Au Transport in Catalyst Coarsening and Si Nanowire Formation

Jul 20, 2014 - IBM T. J. Watson Research Center, Yorktown Heights, New York, United States. § Department of Materials Science and Engineering, Univer...
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Au Transport in Catalyst Coarsening and Si Nanowire Formation B. J. Kim,*,† J. Tersoff,‡ S. Kodambaka,§ Ja-Soon Jang,∥ E. A. Stach,⊥ and F. M. Ross*,‡ †

Department of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, Korea IBM T. J. Watson Research Center, Yorktown Heights, New York, United States § Department of Materials Science and Engineering, University of California, Los Angeles, California, United States ∥ Department of Electronic Engineering, LED-IT Fusion Technology Research Center, Yeungnam University, Gyeongbuk, Korea ⊥ Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York, United States ‡

S Supporting Information *

ABSTRACT: The motion of Au between AuSi liquid eutectic droplets, both before and during vapor−liquid−solid growth, is important in controlling tapering and diameter uniformity in Si nanowires. We measure the kinetics of coarsening of AuSi droplets on Si(001) and Si(111), quantifying the size evolution of droplets during annealing in ultrahigh vacuum using in situ transmission electron microscopy. For individual droplets, we show that coarsening kinetics are modified when disilane or oxygen is added: coarsening rates increase in the presence of disilane but decrease in oxygen. Matching droplet size measurements on Si(001) with coarsening models confirms that Au transport is driven by capillary forces and that the kinetic coefficients depend on the gas environment present. We suggest that the gas effects are qualitatively similar whether transport is attachment limited or diffusion limited. These results provide insight into manipulating nanowire morphologies for advanced device fabrication. KEYWORDS: AuSi eutectic liquid catalyst, vapor−liquid−solid growth, coarsening, in situ transmission electron microscopy

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surfaces have shown results qualitatively3,6 and quantitatively4 consistent with Ostwald ripening. It is also well-known that this Au transport is affected by the growth environment. For example, addition of oxygen prevents droplet volume changes7 and changes in Si precursor gas pressure affect Au motion across the surface and the droplet size distribution.5,8−11 The importance of the Au migration and its dependence on the environment has been demonstrated by experiments enabling nanowire structures to be tailored through Au transport control.3,5,8,12 A more precise understanding of the phenomena involved would enable further progress in nanostructure control with the goal of benefiting from the simplicity of using a dewetted blanket film to form the catalytic droplets, yet still producing well-defined nanowire ensembles. We have therefore made direct measurements to probe the transport processes that control the sizes of nanoscale AuSi droplets on Si. We quantify the diameter changes in AuSi droplets on planar Si(001) surfaces as a function of temperature, examining coarsening in droplets in the size range below 50 nm, and we change the environment to measure how the coarsening of individual droplets on both

he ability to control the structure of epitaxial semiconductor nanowires over large areas and with a high degree of precision makes such nanowires interesting for a range of applications in microelectronics, sensors, battery anodes, and photovoltaics. Epitaxial Si nanowires are commonly grown from catalytic droplets of AuSi on a Si surface,1 and it is well-known that the diameter of each nanowire depends directly on the volume of its catalytic droplet.2 A key ingredient for precise nanowire formation is therefore the ability to control the volume of the droplet, both before and during nanowire growth. A convenient approach to forming catalytic droplets for nanowire growth is by agglomeration and coarsening of a blanket Au film. The droplet sizes can then be tailored to some extent through the coarsening conditions before the start of growth. If lithographic patterning is instead used to define the initial Au particles, volume control is more straightforward, although even lithographically formed droplets that are close together can interact through coarsening. During growth, control of droplet size is essential to enable or prevent (depending on the application) diameter changes along the length of the nanowire. It has been recognized for some time that droplets change their diameter both before and during growth, and that droplet size changes are mediated by transport of Au onto the Si surface and between droplets.3−5 The evolution of the size distribution and density of ensembles of AuSi droplets on Si © 2014 American Chemical Society

