Letterpubs.acs.org/NanoLett

Rational Concept for Reducing Growth Temperature in Vapor−
Liquid−Solid Process of Metal Oxide Nanowires
Zetao Zhu,† Masaru Suzuki,† Kazuki Nagashima,† Hideto Yoshida,‡ Masaki Kanai,† Gang Meng,†
Hiroshi Anzai,† Fuwei Zhuge,† Yong He,† Mickael̈ Boudot,† Seiji Takeda,‡ and Takeshi Yanagida*,††Institute for Materials Chemistry and Engineering, Kyushu University, 6-1 Kasuga-Koen, Kasuga, Fukuoka 816-8580, Japan
Institute of Scientiﬁc and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan‡

ABSTRACT: Vapor−liquid−solid (VLS) growth process of single crystalline metaloxide nanowires has proven the excellent ability to tailor the nanostructures. However,the VLS process of metal oxides in general requires relatively high growth temperatures,
which essentially limits the application range. Here we propose a rational concept toreduce the growth temperature in VLS growth process of various metal oxide nanowires.
Molecular dynamics (MD) simulation theoretically predicts that it is possible to reduce
the growth temperature in VLS process of metal oxide nanowires by precisely controllingthe vapor ﬂux. This concept is based on the temperature dependent “material ﬂux
window” that the appropriate vapor ﬂux for VLS process of nanowire growth decreases
with decreasing the growth temperature. Experimentally, we found the applicability ofthis concept for reducing the growth temperature of VLS processes for various metaloxides including MgO, SnO2, and ZnO. In addition, we show the successful applicationsof this concept to VLS nanowire growths of metal oxides onto tin-doped indium oxide(ITO) glass and polyimide (PI) substrates, which require relatively low growthtemperatures.
KEYWORDS: Metal oxide nanowires, vapor−liquid−solid growth, low temperature growth, material ﬂux window,
temperature dependenceT

without altering metal catalysts is desired for the VLS nanowire
growth of metal oxides. We recently proposed a “material ﬂux
window” concept for designing metal oxide nanowires via a
VLS route.24 Within the framework of this concept, the size ofcritical nucleus at LS interface is smaller than that at VSinterface due to the surface energy gain by the surrounding
liquid catalyst atoms. Therefore, the critical material ﬂux for
VLS nanowire growth is always lower than that for VS ﬁlm
growth. Since VLS nanowire growth competes with VS ﬁlm
growth, the occurrence of nucleation only at the LS interface is
crucial for enhancing the VLS nanowire growth. The
preferential crystal growth only at the LS interface can beobtained by controlling the material ﬂux within the material ﬂux
window between the two critical material ﬂuxes of VLS
nanowire growth and VS ﬁlm growth. Since the growthtemperature inherently aﬀects the nucleation dynamics, thetemperature dependence of the “material ﬂux window” might
give a solution to reduce the growth temperature of VLS
process. However, such temperature dependent “material ﬂux
window” concept has never been examined theoretically andexperimentally. This work proposes a strategy to reduce thegrowth temperature of VLS nanowires composed of metal

he vapor−liquid−solid (VLS) method has shown thepromises to fabricate well-deﬁned single crystalline
nanowires composed of various functional inorganic materials.1−6 By using the VLS growth method, the diameter and thespatial position of nanowires can be tailored by adjusting thesize and the spatial position of metal catalyst.7,8 Furthermore,
the heterostructures within nanowires can be designed bychoosing the growth interface (liquid−solid (LS) or vapor−solid (VS) interfaces) during the VLS process.9 These
interesting features are hardly attainable by other nanowire
growth methods. However, when compared with conventionalliquid methods including hydrothermal nanowire synthesis,10,11
the growth temperature range of VLS process is relatively
high.12,13 Typically, the growth temperatures of VLS growth ofmetal oxides were ranged from 600 to 1000 °C.14−19 This hightemperature operation frequently limits the application range of
VLS method. Within the framework of VLS nanowire growth,
the metal catalysts are required to be a liquid state, which
essentially determines the range of growth temperature.20,21
Although choosing the metal catalysts with lower melting
points is a straightforward approach to reduce the growthtemperature, it is frequently unfeasible due to the aﬃnity
between metal catalysts and desired materials of nanowires.22
This issue is rather critical especially for the VLS nanowire
growth of metal oxides, since metal species, which can beoxidized in the presence of surrounding oxygen, are notpreferred.23 Thus, a strategy to reduce the growth temperature© 2016 American Chemical Society

Received: August 2, 2016
Revised: November 16, 2016
Published: November 29, 2016
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Nano Lettersoxides by considering the temperature dependent “material ﬂux
window”.
Figure 1 shows the schematic of the temperature dependent“material ﬂux window” concept to reduce the growth

Figure 2. (a) Snapshots of MD simulations for nucleation dynamics ofboth LS and VS interfaces when varying the growth temperature andthe vapor ﬂux of MD particles, (b) MD simulation data of growth rates
at both VS and LS interfaces as a function of vapor ﬂux of MD
particles when varying the growth temperature, (c) MD simulation
data of the temperature dependence of the material ﬂux window
between the critical vapor ﬂux for the nucleations at both LS and VS
interfaces.

