Skip to main content
SpringerLink
Log in

Optimal thermoelectric figure of merit of Si/Ge core-shell nanowires

  • Research Article
  • Published:
Nano Research Aims and scope Submit manuscript

Abstract

We investigate the thermoelectric energy conversion efficiency of Si and Ge nanowires, and in particular, that of Si/Ge core-shell nanowires. We show how the presence of a thin Ge shell on a Si core nanowire increases the overall figure of merit. We find the optimal thickness of the Ge shell to provide the largest figure of merit for the devices. We also consider Ge core/Si shell nanowires, and show that an optimal thickness of the Si shell does not exist, since the figure of merit is a monotonically decreasing function of the radius of the nanowire. Finally, we verify the empirical law relating the electron energy gap to the optimal working temperature that maximizes the efficiency of the device.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Nolas, G. S.; Sharp, J.; Goldsmid, H. J. Thermoelectrics: Basic principles and new materials developments; Springer series in material science; Springer Verlag: Berlin, Heidelberg, 2001; Vol. 45.

    Book  Google Scholar 

  2. Goldsmid, H. J. Introduction to Thermoelectricity, 1st ed.; Springer-Verlag: Berlin, 2010; pp 250.

    Book  Google Scholar 

  3. Rurali, R. Colloquium: Structural, electronic, and transport properties of silicon nanowires. Rev. Mod. Phys. 2010, 82, 427–449.

    Article  Google Scholar 

  4. Dubi, Y.; Di Ventra, M. Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions. Rev. Mod. Phys. 2011, 83, 131–155.

    Article  Google Scholar 

  5. Takabatake, T.; Suekuni, K.; Nakayama, T. Phonon-glass electron-crystal thermoelectric clathrates: Experiments and theory. Rev. Mod. Phys. 2014, 86, 669–716.

    Article  Google Scholar 

  6. Tritt, T. M. Thermoelectrics run hot and cold. Science 1996, 272, 1276–1277.

    Article  Google Scholar 

  7. DiSalvo, F. J. Thermoelectric cooling and power generation. Science 1999, 285, 703–706.

    Article  Google Scholar 

  8. Zhao, L. D.; Lo, S. H.; Zhang, Y. S.; Sun, H.; Tan, G. J.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 2014, 508, 373–377.

    Article  Google Scholar 

  9. Hicks, L. D.; Dresselhaus, M. S. Effect of quantum-well structures on the thermoelectric figure of merit. Phys. Rev. B 1993, 47, 12727–12731.

    Article  Google Scholar 

  10. Hochbaum, A. I.; Chen, R. K.; Delgado, R. D.; Liang, W. J.; Garnett, E. C.; Najarian, M.; Majumdar, A.; Yang, P. D. Enhanced thermoelectric performance of rough silicon nanowires. Nature 2008, 451, 163–167.

    Article  Google Scholar 

  11. Boukai, A. I.; Bunimovich, Y.; Tahir-Kheli, J.; Yu, J. K.; Goddard, W. A.; Heath, J. R. Silicon nanowires as efficient thermoelectric materials. Nature 2008, 451, 168–171.

    Article  Google Scholar 

  12. Lee, J. H.; Galli, G. A.; Grossman, J. C. Nanoporous Si as an efficient thermoelectric material. Nano Lett. 2008, 8, 3750–3754.

    Article  Google Scholar 

  13. Vo, T. T. M.; Williamson, A. J.; Lordi, V.; Galli, G. Atomistic design of thermoelectric properties of silicon nanowires. Nano Lett. 2008, 8, 1111–1114.

    Article  Google Scholar 

  14. Tang, J. Y.; Wang, H.-T.; Lee, D. H.; Fardy, M.; Huo, Z. Y.; Russell, T. P.; Yang, P. D. Holey silicon as an efficient thermoelectric material. Nano Lett. 2010, 10, 4279–4283.

