Conductivity-limiting bipolar thermal conductivity in semiconductors
10.1038/srep10136
Crossref journal-article
Springer Science and Business Media LLC
Scientific Reports (297)
Abstract

AbstractIntriguing 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.

Bibliography

Wang, S., Yang, J., Toll, T., Yang, J., Zhang, W., & Tang, X. (2015). Conductivity-limiting bipolar thermal conductivity in semiconductors. Scientific Reports, 5(1).

Authors 6
  1. Shanyu Wang (first)
  2. Jiong Yang (additional)
  3. Trevor Toll (additional)
  4. Jihui Yang (additional)
  5. Wenqing Zhang (additional)
  6. Xinfeng Tang (additional)
References 78 Referenced 113
  1. Price, P. Ambipolar thermodiffusion of electrons and holes in semiconductors. Philos. Mag. 46, 1252–1260 (1955). (10.1080/14786441108520635) / Philos. Mag. by P Price (1955)
  2. Davydov, B. & Shmushkewitch, J. Electrical conductivity of semi-conductors with an ionic lattice in strong fields. J. Phys. 3, 359 (1940). / J. Phys. by B Davydov (1940)
  3. Goldsmid, H. The thermal conductivity of bismuth telluride. Proceed. Phys. Soc. Sec. B 69, 203 (1956). (10.1088/0370-1301/69/2/310) / Proceed. Phys. Soc. Sec. B by H Goldsmid (1956)
  4. Drabble, J. R. & Goldsmid, H. J. Thermal Conduction in Semiconductors Pergamon Press: Oxford, 1961).
  5. Berman, R. Thermal Conduction in Solids. Clarendon Press: Oxford, 1976).
  6. Slack, G. A. & Glassbrenner, C. Thermal conductivity of germanium from 3 °K to 1020 °K. Phys. Rev. 120, 782 (1960). (10.1103/PhysRev.120.782) / Phys. Rev. by GA Slack (1960)
  7. Glassbrenner, C. & Slack, G. A. Thermal conductivity of silicon and germanium from 3 K to the melting point. Phys. Rev. 134, A1058 (1964). (10.1103/PhysRev.134.A1058) / Phys. Rev. by C Glassbrenner (1964)
  8. Gallo, C., Miller, R., Sutter, P. & Ure Jr, R. Bipolar Electronic Thermal Conductivity in Semimetals. J. Appl. Phys. 33, 3144–3145 (1962). (10.1063/1.1728587) / J. Appl. Phys. by C Gallo (1962)
  9. Uher, C. & Goldsmid, H. Separation of the electronic and lattice thermal conductivities in bismuth crystals. phys. stat. solid. (b) 65, 765–772 (1974). (10.1002/pssb.2220650237) / phys. stat. solid. (b) by C Uher (1974)
  10. Magomedov, A.-M. & Pashaev, B. Thermal conductivity of alloys of the bismuth-antimony system in solid and liquid states. Sov. Phys. J. 15, 287–290 (1972). (10.1007/BF00819456) / Sov. Phys. J. by A-M Magomedov (1972)
  11. Abeles, B. Thermal conductivity of germanium in the temperature range 300–1080 K. J. Phys. Chem. Solids 8, 340–343 (1959). (10.1016/0022-3697(59)90357-9) / J. Phys. Chem. Solids by B Abeles (1959)
  12. Kettel, F. Die Wärmeleitfähigkeit von Germanium bei hohen temperaturen. J. Phys. Chem. Solids 10, 52–58 (1959). (10.1016/0022-3697(59)90125-8) / J. Phys. Chem. Solids by F Kettel (1959)
  13. Bowers, R., Ure Jr, R., Bauerle, J. & Cornish, A. InAs and InSb as thermoelectric materials. J. Appl. Phys. 30, 930–934 (1959). (10.1063/1.1735264) / J. Appl. Phys. by R Bowers (1959)
