-hole coupling induced bipolar thermal conduction in semiconductors. Our combined theoretical analysis and experimental measurements show that in semiconductors bipolar thermal transport is in general a “conductivity-limiting” phenomenon, and it is thus controlled by the carrier mobility ratio and by the minority carrier partial electrical conductivity for the intrinsic and extrinsic cases, respectively. Our numerical method quantifies the role of electronic band structure and carrier scattering mechanisms. We have successfully demonstrated bipolar thermal conductivity reduction in doped semiconductors via electronic band structure modulation and/or preferential minority carrier scatterings. We expect this study to be beneficial to the current interests in optimizing thermoelectric properties of narrow gap semiconductors.


Thermal conduction in solids is one of the most fundamental physical processes. It reveals the nature of lattice dynamics as well as phonon scattering mechanisms. Thermal conductivity of solids also influences many technologically important topics including thermal insulation and management of energy storage and conversion systems, microelectronics, data storage devices; efficiency of thermoelectric materials; and stability of sensors and actuators. For semiconductors the low temperature thermal conductivity is not substantially distinct from those of insulators; at elevated temperatures, however, it becomes interesting and yet intriguing due to the vital roles of charge carriers and their interactions. A signature of electron-hole coupling in semiconductors is the bipolar thermal conduction at elevated temperatures, when the calculated lattice thermal conductivity (κ-Τ, where κ is the total thermal conductivity, L the Lorenz number, σ the electrical conductivity, and T the absolute temperature) is significantly higher than the T1 temperature dependence expected for phonon-phonon interaction dominated thermal conductivity1,2,3,4,5,6,7. Similar effect has also been found in semimetals8,9,10. For intrinsic semiconductors, it is well recognized that the mobility ratio between electrons and holes () determines the bipolar thermal conductivity (κb), which maximizes when b = 111,12. Consequently, κb is insignificant for InSb, primarily due to its very large mobility ratio (b > 100)13. In the case of heavily doped semiconductors, the mobility ratio however is no longer a valid guide for understanding or predicting κb, due to the substantially different majority and minority carrier concentrations. For example, recent experiments showed significant κb in p-type heavily-doped skutterudites despite of the mobility ratio between two carriers being greater than 10 (hole mobility ~1–5 cm2/V-s with a concentration of ~1021 cm−3 and electron mobility ~30–50 cm2/V-s with a concentration of ~1018–1019 cm−3 at 800 K, according to our numerical analyses which are presented below)14,15,16,17,18, while the n-type skutterudites do not show appreciable κb, consistent with the rather small b value (~1/50)19,20,21,22,23,24,25,26,27,28,29. Similar observations have been reported for many other semiconductors30,31,32,33,34,35,36,37,38,39. These intriguing results necessitate comprehensive understanding of κb in semiconductors. A recent report attempted to model κb in doped Bi2(Te0.85Se0.15)3 crystals but was unable to capture the specific roles of electronic band structure and carrier scattering mechanisms on κb35.

In this study we report a combined experimental and computational effort that focused on unraveling the general behavior of κb in semiconductors. A numerical method for modeling the temperature dependence of κb for intrinsic as well as extrinsic (heavily doped) semiconductors encompassing a wide range of band gap and electronic band structure has been developed. We find that κb in semiconductors is in general “conductivity-limiting”. In analogous to the bipolar ionic conduction and multiple-step diffusion processes, in which the overall kinetics are determined (limited) by the lower rate species or processes, the bipolar thermal conduction is limited by the charge carrier with lower partial electrical conductivity40,41. Therefore, it is determined by the minority carrier partial electrical conductivity and by the mobility ratio (“mobility-limiting”) in extrinsic and intrinsic semiconductors, respectively. In order to validate these findings, we experimentally demonstrated κb reduction based on electronic band structure modulation and preferential minority carrier scattering. These results largely broaden our understanding of thermal conduction in semiconductors as well as offer insights for optimizing thermoelectric properties of narrow gap semiconductors.

