Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Structures of medium-sized silicon clusters

Nature volume 392, pages 582–585 (1998)Cite this article

Abstract

Silicon is the most important semiconducting material in the microelectronics industry. If current miniaturization trends continue, minimum device features will soon approach the size of atomic clusters. In this size regime, the structure and properties of materials often differ dramatically from those of the bulk. An enormous effort has been devoted to determining the structures of free silicon clusters1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22. Although progress has been made for Sin with n < 8, theoretical predictions for larger clusters are contradictory2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 and none enjoy any compelling experimental support. Here we report geometries calculated for medium-sized silicon clusters using an unbiased global search with a genetic algorithm. Ion mobilities23 determined for these geometries by trajectory calculations are in excellent agreement with the values that we measure experimentally. The cluster geometries that we obtain do not correspond to fragments of the bulk. For n = 12–18 they are built on a structural motif consisting of a stack of Si9 tricapped trigonal prisms. For n ⩾ 19, our calculations predict that near-spherical cage structures become the most stable. The transition to these more spherical geometries occurs in the measured mobilities for slightly larger clusters than in the calculations, possibly because of entropic effects.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Relative deviations of the collision integrals for proposed silicon cluster geometries from the values measured at 298 K.
Figure 2: The LDA global minima for the Sin (n = 12–20) neutrals.
Figure 3: Prolate geometries for n = 19–26 constructed by stacking Si9 TTP subunits.

Similar content being viewed by others

References

  1. Pacchioni, G. & Koutecky, J. Silicon and germanium clusters. A theoretical study of their electronic structures and properties. J. Chem. Phys. 84, 3301–3310 (1986).

    Article  CAS  Google Scholar 

  2. Tomanek, D. & Schluter, M. A. Calculation of magic numbers and the stability of small Si clusters. Phys. Rev. Lett. 56, 1055–1058 (1986).

    Article  CAS  Google Scholar 

  3. Slee, T., Zhenyang, L. & Mingos, D. M. P. Polyhedral skeletal electron pair theory of bare clusters. 1. Small silicon clusters. Inorg. Chem. 28, 2256–2261 (1989).

    Article  CAS  Google Scholar 

  4. Chelikowsky, J. R., Glassford, K. M. & Phillips, J. C. Interatomic force fields for silicon microclusters. Phys. Rev. B 44, 1538–1545 (1991).

    Article  CAS  Google Scholar 

  5. Phillips, J. C. Electron-correlation energies and the structure of Si13. Phys. Rev. B 47, 14132–14135 (1993).

    Article  CAS  Google Scholar 

  6. Vasiliev, I., Ögüt, S. & Chelikowsky, J. R. Ab Initio calculations for the polarizabilities of small semiconductor clusters. Phys. Rev. Lett. 78, 4805–4808 (1997).

    Article  CAS  Google Scholar 

  7. Raghavachari, K. & Rohlfing, C. M. Bonding and stabilities of small silicon clusters: a theoretical study of Si7–Si10. J. Chem. Phys. 89, 2219–2234 (1988).

    Article  CAS  Google Scholar 

  8. Rohlfing, C. M. & Raghavachari, K. Atheoretical study of small silicon clusters using an effective core potential. Chem. Phys. Lett. 167, 559–565 (1990).

    Article  CAS  Google Scholar 

  9. Raghavachari, K. & Rohlfing, C. M. Structures of Si10. Are there conventionally bonded low-energy isomers? Chem. Phys. Lett. 198, 521–525 (1992).

    Article  CAS  Google Scholar 

  10. Messmer, R. P. & Patterson, C. H. Long bonds in silicon clusters: a failure of conventional Møller-Plesset perturbation theory? Chem. Phys. Lett. 192, 277–282 (1992).

    Article  CAS  Google Scholar 

  11. Mistriotis, A. D., Froudakis, G. E., Vendras, P. & Flytzanis, N. Model potential for silicon clusters and surfaces. Phys. Rev. B 47, 10648–10653 (1993).

    Article  CAS  Google Scholar 

  12. Jug, K. & Krack, M. Consistent parameterization of semiempirical MO methods. Int. J. Quant. Chem. 44, 517–531 (1992).

    Article  CAS  Google Scholar 

  13. Gu, B., Li, Z. & Zhu, J. Electrical structure of small icosahedral silicon clusters. J. Phys.: Condens. Matter 5, 5255–5260 (1993).

    CAS  Google Scholar 

  14. Gong, X. G., Zheng, Q. Q. & He, Y. Z. Structural properties of silicon clusters: an empirical potential study. J. Phys.: Condens. Matter 7, 577–584 (1995).

    CAS  Google Scholar 

  15. Menon, M. & Subbaswamy, K. Nonorthogonal tight-binding molecular-dynamics scheme for silicon with improved transferability. Phys. Rev. B 55, 9231–9234 (1996).

    Article  Google Scholar 

  16. Ramakrishna, M. V. & Bahel, A. Combined tight-binding and density functional molecular dynamics investigation of Si12cluster structure. J. Chem. Phys. 104, 9833–9840 (1996).

    Article  CAS  Google Scholar 

  17. Wales, D. J. Electronic structure of small silicon clusters. Phys. Rev. A 49, 2195–2198 (1994).

    Article  CAS  Google Scholar 

  18. Kaxiras, E. & Jackson, K. Shape of small silicon clusters. Phys. Rev. Lett. 71, 727–730 (1993); Structural models for intermediate-sized Si clusters. Z. Phys. D 26, 346–348 (1993).