  14. Liu, R. 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). (10.1016/j.intermet.2011.06.010) / Intermetallics by R Liu (2011)
  15. Cho, J. Y. et al. Thermoelectric properties of p-type skutterudites YbxFe3.5Ni0.5Sb12 (0.8 < x < 1). Acta Mater. 60, 2104–2110 (2012). (10.1016/j.actamat.2011.12.022) / Acta Mater. by JY Cho (2012)
  16. Rogl, G. 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). (10.1016/j.jallcom.2012.04.121) / J. Alloy. Compd. by G Rogl (2012)
  17. Liu, R., Qiu, P., Chen, X., Huang, X. & Chen, L. Composition optimization of p-type skutterudites CeyFexCo4−xSb12 and YbyFexCo4−xSb12 . J. Mater. Res. 26, 1813–1819 (2011). (10.1557/jmr.2011.85) / J. Mater. Res. by R Liu (2011)
  18. Qiu, P. 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). (10.1016/j.jallcom.2010.09.162) / J. Alloy. Compd. by P Qiu (2011)
  19. Shi, X. 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). (10.1021/ja111199y) / J. Am. Chem. Soc. by X Shi (2011)
  20. Ballikaya, S., Uzar, N., Yildirim, S., Salvador, J. R. & Uher, C. High thermoelectric performance of In, Yb, Ce multiple filled CoSb3 based skutterudite compounds. J. Solid State Chem. 193, 31–35 (2012). (10.1016/j.jssc.2012.03.029) / J. Solid State Chem. by S Ballikaya (2012)
  21. Xiong, Z., Chen, X., Huang, X., Bai, S. & Chen, L. High thermoelectric performance of Yb0.26Co4Sb12/yGaSb nanocomposites originating from scattering electrons of low energy. Acta. Mater. 58, 3995–4002 (2010). (10.1016/j.actamat.2010.03.025) / Acta. Mater. by Z Xiong (2010)
  22. Bai, S. et al. Enhanced thermoelectric performance of dual-element-filled skutterudites BaxCeyCo4Sb12 . Acta. Mater. 57, 3135–3139 (2009). (10.1016/j.actamat.2009.03.018) / Acta. Mater. by S Bai (2009)
  23. Zhao, X. et al. Synthesis and thermoelectric properties of Sr-filled skutterudite SryCo4Sb12 . J. Appl. Phys. 99, 053711-053711-053714 (2006). (10.1063/1.2172705)
  24. Chen, L. et al. Anomalous barium filling fraction and n-type thermoelectric performance of BayCo4Sb12 . J. Appl. Phys. 90, 1864–1868 (2001). (10.1063/1.1388162) / J. Appl. Phys. by L Chen (2001)
  25. Li, H., Tang, X., Zhang, Q. & Uher, C. High performance InxCeyCo4Sb12 thermoelectric materials with in situ forming nanostructured InSb phase. Appl. Phys. Lett. 94, 102114 (2009). (10.1063/1.3099804) / Appl. Phys. Lett. by H Li (2009)
  26. Shi, X. et al. Low thermal conductivity and high thermoelectric figure of merit in n-type BaxYbyCo4Sb12 double-filled skutterudites. Appl. Phys. Lett. 92, 182101 (2008). (10.1063/1.2920210) / Appl. Phys. Lett. by X Shi (2008)
  27. Dyck, J. S. et al. Thermoelectric properties of the n-type filled skutterudite Ba0.3Co4Sb12 doped with Ni. J. Appl. Phys. 91, 3698–3705 (2002). (10.1063/1.1450036) / J. Appl. Phys. by JS Dyck (2002)