Figure 1. Schematic of the temperature dependent “material ﬂux
window” concept to reduce the growth temperature of VLS nanowire
growth for metal oxides. Upper schematic ﬁgure shows thetemperature dependence of materials ﬂux window, where thenucleation preferentially occurs at LS interface. Lower ﬁgure shows
the temperature dependence of critical vapor ﬂuxes, above which a
nucleation occurs, for both VS and LS interfaces.

temperature of VLS process. As illustrated, this concept
describes that the appropriate vapor ﬂux for VLS process of
nanowire growth decreases with decreasing the growthtemperature. This concept is derived from the following MD
simulations, as shown in Figure 2. The details of the MD
simulations are shown in the Methods Section and reference
25. The nucleation rates of both VLS growth and VS growth
are calculated by the modiﬁed Lenard-Jones (L-J) potential
models. Figure 2a shows the snapshots of MD simulations fornucleation dynamics of both LS and VS interfaces when varying
the growth temperature and the vapor ﬂux of MD particles.
These snapshots highlight that the VLS growth process of
nanowires can be maintained even decreasing the growthtemperature (T: reduced temperature, 0.307 to 0.270) via
decreasing the vapor ﬂux. This simulation trend can be moreclearly seen in Figure 2b, which shows the eﬀect of growthtemperature on the calculated growth rates at both LS and VS
interfaces as a function of vapor ﬂux of MD particles. As shownin Figure 2b, the material ﬂux window, where nanowires can begrown (i.e., a nucleation occurs only at LS interface), tends toshift toward the lower range of vapor ﬂux density as the growthtemperature decreases from T = 0.307 to T = 0.270. As seen in
Figure 2b, all plotted data can be well ﬁtted by the following
equation of nucleation rate j,⎡⎤−la2πγ 2⎥j(ρsup ) ∝ [ln(ρsup /ρeq )]3/2 exp⎢⎢⎣ (kBT )2 ln(ρsup /ρeq ) ⎥⎦This formula is based on the classical nucleation theory,26
where γ is the two-dimensional surface tension (energy)
deﬁned at the boundary of two-dimensional nuclear clusters at
the solid surface, la is the lattice constant parameter of solid,
which is set to be 1.145 in these calculations, kB is theBoltzmann constant and T is temperature. ρeq is the saturated
vapor density, whose value is obtained from preliminary
simulations to be ρeq = 1.80 × 10−4 at T = 0.307, and ρeq =2.99 × 10−5 at T = 0.270. ρsup is the supplied vapor density. The
values of surface tension for each of VS and VLS (LS interface)system, γvs and γls as the ﬁtting parameter, are estimated to be
γvs = 0.37 and γls = 0.25 at T = 0.307, and γvs = 0.42 and γls =0.20 at T = 0.270.
Eq 1 implies that the solid constantly grows when the ﬂux
density is higher than the following critical value ρc as expressedin the eq 2 (the maximum of the curvature of the theoreticalcurve),⎡
l 2πγ 2 ⎤
ρc ≅ ρeq exp⎢0.8 a 2 ⎥⎣ (kBT ) ⎦(2)

Thus, these theoretical considerations highlight that theobserved shift of the material ﬂux window as a function of T (inFigure 2b) is essentially due to the shift of saturate vapor
density ρeq, which exponentially depends on T. Eq 2 also leads
the width of the material ﬂux window W, viewed in thelogarithmic scale of the ﬂux density, as

(1)
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Figure 3. (a) Eﬀects of Mg metal vapor ﬂux and the growth temperature on the VLS nanowire formation of MgO. SEM images are shown in theﬁgure. (b) Eﬀect of Mg metal vapor ﬂux on the temperature dependence of MgO nanowire density formed via a VLS route. The inset shows theeﬀect of Mg metal vapor ﬂux on the critical temperature Tc, above which the nanowire structures can be formed via a VLS process. (c) Eﬀect ofoxygen partial pressure on the temperature dependence of MgO nanowire density formed via a VLS route. The inset shows the eﬀect of oxygen
partial pressure on the critical temperature Tc, above which the nanowire structures can be formed via a VLS process.