Results and Discussion

Bipolar thermal conductivity in semiconductors can be expressed as1,2,3,4

where σi and αi (subscript i = n, p) are the partial electrical conductivity and Seebeck coefficient for electrons and holes, respectively. For a single parabolic band, the Seebeck coefficient of each carrier can be written as42

where kB is the Boltzmann constant, e the free electron charge, ξ the reduce Fermi energy, λ the carrier scattering parameter, Fx the Fermi integral of the order of x. Therefore , where Eg is the band gap4. For acoustic phonon scattering (λ  = −1/2), the term can be written as which is associated with the total energy carried by electron-hole pairs (band gap energy and kinetic energies). The electrical conductivity of each carrier is

where i=n, p designates the carrier concentrations of electron and hole, respectively.

“Conductivity-Limiting” Bipolar Thermal Conductivity

To elucidate the bipolar thermal conduction behavior in semiconductors, we may rearrange Eq. (1) into (assuming acoustic phonon scattering λ = −1/2, which is valid for most thermoelectric materials)

For a given material at a fixed T, the variation of as a function of ξp or ξn is rather negligible, while the carrier concentrations and the partial electrical conductivity σi (right side of Eq. (4)) could change by several orders of magnitude because of the activation behavior of the charge carriers. Here and are the reduced kinetic energies of holes () and electrons (), respectively, which only slightly change their numerical values when varying the Fermi level43. To verify these analyses, numerical data for p-type skutterudites (RxFe3NiSb12) with Eg = 0.2 eV, mp* = 5 m0, mn* = 2 m0, at 800 K are plotted in fig. 1, where mp*, mn*, and m0 are the effective mass of holes, effective mass of electrons, and free electron mass, respectively. The details of the calculations will be discussed below. As shown in fig. 1(a), with increasing ξp from –1 (weakly-degenerate) to 2 (degenerate), only increases from 4.2 to 5.3, ~25% increases; whereas p increases by a factor of ~10 and the minority carrier partial conductivity σn decreases by a factor of ~20. These suggest that for semiconductors in general, Eq. (1) or (4) can be approximated as , therefore κb in semiconductors is actually “conductivity-limiting”, analogous to the rate-limiting phenomena in kinetic diffusion processes41. For intrinsic semiconductors, since n = p, Eq. (4) can be further approximated to be , consistent with the large body of literature already developed. In the case of extrinsic semiconductors (np or pn) κb is primarily determined by the partial electrical conductivity of the minority carriers, not by the mobility ratio. A linear dependence of κb vs. σn at 800 K for p-type doped skutterudites, as shown in fig. 1(b), further substantiates our proposed “conductivity-limiting” concept for bipolar thermal conduction in semiconductors.

Figure 1
Figure 1

(a) Numerically calculated total reduced kinetic energy for holes and electrons, hole (majority carrier) concentration, and electron (minority carrier) partial electrical conductivity as a function of the reduced Fermi level (ξp); (b) calculated κb as a function of minority carrier partial electrical conductivity σn. The dashed line is a guide for eye. The calculations were carried out for p-type skutterudites (RxFe3NiSb12) with Eg = 0.2 eV, mp* = 5m0, mn* = 2m0, at 800 K.

Numerical Modeling

Data presented in fig. 1 were calculated by our numerical method for modeling the temperature dependence of κb in semiconductors. Our numerical method aimed at discerning the underlying physics that controls κb, including the electronic band structure features and carrier scattering mechanisms. We use the experimental carrier concentration values as those of the majority carriers. Based on the majority carrier concentration and Seebeck coefficient at room temperature, and the maximum Seebeck coefficient value at elevated temperatures, we can determine the Fermi level, the majority carrier effective mass and Eg44,45. The minority carrier effective mass is used as an adjustable parameter. The majority and minority carrier concentrations and their temperature dependences are calculated based on semiconductor statistics46. In order to obtain the T dependence of mobility, we first modeled its carrier concentration dependence at room temperature. We then assumed that the carriers are predominantly scattered by the acoustic phonons, therefore and . For example, the room temperature carrier mobility of n-type and p-type 3d transition metal-based skutterudite antimonides Rx(Fe,Co,Ni)4Sb12 as a function of carrier concentration is shown in fig. 2, where R represents fillers and x the filling fraction. The data were taken from the literatures14,15,16,17,18,19,20,21,22,23,24,25,26,27,47,48,49,50,51,52,53,54,55,56,57,58,59 and were well represented by an empirical expression (the solid lines in fig. 2)60