  28. Singh, D. J. & Du, M.-H. Properties of alkaline-earth-filled skutterudite antimonides: A(FeNi)4Sb12 (A= Ca, Sr and Ba). Phys. Rev. B 82, 075115 (2010). (10.1103/PhysRevB.82.075115) / Phys. Rev. B by DJ Singh (2010)
  29. Yang, J., Wang, S., Yang, J., Zhang, W. & Chen, L. Electron and Phonon Transport in n-and p-type Skutterudites. in MRS Proceed. 1490, 9–18 (Cambridge Univ Press).(2013). (10.1557/opl.2013.216) / MRS Proceed by J Yang (2013)
  30. Joffe, A. Heat transfer in semiconductors. Can. J. Phys. 34, 1342–1355 (1956). (10.1139/p56-150) / Can. J. Phys. by A Joffe (1956)
  31. Shanks, H., Maycock, P., Sidles, P. & Danielson, G. Thermal conductivity of silicon from 300 to 1400 K. Phys. Rev. 130, 1743 (1963). (10.1103/PhysRev.130.1743) / Phys. Rev. by H Shanks (1963)
  32. Dismukes, J., Ekstrom, L., Steigmeier, E., Kudman, I. & Beers, D. Thermal and Electrical Properties of Heavily Doped Ge-Si Alloys up to 1300 °K. J. Appl. Phys. 35, 2899–2907 (1964). (10.1063/1.1713126) / J. Appl. Phys. by J Dismukes (1964)
  33. Nikitin, E., Tamarin, P. & Tarasov, V. Thermal and electrical properties of cobalt monosilicide between 4.2 and 1600 K. Sov. Phys. Solid. Stat. 11, 2002–2004 (1970). / Sov. Phys. Solid. Stat. by E Nikitin (1970)
  34. Martin, J. Thermal conductivity of Mg2Si, Mg2Ge and Mg2Sn. J. Phys. Chem. Solids 33, 1139–1148 (1972). (10.1016/S0022-3697(72)80273-7) / J. Phys. Chem. Solids by J Martin (1972)
  35. Yelgel, Ö. C. & Srivastava, G. Thermoelectric properties of n-type Bi2(Te0.85Se0.15)3 single crystals doped with CuBr and SbI3 . Phys. Rev. B 85, 125207 (2012). (10.1103/PhysRevB.85.125207) / Phys. Rev. B by ÖC Yelgel (2012)
  36. Jiang, J., Chen, L., Bai, S., Yao, Q. & Wang, Q. Thermoelectric properties of textured p-type (Bi,Sb)2Te3 fabricated by spark plasma sintering. Scrip. Mater. 52, 347–351 (2005). (10.1016/j.scriptamat.2004.10.038) / Scrip. Mater. by J Jiang (2005)
  37. Wang, S. 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). (10.1039/c2jm34608g) / J. Mater. Chem. by S Wang (2012)
  38. Puneet, P. 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). (10.1038/srep03212) / Sci. Rep. by P Puneet (2013)
  39. Wang, S. et al. Anisotropic multicenter bonding and high thermoelectric performance in electron-poor CdSb. Chem. Mater. 27, 1071–1081 (2015). (10.1021/cm504398d) / Chem. Mater. by S Wang (2015)
  40. Kingery, W. D. Introduction To Ceramics. John Wiley & Sons: New York, 1960).
  41. Crank, J. The Mathematics of Diffusion. Clarendon Press: Oxford, 1975).
  42. Fistul, V. I. Heavily doped semiconductors. Plenum Press: New York, 1969). (10.1007/978-1-4684-8821-0_7)
  43. Ioffe, A. F. Physics of Semiconductors Academic Press: New York, 1960).
  44. Goldsmid, H. J. Electronic Refrigeration. Pion Limited: London, 1986).
  45. Goldsmid, H. & Sharp, J. Estimation of the thermal band gap of a semiconductor from Seebeck measurements. J. Electron. Mater. 28, 869–872 (1999). (10.1007/s11664-999-0211-y) / J. Electron. Mater. by H Goldsmid (1999)