Received: April 28, 2014 Revised: July 7, 2014 Published: July 20, 2014 4554

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Si(001) and Si(111) varies when the conditions change from ultrahigh vacuum (UHV) to low pressures of oxygen or disilane. We fit the Si(001) droplet size evolution data at each temperature with a simple coarsening model, showing that the Au transport is driven by capillary forces. We find that individual droplets on both Si(001) and Si(111) coarsen more rapidly in the presence of disilane and more slowly in the presence of oxygen, implying that the kinetic coefficients depend on the environment. While more complete results were obtained for Si(001), this general picture of evolution dominated by classic coarsening, and rate constants sensitive to the ambient vapor, applies for both Si(001) and Si(111), the common surface for nanowire growth. The results help us understand how the growth environment may be used to control nanowire diameter and distribution. The coarsening experiments were carried out by depositing a blanket Au film on Si under UHV then observing subsequent kinetics during heating under various conditions. The observations were made in a multichamber UHV system with base pressure 2 × 10−10 Torr, consisting of a transmission electron microscope (TEM) with in situ physical and chemical vapor deposition facilities.13 The experimental procedure for Si(001) starts by cutting 2 × 4 mm samples from silicon-oninsulator wafers that consist of a 200 nm thick device layer on a 2 μm thick SiO2 layer on a doped Si(001) substrate. Etching from the back side was used to remove the substrate and oxide layer from a membrane region approximately 50 μm in diameter in the center of each sample. For Si(111), bulk wafers were etched. Each sample was chemically cleaned, inserted into the vacuum system, and degassed at ∼600 °C for 2 h (using resistive heating, calibrated with an infrared pyrometer; we expect the substrate temperatures to be accurate to within ±20 °C14). Finally, the native oxide was removed by resistively heating above 900 °C for a few seconds. This procedure thins the membrane to below 100 nm and results in a clean but stepped Si surface.15 A 2−3 nm Au film was then evaporated onto the silicon without deliberate heating, using a home-built Knudsen cell. This thickness of Au was chosen because it is optimal for nanowire growth in our microscope.13 The thickness was measured using a crystal monitor that had been calibrated via ex situ ion scattering data. Finally, the sample was transferred to the TEM for imaging. Directly after Au deposition and cooling, imaging showed the sample surfaces to be covered with three-dimensional Au crystallites of sizes ranging from 10 to 50 nm. This suggests that some agglomeration of the Au film had already taken place due to unintentional heating by the evaporator. On heating in UHV above the Au/Si eutectic temperature of ∼370 °C, the Au crystallites transformed into liquid droplets by reacting with Si from the substrate. Further heating (still under UHV) resulted in a clearly visible coarsening process occurring over several minutes. An example set of bright-field images of Si(001) obtained from a movie recorded at 30 frames per second during heating is shown in Figure 1. On Si(001), droplets show a visibly square shape due to anisotropy of the liquid/Si interface.16 On Si(111), any deformations reflecting crystal symmetry are less visible and the islands are more circular in shape; an example is shown in Supporting Information Figure S1. During the annealing in Figure 1, the smaller droplets clearly shrink and disappear while larger ones grow, maintaining their shape. The evolution of all the droplets in the field of view is shown in Figure 2 along with similar data obtained over a temperature range that spans the conditions used13 for

Figure 1. TEM bright-field images of liquid AuSi droplets on Si(001) recorded during annealing in UHV at 525 °C at the times indicated (with t = 0 when the observation began). The vacuum during annealing was 5.6 × 10−10 Torr.

Figure 2. (a−d) Droplet radius R versus t during UHV annealing of AuSi droplets on Si(001) at the temperatures indicated. The curves show fits from attachment limited coarsening with parameters L and α for each temperature.

