Simple Models for Complex Behavior in Nanowire Growth
Written by Arthur L. Robinson
In his Von Hippel Award presentation Wednesday evening, Jerry Tersoff of the IBM T.J. Watson Research Center observed from experience that problems arising from experimental puzzles were able to bring out the best of him as a theorist. For example, a theme of his research has been to find simple models that capture some element of some very complex experimental situation. To illustrate this approach, Tersoff turned to growth of semiconductor nanowires, which provide unique opportunities for studying crystal growth. Their small diameter guarantees single-crystal growth, and they can be grown in a transmission electron microscope (TEM). Because nanowires are so thin, they are electron transparent, and researchers can capture the entire growth region in a single image, recording growth in situ under UHV conditions, in effect a laboratory for studying fundamental issues of crystal growth. A number of remarkable phenomena have been discovered in this way, some of which are specific to nanowires. In his presentation, Tersoff described a few of these intriguing observations and demonstrated how even very simple models can give useful insight into the behavior and in the process deepening our understanding of nanoscale materials.
Nanowires actually have a long history, going back to the 1960s, when researchers were able to grow vertical silicon whiskers on a silicon substrate by depositing a gold layer on the substrate and heating. The resulting gold-silicon liquid acts as a catalyst for silicon growth when exposed to a silane (S2H6) source. Today wires with 10- to 100-nm diameters can be readily grown in this way (but without gold, which would be detrimental to devices) for use in photovoltaics and transistors based on self-assembled semiconductor nanostructures with dimensions smaller than lithography can handle.
One benefit of studying with the TEM emerged right away. The conventional view had been that the ideal wires were long and straight, but reality intervened with a closer look by experimentalists at the walls, which actually had a sawtooth edge. This finding drew Tersoff into the discussion, and the deal was sealed when around 2010 researchers showed images in which the wires could sometimes grow in a temperature-controlled zigzag path and were not always normal to the substrate surface. Tersoff asked what kind of model could capture such “weird” behaviors and ruled out atomistic simulations as too unwieldy. What he and a colleague came up with was what he called a two-dimensional faceted continuum model based on three “elementary processes”: facet growth, droplet statics, and introduction of new facets.
Unpacking the three elements, Tersoff explained that facet growth was by means of liquid phase epitaxy from supersaturated liquid. Droplet statics was about droplet stability as the droplet size changed. The really new element, facet addition, included all infinitesimal process that add only one edge with a parameter characterizing edge energy as a barrier to growing new facets. Tersoff said that the spirit of their model resembles that of a 1990s model for faceted crystal growth but with addition of the droplets. Subsequent extensive simulations suggested that these three elements are sufficient to explain many of the observed observations.
Applying the model to growth of the original vertical silicon wire with sawtoothed edges seemed too complicated for the first attempt, so Tersoff’s group first turned to a longer and more uniform configuration that grows at an angle relative to the substrate surface but is not sawtoothed. The calculation is an iterative one with checks for stability of droplets and facets at each time step. The simulation reproduced the nanowire, and it was even possible to account for changing parameters like temperature that, for example, caused the gold to diffuse out of the droplet, introducing a taper in the wire by means of jogs to account for the changing diameter. They also found that changing the edge-energy parameter could change the growth mode, with behaviors like crawling, resulting in lateral growth, and kinking. Returning to the vertical wire configuration, the researchers found that they could reproduce the sawtooth, which was due to a geometrical frustration when there is no plane normal to the growth plane to serve as the wall. By introducing three new facets with a slightly higher edge energy, the growth was stabilized without eliminating the geometrical frustration but generated the sawtooth. The model also correctly predicted the change in the sawtooth period with nanowire diameter. Finally, experiments verified the change in growth mode from vertical with sawtooth to tilted without sawtooth by introducing oxygen into the growth chamber to vary the energy parameter.
Summing up his presentation, Tersoff concluded that he and his colleagues had identified three elementary processes in nanowire growth and captured these three elements in a dynamical facet-growth model that enabled direct simulations of complex growth, including kinking and crawling behaviors and sawtooth growth. They also used the model to discover new oscillatory growth modes, and pave the way for detailed comparison of experiment and simulation to advance the understanding of nanowire growth.
The Materials Research Society’s highest honor, the Von Hippel Award, is conferred annually to an individual in recognition of the recipient’s outstanding contribution to interdisciplinary research on materials.