  46. Blakemore, J. S. Semiconductor Statistics. (New York: Courier Dover Publications, 2002).
  47. Caillat, T., Borshchevsky, A. & Fleurial, J. P. Properties of single crystalline semiconducting CoSb3 . J. Appl. Phys. 80, 4442–4449 (1996). (10.1063/1.363405) / J. Appl. Phys. by T Caillat (1996)
  48. Yang, J., Meisner, G., Morelli, D. & Uher, C. Iron valence in skutterudites: Transport and magnetic properties of Co1-xFexSb3 . Phys. Rev. B 63, 014410 (2000). (10.1103/PhysRevB.63.014410) / Phys. Rev. B by J Yang (2000)
  49. Zhou, C., Morelli, D., Zhou, X., Wang, G. & Uher, C. Thermoelectric properties of P-type Yb-filled skutterudite YbxFeyCo4−ySb12 . Intermetallics 19, 1390–1393 (2011). (10.1016/j.intermet.2011.04.015) / Intermetallics by C Zhou (2011)
  50. Yang, K. et al. Synthesis and thermoelectric properties of double-filled skutterudites CeyYb0.5-yFe1.5Co2.5Sb12 . J. Alloy. Compd. 467, 528–532 (2009). (10.1016/j.jallcom.2007.12.065) / J. Alloy. Compd. by K Yang (2009)
  51. Leszczynski, J. et al. Electronic band structure, magnetic, transport and thermodynamic properties of In-filled skutterudites InxCo4Sb12 . J. Phys. D Appl. Phys. 46, 495106 (2013). (10.1088/0022-3727/46/49/495106) / J. Phys. D Appl. Phys by J Leszczynski (2013)
  52. Salvador, J., Yang, J., Wang, H. & Shi, X. Double-filled skutterudites of the type YbxCayCo4Sb12: Synthesis and properties. J. Appl. Phys. 107, 043705 (2010). (10.1063/1.3296186) / J. Appl. Phys. by J Salvador (2010)
  53. Pei, Y. et al. Improving thermoelectric performance of caged compounds through light-element filling. Appl. Phys. Lett. 95, 042101 (2009). (10.1063/1.3182800) / Appl. Phys. Lett. by Y Pei (2009)
  54. Pei, Y., Chen, L., Bai, S., Zhao, X. & Li, X. Effect of Pd substitution on thermoelectric properties of Ba0.3PdxCo4-xSb12 . Script. Mater. 56, 621–624 (2007). (10.1016/j.scriptamat.2006.12.012) / Script. Mater by Y Pei (2007)
  55. Zhao, W. 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). (10.1021/ja8089334) / J. Am. Chem. Soc. by W Zhao (2009)
  56. Yang, J. et al. Low temperature transport and structural properties of misch-metal-filled skutterudites. J. Appl. Phys. 102, 083702 (2007). (10.1063/1.2794716) / J. Appl. Phys. by J Yang (2007)
  57. Kuznetsov, V., Kuznetsova, L. & Rowe, D. Effect of partial void filling on the transport properties of NdxCo4Sb12 skutterudites. J. Phys. Condens. Mat. 15, 5035–5048 (2003). (10.1088/0953-8984/15/29/315) / J. Phys. Condens. Mat. by V Kuznetsov (2003)
  58. Nolas, G., Cohn, J. & Slack, G. Effect of partial void filling on the lattice thermal conductivity of skutterudites. Phys. Rev. B 58, 164 (1998). (10.1103/PhysRevB.58.164) / Phys. Rev. B by G Nolas (1998)
  59. Morelli, D. T., Meisner, G. P., Chen, B., Hu, S. & Uher, C. Cerium filling and doping of cobalt triantimonide. Phys. Rev. B 56, 7376 (1997). (10.1103/PhysRevB.56.7376) / Phys. Rev. B by DT Morelli (1997)
  60. Slack, G. A. & Hussain, M. A. The maximum possible conversion efficiency of silicon-germanium thermoelectric generators. J. Appl. Phys. 70, 2694–2718 (1991). (10.1063/1.349385) / J. Appl. Phys. by GA Slack (1991)
  61. Xie, W. et al. Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites. Nano Lett. 10, 3283–3289 (2010). (10.1021/nl100804a) / Nano Lett. by W Xie (2010)
  62. Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nat. Mater. 7, 105–114 (2008). (10.1038/nmat2090) / Nat. Mater. by GJ Snyder (2008)
  63. Dresselhaus, M. S. et al. New Directions for Low-Dimensional Thermoelectric Materials. Adv. Mater. 19, 1043–1053 (2007). (10.1002/adma.200600527) / Adv. Mater. by MS Dresselhaus (2007)
