Skip to main content
SpringerLink
Log in

Modified valence force field approach for phonon dispersion: from zinc-blende bulk to nanowires

Methodology and computational details

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

The correct estimation of the thermal properties of ultra-scaled CMOS and thermoelectric semiconductor devices demands for accurate phonon modeling in such structures. This work provides a detailed description of the modified valence force field (MVFF) method to obtain the phonon dispersion in zinc-blende semiconductors. The model is extended from bulk to nanowires after incorporating proper boundary conditions. The computational demands by the phonon calculation increase rapidly as the wire cross-section size increases. It is shown that nanowire phonon spectra differ considerably from the bulk dispersions. This manifests itself in the form of different physical and thermal properties in these wires. We believe that this model and approach will prove beneficial in the understanding of the lattice dynamics in the next generation ultra-scaled semiconductor devices.

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. Buin, A., Verma, A., Anantram, M.: Carrier-phonon interaction in small cross-sectional silicon nanowires. J. Appl. Phys. 104, 053716 (2008)

    Article  Google Scholar 

  2. Buin, A.K., Verma, A., Svizhenko, A., Anantram, M.P.: Significant enhancement of hole mobility in [110] silicon nanowires compared to electrons and Bulk silicon. Nano Lett. 8(2), 760–765 (2008) pMID: 18205425 [online]. Available: http://pubs.acs.org/doi/abs/10.1021/nl0727314

    Article  Google Scholar 

  3. Mingo, N., Yang, L.: Phonon transport in nanowires coated with an amorphous material: an atomistic Green’s function approach. Phys. Rev. B 68(24), 245406 (2003)

    Article  Google Scholar 

  4. Mingo, N., Yang, L., Li, D., Majumdar, A.: Predicting the thermal conductivity of Si and Ge nanowires. Nano Lett. 3(12), 1713–1716 (2003)

    Article  Google Scholar 

  5. Wang, J., Wang, J.-S.: Dimensional crossover of thermal conductance in nanowires. Appl. Phys. Lett. 90(24), 241908 (2007)

    Article  Google Scholar 

  6. Peelaers, H., Partoens, B., Peeters, F.M.: Phonon band structure of Si nanowires: a stability analysis. Nano Lett. 9(1), 107–111 (2009)

    Article  Google Scholar 

  7. Keating, P.N.: Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev. 145(2), 637–645 (1966)

    Article  Google Scholar 

  8. Sui, Z., Herman, I.P.: Effect of strain on phonons in Si, Ge, and Si/Ge heterostructures. Phys. Rev. B 48(24), 17938–17953 (1993)

    Article  Google Scholar 

  9. Fu, H., Ozolins, V., Alex, Z.: Phonons in GaP quantum dots. Phys. Rev. B 59(4), 2881–2887 (1999)

    Article  Google Scholar 

  10. McMurry, H., Solbrig, A. Jr., Boyter, J.: The use of valence force potentials in calculating crystal vibrations. J. Phys. Chem. Solids 28(12), 2359–2368 (1967)

    Article  Google Scholar 

  11. Weber, W.: Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α-Sn. Phys. Rev. B 15(10), 4789–4803 (1977)

    Article  Google Scholar 

  12. Rustagi, K., Weber, W.: Adiabatic bond charge model for the phonons in A(III)B(V) semiconductors. Solid State Commun. 18, 673–675 (1976)

    Article  Google Scholar 

  13. Markussen, T., Jauho, A.-P., Brandbyge, M.: Heat conductance is strongly anisotropic for pristine silicon nanowires. Nano Lett. 8(11), 3771–3775 (2008)

    Article  Google Scholar 

  14. McMurry, H.L., Solbrig, A.W., Boyter, J.K., Noble, C.: The use of valence force potentials in calculating crystal vibrations. J. Phys. Chem. Solids 28, 2359–2368 (1967)

    Article  Google Scholar 

  15. Zou, J., Balandin, A.: Phonon heat conduction in a semiconductor nanowire. J. Appl. Phys. 89(5), 2932–2938 (2001)

    Article  Google Scholar 

  16. Zhang, Y., Cao, J.X., Xiao, Y., Yan, X.H.: Phonon spectrum and specific heat of silicon nanowires. J. Appl. Phys. 102(10), 104303 (2007)

    Article  Google Scholar 

  17. Li, X., Maute, K., Dunn, M.L., Yang, R.: Strain effects on the thermal conductivity of nanostructures. Phys. Rev. B 81(24), 245318 (2010)