nanowire growth in our microscope. Note that droplets observed under continuous and intermittent electron beam irradiation exhibited similar diameter changes, indicating that the electron beam does not have a strong effect on the coarsening kinetics. To examine the effect of gas environment on this coarsening process, we supplied either 1 × 10−6 Torr Si2H6 or 1.2 × 10−7 Torr O2 to a set of droplets during coarsening without changing the temperature. Typical results are shown in Figure 3a,d for Si(001) and Supporting Information Figure S1 for Si(111), for droplets that were decreasing in volume at the time the gas environment was changed. In the case of oxygen, the gas introduction causes a visible break in the slope of volume versus time; it is clear that the rate of shrinking decreases (Figure 3b; Supporting Information Figure S1a,c). A similar slowdown was measured on Si(001) at other temperatures (Figure 3c). A slowdown in kinetics under O2 to a rate lower than in UHV is consistent with prior observations.7 In the case of disilane (Figure 3d−f; Supporting Information Figure S1b,d), we observe the opposite effect; the rate of shrinking of an individual droplet accelerates when the gas pressure rises. On Si(111) and (211), it is known that precursor gas pressure can strongly affect Au motion; at pressures 10−2 to 1 Torr, much higher than used here, silane or disilane agglomerate Au films and prevent Au diffusion out of AuSi droplets.5,8−11 These effects are thought to be related to the coverage of adsorbed H, 4555

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assumptions: Only surface diffusion of Au is considered, because this is likely to dominate over diffusion through the bulk. We also take the droplet shape as independent of diameter, as expected from elementary wetting theory, and confirmed by measurements of image contrast for Si(001) described in the Supporting Information (Figure S2). Furthermore, since the droplets are always in contact with the Si substrate, we assume that they maintain a constant composition, given by the Si liquidus line in the AuSi phase diagram (15−17 molar % Si22 at the temperatures used). This implies that coarsening via addition or removal of Au atoms is associated with dissolution or precipitation of Si from/onto the substrate beneath the droplet. Finally, we assume the properties of the surrounding terrace are uniform right up to the droplet edge. More complex scenarios are possible, but as we show below, this standard model can explain our experimental results. The coarsening of three-dimensional droplets (or solid islands) on a flat surface has been analyzed in detail both theoretically and experimentally20,23−29 with experiments generally involving statistical analysis of the droplet size distribution, but also through measurements of individual droplet evolution.30 Two limiting cases can be distinguished, in which the rate of droplet coarsening is limited either by attachment/detachment of atoms at the droplet edge or by diffusion of atoms across the surface between droplets. In general, diffusion will be the rate-limiting step for very large length scales, while attachment is expected to be rate-limiting at very small length scales.20 However, the crossover length depends strongly on the materials and especially the temperature. Because of the small dimensions here, and because Au is known to diffuse rapidly, we anticipate that attachment is probably rate limiting. We therefore focus on this case. The droplet sizes then evolve by exchange between the droplet edges and a reservoir of surface adatoms. Thus, dV/dt ∝ 2πR(μs − μd), where V is the droplet volume, 2πR is its perimeter, μd is its chemical potential, and μs is the chemical potential of the Au adatoms on the surface. Using V ∝ R3 and μd ∝ R−1 (the Gibbs−Thomson effect, where μ is taken relative to the bulk eutectic liquid), we can rewrite this as

Figure 3. (a) An AuSi droplet on Si(001) after annealing at 550 °C in UHV and then in 1.2 × 10−7 Torr O2 at the times indicated in seconds. (b,c) R3 versus t of the droplet in (a) and another at 475 °C. The black and purple data points are measured in UHV and oxygen, respectively. There is an approximately linear relationship between R3 and t in each regime but with different slope. (d) An AuSi droplet on Si(001) after annealing at 550 °C in UHV and then in 1 × 10−6 Torr Si2H6 at the times indicated. (e,f) R3 versus t of the droplet in (d) and another at 475 °C. The black and blue data points are measured in UHV and disilane, respectively. There is an approximately linear relationship between R3 and t in each regime.

which increases with precursor pressure.17 Hence, although the structure of Si(001) and (111) are very different, it seems plausible that disilane pressure affects Au migration kinetics on both surfaces via the coverage of H. Indeed, on Si(001), H coverage is known experimentally and theoretically to affect motion of other species, specifically Si.18,19 The results above emphasize the dynamic evolution occurring in these droplets and illustrate directly the importance of the gas environment in controlling the evolution of individual droplets. When a group of droplets changes in size and density, several possible mechanisms could be contributing.20 Coalescence of droplets is one possibility, but we find that coalescence does not play a role here. The droplets are separated enough not to impinge, and we observed no motion of droplets across the surface (apart from some local motion of the smallest droplets during the disilane exposure, as in Figure 3d and Supporting Information Figure S1b). We can also neglect Au evaporation and condensation, because the vapor pressure of Au is very low (in the 10−10 Torr range) at the temperatures examined.21 We therefore focus on Ostwald ripening, where large droplets grow at the expense of smaller droplets through diffusion of material between droplets driven by the Gibbs− Thomson effect. We calculate evolution under the following

dR 1⎛1 1⎞ =α ⎜ − ⎟ dt R⎝L R⎠

(1)

