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.

Plateau–Rayleigh crystal growth of periodic shells on one-dimensional substrates

Subjects

Abstract

The Plateau–Rayleigh instability was first proposed in the mid-1800s to describe how a column of water breaks apart into droplets to lower its surface tension. This instability was later generalized to account for the constant volume rearrangement of various one-dimensional liquid and solid materials. Here, we report a growth phenomenon that is unique to one-dimensional materials and exploits the underlying physics of the Plateau–Rayleigh instability. We term the phenomenon Plateau–Rayleigh crystal growth and demonstrate that it can be used to grow periodic shells on one-dimensional substrates. Specifically, we show that for certain conditions, depositing Si onto uniform-diameter Si cores, Ge onto Ge cores and Ge onto Si cores can generate diameter-modulated core–shell nanowires. Rational control of deposition conditions enables tuning of distinct morphological features, including diameter-modulation periodicity and amplitude and cross-sectional anisotropy. Our results suggest that surface energy reductions drive the formation of periodic shells, and that variation in kinetic terms and crystal facet energetics provide the means for tunability.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Plateau–Rayleigh (P–R) crystal growth of periodic shell nanowires with tunable morphology.
Figure 2: Experimental synthetic control and model for P–R crystal growth.
Figure 3: Generality and scope of P–R crystal growth.
Figure 4: Optical properties of Si periodic shell nanowires.
Figure 5: P–R crystal growth of periodic shell heterostructures.

References

  1. Lauhon, L. J., Gudiksen, M. S., Wang, D. & Lieber, C. M. Epitaxial core–shell and core–multi-shell nanowire heterostructures. Nature 420, 57–61 (2002).

    CAS  Article  Google Scholar 

  2. Heiss, M. et al. Self-assembled quantum dots in a nanowire system for quantum photonics. Nature Mater. 12, 439–444 (2013).

    CAS  Article  Google Scholar 

  3. Wallentin, J. et al. InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit. Science 339, 1057–1060 (2013).

    CAS  Article  Google Scholar 

  4. Kempa, T. J. et al. Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics. Proc. Natl Acad. Sci. USA 109, 1407–1412 (2012).

    CAS  Article  Google Scholar 

  5. Kempa, T. J., Day, R. W., Kim, S-K., Park, H-G. & Lieber, C. M. Semiconductor nanowires: a platform for exploring limits and concepts for nano-enabled solar cells. Energy Environ. Sci. 6, 719–733 (2013).

    CAS  Article  Google Scholar 

  6. De la Mata, M. et al. A review of MBE grown 0D, 1D and 2D quantum structures in a nanowire. J. Mater. Chem. C 1, 4300–4312 (2013).

    CAS  Article  Google Scholar 

  7. Kim, S-K. et al. Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design. Nano Lett. 12, 4971–4976 (2012).

    CAS  Article  Google Scholar 

  8. Hochbaum, A. I. et al. Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163–167 (2008).

    CAS  Article  Google Scholar 

  9. Lim, S. K., Crawford, S., Haberfehlner, G. & Gradečak, S. Controlled modulation of diameter and composition along individual III−V nitride nanowires. Nano Lett. 13, 331–336 (2013).

    CAS  Article  Google Scholar 

  10. Musin, I. R., Boyuk, D. S. & Filler, M. A. Surface chemistry controlled diameter-modulated semiconductor nanowire superstructures. J. Vac. Sci. Technol. B 31, 020603 (2013).

    Article  Google Scholar 

  11. Hocevar, M. et al. Growth and optical properties of axial hybrid III–V/silicon nanowires. Nature Commun. 3, 1266 (2012).

    Article  Google Scholar 

  12. Hillerich, K. et al. Strategies to control morphology in hybrid group III−V/group IV heterostructure nanowires. Nano Lett. 13, 903–908 (2013).

    CAS  Article  Google Scholar 

  13. Givargizov, E. I. Periodic instability in whisker growth. J. Cryst. Growth 20, 217–226 (1973).

    CAS  Article  Google Scholar 

  14. Zhang, H. Z. et al. Dependence of the silicon nanowire diameter on ambient pressure. Appl. Phys. Lett. 73, 3396 (1998).

    CAS  Article  Google Scholar 

  15. Oliveira, D. S., Tizei, L. H. G., Ugarte, D. & Cotta, M. A. Spontaneous periodic diameter oscillations in InP nanowires: the role of interface instabilities. Nano Lett. 13, 9–13 (2012).

    Article  Google Scholar 

  16. Ma, Z. et al. Vapor–liquid–solid growth of serrated GaN nanowires: shape selection driven by kinetic frustration. J. Mater. Chem. C 1, 7294–7302 (2013).

    CAS  Article  Google Scholar 

  17. Christesen, J. D., Pinion, C. W., Grumstrup, E. M., Papanikolas, J. M. & Cahoon, J. F. Synthetically encoding 10 nm morphology in silicon nanowires. Nano Lett. 13, 6281–6286 (2013).

    CAS  Article  Google Scholar 

  18. Tian, J. et al. Boron carbide and silicon oxide hetero-nanonecklaces via temperature modulation. Cryst. Growth Des. 8, 3160–3164 (2008).

    CAS  Article  Google Scholar 

  19. Goldthorpe, I. A., Marshall, A. F. & McIntyre, P. C. Synthesis and strain relaxation of Ge-core/Si-shell nanowire arrays. Nano Lett. 8, 4081–4086 (2008).

    CAS  Article  Google Scholar 

  20. Schmidt, V., McIntyre, P. C. & Gosele, U. Morphological instability of misfit-strained core–shell nanowires. Phys. Rev. B 77, 235302 (2008).

    Article  Google Scholar 

  21. Plateau, J. A. F. Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity. Annu. Rep. Smithsonian Institution 270–285 (1863).

  22. Rayleigh, L. On the instability of jets. Proc. London Math. Soc. 10, 4–13 (1878).

    Article  Google Scholar 

  23. Eggers, J. Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–929 (1997).

    CAS  Article  Google Scholar 

  24. Nichols, F. A. & Mullins, W. W. Surface- (interface-) and volume-diffusion contributions to morphological changes driven by capillarity. Trans. Metall. Soc. AIME 233, 1840–1848 (1965).

    CAS  Google Scholar 

  25. Nichols, F. A. & Mullins, W. W. Morphological changes of a surface of revolution due to capillarity-induced surface diffusion. J. Appl. Phys. 36, 1826–1835 (1965).

    Article  Google Scholar 

  26. Nichols, F. A. On the spheroidization of rod-shaped particles of finite length. J. Mater. Sci. 11, 1077–1082 (1976).

    Article  Google Scholar 

  27. Barwicz, T., Cohen, G. M., Reuter, K. B., Bangsaruntip, S. & Sleight, J. W. Anisotropic capillary instability of silicon nanostructures under hydrogen anneal. Appl. Phys. Lett. 100, 0931091–0931093 (2012).

    Article  Google Scholar 

  28. Rauber, M., Muench, F., Toimil-Molares, M. E. & Ensinger, W. Thermal stability of electrodeposited platinum nanowires and morphological transformations at elevated temperatures. Nanotechnology 23, 475710 (2012).

    CAS  Article  Google Scholar 

  29. Peng, H. Y. et al. Bulk-quantity Si nanosphere chains prepared from semi-infinite length Si nanowires. J. Appl. Phys. 89, 727 (2001).

    CAS  Article  Google Scholar 

  30. Smith, D. L. Thin-Film Deposition: Principles & Practice Ch. 5 (McGraw-Hill, 1995).

    Google Scholar 

  31. Lim, S-H., Song, S., Park, T-S., Yoon, E. & Lee, J-H. Si adatom diffusion on Si (100) surface in selective epitaxial growth of Si. J. Vac. Sci. Technol. B 21, 2388 (2003).

    CAS  Article  Google Scholar 

  32. Fissel, A. & Richter, W. MBE growth kinetics of Si on heavily-doped Si(111):P: a self-surfactant effect. Mater. Sci. Eng. B 73, 163–167 (2000).

    Article  Google Scholar 

  33. Wulff, G. Zur frage der geschwindigkeit des wachstums und der auflösung der kristallflächen. Z. Kristall. Mineral. 34, 449 (1901).

    CAS  Google Scholar 

  34. Lu, G-H., Huang, M., Cuma, M. & Liu, F. Relative stability of Si surfaces: a first-principles study. Surf. Sci. 588, 61–70 (2005).

    CAS  Article  Google Scholar 

  35. Mo, Y-W., Kleiner, J., Webb, M. B. & Lagally, M. G. Surface self-diffusion of Si on Si(001). Surf. Sci. 268, 275–295 (1992).

    CAS  Article  Google Scholar 

  36. Cho, K. & Kaxiras, E. Intermittent diffusion on the reconstructed Si(111) surface. Europhys. Lett. 39, 287–292 (1997).

    CAS  Article  Google Scholar 

  37. Xiang, Q. et al. Interfacet mass transport and facet evolution in selective epitaxial growth of Si by gas source molecular beam epitaxy. J. Vac. Sci. Technol. B 14, 2381–2386 (1996).

    CAS  Article  Google Scholar 

  38. Cao, L. et al. Engineering light absorption in semiconductor nanowire devices. Nature Mater. 8, 643–647 (2009).

    CAS  Article  Google Scholar 

  39. Gloppe, A. et al. Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field. Nature Nanotech. 9, 920–926 (2014).

    CAS  Article  Google Scholar 

  40. Ramos, D. et al. Optomechanics with silicon nanowires by harnessing confined electromagnetic modes. Nano Lett. 12, 932–937 (2012).

    CAS  Article  Google Scholar 

  41. Tamayo, J., Kosaka, P. M., Ruz, J. J., Paulo, A. S. & Calleja, M. Biosensors based on nanomechanical systems. Chem. Soc. Rev. 42, 1287–1311 (2013).

    CAS  Article  Google Scholar 

  42. Yariv, A. & Yeh, P. Photonics (Oxford Univ. Press, 2006).

    Google Scholar 

  43. England, G. et al. Bioinspired micrograting arrays mimicking the reverse color diffraction elements evolved by the butterfly Pierella luna. Proc. Natl Acad. Sci. USA 111, 15630–15634 (2014).

    CAS  Article  Google Scholar 

  44. Cui, Y., Lauhon, L. J., Gudiksen, M. S., Wang, J. & Lieber, C. M. Diameter-controlled synthesis of single-crystal silicon nanowires. Appl. Phys. Lett. 78, 2214–2216 (2001).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The authors thank A. Graham for assistance with electron microscopy. R.W.D. acknowledges a Graduate Research Fellowship from the National Science Foundation (NSF). M.N.M. acknowledges a Fannie and John Hertz Foundation Graduate Fellowship and an NSF Graduate Research Fellowship. R.G. acknowledges the support of a Japan Student Services Organization Graduate Research Fellowship. Y-S.N. acknowledges support for this work by the TJ Park Science Fellowship. C.M.L. acknowledges support of this research by a Department of Defense, National Security Science and Engineering Faculty Fellowships (N00244-09-1-0078) award and from Abengoa Solar New Technologies SA. H.-G.P. acknowledges support by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (no. 2009-0081565). S-K.K. acknowledges support of this work by the Basic Science Research Program through the NRF funded by the Ministry of Science, ICT & Future Planning (NRF-2013R1A1A1059423). This work was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported by the NSF under award no. ECS-0335765. CNS is part of Harvard University.

Author information

Authors and Affiliations

Authors

Contributions

R.W.D., M.N.M., H-G.P. and C.M.L. designed the experiments. R.W.D., M.N.M., R.G., Y-S.N. and S-K.K. performed the experiments. R.W.D., M.N.M. and C.M.L. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Hong-Gyu Park or Charles M. Lieber.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2782 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Day, R., Mankin, M., Gao, R. et al. Plateau–Rayleigh crystal growth of periodic shells on one-dimensional substrates. Nature Nanotech 10, 345–352 (2015). https://doi.org/10.1038/nnano.2015.23

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2015.23

This article is cited by

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research