    Article  Google Scholar 

  15. Chen, Y.; Jayasekera, T.; Calzolari, A.; Kim, K. W.; Buongiorno Nardelli, M. Thermoelectric properties of graphene nanoribbons, junctions and superlattices. J. Phys. Condens. Matter 2010, 22, 372202.

    Article  Google Scholar 

  16. Amato, M.; Ossicini, S.; Rurali, R. Band-offset driven efficiency of the doping of SiGe core-shell nanowires. Nano Lett. 2011, 11, 594–598.

    Article  Google Scholar 

  17. Lee, E. K.; Yin, L.; Lee, Y.; Lee, J. W.; Lee, S. J.; Lee, J.; Cha, S. N.; Whang, D.; Hwang, G. S.; Hippalgaonkar, K. et al. Large thermoelectric figure-of-merits from SiGe nanowires by simultaneously measuring electrical and thermal transport properties. Nano Lett. 2012, 12, 2918–2923.

    Article  Google Scholar 

  18. Markussen, T. Surface disordered Ge-Si core-shell nanowires as efficient thermoelectric materials. Nano Lett. 2012, 12, 4698–4704.

    Article  Google Scholar 

  19. Curtin, B. M.; Codecido, E. A.; Kramer, S.; Bowers, J. E. Field-effect modulation of thermoelectric properties in multigated silicon nanowires. Nano Lett. 2013, 13, 5503–5508.

    Article  Google Scholar 

  20. Jiang, X. C.; Xiong, Q. H.; Nam, S.; Qian, F.; Li, Y.; Lieber, C. M. InAs/InP radial nanowire heterostructures as high electron mobility devices. Nano Lett. 2007, 7, 3214–3218.

    Article  Google Scholar 

  21. Tian, Y.; Sakr, M. R.; Kinder, J. M.; Liang, D.; MacDonald, M. J.; Qiu, R. L. J.; Gao, H. J.; Gao, X. P. A. One dimensional quantum confinement effect modulated thermoelectric properties in InAs nanowires. Nano Lett. 2012, 12, 6492–6497.

    Article  Google Scholar 

  22. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186.

    Article  Google Scholar 

  23. Ceperley, D. M.; Alder, B. J. The ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 1980, 45, 566–569.

    Article  Google Scholar 

  24. Perdew, J. P.; Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23, 5048–5079.

    Article  Google Scholar 

  25. Yang, K. K.; Chen, Y. P.; D’Agosta, R.; Xie, Y. E.; Zhong, J. X.; Rubio, A. Enhanced thermoelectric properties in hybrid graphene/boron nitride nanoribbons. Phys. Rev. B 2012, 86, 045425.

    Article  Google Scholar 

  26. D’Agosta, R. Towards a dynamical approach to the calculation of the figure of merit of thermoelectric nanoscale devices. Phys. Chem. Chem. Phys. 2013, 15, 1758–1765.

    Article  Google Scholar 

  27. Yang, K.; Cahangirov, S.; Cantarero, A.; Rubio, A.; D’Agosta, R. Thermoelectric properties of atomically thin silicene and germanene nanostructures. Phys. Rev. B 2014, 89, 125403.

    Article  Google Scholar 

  28. Keating, P. Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev. 1966, 145, 637.

    Article  Google Scholar 

  29. Mingo, N. Anharmonic phonon flow through molecular-sized junctions. Phys. Rev. B 2006, 74, 125402.

    Article  Google Scholar 

  30. Wang, J. S.; Wang, J.; Zeng, N. Nonequilibrium Green’s function approach to mesoscopic thermal transport. Phys. Rev. B 2006, 74, 033408.

    Article  Google Scholar 

  31. Yamamoto, T.; Watanabe, K. Nonequilibrium Green’s function approach to phonon transport in defective carbon nanotubes. Phys. Rev. Lett. 2006, 96, 255503.