Here α is a rate coefficient, into which we have absorbed geometrical factors for simplicity. It is thermally activated with the form exp[−(Ea + Ed)]/kT, where (Ea + Ed) is the barrier for an Au atom to leave a droplet, as shown in Figure 4. L is the size above which droplets grow and below which they shrink. If we knew the full droplet-size distribution, L could be determined by mass conservation; but because of our limited field of view we cannot measure L experimentally very accurately. We therefore treat both L and α as unknown parameters. In general, L increases during coarsening, due to the removal of the smallest droplets and growth of the largest ones. However, we show below that because of the short time periods involved in these experiments, assuming constant L over the time interval of the measurements allows the data to be fitted well. Then integrating eq 1 gives an explicit expression for the evolution α(t − t0) = 4556

⎛ 1 2 R⎞ LR + L2R + L3 ln⎜1 − ⎟ ⎝ 2 L⎠

(2)

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The model fit is compared directly with the raw data for Si(001) in Figure 2a, where the solid curves are fits to eq 2. Repeating this procedure for each temperature (Figure 2b−d and Supporting Information Figures S3 and S4), we find that we can obtain excellent fits for all the droplets using a single value of α and of L at each temperature. These values are shown in each panel of Figure 2. We consider this as direct confirmation that the evolution is driven by the Gibbs− Thomson effect, as in classic coarsening. Note that the kinetic coefficient α increases with temperature, as expected. It is interesting to note that, although fitting L requires examination of both large and small droplets, the model fits for α are based primarily on the behavior of the smallest droplets as they shrink. For nanowire growth, the evolution of the particles that survive is more relevant. However, small droplets change more rapidly and thus in a more constant environment; over the time that a large droplet grows enough to measure accurately, nearby smaller droplets have disappeared, affecting its evolution. The changes in α with ambient gas shown in Figure 3 will be relevant to large as well as smaller droplets. So far, we have assumed attachment-limited kinetics. We have also examined diffusion-limited kinetics, but we find that the behavior is too similar to distinguish based on our limited data set. This is perhaps not surprising;20,31 the most distinctive features in the behavior come from the size-dependence of the capillary driving force, which is the same regardless of which transport step is rate-limiting. Given the fact that either attachment or diffusion-limited kinetics can fit our data, how should we understand the environmental effects on transport shown in Figure 3? It is clear that oxygen or disilane modify the evolution of individual droplets quite strongly. One might suppose that diffusionlimited evolution is controlled by surface parameters, while attachment-limited evolution is controlled by a property of the droplet edge. If so, one might expect a qualitatively different effect from gases depending on whether the evolution is limited by diffusion or attachment. To answer this question, it is helpful to relate the kinetic parameters to the microscopic energetics of Au adatoms on the surface. Consider Au adatoms jumping from the droplet to neighboring sites on the surface, and back, with an energy landscape illustrated schematically in Figure 4. The surface is an energetically unfavorable location for Au compared with the liquid, the difference being Ea. (We are considering transport to be via a mobile species such as adatoms. This does not include any immobile Au incorporated into the surface reconstruction.) This energy difference between surface and droplet sites does not depend on properties of the droplet edge. There is an extra barrier Ed at the droplet edge, although in general we may have Ed = 0. Once on the surface, there is a barrier Em to adatom migration. In eq 1, the rate coefficient α is thermally activated with the form exp(−Ea/kT)exp(−Ed/kT). (For transport from the surface to the droplet, the only barrier is Ed. But the number of available atoms, and hence the rate of evolution, is proportional to exp(−Ea/kT), giving detailed balance.) A corresponding analysis for diffusion-limited transport gives an analogous rate coefficient that is thermally activated with the form exp(−Ea/kT)exp(−Em/kT), reflecting the adatom density and mobility. Any modification of the surface by environmental gases will change the adatom formation energy Ea, changing the kinetics by a factor exp(−Ea/kT) in both attachment and diffusion limited cases. The barriers Em and Ed will also be