Figure 2
Figure 2

Room temperature carrier mobility as a function of carrier concentration for (a) p-type and (b) n-type Rx(Fe,Co,Ni)4Sb12 skutterudites. The solid lines are least squares fits to the data using Eq. (5). Data used here are taken from Refs. 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 and 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59.

where iRef is the reference carrier concentration, approximately where degeneracy sets in, a is a fitting parameter, and and are the minimum and maximum possible mobility, respectively. In general, the carrier concentration dependence of mobility for all semiconductors studied in this work can be well accounted by this phenomenological formula and the fitting parameters are summarized in the Table S1 (Supporting Information, SI).

Based on Eqs. (1)–(3) and (5) and the aforementioned method, we were able to numerically fit the temperature dependence of κb in intrinsic and extrinsic semiconductors with a large variation of band gap, the Fermi level, and effective mass values. Figure 3(a) shows the excellent agreement between the experimental data (symbols) for intrinsic Si single crystal7 and degenerate polycrystalline skutterudite Yb0.7Fe3NiSb12 in a wide temperature range. Figure 3(b) shows the calculated () and experimental () values of κb for a variety of materials at various temperatures, including (Bi,Sb)2(Te,Se)337,61, skutterudites, Si, and Ge6,7. The dashed line in fig. 3(b) represents . These results suggest that our method well accounts for the temperature dependence of κb in semiconductors (all relevant parameters used in our calculations are summarized in Table S2, SI). Since κb is determined by the minority carrier partial electrical conductivity in doped semiconductors, the minority carrier effective mass and its mobility, as well as Eg will have strong influence. The extent to which these parameters affect κb is illustrated in Fig. S1 (SI). This also suggests that κb modification can be achieved by manipulating these parameters.

Figure 3
Figure 3

(a) Experimental (symbols) and fitted (solid lines) bipolar thermal conductivity of intrinsic Si single crystal and degenerate Yb0.7Fe3NiSb12 vs. T. (b) Experimental (κbExp) and calculated (κbCal) bipolar thermal conductivity for intrinsic Si and Ge single crystals, and degenerate Bi2Te3-based zone melted (ZM) compounds and p-type skutterudites at various temperatures. The dashed line represents κbCal=κbExp.

Bipolar Thermal Conductivity Reduction

In order to examine the validity of the minority carrier dominated bipolar thermal conduction in heavily doped semiconductors, and to utilize the concept of modifying κb presented, we investigated ways of κb reduction motivated by the recent quest for high efficiency thermoelectric materials that necessitate low thermal conductivity62,63,64,65. It is well known that in filled skutterudites66, the triple degenerate conduction band minimum (CBM) is primarily composed of d-orbitals from the transition metals (TMs), with some contribution from Sb p-states (p-d hybridization). Thus the density of states (DOS) at the CBM can be effectively adjusted by varying the TMs. Our first principles calculations reveal that in the p-type Ba-filled skutterudites, DOS at the CBM decreases significantly with decreasing Fe/Co ratio on the TM sites from 2:2 to 1:3, as shown in fig. 4(a), mainly due to the higher energy and thus more contribution of 3d orbitals of Fe as compared with those of Co. The distinct DOS of minority carrier band further suggests that κb for p-type Ba0.5Co3FeSb12 should be smaller than BaCo2Fe2Sb12 due to the minority carrier partial conductivity reduction. Data for 800 K κb vs. the majority carrier (hole) concentration for a series of BaxCo3FeSb12 and BayCo2Fe2Sb12 samples are plotted in fig. 4(b), and the lines represent fitting to the data using the minority carrier effective masses and , respectively. This electronic band modulation induced κb reduction substantiates the dominant role of the minority carriers. Because of the commonly triple-degenerate and 3d-orbital-dominated nature of the CBM, the minority carrier effective masses of the p-type skutterudites are usually much higher than those of the n-type, in which the minority carrier band is mainly composed of single-degenerate Sb p-orbital-featured light bands67. Therefore, the predominant underlying reason for large differences in κb between the n- and p-type skutterudites is actually due to the effective mass differences between the corresponding conduction and valence (minority) bands.

