Skip to main content
SpringerLink
Log in

Liquid droplet dynamics and complex morphologies in vapor–liquid–solid nanowire growth

  • Articles
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

The morphology of semiconducting nanowires, including kinked and branched wires, must be controlled in order to produce functional devices. Here, we describe some of the experimental and theoretical work involving complex morphologies of Au-catalyzed Si nanowires grown using the vapor–liquid–solid technique. Although there is a broad parameter space to explore, experiments have highlighted the importance of the precursor and impurity partial pressures on kinking behavior. Theoretical and modeling work has indicated that the stability of and transitions in droplet configuration are important for growth direction changes that can lead to complex morphologies. We describe recent phase-field simulations of nanowire growth that address the dynamics of liquid droplets during vapor–liquid–solid growth, as well as the implications of these results for the formation of wires with complex morphology.

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.

FIG. 1.
FIG. 2.
FIG. 3.
FIG. 4.
TABLE I
FIG. 5.
FIG. 6.
FIG. 7.
FIG. 8.
FIG. 9.
FIG. 10.

Similar content being viewed by others

References

  1. S. Nam, X. Jiang, Q. Xiong, D. Ham, and C.M. Lieber: Vertically integrated, three-dimensional nanowire complementary metal-oxide-semiconductor circuits. Proc. Natl. Acad. Sci. 106, 21035 (2009).

    Article  CAS  Google Scholar 

  2. M.J. Bierman and S. Jin: Potential applications of hierarchical branching nanowires in solar energy conversion. Energy Environ. Sci. 2, 1050 (2009).

    Article  CAS  Google Scholar 

  3. M.D. Kelzenberg, S.W. Boettcher, J.A. Petykiewicz, D.B. Turner-Evans, M.C. Putnam, E.L. Warren, J.M. Spurgeon, R.M. Briggs, N.S. Lewis, and H.A. Atwater: Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications. Nature Mater. 9, 239 (2010).

    Article  CAS  Google Scholar 

  4. C.K. Chan, H. Peng, G. Liu, K. McIlwrath, X.F. Zhang, R.A. Huggins, Y. Cui: High-performance lithium battery anodes using silicon nanowires. Nature Nanotechnol. 3, 31 (2008).

    Article  CAS  Google Scholar 

  5. Y. Cui, Q. Wei, H. Park, and C.M. Lieber: Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species. Science 293, 1289 (2001).

    Article  CAS  Google Scholar 

  6. F. Patolsky, G. Zheng, O. Hayden, M. Lakadamyali, X. Zhuang, and C.M. Lieber: Electrical detection of single viruses. Proc. Natl. Acad. Sci. 101, 14017 (2004).

    Article  CAS  Google Scholar 

  7. G. Zheng, F. Patolsky, Y. Cui, W.U. Wang, and C.M. Lieber: Multiplexed electrical detection of cancer markers with nanowire sensor arrays. Nature Biotechnol. 23, 1294 (2005).

    Article  CAS  Google Scholar 

  8. W. Kim, J.K. Ng, M.E. Kunitake, B.R. Conklin, and P. Yang: Interfacing silicon nanowires with mammalian cells. J. Am. Chem. Soc. 129, 7228 (2007).

    Article  CAS  Google Scholar 

  9. B. Tian, T. Cohen-Karni, Q. Qing, X. Duan, P. Xie, and C.M. Lieber: Three-dimensional, flexible nanoscale field-effect transistors as localized bioprobes. Science 329, 830 (2010).

    Article  CAS  Google Scholar 

  10. R.S. Wagner and W.C. Ellis: Vapor-liquid-solid mechanism of single crystal growth. Appl. Phys. Lett. 4, 89 (1964).

    Article  CAS  Google Scholar 

  11. R.S. Wagner and C.J. Doherty: Mechanism of branching and kinking during VLS crystal growth. J. Electrochem. Soc. 115, 93 (1968).

    Article  CAS  Google Scholar 

  12. B. Tian, P. Xie, T.J. Kempa, D.C. Bell, and C. Lieber: Single-crystalline kinked semiconductor nanowire superstructures. Nature Nanotechnol. 4, 824 (2009).

    Article  CAS  Google Scholar 

  13. G.A. Bootsma and H.J. Gassen: Quantitative study on growth of silicon whiskers from silane and germanium whiskers from germane. J. Cryst. Growth 10, 223 (1971).

    Article  CAS  Google Scholar 

  14. J. Westwater, D.P. Gosain, S. Tomiya, S. Usui, and H. Ruda: Growth of silicon nanowires via gold/silane vapor-liquid-solid reaction. J. Vac. Sci. Technol. B 15, 554 (1997).

    Article  CAS  Google Scholar 

  15. J.B. Hannon, S. Kodambaka, F.M. Ross, and R.M. Tromp: The influence of the surface migration of gold on the growth of silicon nanowires. Nature 440, 69 (2006).

    Article  CAS  Google Scholar 

  16. S. Kodambaka, J.B. Hannon, R.M. Tromp, and F.M. Ross: Control of Si nanowire growth by oxygen. Nano Lett. 6, 1292 (2006).

    Article  CAS  Google Scholar 

  17. T. Kawashima, T. Mizutani, T. Nakagawa, H. Torii, T. Saitoh, K. Komori, and M. Fujii: Control of surface migration of gold particles on Si nanowires. Nano Lett. 8, 362 (2008).

    Article  CAS  Google Scholar 

  18. A. Lugstein, M. Steinmair, Y.J. Hyun, G. Hauer, P. Pongratz, and E. Bertagnolli: Pressure-induced orientation control of the growth of epitaxial silicon nanowires. Nano Lett. 8, 2310 (2008).

    Article  CAS  Google Scholar 

  19. P. Madras, E. Dailey, and J. Drucker: Kinetically induced kinking of vapor–liquid–solid grown epitaxial Si nanowires. Nano Lett. 9, 3826 (2009).

    Article  CAS  Google Scholar 

  20. P. Madras, E. Dailey, and J. Drucker: Spreading of liquid AuSi on vapor–liquid solid–grown Si nanowires. Nano Lett. 10, 1759 (2010).

    Article  CAS  Google Scholar 

  21. E. Dailey, P. Madras, and J. Drucker: Au on vapor–liquid–solid grown Si nanowires: Spreading of liquid AuSi from the catalytic seed. J. Appl. Phys. 108, 064320 (2010).

    Article  CAS  Google Scholar 

  22. E. Dailey, P. Madras, and J. Drucker: Composition and growth direction control of epitaxial vapor–liquid–solid-grown SiGe nanowires. Appl. Phys. Lett. 97, 143106 (2010).

    Article  CAS  Google Scholar 

  23. K.W. Schwarz and J. Tersoff: From droplets to nanowires: Dynamics of vapor–liquid–solid growth. Phys. Rev. Lett. 102, 206101 (2009).

    Article  CAS  Google Scholar 

  24. K.W. Schwarz and J. Tersoff: Elementary processes in nanowire growth. Nano Lett. 11, 316 (2011).

    Article  CAS  Google Scholar 

  25. S.M. Roper, A.M. Anderson, S.H. Davis, and P.W. Voorhees: Radius selection and droplet unpinning in vapor–liquid–solid-grown nanowires. J. Appl. Phys. 107, 114320 (2010).

    Article  CAS  Google Scholar 

  26. M.S. McCallum, P.W. Voorhees, M.J. Miksis, S.H. Davis, and H. Wong: Capillary instabilities in solid thin films: Lines. J. Appl. Phys. 79, 7604 (1996).

    Article  CAS  Google Scholar 

  27. V. Schmidt, S. Senz, and U. Gösele: The shape of epitaxially grown silicon nanowires and the influence of line tension. Appl. Phys. A 445 (2005).

    Google Scholar 

  28. S.M. Roper, S.H. Davis, S.A. Norris, A.A. Golovin, P.W. Voorhees, and M. Weiss: Steady growth of nanowires via the vapor–liquid–solid method. J. Appl. Phys. 102, 034304 (2007).

    Article  CAS  Google Scholar 

  29. E.B. Dussan, V: On the spreading of liquids on solid surfaces: Static and dynamic contact lines. Annu. Rev. of Fluid Mech. 11, 371 (1979).

    Article  Google Scholar 

  30. P.G. de Gennes: Wetting—Statics and dynamics. Rev. Mod. Phys. 57, 827 (1985).

    Article  Google Scholar 

  31. T.D. Blake: The physics of moving wetting lines. J. Colloid Interface Sci. 299, 1 (2006).

    Article  CAS  Google Scholar 

  32. S. Rosenblat and S.H. Davis: How do liquid drops spread on solids? In Frontiers in Fluid Mechanics (S.H. Davis and J.L. Lumley, eds.; Springer–Verlag, New York, 1985).

  33. T.D. Blake and J.M. Haynes: Kinetics of Liquid/Liquid displacement. J. Colloid and Interface Sci. 30, 421 (1969).

    Article  CAS  Google Scholar 

  34. T.D. Blake, A. Clarke, J. DeConinck, and M. deRuijter: Contact angle relaxation during droplet spreading: Comparison between molecular kinetic theory and molecular dynamics. Langmuir 13, 2164 (1997).

    Article  CAS  Google Scholar 

  35. R.L. Hoffman: A study of the advancing interface: I. Interface shape in liquid–gas systems. J. Colloid Interface Sci. 50, 228 (1975).

    Article  CAS  Google Scholar 

  36. R.L. Hoffman: A study of the advancing interface: II. Theoretical prediction of the dynamic contact angle in liquid–gas systems. J. Colloid Interface Sci. 94, 470 (1983).

    Article  CAS  Google Scholar 

  37. S. Schiaffino and A.A. Sonin: Molten droplet deposition and solidification at low Weber numbers. Phys. Fluids 9, 3172 (1997).

    Article  CAS  Google Scholar 

  38. D. Wheeler, J.A. Warren, and W.J. Boettinger: Modeling the early stages of reactive wetting. Phys. Rev. E 82, 051601 (2010).

    Article  CAS  Google Scholar 

  39. W.J. Boettinger, J.A. Warren, C. Beckermann, and A. Karma: Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32, 163 (2002).

    Article  CAS  Google Scholar 

  40. L.Q. Chen: Phase-field models for microstructure evolution. Annu. Rev. Mater. Res. 32, 113 (2002).

    Article  CAS  Google Scholar 

  41. P. Seppecher: Moving contact lines in the Cahn–Hilliard theory. Int. J. Eng. Sci. 34, 977 (1996).

    Article  Google Scholar 

  42. H. Ding and P.D.M Spelt: Inertial effects in droplet spreading: A comparison between diffuse-interface and level-set simulations. J. Fluid Mech. 576, 1 (2007).

    Article  Google Scholar 

  43. H. Ding, M.N.H Gilani, and P.D.M Spelt: Sliding, pinch-off and detachment of a droplet on a wall in shear flow. J. Fluid Mech. 644, 217 (2010).

    Article  Google Scholar 

  44. W. Villanueva, K. Gronhagen, G. Amberg, and J. Agren: Multicomponent and multiphase modeling and simulation of reactive wetting. Phys. Rev. E 77, 056313 (2008).

    Article  CAS  Google Scholar 

  45. W. Villanueva, W.J. Boettinger, J.A. Warren, and G. Amberg: Effect of phase change and solute diffusion on spreading on a dissolving substrate. Acta Mater. 57, 6022 (2009).

    Article  CAS  Google Scholar 

  46. A. Karma and W. Rappel: Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys. Rev. E 53, R3017 (1996).

    Article  CAS  Google Scholar 

  47. R.F. Sekerka and Z. Bi: Phase field model of multicomponent alloy solidification with hydrodynamics. In Interfaces for the 21st Century: New Research Directions in Fluid Mechanics and Materials Science (G.B. McFadden, ed.; Imperial College Press, London, 2002).

  48. R.F. Sekerka: Irreversible thermodynamic basis of phase field models. Phil. Mag. 91, 3 (2011).

    Article  CAS  Google Scholar 

  49. J.E. Guyer, D. Wheeler, and J.A. Warren: FiPy: Partial differential equations with Python. Comput. Sci. Eng. 11, 6 (2009).

    Article  CAS  Google Scholar 

  50. H. Adhikari, A.F. Marshall, I.A. Goldthorpe, C.E.D Chidsey, and P.C. McIntyre: Metastability of Au-Ge liquid nanocatalysts: Ge vapor–liquid–solid nanowire growth far below the bulk eutectic temperature. ACS Nano. 1, 415 (2007).

    Article  CAS  Google Scholar 

  51. E.J. Schwalbach and P.W. Voorhees: Phase equilibrium and nucleation in VLS-grown nanowires. Nano Lett. 8, 3739 (2008).

    Article  CAS  Google Scholar 

  52. B.J. Kim, J. Tersoff, C.Y. Wen, M.C. Reuter, E.A. Stach, and F.M. Ross: Determination of size effects during the phase transition of a nanoscale Au-Si eutectic. Phys. Rev. Lett. 103, 155701 (2009).

    Article  CAS  Google Scholar 

  53. T. Iida and R. Guthrie: The Physical Properties of Liquid Metals (Oxford University Press, New York, 1993).

    Google Scholar 

  54. L.E. Malvern: Introduction to the Mechanics of a Continuous Medium (Prentice-Hall, Englewood Cliffs, NJ, 1969).

    Google Scholar 

  55. E.B. Dussan V and S.H. Davis: Motion of a fluid-fluid interface along a solid-surface. J. Fluid Mech. 65, 71 (1974).

    Article  Google Scholar 

  56. E.J. Schwalbach: Northwestern University, Evanston, IL. Unpublished results, 2011.

    Google Scholar 

  57. R. Kobayashi: Modeling and numerical simulations of dendritic crystal-growth. Phys. D 63, 410 (1993).

    Article  Google Scholar 

  58. A.A. Wheeler and G.B. McFadden: On the notion of a ξ-vector and a stress tensor for a general class of anisotropic diffuse interface models. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 453, 1611 (1997).

    Article  CAS  Google Scholar 

Download references

Acknowledgment

This research is supported by National Science Foun-dation Grant CMMI-0507053. E.J.S. acknowledges sup-port from a National Defense Science and Engineering Graduate Fellowship. Computational resources were provided by the Quest cluster at Northwestern Univer-sity. The authors acknowledge fruitful discussions with A.M. Anderson, S.M. Roper, and J. Tersoff.

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois, 60208, USA

    E. J. Schwalbach & P. W. Voorhees

  2. Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois, 60208, USA

    S. H. Davis

  3. Metallurgy Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899, USA

    D. Wheeler & J. A. Warren

Authors
  1. E. J. Schwalbach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. H. Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. W. Voorhees
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Wheeler
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. A. Warren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. W. Voorhees.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schwalbach, E.J., Davis, S.H., Voorhees, P.W. et al. Liquid droplet dynamics and complex morphologies in vapor–liquid–solid nanowire growth. Journal of Materials Research 26, 2186–2198 (2011). https://doi.org/10.1557/jmr.2011.96

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2011.96

Search

Navigation