Figure 4. Schematic of the energy landscape for an Au atom, including the AuSi liquid and the atomically corrugated surface. Ea is the formation energy of a Au adatom on the surface from the liquid reservoir. Ed is the barrier (if any) for an adatom to cross back from the surface to the liquid. Em is the barrier for adatom migration on the surface. In this standard model, the terrace properties are assumed to be uniform right up to the droplet edge. The diagram illustrates the expected Ea > Ed.

For shrinking droplets, t0 is the time at which the droplet volume becomes zero. For sufficiently small droplets, we can expand to lowest order in R/L, giving 3α(t0 − t ) = R3

or

R ∝ (t0 − t )1/3

(3)

We fit this model to the Si(001) data in Figures 2 and 5. We first note that at each temperature, a rough estimate for L can

Figure 5. (a) R3 versus t for all AuSi droplets on Si(001) in the field of view during anneal at 545 °C. (b) A similar plot but for only the four droplets with decreasing volume, showing approximately linear behavior at small R. (c) The right-hand side of eq 2 versus t. (d) The right-hand side of eq 2 versus t − t0, showing that the four data sets for which t0 is defined collapse onto a straight line.

be obtained by direct examination of the data: for example, in Figure 2a, L ∼ 40 nm. We then consider the simpler eq 3. Because this applies for small R, a plot of R3 versus t should become linear as each droplet shrinks. Figure 5a shows R3 versus t for the full data set at T = 545 °C, while Figure 5b shows the same plot for the smallest R values. This confirms that for R ≤ 25−30 nm the data become quite linear. Importantly, the lines have similar gradients, consistent with eq 3, so we can directly obtain a value for α for the ensemble of droplets and a value for t0 for each individual (shrinking) droplet. If instead of R3 we plot the righthand side of eq 2 versus t, the data should become linear for all sizes. This is confirmed in Figure 5 panels c,d where we displace each data set laterally by t0 and vary L to determine the value of L at which the data collapse onto a straight line. 4557

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Basic Energy Sciences, under Contract DE-AC02 98CH10886. We acknowledge P. Venables (ASU) and M. Filler (GaTech) for very helpful discussions and Yong-Ryun Jo (GIST) for assistance with data analysis.

affected, so the effect of gases on detachment and diffusion will be quantitatively somewhat different, but both of these barriers are typically smaller than the formation energy Ea. The kinetic model described above and in Figure 4 is expected to apply equally for the different Si surfaces. Thus, the general results are expected to remain valid for both Si(001) and (111). The values of the parameters α and L will be different, but we still expect the same key aspect of evolution dominated by classic coarsening, and we have shown a rate constant sensitive to the ambient vapor for both surfaces. In conclusion, we have shown that the time evolution of AuSi droplets on both Si(001) and Si(111) surfaces can be strongly modified by changing the gas environment. Modeling of the droplet size evolution on Si(001) shows that the droplets develop according to capillarity-driven coarsening, that is, Ostwald ripening, and direct observation shows how the gas environment modifies the kinetic coefficients that control the process for both Si(001) and (111). These results suggest opportunities for producing novel nanowire-based structures. It is already known that droplet coarsening during annealing in UHV can result in changed nanowire diameters,3,32 and that nanowire nucleation locations5 and growth direction7,33 can be controlled through Au transport. Also known is that addition of disilane reverts an oxygen-exposed surface back to a surface on which Au is mobile.7 The combination of tapered or stepped diameter nanostructures produced via droplet coarsening with the opposing and reversible effects of oxygen and disilane therefore add flexibility to the toolbox for nanowire growth. One could imagine deliberately including large AuSi droplets to drive coarsening, and switching coarsening on and off using oxygen and disilane. Other materials, such as Ge, B,34 P, or As, might also alter Au transport kinetics on Si. The control of Au transport by these and other means may be useful in manipulating nanowire morphologies.