Figure 4
Figure 4

(a) The density of states around the CBM for BaCo2Fe2Sb12 and BaCo3FeSb12. (b) Bipolar thermal conductivity at 800 K as a function of hole (majority carrier) concentration for BaxCo2Fe2Sb12 and BayCo3FeSb12. The lines in (b) are fits to the data using different minority carrier effective mass values.

Our second example of κb reduction takes the advantage of preferential scattering of the minority carriers. Normally in heavily doped semiconductors, the minority carriers are non-degenerate. Given the electronic band structure of a material and the Fermi level (determined by the majority carrier concentration), one can calculate the range of minority carrier wavelength46. For example, the electron wavelength in a heavily-doped p-type Bi2Te3 (p = 3.5 × 1019 cm−3) is approximately between 10 nm and 50 nm, as shown in fig. 5(a). We compare κb of p-type zone melted (ZM) and nanostructured (Nano) Bi0.5Sb1.5Te3 prepared by the melt spinning combined with subsequent spark plasma sintering (MS-SPS) technique61. Figure 5(b) shows, at comparable majority carrier concentrations between the ZM and Nano samples, a significant κb reduction is achieved when nanoprecipitates are introduced into the sample. The minority carrier partial electrical conductivity is determined by Eg, minority effective mass and mobility. The estimated small Eg variation between ZM and Nano is only responsible for 20% of the κb reduction. For a large system like nanostructured Bi0.5Sb1.5Te3, a full electronic band structure calculation is computationally unfeasible. It is difficult to directly determine mn* (minority carrier) at the CBM. The estimated mn* values of n-type doped ZM and Nano Bi2Te2.7Se0.3 are 1.0 m0 and 1.1 m0, respectively38,68. If we assume comparable mn* at CBM between the ZM and Nano samples, the major part of κb reduction between the p-type ZM and Nano Bi0.5Sb1.5Te3 with comparable majority hole concentrations could be attributed to the reduction of minority carrier mobility (μn) corroborated by our κb fittings, where μn = 4095 cm2/V-s for the ZM and 1115 cm2/V-s for the Nano. The TEM image (inset of fig. 5(b)) shows that the sizes of nanoprecipitates closely match those of the minority electron wavelengths. Given the majority hole wavelength is estimated to be ~2 nm, we postulate a strong preferential minority carrier scattering by the nanoprecipitates in the Nano Bi0.5Sb1.5Te3. Similar κb reduction can also be observed in nanostructured n-type Bi2(Te,Se)3 compounds38,69,70. Extensive recent studies have established the role of nanostructure on lattice thermal conductivity reduction63,65, we propose an “preferential minority carrier scatterings” for κb reduction, which is partially responsible for the thermoelectric performance gains reported, especially at elevated temperatures61,71. Recent theoretical work has also demonstrated that similar κb reduction via heterostructure barriers scattering is possible72. Finally we caution that nanostructure induced band structure modulation reported in AgPbmSbTe2-m might be possible for Bi0.5Sb1.5Te373, which could be responsible for part of the κb reduction.

Figure 5
Figure 5

(a) The calculated electron wavelength, and the product of the Fermi-Dirac distribution function and electronic density of states f(E) g(E) vs. energy with the zero point corresponding to the conduction band minimum (Ec). (b) The experimental and modeled bipolar thermal conductivity vs. temperature, for p-type zone melted (ZM) and nanostructured (MS-SPS) Bi0.5Sb1.5Te3. The inset is a TEM picture of the MS-SPS bulk sample which shows 10–50 nm nanoprecipitates. (The room temperature minority carrier mobilities of ZM and Nano samples are μn = 4095 and 1115 cm2/V-s, respectively).


