Thermoelectric Nanomaterials pp 3-32 | Cite as
Material Design Considerations Based on Thermoelectric Quality Factor
Abstract
In this chapter several aspects of the electronic and phonon structure are considered for the design and engineering of advanced thermoelectric materials. For a given compound, its thermoelectric figure of merit, zT, is fully exploited only when the free carrier density is optimized. Achieving higher zT beyond this requires the improvement in the material quality factor B. Using experimental data on lead chalcogenides as well as examples of other good thermoelectric materials, we demonstrate how the fundamental material parameters: effective mass, band anisotropy, deformation potential, and band degeneracy, among others, impact the thermoelectric properties and lead to desirable thermoelectric materials. As the quality factor B is introduced under the assumption of acoustic phonon (deformation potential) scattering, a brief discussion about carrier scattering mechanisms is also included. This simple model with the use of an effective deformation potential coefficient fits the experimental properties of real materials with complex structures and multi-valley Fermi surfaces remarkably well—which is fortunate as these are features likely found in advanced thermoelectric materials.
Keywords
Optical Phonon Thermoelectric Material Acoustic Phonon Deformation Potential Lead ChalcogenideReferences
- 1.R.P. Chasmar, R. Stratton, J. Electron. Control 7, 52–72 (1959)CrossRefGoogle Scholar
- 2.H.J. Goldsmid, Introduction to Thermoelectricity (Springer, Berlin, Heidelberg, 2010)Google Scholar
- 3.H.J. Goldsmid, Thermoelectric Refrigeration (Temple Press Books LTD, London, 1964)CrossRefGoogle Scholar
- 4.G.S. Nolas, J. Sharp, H.J. Goldsmid, Thermoelectrics Basic Principles and New Materials Developments (Springer, Berlin, Heidelberg, 2001)Google Scholar
- 5.G.D. Mahan, Solid State Physics, (Academic Press Inc., San Diego , 1998), vol. 51, pp. 81–157Google Scholar
- 6.G.A. Slack, in CRC Thermoelectric Handbook, ed. by D.M. Rowe (CRC Press LLC, Boca Raton, 1995)Google Scholar
- 7.Y. Pei, A.D. LaLonde, H. Wang, G.J. Snyder, Energy Environ. Sci. 5(7), 7963–7969 (2012)CrossRefGoogle Scholar
- 8.C. Herring, Bell Syst. Tech. J. 34(2), 237–290 (1955)CrossRefGoogle Scholar
- 9.Y.I. Ravich, B.A. Efimova, I.A. Smirnov, Semiconducting Lead Chalcogenides (Plenum Press, New York, 1970)CrossRefGoogle Scholar
- 10.C. Herring, E. Vogt, Phys. Rev. 101(3), 944 (1956)CrossRefGoogle Scholar
- 11.Y. Takagiwa, Y. Pei, G. Pomrehn, G. J. Snyder, Appl. Phys. Lett. 101, 092102 (2012)Google Scholar
- 12.J. Bardeen, W. Shockley, Phys. Rev. 80(1), 72 (1950)CrossRefGoogle Scholar
- 13.E.S. Toberer, C.A. Cox, S.R. Brown, T. Ikeda, A.F. May, S.M. Kauzlarich, G.J. Snyder, Adv. Funct. Mater. 18(18), 2795–2800 (2008)CrossRefGoogle Scholar
- 14.A.F. May, E.S. Toberer, A. Saramat, G.J. Snyder, Phys. Rev. B 80(12), 125205 (2009)CrossRefGoogle Scholar
- 15.Y.I. Ravich, B.A. Efimova, V.I. Tamarchenko, Phys. Status Solidi B-Basic Res. 43(2), 453–469 (1971)CrossRefGoogle Scholar