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(1) Wagner, R. S.; Ellis, W. C. Vapor-liquid-solid mechanism of single crystal growth. Appl. Phys. Lett. 1964, 4, 89. (2) Cui, Y.; Lauhon, L. J.; Gudiksen, M. S.; Wang, J.; Lieber, C. M. Diameter-controlled synthesis of single-crystal silicon nanowires. Appl. Phys. Lett. 2001, 78, 2214. (3) Hannon, J. B.; Kodambaka, S.; Ross, F. M.; Tromp, R. M. Fundamental limits on the growth of Si nanowires. Nature 2006, 440, 69−71. (4) Ruffino, F.; Canino, A.; Grimaldi, M. G.; Giannazzo, F.; Roccaforte, F.; Raineri, V. Kinetic mechanism of the thermal-induced self-organization of Au/Si nanodroplets on Si(100): size and roughness evolution. J. Appl. Phys. 2008, 104, 024310. (5) Dailey, E.; Drucker, J. “Seedless” vapor-liquid-solid growth of Si and Ge nanowires: The origin of bimodal diameter distributions. J. Appl. Phys. 2009, 105, 064317. (6) Sui, M.; Li, M.-Y.; Kim, E.-S.; Lee, J. Annealing temperature effect on self-assembled Au droplets on Si (111). Nanoscale Res. Lett. 2013, 8, 525. (7) Kodambaka, S.; Hannon, J. B.; Tromp, R. M.; Ross, F. M. Control of Si Nanowire Growth by Oxygen. Nano Lett. 2006, 6, 1292−6. (8) Dailey, E.; Madras, P.; Drucker, J. Au on vapor-liquid-solid grown Si nanowires: Spreading of liquid AuSi from the catalytic seed. J. Appl. Phys. 2010, 108, 064320. (9) den Hertog, M. I.; Rouviere, J.-L.; Dhalluin, F.; Desré, P. J.; Gentile, P.; Ferret, P.; Oehler, F.; Baron, T. Control of Gold Surface Diffusion on Si Nanowires. Nano Lett. 2008, 8, 1544. (10) Kawashima, T.; Mizutani, T.; Nakagawa, T.; Torii, H.; Saitoh, T.; Komori, K.; Fujii, M. Control of Surface Migration of Gold Particles on Si Nanowires. Nano Lett. 2008, 8, 362−8. (11) Xu, T.; Nys, J. P.; Addad, A.; Lebedev, O. I.; Urbieta, A.; Salhi, B.; Berthe, M.; Grandidier, B.; Stiévenard, D. Faceted sidewalls of silicon nanowires: Au-induced structural reconstructions and electronic properties. Phys. Rev. B 2010, 81, 115403. (12) Cao, L.; Garipcan, B.; Atchison, J. S.; Ni, C.; Nabet, B.; Spanier, J. E. Instability and Transport of Metal Catalyst in the Growth of Tapered Silicon Nanowires. Nano Lett. 2006, 6, 1852. (13) Ross, F. M. Controlling nanowire structures through real time growth studies. Rep. Prog. Phys. 2010, 73, 114501−22. (14) Stach, E. A.; Hull, R.; Tromp, R. M.; Reuter, M. C.; Copel, M.; LeGoues, F. K.; Bean, J. C. Effect of the surface upon misfit dislocation velocities during the growth and annealing of SiGe/Si (001) heterostructures. J. Appl. Phys. 1998, 83, 1931. (15) Tromp, R. M.; Ross, F. M. Advances in in situ ultra-high vacuum transmission electron microscopy: Growth of SiGe on Si. Annu. Rev. Mater. Sci. 2000, 30, 431−449. (16) Ressel, B.; Prince, K. C.; Heun, S.; Homma, Y. Wetting of Si surfaces by Au−Si liquid alloys. J. Appl. Phys. 2003, 93, 3886. (17) Shin, N.; Filler, M. A. Controlling Silicon Nanowire Growth Direction via Surface Chemistry. Nano Lett. 2012, 12, 2865−2870. (18) Nara, J.; Sasaki, T.; Ohno, T. Adsorption and diffusion of Si atoms on the H-terminated Si(001) surface: Si migration assisted by H mobility. Phys. Rev. Lett. 1997, 79, 4421−4424. (19) Copel, M.; Tromp, R. M. H Coverage Dependence of Si(001) Homoepitaxy. Phys. Rev. Lett. 1994, 72, 1236−1239. (20) Zinke-Allmang, M.; Feldman, L. C.; Grabow, M. H. Clustering on surfaces. Surf. Sci. Rep. 1992, 16, 377. (21) Lide, D. R. (ed), CRC Handbook of Chemistry and Physics, 84th ed., online version; CRC Press: Boca Raton, FL, 2003; Section 4, Properties of the Elements and Inorganic Compounds; Vapor Pressure of the Metallic Elements.