  64. Yang, J., Yip, H. L. & Jen, A. K. Y. Rational design of advanced thermoelectric materials. Adv. Energy Mater. 3, 549–565 (2013). (10.1002/aenm.201200514) / Adv. Energy Mater by J Yang (2013)
  65. Minnich, A., Dresselhaus, M., Ren, Z. & Chen, G. Bulk nanostructured thermoelectric materials: current research and future prospects. Energy Environ. Sci. 2, 466–479 (2009). (10.1039/b822664b) / Energy Environ. Sci. by A Minnich (2009)
  66. Yang, J. 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). (10.1103/PhysRevB.84.235205) / Phys. Rev. B by J Yang (2011)
  67. Sofo, J. & Mahan, G. Electronic structure of CoSb3: A narrow-band-gap semiconductor. Phys. Rev. B 58, 15620 (1998). (10.1103/PhysRevB.58.15620) / Phys. Rev. B by J Sofo (1998)
  68. Wang, S., Li, H., Lu, R., Zheng, G. & Tang, X. Metal nanoparticle decorated n-type Bi2Te3-based materials with enhanced thermoelectric performances. Nanotechnology 24, 285702 (2013). (10.1088/0957-4484/24/28/285702) / Nanotechnology by S Wang (2013)
  69. Wang, S., Xie, W., Li, H. & Tang, X. Enhanced performances of melt spun Bi2(Te,Se)3 for n-type thermoelectric legs. Intermetallics 19, 1024–1031 (2011). (10.1016/j.intermet.2011.03.006) / Intermetallics by S Wang (2011)
  70. Wang, S., Xie, W., Li, H. & Tang, X. High performance n-type (Bi,Sb)2(Te,Se)3 for low temperature thermoelectric generator. J. Phys. D Appl. Phys. 43, 335404 (2010). (10.1088/0022-3727/43/33/335404) / J. Phys. D Appl. Phys by S Wang (2010)
  71. Poudel, B. et al. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 320, 634–638 (2008). (10.1126/science.1156446) / Science by B Poudel (2008)
  72. Bahk, J.-H. & Shakouri, A. Enhancing the thermoelectric figure of merit through the reduction of bipolar thermal conductivity with heterostructure barriers. Appl. Phys. Lett. 105, 052106 (2014). (10.1063/1.4892653) / Appl. Phys. Lett. by J-H Bahk (2014)
  73. Zhang, Y., Ke, X., Chen, C., Yang, J. & Kent, P. R. Nanodopant-induced band modulation in AgPbmSbTe2+m-type thermoelectrics. Phys. Rev. Lett. 106, 206601 (2011). (10.1103/PhysRevLett.106.206601) / Phys. Rev. Lett. by Y Zhang (2011)
  74. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996). (10.1103/PhysRevLett.77.3865) / Phys. Rev. Lett. by JP Perdew (1996)
  75. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994). (10.1103/PhysRevB.50.17953) / Phys. Rev. B by PE Blöchl (1994)
  76. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999). (10.1103/PhysRevB.59.1758) / Phys. Rev. B by G Kresse (1999)
  77. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996). (10.1103/PhysRevB.54.11169) / Phys. Rev. B by G Kresse (1996)
  78. Yang, J. et al. Evaluation of Half-Heusler Compounds as Thermoelectric Materials Based on the Calculated Electrical Transport Properties. Adv. Funct. Mater. 18, 2880–2888 (2008). (10.1002/adfm.200701369) / Adv. Funct. Mater. by J Yang (2008)
Dates
Type When
Created 10 years, 3 months ago (May 13, 2015, 12:11 p.m.)
Deposited 2 years, 7 months ago (Jan. 5, 2023, 9:12 a.m.)
Indexed 4 days, 15 hours ago (Aug. 28, 2025, 8:22 a.m.)
Issued 10 years, 3 months ago (May 13, 2015)
Published 10 years, 3 months ago (May 13, 2015)
Published Online 10 years, 3 months ago (May 13, 2015)
Funders 0

None

@article{Wang_2015, title={Conductivity-limiting bipolar thermal conductivity in semiconductors}, volume={5}, ISSN={2045-2322}, url={http://dx.doi.org/10.1038/srep10136}, DOI={10.1038/srep10136}, number={1}, journal={Scientific Reports}, publisher={Springer Science and Business Media LLC}, author={Wang, Shanyu and Yang, Jiong and Toll, Trevor and Yang, Jihui and Zhang, Wenqing and Tang, Xinfeng}, year={2015}, month=may }