- 16.L.G. Ferreira, Phys. Rev. 137(5A), 1601–1609 (1965)Google Scholar
- 17.K. Seeger, Semiconductor Physics An Introduction, 9th edn. (Springer, Berlin, Heidelberg, 2004)Google Scholar
- 18.H. Wang, Y. Pei, A.D. LaLonde, G.J. Snyder, Proc. Nat. Acad. Sci. 109(25), 9705–9709 (2012)CrossRefGoogle Scholar
- 19.G.E. Pikus, G.L. Bir, Sov. Phys. Solid State 1(11), 1502–1517 (1960)Google Scholar
- 20.G.L. Bir, G.E. Pikus, Sov. Phys. Solid State 2(9), 2039–2051 (1961)Google Scholar
- 21.M.V. Fischetti, S.E. Laux, J. Appl. Phys. 80(4), 2234–2252 (1996)CrossRefGoogle Scholar
- 22.I.I. Zasavitskii, E. Silva, E. Abramof, P.J. McCann, Phys. Rev. B 70(11), 115302 (2004)Google Scholar
- 23.H.Z. Wu, N. Dai, P.J. McCann, Phys. Rev. B 66(4), 045303 (2002)Google Scholar
- 24.Springer Materials the Landolt-Börnstein DatabaseGoogle Scholar
- 25.B.-L. Huang, M. Kaviany, Phys. Rev. B 77(12), 125209 (2008)Google Scholar
- 26.T. Caillat, A. Borshchevsky, J.P. Fleurial, J. Appl. Phys. 80(8), 4442–4449 (1996)CrossRefGoogle Scholar
- 27.J.O. Sofo, G.D. Mahan, Phys. Rev. B 58(23), 15620–15623 (1998)CrossRefGoogle Scholar
- 28.J.L. Feldman, D.J. Singh, Phys. Rev. B 53(10), 6273–6282 (1996)CrossRefGoogle Scholar
- 29.A. May, J.-P. Fleurial, G. Snyder, Phys. Rev. B 78(12), 125205 (2008)Google Scholar
- 30.A.F. May, D.J. Singh, G.J. Snyder, Phys. Rev. B 79(15), 153101 (2009)CrossRefGoogle Scholar
- 31.K. Tukioka, Jpn. J. Appl. Phys. Part 1 - Regul. Pap. Short Notes Rev. Pap. 30(2), 212–217 (1991)Google Scholar
- 32.B.M. Askerov, Electron Transport Phenomena in Semiconductors (World Scientific Publishing Co. Pte. Ltd., Singapor, 1991)Google Scholar
- 33.D.J. Howarth, E.H. Sondheimer, Proc. Royal Society Lond. Ser. Math. Phys. sci. 219(1136), 53–74 (1953)Google Scholar
- 34.V.W.L. Chin, R.J. Egan, T.L. Tansley, J. Appl. Phys. 69(6), 3571–3577 (1991)CrossRefGoogle Scholar
- 35.D.I. Bilc, S.D. Mahanti, M.G. Kanatzidis, Phys. Rev. B 74(12), 125202 (2006)CrossRefGoogle Scholar
- 36.L.Y. Morgovskii, Y.I. Ravich, Soviet Physics Semiconductors-Ussr 5(5), 860 (1971)Google Scholar
- 37.C. Jacoboni, L. Reggiani, Rev. Mod. Phys. 55(3), 645–705 (1983)CrossRefGoogle Scholar
- 38.W.A. Harrison, Phys. Rev. 104(5), 1281 (1956)CrossRefGoogle Scholar
- 39.K. Takeda, N. Matsumoto, J. Phys. C-Solid State Phys. 17(28), 5001–5015 (1984)CrossRefGoogle Scholar
- 40.J.D. Wiley, M. Didomeni, Phys. Rev. B 2(2), 427 (1970)Google Scholar
- 41.J.D. Wiley, Solid State Commun. 8(22), 1865–1868 (1970)CrossRefGoogle Scholar
- 42.M. Costato, G. Gagliani, C. Jacoboni, L. Reggiani, J. Phys. Chem. Solids 35(12), 1605–1614 (1974)CrossRefGoogle Scholar
- 43.Y.I. Ravich, Sov. Phys. Semiconductors-Ussr 3(10), 1278 (1970)Google Scholar
- 44.R. Dalven, Phys. Rev. B 3(6), 1953–1954 (1971)CrossRefGoogle Scholar
- 45.H. Ehrenreich, J. Appl. Phys. 32(10), 2155–2166 (1961)CrossRefGoogle Scholar
- 46.D.L. Rode, Phys. Rev. B 2(4), 1012–1024 (1970)CrossRefGoogle Scholar
- 47.D.L. Rode, Phys. Rev. B-Solid State 2(10), 4036–4044 (1970)CrossRefGoogle Scholar
- 48.A.R. Hutson, Phys. Rev. 108(2), 222–230 (1957)CrossRefGoogle Scholar