    Article  Google Scholar 

  32. Wang, J. S. Quantum thermal transport from classical molecular dynamics. Phys. Rev. Lett. 2007, 99, 160601.

    Article  Google Scholar 

  33. Wang, J. S.; Wang, J.; Lüe, J. T. Quantum thermal transport in nanostructures. Eur. Phys. J. B 2008, 62, 381–404.

    Article  Google Scholar 

  34. Chen, J.; Zhang, G.; Li, B. Tunable thermal conductivity of Si1-xGex nanowires. Appl. Phys. Lett. 2009, 95, 073117.

    Article  Google Scholar 

  35. Wan, W. H.; Xiong, B. G.; Zhang, W. X.; Feng, J.; Wang, E. G. The effect of electron-phonon coupling on the thermal conductivities of silicon nanowires. J. Phys. Condens. Matter 2012, 24, 295402.

    Article  Google Scholar 

  36. Shanks, H. R.; Sidles, P. H.; Maycock, P. D.; Danielson, G. C. Thermal conductivity of silicon from 300 to 1400 K. Phys. Rev. 1963, 130, 1743.

    Article  Google Scholar 

  37. Rücker, H.; Methfessel, M. Anharmonic Keating model for group-IV semiconductors with application to the lattice dynamics in alloys of Si, Ge, and C. Phys. Rev. B 1995, 52, 11059–11072.

    Article  Google Scholar 

  38. Thonhauser, T.; Mahan, G. D. Phonon modes in Si [111]_nanowires. Phys. Rev. B 2004, 69, 075213.

    Article  Google Scholar 

  39. Shelley, M.; Mostofi, A. A. Prediction of high ZT in thermoelectric silicon nanowires with axial germanium heterostructures. Europhys. Lett. 2011, 94, 67001.

    Article  Google Scholar 

  40. Moon, J.; Kim, J. H.; Chen, Z. C. Y.; Xiang, J.; Chen, R. K. Gate-modulated thermoelectric power factor of hole gas in Ge-Si core-shell nanowires. Nano Lett. 2013, 13, 1196–1202.

    Article  Google Scholar 

  41. Wingert, M. C.; Chen, Z. C. Y.; Dechaumphai, E.; Moon, J.; Kim, J. H.; Xiang, J.; Chen, R. K. Thermal conductivity of Ge and Ge-Si core-shell nanowires in the phonon confinement regime. Nano Lett. 2011, 11, 5507–5513.

    Article  Google Scholar 

  42. Yu, B.; Zebarjadi, M.; Wang, H. H.; Lukas, K.; Wang, H. Z.; Wang, D. Z.; Opeil, C.; Dresselhaus, M.; Chen, G.; Ren, Z. F. Enhancement of thermoelectric properties by modulation-doping in silicon germanium alloy nanocomposites. Nano Lett. 2012, 12, 2077–2082.

    Article  Google Scholar 

  43. Goldmid, H. J.; Sharp, J. W. Estimates of the thermal band gap of a semiconductor from Seebeck measurements. J. Electron. Mater. 1999, 28, 869.

    Article  Google Scholar 

  44. Goldsmid, H. J. The thermal conductivity of bismuth telluride. Proc. Phys. Soc. B 1956, 69, 203–209.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nano-Bio Spectroscopy Group and ETSF Scientific Development Center, Departamento de Fisica de Materiales, Universidad del Pais Vasco UPV/EHU, San Sebastian, 20018, Spain

    Kaike Yang, Angel Rubio & Roberto D’Agosta

  2. Instituto de Ciencia de Materiales, Universidad de Valencia, Valencia, 46071, Spain

    Andres Cantarero

  3. Ikerbasque, Basque foundation for Science, Bilbao, 48013, Spain

    Roberto D’Agosta

Authors
  1. Kaike Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andres Cantarero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Angel Rubio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Roberto D’Agosta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Angel Rubio or Roberto D’Agosta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, K., Cantarero, A., Rubio, A. et al. Optimal thermoelectric figure of merit of Si/Ge core-shell nanowires. Nano Res. 8, 2611–2619 (2015). https://doi.org/10.1007/s12274-015-0766-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12274-015-0766-2

Keywords

Search

Navigation