To conclude, our combined theoretical analysis and experimental measurements have established that in semiconductors bipolar thermal transport is in general a “conductivity-limiting” phenomenon, which is controlled by the carrier mobility ratio and the minority carrier partial electrical conductivity for the intrinsic and extrinsic cases, respectively. The numerical method we developed quantifies the role of electronic band structure and carrier scattering mechanisms. We have also demonstrated feasible strategies for manipulating the bipolar thermal conductivity in doped semiconductors via electronic band structure modulation and/or preferential minority carrier scatterings. We expect our study to be beneficial to the current interests in optimizing thermoelectric properties of narrow gap semiconductors.


Samples in this study were synthesized by a combination of induction melting and long-term high-temperature annealing, by zone melting, or by MS-SPS, and the details of which were documented elsewhere19,61. High-resolution transmission electron microscopy (TEM) images were collected using a JEM-2100F TEM. Electrical conductivity (σ) and Seebeck coefficient (α) were simultaneously measured by an Ulvac ZEM-3 under a low-pressure helium atmosphere. Thermal conductivity was calculated from the measured thermal diffusivity (D), specific heat (Cp), and density (d) using the relationship κ = DCpd. Thermal diffusivity D was tested by laser flash diffusivity method using a Netzsch LFA-457 system, and Cp was measured by a Netzsch DSC 404F1 using sapphire as the reference. The accuracy of the κ measurements is estimated to be ~10% and the precision <5%. κb were extrapolated from κb + κL = κ-LσT by assuming lattice thermal conductivity κL is inversely proportional to T. Hall measurements were performed on a Janis cryostat equipped with a 9 Tesla superconducting magnet. The carrier concentration of electron (n) or hole (p) and the corresponding Hall mobility μn or μp (subscript n represents the electron and p the hole) were estimated from the measured Hall coefficient (RH) and electrical conductivity by the relation and , respectively.

The first-principles electronic band structure calculations were performed with the generalized gradient approximation functional of Perdew, Burke, and Ernzerhof74, with projected augmented wave method75,76, as implemented in Vienna ab initio simulation package (VASP)77. The computational techniques are similar to those published previously66,78. The de Broglie wavelengths (λ) is defined as, λ = h/m*v, where h, m*, and v are the Planck constant, carrier effective mass, and drift velocity, respectively. m*, v and λ of degenerate majority carriers are almost energy independent (kBT within the Fermi level), while for non-degenerate minority carriers these values are energy dependent, which are derived from band structure. The detailed calculation method is shown in Supporting Information, and the calculated density of state, mn* and vn of electrons for p-type Bi2Te3 (ξp = 0.25, mp* = 1.3 m0) are shown in figure S2 (SI).

Additional Information

How to cite this article: Wang, S. et al. Conductivity-limiting bipolar thermal conductivity in semiconductors. Sci. Rep. 5, 10136; doi: 10.1038/srep10136 (2015).


  1. 1.

    Ambipolar thermodiffusion of electrons and holes in semiconductors. Philos. Mag. 46, 1252–1260 (1955).

  2. 2.

    & Electrical conductivity of semi-conductors with an ionic lattice in strong fields. J. Phys. 3, 359 (1940).

  3. 3.

    The thermal conductivity of bismuth telluride. Proceed. Phys. Soc. Sec. B 69, 203 (1956).

  4. 4.

    & Thermal Conduction in Semiconductors Pergamon Press: Oxford, 1961).

  5. 5.

    Thermal Conduction in Solids. Clarendon Press: Oxford, 1976).

  6. 6.

    & Thermal conductivity of germanium from 3 °K to 1020 °K. Phys. Rev. 120, 782 (1960).

  7. 7.

    & Thermal conductivity of silicon and germanium from 3 K to the melting point. Phys. Rev. 134, A1058 (1964).

  8. 8.

    , , & Bipolar Electronic Thermal Conductivity in Semimetals. J. Appl. Phys. 33, 3144–3145 (1962).

  9. 9.