ASSOCIATED CONTENT

S Supporting Information *

Figure S1: Changes in the rate of shrinking of AuSi droplets on Si(111) on addition of disilane and oxygen. Figure S2: Droplet shape on Si(001) as a function of diameter. Figures S3 and S4: Fitting procedure for coarsening on Si(001) at all temperatures. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: (B.J.K.) [email protected]. *E-mail: (F.M.R.) [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS B.J.K. acknowledges support from the Research Institute for Solar and Sustainable Energies (RISE) at Gwangju Institute of Science and Technology (GIST) and from the National Research Foundation of Korea (NRF) under Grant NRF2013S1A2A2035468. B.J.K. and J.S.J. acknowledge support from the Ministry of Trade, Industry, and Energy (MTIE) through the industrial infrastructure program under Grant 10033630. E.A.S. acknowledges the support of the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Office of 4558

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(22) Binary Alloy Phase Diagrams; Okamoto, H., Massalski, T. B., Eds.; American Society for Metals: Materials Park, OH, 1986; Vol. I. (23) Chakraverty, B. K. Kinetics of clustering processes. Surf. Sci. 1966, 4, 205−220. (24) Voorhees, P. W.; Glicksman, M. E. Solution to the multi-particle diffusion problem with appplications to Ostwald ripening. I. Theory. Acta Met. 1984, 32, 2001−2011. (25) Atwater, H. A.; Yang, C. M. J. Appl. Phys. 1990, 67, 6202. (26) Fradkov, V. E.; Mani, S. S.; Glicksman, M. E.; Rogers, J. R.; Downey, J. P.; Witherow, W. K.; Facemire, B. R.; Frazier, D. O. Coarsening of three dimensional droplets by two dimensional diffusion: Part 2. Theory. J. Electron. Mater. 1994, 23, 1007−1013. (27) Shorlin, K.; Yu, S.; Kryiov; Zinke-Allmang, M. Physica A 1998, 161, 248−265. (28) Viñals, J.; Mullins, W. W. Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix. J. Appl. Phys. 1998, 83, 621. (29) Shorlin, K.; Zinke-Allmang, M.; Fraser, D. Statistical analysis of the spatial distribution of simulated island formation on a surface. Phys. Rev. B 2002, 66, 165403. (30) Rogers, J. R.; Downey, J. P.; Witherow, W. K.; Facemire, B. R.; Frazier, D. O.; Fradkov, V. E.; Mani, S. S.; Glicksman, M. E. Coarsening of three dimensional droplets by two dimensional diffusion: Part 1. Experiment. J. Electron. Mater. 1994, 23, 999−1006. (31) Xia, H.; Zinke-Allmang, M. Rate equation approach to the late stages of cluster ripening. Physica A 1998, 261, 176−187. (32) Hillerich, K.; Dick, K. A.; Wen, C.-Y.; Reuter, M. C.; Kodambaka, S.; Ross, F. M. Strategies To Control Morphology in Hybrid Group III−V/Group IV Heterostructure Nanowires. Nano Lett. 2013, 13, 903−908. (33) Pan, L.; Lew, K.; Redwing, J. M.; Dickey, E. C. Effect of diborane on the microstructure of boron-doped silicon nanowires. J. Cryst. Growth 2005, 277, 428−436. (34) Madras, P.; Dailey, E.; Drucker, J. Kinetically Induced Kinking of Vapor−Liquid−Solid Grown Epitaxial Si Nanowires. Nano Lett. 2009, 9, 3826−30.

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