- 49.Y.I. Ravich, B.A. Efimova, V.I. Tamarchenko, Phys. Status Solidi B-Basic Res. 43(1), 11–33 (1971)CrossRefGoogle Scholar
- 50.D.M. Zayachuk, Semiconductors 31(2), 173–176 (1997)CrossRefGoogle Scholar
- 51.C.M. Bhandari, D.M. Rowe, J. Phys. D: Appl. Phys. 18(5), 873 (1985)CrossRefGoogle Scholar
- 52.R.L. Petritz, W.W. Scanlon, Phys. Rev. 97(6), 1620–1626 (1955)CrossRefGoogle Scholar
- 53.S. Johnsen, J.Q. He, J. Androulakis, V.P. Dravid, I. Todorov, D.Y. Chung, M.G. Kanatzidis, J. Am. Chem. Soc. 133(10), 3460–3470 (2011)CrossRefGoogle Scholar
- 54.R.S. Allgaier, W.W. Scanlon, Phy. Rev. 111(4), 1029–1037 (1958)CrossRefGoogle Scholar
- 55.L.D. Zhao, S.H. Lo, J. He, H. Li, K. Biswas, J. Androulakis, C.I. Wu, T.P. Hogan, D.Y. Chung, V.P. Dravid, M.G. Kanatzidis, J. Am. Chem. Soc. 133(50), 20476–20487 (2011)CrossRefGoogle Scholar
- 56.H. Wang, E. Schechtel, Y. Pei and G. J. Snyder, Adv. Energy Mater. 3, 488–498 (2013)Google Scholar
- 57.E.G. Bylander, M. Hass, Solid State Commun. 4(1), 51–53 (1966)CrossRefGoogle Scholar
- 58.Y. Kanai, K. Shohno, Jpn. J. Appl. Phys. 2, 6–10 (1963)CrossRefGoogle Scholar
- 59.Y. I. Ravich, in Lead Chalcogenides Physics and Applications, vol. 18, ed. by D. Khokhlov (Taylor and Francis, New York, 2003)Google Scholar
- 60.P. Ghosez, M. Veithen, J. Phys.-Condes. Matter 19(9), 096002 (2007)Google Scholar
- 61.G. Kliche, Infrared Phys. 24(2), 171–177 (1984)Google Scholar
- 62.G.S. Nolas, G.A. Slack, T. Caillat, G.P. Meisner, J. Appl. Phys. 79(5), 2622–2626 (1996)CrossRefGoogle Scholar
- 63.L. Chaput, J. Tobola, P. Pécheur, H. Scherrer, Phys. Rev. B 73(4), 045121 (2006)Google Scholar
- 64.P. Larson, S.D. Mahanti, M.G. Kanatzidis, Phys. Rev. B 62(19), 12754–12762 (2000)CrossRefGoogle Scholar
- 65.T.J. Zhu, K. Xiao, C. Yu, J.J. Shen, S.H. Yang, A.J. Zhou, X.B. Zhao, J. He, J. Appl. Phys. 108(4), 044903–044905 (2010)CrossRefGoogle Scholar
- 66.C. Yu, T.-J. Zhu, R.-Z. Shi, Y. Zhang, X.-B. Zhao, J. He, Acta Mater. 57(9), 2757–2764 (2009)CrossRefGoogle Scholar
- 67.X. Shi, J. Yang, J.R. Salvador, M.F. Chi, J.Y. Cho, H. Wang, S.Q. Bai, J.H. Yang, W.Q. Zhang, L.D. Chen, J. Am. Chem. Soc. 133(20), 7837–7846 (2011)CrossRefGoogle Scholar
- 68.Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, G.J. Snyder, Nature 473(7345), 66–69 (2011)CrossRefGoogle Scholar
- 69.Y. Takagiwa, Y. Pei, G. Pomrehn, G. J. Snyder, APL Materials in press (2013)Google Scholar
- 70.Y. Pei, A. LaLonde, S. Iwanaga, G.J. Snyder, Energy Environ. Sci. 4, 2085–2089 (2011)CrossRefGoogle Scholar
- 71.H. Wang, Y. Pei, A.D. Lalonde, G.J. Snyder, Adv. Mater. 23(11), 1366–1370 (2011)CrossRefGoogle Scholar
- 72.V.K. Zaitsev, M.I. Fedorov, E.A. Gurieva, I.S. Eremin, P.P. Konstantinov, A.Y. Samunin, M.V. Vedernikov, Phys. Rev. B 74(4), 045207 (2006)Google Scholar
- 73.S.K. Bux, M.T. Yeung, E.S. Toberer, G.J. Snyder, R.B. Kaner, J.-P. Fleurial, J. Mater. Chem. 21(33), 12259 (2011)CrossRefGoogle Scholar
- 74.W. Liu, X. Tan, K. Yin, H. Liu, X. Tang, J. Shi, Q. Zhang, C. Uher, Phys. Rev. Lett. 108(16), 166601 (2012)CrossRefGoogle Scholar
- 75.X. Liu, H. Wang, L. Hu, H. Xie, G. Jiang, G. J. Snyder, X. Zhao, T. Zhu, Adv. Energ. Mater. doi: 10.1002/aenm.201300174 (2013)