    & Separation of the electronic and lattice thermal conductivities in bismuth crystals. phys. stat. solid. (b) 65, 765–772 (1974).

  10. 10.

    & Thermal conductivity of alloys of the bismuth-antimony system in solid and liquid states. Sov. Phys. J. 15, 287–290 (1972).

  11. 11.

    Thermal conductivity of germanium in the temperature range 300–1080 K. J. Phys. Chem. Solids 8, 340–343 (1959).

  12. 12.

    Die Wärmeleitfähigkeit von Germanium bei hohen temperaturen. J. Phys. Chem. Solids 10, 52–58 (1959).

  13. 13.

    , , & InAs and InSb as thermoelectric materials. J. Appl. Phys. 30, 930–934 (1959).

  14. 14.

    et al. p-Type skutterudites RxMyFe3CoSb12 (R, M = Ba, Ce, Nd, and Yb): Effectiveness of double-filling for the lattice thermal conductivity reduction. Intermetallics 19, 1747–1751 (2011).

  15. 15.

    et al. Thermoelectric properties of p-type skutterudites YbxFe3.5Ni0.5Sb12 (0.8 < x < 1). Acta Mater. 60, 2104–2110 (2012).

  16. 16.

    et al. Thermoelectric properties of p-type didymium (DD) based skutterudites DDy(Fe1-xNix)4Sb12 (0.13 < x < 0.25, 0.46 < y < 0.68). J. Alloy. Compd. 537, 242–249 (2012).

  17. 17.

    , , , & Composition optimization of p-type skutterudites CeyFexCo4−xSb12 and YbyFexCo4−xSb12. J. Mater. Res. 26, 1813–1819 (2011).

  18. 18.

    et al. Effects of Sn-doping on the electrical and thermal transport properties of p-type Cerium filled skutterudites. J. Alloy. Compd. 509, 1101–1105 (2011).

  19. 19.

    et al. Multiple-filled skutterudites: high thermoelectric figure of merit through separately optimizing electrical and thermal transports. J. Am. Chem. Soc. 133, 7837–7846 (2011).

  20. 20.

    , , , & High thermoelectric performance of In, Yb, Ce multiple filled CoSb3 based skutterudite compounds. J. Solid State Chem. 193, 31–35 (2012).

  21. 21.

    , , , & High thermoelectric performance of Yb0.26Co4Sb12/yGaSb nanocomposites originating from scattering electrons of low energy. Acta. Mater. 58, 3995–4002 (2010).

  22. 22.

    et al. Enhanced thermoelectric performance of dual-element-filled skutterudites BaxCeyCo4Sb12. Acta. Mater. 57, 3135–3139 (2009).

  23. 23.

    et al. Synthesis and thermoelectric properties of Sr-filled skutterudite SryCo4Sb12. J. Appl. Phys. 99, 053711-053711-053714 (2006).

  24. 24.

    et al. Anomalous barium filling fraction and n-type thermoelectric performance of BayCo4Sb12. J. Appl. Phys. 90, 1864–1868 (2001).

  25. 25.

    , , & High performance InxCeyCo4Sb12 thermoelectric materials with in situ forming nanostructured InSb phase. Appl. Phys. Lett. 94, 102114 (2009).

  26. 26.

    et al. Low thermal conductivity and high thermoelectric figure of merit in n-type BaxYbyCo4Sb12 double-filled skutterudites. Appl. Phys. Lett. 92, 182101 (2008).

  27. 27.

    et al. Thermoelectric properties of the n-type filled skutterudite Ba0.3Co4Sb12 doped with Ni. J. Appl. Phys. 91, 3698–3705 (2002).

  28. 28.

    & Properties of alkaline-earth-filled skutterudite antimonides: A(FeNi)4Sb12 (A= Ca, Sr, and Ba). Phys. Rev. B 82, 075115 (2010).

  29. 29.

    , , , & Electron and Phonon Transport in n-and p-type Skutterudites. in MRS Proceed. 1490, 9–18 (Cambridge Univ Press).(2013).

  30. 30.

    Heat transfer in semiconductors. Can. J. Phys. 34, 1342–1355 (1956).

  31. 31.

    , , & Thermal conductivity of silicon from 300 to 1400 K. Phys. Rev. 130, 1743 (1963).

  32. 32.

    , , , & Thermal and Electrical Properties of Heavily Doped Ge-Si Alloys up to 1300 °K. J. Appl. Phys. 35, 2899–2907 (1964).

  33. 33.

    , & Thermal and electrical properties of cobalt monosilicide between 4.2 and 1600 K. Sov. Phys. Solid. Stat. 11, 2002–2004 (1970).

  34. 34.

    Thermal conductivity of Mg2Si, Mg2Ge and Mg2Sn. J. Phys. Chem. Solids 33, 1139–1148 (1972).

  35. 35.

    & Thermoelectric properties of n-type Bi2(Te0.85Se0.15)3 single crystals doped with CuBr and SbI3. Phys. Rev. B 85, 125207 (2012).

  36. 36.

    , , , & Thermoelectric properties of textured p-type (Bi,Sb)2Te3 fabricated by spark plasma sintering. Scrip. Mater. 52, 347–351 (2005).

  37. 37.

    et al. Enhanced thermoelectric properties of Bi2(Te1−xSex)3-based compounds as n-type legs for low-temperature power generation. J. Mater. Chem. 22, 20943–20951 (2012).

  38. 38.

    et al. Preferential Scattering by Interfacial Charged Defects for Enhanced Thermoelectric Performance in Few-layered n-type Bi2Te3. Sci. Rep. 3, 3212; 10.1038/srep03212 (2013).

  39. 39.

    et al. Anisotropic multicenter bonding and high thermoelectric performance in electron-poor CdSb. Chem. Mater. 27, 1071–1081 (2015).

  40. 40.

    Introduction To Ceramics. John Wiley & Sons: New York, 1960).

  41. 41.

    The Mathematics of Diffusion. Clarendon Press: Oxford, 1975).

  42. 42.

    Heavily doped semiconductors. Plenum Press: New York, 1969).

  43. 43.

    Physics of Semiconductors Academic Press: New York, 1960).

  44. 44.

    Electronic Refrigeration. Pion Limited: London, 1986).

  45. 45.

    & Estimation of the thermal band gap of a semiconductor from Seebeck measurements. J. Electron. Mater. 28, 869–872 (1999).

  46. 46.

    Semiconductor Statistics. (New York: Courier Dover Publications, 2002).

  47. 47.

    , & Properties of single crystalline semiconducting CoSb3. J. Appl. Phys. 80, 4442–4449 (1996).

  48. 48.

    , , & Iron valence in skutterudites: Transport and magnetic properties of Co1-xFexSb3. Phys. Rev. B 63, 014410 (2000).

  49. 49.

    , , , & Thermoelectric properties of P-type Yb-filled skutterudite YbxFeyCo4−ySb12. Intermetallics 19, 1390–1393 (2011).

  50. 50.

    et al. Synthesis and thermoelectric properties of double-filled skutterudites CeyYb0.5-yFe1.5Co2.5Sb12. J. Alloy. Compd. 467, 528–532 (2009).

  51. 51.

    et al. Electronic band structure, magnetic, transport and thermodynamic properties of In-filled skutterudites InxCo4Sb12. J. Phys. D Appl. Phys. 46, 495106 (2013).

  52. 52.

    , , & Double-filled skutterudites of the type YbxCayCo4Sb12: Synthesis and properties. J. Appl. Phys. 107, 043705 (2010).

  53. 53.

    et al. Improving thermoelectric performance of caged compounds through light-element filling. Appl. Phys. Lett. 95, 042101 (2009).

  54. 54.

    , , , & Effect of Pd substitution on thermoelectric properties of Ba0.3PdxCo4-xSb12. Script. Mater. 56, 621–624 (2007).

  55. 55.

    et al. Enhanced thermoelectric performance in barium and indium double-filled skutterudite bulk materials via orbital hybridization induced by indium filler. J. Am. Chem. Soc. 131, 3713–3720 (2009).