    Article  CAS  Google Scholar 

  19. Pederson, M. R., Jackson, K., Porezag, D. V., Hajnal, Z. & Frauenheim, T. Vibrational signatures for low-energy intermediate-sized Si clusters. Phys. Rev. B 54, 2863–2867 (1996).

    Article  CAS  Google Scholar 

  20. Grossman, J. C. & Mitas, L. Quantum Monte Carlo determination of electronic and structural properties of Sinclusters. Phys. Rev. Lett. 74, 1323–1326 (1995); Family of low-energy elongated Sin(n ≤ 50) clusters. Phys. Rev. B 52, 16735–16738 (1995).

    Article  CAS  Google Scholar 

  21. Rothlisberger, U., Andreoni, W. & Giannozzi, P. Thirteen-atom clusters: equilibrium geometries, structural transformations, and trends in Na, Mg, Al, and Si. J. Chem. Phys. 96, 1248–1256 (1992).

    Article  Google Scholar 

  22. Song, J., Ulloa, S. E. & Drabold, D. A. Soliton-induced lattice relaxation and the electronic and vibrational spectra of silicon clusters. Phys. Rev. B 53, 8042–8051 (1996).

    Article  CAS  Google Scholar 

  23. Jarrold, M. F. & Constant, V. A. Silicon cluster ions: evidence for a structural transition. Phys. Rev. Lett. 67, 2994–2997 (1991).

    Article  CAS  Google Scholar 

  24. Arnold, C. C. & Neumark, D. M. Study of Si4and Si−4using threshold photodetachment (ZEKE) spectroscopy. J. Chem. Phys. 99, 3353–3362 (1993).

    Article  CAS  Google Scholar 

  25. Honea, E. C.et al. Raman spectra of size-selected silicon clusters and comparison with calculated structures. Nature 366, 42–44 (1993).

    Article  CAS  Google Scholar 

  26. Li, S., Van Zee, R. J., Weltner Jr, W. & Raghavachari, K. Si3-Si7. Experimental and theoretical infrared spectra. Chem. Phys. Lett. 243, 275–280 (1995).

    Article  CAS  Google Scholar 

  27. Von Helden, G., Hsu, M. T., Gotts, N. G. & Bowers, M. T. Carbon cluster cations with up to 84 atoms: structures, formation mechanism, and reactivity. J. Phys. Chem. 97, 8182–8192 (1993).

    Article  CAS  Google Scholar 

  28. Mesleh, M. F., Hunter, J. M., Shvartsburg, A. A., Schatz, G. C. & Jarrold, M. F. Structural information from ion mobility measurements: effects of the long-range potential. J. Phys. Chem. 100, 16082–16086 (1996).

    Article  CAS  Google Scholar 

  29. Deaven, D. M. & Ho, K. M. Molecular geometry optimization with a genetic algorithm. Phys. Rev. Lett. 75, 288–291 (1995).

    Article  CAS  Google Scholar 

  30. Jarrold, M. F. Drift tube studies of atomic clusters. J. Phys. Chem. 99, 11–21 (1995).

    Article  CAS  Google Scholar 

  31. Shvartsburg, A. A., Hudgins, R. R., Dugourd, Ph. & Jarrold, M. F. Structural elucidation of fullerene dimers using high-resolution ion mobility measurements and trajectory calculation simulations. J.Phys. Chem. A 101, 1684–1688 (1997).

    Article  CAS  Google Scholar 

  32. Bylaska, E. J., Taylor, P. R., Kawai, R. & Weare, J. H. LDA predictions of C20isomerizations: neutral and charged species. J. Phys. Chem. 100, 6966–6972 (1996).

    Article  CAS  Google Scholar 

  33. Martin, J. M. L. C28: the smallest stable fullerene? Chem. Phys. Lett. 255, 1–6 (1996).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank J. Chelikowsky, D. Drabold, G. Froudakis, J. Grossman, K. Jackson, K. Jug, M. Krack, U. Landman, H. Mayne, M. Menon, L. Mitas, L. Munro, K. Raghavachari, C. Rohlfing, K.Subbaswamy and D. Wales for providing us with their optimized silicon cluster geometries and for discussions; we also thank R. Hudgins for assistance with the experimental work. This research was supported by the NSF, the US Army Research Office, the Office of Basic Energy Sciences, the High Performance Computing and Communications initiative (including a grant of computer time at the National Energy Research Supercomputing Center), and Ames Laboratory operated for the US DOE by Iowa State University.

Author information

Authors and Affiliations

  1. Ames Laboratory-USDOE and Department of Physics and Astronomy, Iowa State University, Ames, 50011, Iowa, USA

    Kai-Ming Ho, Bicai Pan, Zhong-Yi Lu, Cai-Zhuang Wang & Jacob G. Wacker

  2. Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, 60208, Illinois, USA

    Alexandre A. Shvartsburg, James L. Fye & Martin F. Jarrold

Authors
  1. Kai-Ming Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexandre A. Shvartsburg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bicai Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhong-Yi Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Cai-Zhuang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jacob G. Wacker
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. James L. Fye
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Martin F. Jarrold
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin F. Jarrold.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ho, KM., Shvartsburg, A., Pan, B. et al. Structures of medium-sized silicon clusters. Nature 392, 582–585 (1998). https://doi.org/10.1038/33369

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/33369

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing