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
Open Access articles citing this article.
Nature Communications Open Access 15 April 2021
Nature Communications Open Access 10 December 2019
Alloy-assisted deposition of three-dimensional arrays of atomic gold catalyst for crystal growth studies
Nature Communications Open Access 08 December 2017
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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).
Heiss, M. et al. Self-assembled quantum dots in a nanowire system for quantum photonics. Nature Mater. 12, 439–444 (2013).
Wallentin, J. et al. InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit. Science 339, 1057–1060 (2013).
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).
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).
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).
Kim, S-K. et al. Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design. Nano Lett. 12, 4971–4976 (2012).
Hochbaum, A. I. et al. Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163–167 (2008).
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).
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).
Hocevar, M. et al. Growth and optical properties of axial hybrid III–V/silicon nanowires. Nature Commun. 3, 1266 (2012).
Hillerich, K. et al. Strategies to control morphology in hybrid group III−V/group IV heterostructure nanowires. Nano Lett. 13, 903–908 (2013).
Givargizov, E. I. Periodic instability in whisker growth. J. Cryst. Growth 20, 217–226 (1973).
Zhang, H. Z. et al. Dependence of the silicon nanowire diameter on ambient pressure. Appl. Phys. Lett. 73, 3396 (1998).
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).
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).
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).
Tian, J. et al. Boron carbide and silicon oxide hetero-nanonecklaces via temperature modulation. Cryst. Growth Des. 8, 3160–3164 (2008).
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).
Schmidt, V., McIntyre, P. C. & Gosele, U. Morphological instability of misfit-strained core–shell nanowires. Phys. Rev. B 77, 235302 (2008).
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).
Rayleigh, L. On the instability of jets. Proc. London Math. Soc. 10, 4–13 (1878).
Eggers, J. Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–929 (1997).
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).
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).
Nichols, F. A. On the spheroidization of rod-shaped particles of finite length. J. Mater. Sci. 11, 1077–1082 (1976).
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).
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).
Peng, H. Y. et al. Bulk-quantity Si nanosphere chains prepared from semi-infinite length Si nanowires. J. Appl. Phys. 89, 727 (2001).
Smith, D. L. Thin-Film Deposition: Principles & Practice Ch. 5 (McGraw-Hill, 1995).
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).
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).
Wulff, G. Zur frage der geschwindigkeit des wachstums und der auflösung der kristallflächen. Z. Kristall. Mineral. 34, 449 (1901).
Lu, G-H., Huang, M., Cuma, M. & Liu, F. Relative stability of Si surfaces: a first-principles study. Surf. Sci. 588, 61–70 (2005).
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).
Cho, K. & Kaxiras, E. Intermittent diffusion on the reconstructed Si(111) surface. Europhys. Lett. 39, 287–292 (1997).
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).
Cao, L. et al. Engineering light absorption in semiconductor nanowire devices. Nature Mater. 8, 643–647 (2009).
Gloppe, A. et al. Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field. Nature Nanotech. 9, 920–926 (2014).
Ramos, D. et al. Optomechanics with silicon nanowires by harnessing confined electromagnetic modes. Nano Lett. 12, 932–937 (2012).
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).
Yariv, A. & Yeh, P. Photonics (Oxford Univ. Press, 2006).
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).
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).
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.
The authors declare no competing financial interests.
About this article
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
This article is cited by
Applied Physics A (2022)
Self-assembled monolayer modulated Plateau-Rayleigh instability and enhanced chemical stability of silver nanowire for invisibly patterned, stable transparent electrodes
Nano Research (2022)
Nature Communications (2021)
Nature Communications (2019)
Nano Research (2019)