- 76.D.A. Pshenay-Severin, M.I. Fedorov, Phys. Solid State 49(9), 1633–1637 (2007)CrossRefGoogle Scholar
- 77.Q. Zhang, J. He, T.J. Zhu, S.N. Zhang, X.B. Zhao, T.M. Tritt, Appl. Phys. Lett. 93(10), 102109 (2008)CrossRefGoogle Scholar
- 78.F. Ben Zid, A. Bhouri, H. Mejri, M. Said, N. Bouarissa, J.L. Lazzari, F.A. d’Avitaya, J. Derrien, Physica B 322(3–4), 225–235 (2002)CrossRefGoogle Scholar
- 79.P.E. Batson, J.F. Morar, Appl. Phys. Lett. 59(25), 3285–3287 (1991)CrossRefGoogle Scholar
- 80.X.W. Wang, H. Lee, Y.C. Lan, G.H. Zhu, G. Joshi, D.Z. Wang, J. Yang, A.J. Muto, M.Y. Tang, J. Klatsky, S. Song, M.S. Dresselhaus, G. Chen, Z.F. Ren, Appl. Phys. Lett. 93(19), 193121 (2008)CrossRefGoogle Scholar
- 81.M.N. Tripathi, C.M. Bhandari, J. Phys. Condes. Matter 15(31), 5359–5370 (2003)Google Scholar
- 82.A.J. Minnich, H. Lee, X.W. Wang, G. Joshi, M.S. Dresselhaus, Z.F. Ren, G. Chen, D. Vashaee, Phys. Rev. B 80(15), 155327 (2009)CrossRefGoogle Scholar
- 83.G.A. Slack, M.A. Hussain, J. Appl. Phys. 70(5), 2694–2718 (1991)CrossRefGoogle Scholar
- 84.M. I. Fedorov, D. A. Pshenay-Severin, V. K. Zaitsev, S. Sano, M. V. Vedernikov, Features of Conduction Mechanism in n-type Mg2Si1-xSnx Solid Solutions. (IEEE, New York, 2003)Google Scholar
- 85.D.A. Pshenay-Severin, M.I. Fedorov, Phys. Solid State 52(7), 1342–1347 (2010)CrossRefGoogle Scholar
- 86.H. Brooks, Theory of the Electrical Properties of Germanium Silicon (Academic Press Inc, NY, 1955)Google Scholar
- 87.W.P. Mason, T.B. Bateman, Phys. Rev. Lett. 10(5), 151–154 (1963)CrossRefGoogle Scholar
- 88.C.B. Vining, J. Appl. Phys. 69(1), 331–341 (1991)CrossRefGoogle Scholar
- 89.D. Long, Phy. Rev. 120(6), 2024–2032 (1960)CrossRefGoogle Scholar
- 90.J.E. Aubrey, W. Gubler, T. Henningsen, S.H. Koenig, Phys. Rev. 130(5), 1667–1670 (1963)CrossRefGoogle Scholar
- 91.F.J. Morin, J.P. Maita, Phys. Rev. 96(1), 28–35 (1954)CrossRefGoogle Scholar
- 92.G.W. Ludwig, R.L. Watters, Phys. Rev. 101(6), 1699–1701 (1956)CrossRefGoogle Scholar
- 93.J.G. Nash, J.W. Holmkennedy, Phys. Rev. B 15(8), 3994–4006 (1977)CrossRefGoogle Scholar
- 94.P.D. Yoder, V.D. Natoli, R.M. Martin, J. Appl. Phys. 73(9), 4378–4383 (1993)CrossRefGoogle Scholar
- 95.S.V. Obukhov, V.G. Tyuterev, Phys. Solid State 51(6), 1110–1113 (2009)CrossRefGoogle Scholar
- 96.Z. Wang, S. D. Wang, S. Obukhov, N. Vast, J. Sjakste, V. Tyuterev, N. Mingo, Phys. Rev. B 83(20), 205208 (2011)Google Scholar
- 97.F. Murphy-Armando, S. Fahy, Phys. Rev. B 78(3), 035202 (2008)Google Scholar
- 98.D.M. Rowe, C.M. Bhandari, J. Phys. Lett. 46(1), L49–L52 (1985)CrossRefGoogle Scholar
- 99.H. Wang, A.D. LaLonde, Y. Pei, and G. J. Snyder, Adv. Funct. Mater. 23, 1586–1596, (2013)Google Scholar
- 100.Y. Z. Pei, A. D. LaLonde, N. A. Heinz, X. Y. Shi, S. Iwanaga, H. Wang, L. D. Chen, G. J. Snyder, Adv. Mater. 23(47), 5674–5678 (2011)Google Scholar
- 101.J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, G.J. Snyder, Science 321(5888), 554–557 (2008)Google Scholar
- 102.C.M. Jaworski, B. Wiendlocha, V. Jovovic, J.P. Heremans, Energy Environ. Sci. 4, 4155–4162 (2011)CrossRefGoogle Scholar