    Article  Google Scholar 

  18. Thonhauser, T., Mahan, G.D.: Phonon modes in Si [111] nanowires. Phys. Rev. B 69(7), 075213 (2004)

    Article  Google Scholar 

  19. Zhao, H., Tang, Z., Li, G., Aluru, N.R.: Quasiharmonic models for the calculation of thermodynamic properties of crystalline silicon under strain. J. Appl. Phys. 99(6), 064314 (2006)

    Article  Google Scholar 

  20. Lazarenkova, O.L., von Allmen, P., Oyafuso, F., Lee, S., Klimeck, G.: Effect of anharmonicity of the strain energy on band offsets in semiconductor nanostructures. Appl. Phys. Lett. 85(18), 4193–4195 (2004)

    Article  Google Scholar 

  21. Hendrikse, Z.W., Elout, M.O., Maaskant, W.J.A.: Computation of the independent elements of the dynamical matrix. Comput. Phys. Commun. 86(3), 297–311 (1995)

    Article  Google Scholar 

  22. Landauer, R.: Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Dev. 1(3), 223–231 (1957)

    Article  MathSciNet  Google Scholar 

  23. Wallace, D.C.: Thermodynamics of Crystals. Dover, New York (1998)

    Google Scholar 

  24. Weinstein, B.A., Piermarini, G.J.: Raman scattering and phonon dispersion in Si and GaP at very high pressure. Phys. Rev. B 12(4), 1172–1186 (1975)

    Article  Google Scholar 

  25. Dongarra, J.: Survey of sparse matrix storage formats, (1995) [online]. Available: http://www.netlib.org/linalg/html_templates/node90.html

  26. Dongarra, J.: Mathworks, Matlab eig reference (2010) [online]. Available: http://www.mathworks.com/help/techdoc/ref/eig.html

  27. Dongarra, J.: Matlab eig reference (2010) [online]. Available: http://www.mathworks.com/help/techdoc/ref/eigs.html

  28. Klimeck, G., Oyafuso, F., Boykin, T.B., Bowen, R.C., von Allmen, P.: Development of a nanoelectronic 3-D (NEMO 3-D) simulator for multimillion atom simulations and its application to alloyed quantum dots. Comput. Model. Eng. Sci. (CMES) 3(5), 601–642 (2002)

    MATH  Google Scholar 

  29. Paul A., Luisier, M., Neophytou, N., Kim, R., Geng, J., McLennan, M., Lundstrom, M., Klimeck, G.: Band Structure Lab, May 2006 [online]. Available: http://nanohub.org/resources/1308

  30. Nilsson, G., Nelin, G.: Study of the homology between silicon and germanium by thermal neutron spectrometry. Phys. Rev. B 6(10), 3777–3786 (1972)

    Article  Google Scholar 

  31. Electronic archive, new semiconductor materials—characteristics and properties, Ioffe Physico-Technical Institute Website, 2001, http://www.ioffe.ru/SVA/NSM/Semicond/

  32. Madelung, O.: Semiconductors—HandBook, 3rd edn. Springer, Berlin (2004)

    Google Scholar 

  33. de Gironcoli, S.: Phonons in Si-Ge systems: An ab initio interatomic-force-constant approach. Phys. Rev. B 46(4), 2412–2419 (1992)

    Article  Google Scholar 

  34. Eryiğit, R., Herman, I.P.: Lattice properties of strained GaAs, Si, and Ge using a modified bond-charge model. Phys. Rev. B 53(12), 7775–7784 (1996)

    Article  Google Scholar 

  35. Lazarenkova, O.L., von Allmen, P., Oyafuso, F., Lee, S., Klimeck, G.: An atomistic model for the simulation of acoustic phonons, strain distribution, and Grüneisen coefficients in zinc-blende semiconductors. Superlattices Microst. 34(3–6), 553–556 (2003)

    Article  Google Scholar 

  36. Blackford, L.S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia (1997)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering and Network for Computational Nanotechnology, Purdue University, 47907, West Lafayette, USA

    Abhijeet Paul, Mathieu Luisier & Gerhard Klimeck

Authors
  1. Abhijeet Paul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mathieu Luisier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gerhard Klimeck
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhijeet Paul.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paul, A., Luisier, M. & Klimeck, G. Modified valence force field approach for phonon dispersion: from zinc-blende bulk to nanowires. J Comput Electron 9, 160–172 (2010). https://doi.org/10.1007/s10825-010-0332-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-010-0332-9

Keywords

Search

Navigation