  56. 56.

    et al. Low temperature transport and structural properties of misch-metal-filled skutterudites. J. Appl. Phys. 102, 083702 (2007).

  57. 57.

    , & Effect of partial void filling on the transport properties of NdxCo4Sb12 skutterudites. J. Phys. Condens. Mat. 15, 5035–5048 (2003).

  58. 58.

    , & Effect of partial void filling on the lattice thermal conductivity of skutterudites. Phys. Rev. B 58, 164 (1998).

  59. 59.

    , , , & Cerium filling and doping of cobalt triantimonide. Phys. Rev. B 56, 7376 (1997).

  60. 60.

    & The maximum possible conversion efficiency of silicon-germanium thermoelectric generators. J. Appl. Phys. 70, 2694–2718 (1991).

  61. 61.

    et al. Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites. Nano Lett. 10, 3283–3289 (2010).

  62. 62.

    & Complex thermoelectric materials. Nat. Mater. 7, 105–114 (2008).

  63. 63.

    et al. New Directions for Low-Dimensional Thermoelectric Materials. Adv. Mater. 19, 1043–1053 (2007).

  64. 64.

    , & Rational design of advanced thermoelectric materials. Adv. Energy Mater. 3, 549–565 (2013).

  65. 65.

    , , & Bulk nanostructured thermoelectric materials: current research and future prospects. Energy Environ. Sci. 2, 466–479 (2009).

  66. 66.

    et al. Trends in electrical transport of p-type skutterudites RFe4Sb12 (R= Na, K, Ca, Sr, Ba, La, Ce, Pr, Yb) from first-principles calculations and Boltzmann transport theory. Phys. Rev. B 84, 235205 (2011).

  67. 67.

    & Electronic structure of CoSb3: A narrow-band-gap semiconductor. Phys. Rev. B 58, 15620 (1998).

  68. 68.

    , , , & Metal nanoparticle decorated n-type Bi2Te3-based materials with enhanced thermoelectric performances. Nanotechnology 24, 285702 (2013).

  69. 69.

    , , & Enhanced performances of melt spun Bi2(Te,Se)3 for n-type thermoelectric legs. Intermetallics 19, 1024–1031 (2011).

  70. 70.

    , , & High performance n-type (Bi,Sb)2(Te,Se)3 for low temperature thermoelectric generator. J. Phys. D Appl. Phys. 43, 335404 (2010).

  71. 71.

    et al. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 320, 634–638 (2008).

  72. 72.

    & Enhancing the thermoelectric figure of merit through the reduction of bipolar thermal conductivity with heterostructure barriers. Appl. Phys. Lett. 105, 052106 (2014).

  73. 73.

    , , , & Nanodopant-induced band modulation in AgPbmSbTe2+m-type thermoelectrics. Phys. Rev. Lett. 106, 206601 (2011).

  74. 74.

    , & Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

  75. 75.

    Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).

  76. 76.

    & From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).

  77. 77.

    & Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

  78. 78.

    et al. Evaluation of Half-Heusler Compounds as Thermoelectric Materials Based on the Calculated Electrical Transport Properties. Adv. Funct. Mater. 18, 2880–2888 (2008).

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This work was supported by US Department of Energy under corporate agreement DE-FC26-04NT42278, by GM, and by National Science Foundation under award number 1235535.

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Author notes

    • Shanyu Wang
    •  & Jiong Yang

    These authors contributed equally to this work.


  1. Materials Science and Engineering Department, University of Washington, Seattle, WA 98195-2120, USA

    • Shanyu Wang
    • , Jiong Yang
    • , Trevor Toll
    •  & Jihui Yang
  2. State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China

    • Wenqing Zhang
  3. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China

    • Xinfeng Tang


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Jihui Yang designed research; S.W., Jiong Yang, and T.T. performed research; Jihui Yang, W.Z. and X.T. analyzed data; and Jihui Yang, S.W., and Jiong Yang wrote the paper. All authors reviewed the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Jihui Yang or Wenqing Zhang or Xinfeng Tang.

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