DOI: 10.1063/1.3676451. Stability and topological transformations of liquid droplets on vapor-liquid-solid nanowires

Stability and topological transformations of liquid droplets on vapor-liquid-solid nanowires

10.1063/1.3676451

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

The Vapor-Liquid-Solid method is one of the most popular techniques for growing semiconducting nanowires, and the stability of the liquid droplet is an important factor controlling wire morphology and, ultimately, functionality. Earlier theoretical work on axisymmetric systems indicates that the lowest-energy liquid configuration varies with surface energies, wire radius, and fluid volume. We test these predictions with a fully dynamic phase-field model that incorporates viscous fluid flow. Under conditions predicted by this earlier theoretical work, we observe the pinning of the liquid to the top face of a nanowire, a condition necessary for wire growth. To study the stability of the droplet, we apply perturbations to the liquid shape and find that the system can transition to a metastable configuration, a local minimum in the energy landscape. Furthermore, the transition pathway to this local minimum depends on the magnitude of the perturbations. Under conditions that favor a liquid on the sidewalls of the wire, we observe a spontaneous transition of the liquid from a droplet to an annular configuration through an intermediate state that is not predicted by theory. The time scales and contact-line speeds for these transitions are determined through simulation and are consistent with approximations based on simple dimensional analysis.

Bibliography

Schwalbach, E. J., Davis, S. H., Voorhees, P. W., Warren, J. A., & Wheeler, D. (2012). Stability and topological transformations of liquid droplets on vapor-liquid-solid nanowires. Journal of Applied Physics, 111(2).

Authors 5

Edwin J. Schwalbach (first)
Stephen H. Davis (additional)
Peter W. Voorhees (additional)
James A. Warren (additional)
Daniel Wheeler (additional)

References 29 Referenced 17

10.1063/1.1753975 / Appl. Phys. Lett. (1964)
10.1149/1.2411032 / J. Electrochem. Soc. (1968)
10.1126/science.1192033 / Science (2010)
10.1039/b912095e / Energy Environ. Sci. (2009)
10.1557/jmr.2011.96 / J. Mater. Res. (2011)
10.1116/1.589291 / J. Vac. Sci. Technol., B (1997)
10.1021/nl072366g / Nano Lett. (2008)
10.1021/nl8011006 / Nano Lett. (2008)
10.1038/nnano.2009.304 / Nat. Nanotechnol. (2009)
10.1021/nl100249j / Nano Lett. (2010)
10.1063/1.3487971 / J. Appl. Phys. (2010)
10.1063/1.3497079 / Appl. Phys. Lett. (2010)
10.1063/1.3434403 / J. Appl. Phys. (2010)
10.1103/PhysRevLett.102.206101 / Phys. Rev. Lett. (2009)
10.1021/nl1027815 / Nano Lett. (2011)
10.1146/annurev.matsci.32.101901.155803 / Ann. Rev. Mat. Res. (2002)
10.1016/0020-7225(95)00141-7 / Int. J. Eng. Sci. (1996)
10.1017/S0022112007004910 / J. Fluid Mech. (2007)
10.1103/PhysRevE.77.056313 / Phys. Rev. E (2008)
10.1016/j.actamat.2009.08.033 / Acta Mater. (2009)
10.1017/S0022112009992217 / J. Fluid Mech. (2010)
10.1103/PhysRevE.82.051601 / Phys. Rev. E (2010)
10.1063/1.869434 / Phys. Fluids (1997)
10.1007/BF02884878 / Bull. Alloy Phase Diagrams (1983)
{'first-page': '147', 'volume-title': 'Interfaces for the 21st Century', 'year': '2002', 'key': '2023070601040431300_c25'} / Interfaces for the 21st Century (2002)
10.1080/14786435.2010.491805 / Philos. Mag. (2011)
10.1109/MCSE.2009.52 / Comput. Sci. Eng. (2009)
{'volume-title': 'The Physical Properties of Liquid Metals', 'year': '1993', 'key': '2023070601040431300_c28'} / The Physical Properties of Liquid Metals (1993)
10.1016/0021-9797(77)90052-2 / J. Colloid Interface Sci. (1977)

Dates

Type	When
Created	13 years, 7 months ago (Jan. 19, 2012, 6:25 p.m.)
Deposited	2 years, 1 month ago (July 5, 2023, 11:03 p.m.)
Indexed	1 month ago (July 30, 2025, 6:57 a.m.)
Issued	13 years, 7 months ago (Jan. 15, 2012)
Published	13 years, 7 months ago (Jan. 15, 2012)
Published Online	13 years, 7 months ago (Jan. 19, 2012)
Published Print	13 years, 7 months ago (Jan. 15, 2012)

Funders 0

None

BibTeX

@article{Schwalbach_2012, title={Stability and topological transformations of liquid droplets on vapor-liquid-solid nanowires}, volume={111}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.3676451}, DOI={10.1063/1.3676451}, number={2}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Schwalbach, Edwin J. and Davis, Stephen H. and Voorhees, Peter W. and Warren, James A. and Wheeler, Daniel}, year={2012}, month=jan }

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