W ≡ ln ρc,VS − ln ρc,LS ≅ 0.8

la2π (γvs 2 − γls 2)
2(kBT )

observed. To more quantitatively examine this eﬀect of vapor
ﬂux on the VLS nanowire formation, we measured thenanowire density when varying the Mg vapor ﬂux (ranged
from 4.2 to 34.1 × 1017 cm−2s−1) and the growth temperature(ranged from 250 to 850 °C) with the constant oxygen partialpressure (10−3 Pa), as shown in Figure 3b. When varying the
growth temperature, there was a critical temperature, above
which the nanowire structures were formed. For example, at thehighest Mg vapor ﬂux of 34.1 × 1017 cm−2s−1, any nanowire
structures were not observable below the critical temperature,
600 °C, and the nanowire structures emerged above the criticaltemperature. As shown in the inset ﬁgure, the criticaltemperature decreases with decreasing the growth temperature
down to 350 °C. Furthermore, the similar trend was also
conﬁrmed even when varying only the oxygen partial pressure(e.g., oxygen vapor ﬂux) with the constant Mg vapor ﬂux, as
seen in Figure 3c, which shows the nanowire density data whenvarying the oxygen partial pressures ranged from 10−3 Pa to 1
Pa and the growth temperature (ranged from 250 to 850 °C)
with the constant Mg vapor ﬂux (8.8 × 1017 cm−2s−1).
Decreasing the oxygen partial pressure from 1 Pa to 10−3 Padecreases the critical temperature for the VLS nanowire growthfrom 450 to 350 °C. Thus, the growth temperature for MgO
nanowire growth via a VLS route can be reduced by decreasing
the vapor ﬂux, which is consistent with the theoretical(3)This value tends to increase as temperature decreases (W =2.6 at T = 0.307, and W = 6.2 at T = 0.270), as shown in Figure
2c. These MD simulation results and the analysis based on
nucleation theory suggest that it should be experimentallypossible to reduce the growth temperature of VLS nanowire
growth by appropriately decreasing the vapor ﬂux.
Figure 3 shows the experimental validation of above
theoretical framework by utilizing the VLS growth of MgO
nanowires with Au catalysts. The experimental details of
nanowire growth can be seen in the Methods Section. Figure 3ashows the scanning electron microscopy (SEM) images of
MgO nanowires formed via a VLS route. The growthtemperatures were 400 and 800 °C, and the Mg metal ﬂuxes
were 8.8 × 1017 cm−2s−1 and 34.1 × 1017 cm−2s−1 with theconstant oxygen partial pressure (10−3 Pa). Although at thehigher growth temperature, 800 °C, the nanowire structures
could be formed at both vapor ﬂux cases, there was thesigniﬁcant eﬀect of vapor ﬂux on the appearance of nanowire
structures at the lower growth temperature, 400 °C. At thelower growth temperature, 400 °C, the nanowire shape wasobservable only for the lower vapor ﬂux case, but not for thehigher vapor ﬂux case, where only grain-ﬁlm structure was
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Figure 4. (a) Growth rates of VLS nanowires and thin ﬁlms when varying the growth temperature at the constant Mg metal vapor ﬂux of 4.2 × 1017
cm−2s−1. (b) Growth rates of VLS nanowires and thin ﬁlms when varying the growth temperature at the constant Mg metal vapor ﬂux of 24.5 × 1017
cm−2s−1.

predictions in Figure 2. Within the framework of “material ﬂux
window”, the successful reduction of growth temperature via
controlling the vapor ﬂux should originate from the suppressionof a nucleation at VS interface.24 To conﬁrm this, we measured
the growth temperature dependence of thin ﬁlm (VS) growthrate by varying Mg metal vapor ﬂux, as shown in Figure 4. For
comparison, the data of nanowire growth rates are also shown.
Clearly, the VS thin ﬁlm growth is signiﬁcantly suppressed bydecreasing the Mg metal vapor ﬂux. For example, at the growthtemperature of 500 °C, the VS thin ﬁlm growth is almost zerofor the lower vapor ﬂux, 4.2 × 1017 cm−2s−1, whereas for thehigher vapor ﬂux, 24.5 × 1017 cm−2s−1, such VS thin ﬁlm
growth is signiﬁcant (around 0.6 nm/min). Thus, thetemperature dependent “material ﬂux window” is a key
phenomenon to successfully reduce the growth temperatureof nanowires via a VLS route.
Next we examine the applicability of above strategy to reduce
the growth temperature for VLS nanowire growths of various
metal oxides. Figure 5 shows the SEM images of SnO2 andZnO nanowires formed via the VLS route with Au catalysts.
The growth temperatures were 400 and 750 °C, and the Sn and
Zn metal ﬂuxes were ranged from 3.3 × 1017 cm−2s−1 to 39.1 ×1017 cm−2s−1 with the constant oxygen partial pressure (10−3Pa). The other experimental details of nanowire growths can beseen in the Methods Section. At the higher growth temperature, 750 °C, the nanowire structures of both SnO2 and ZnO
were observable independent of the vapor ﬂux cases. On theother hand, at the lower growth temperature, 400 °C, thenanowire structures were observable only for the lower vapor
ﬂux, 3.3 × 1017 cm−2s−1 (SnO2) and 4.3 × 1017 cm−2s−1 (ZnO).
Thus, decreasing the metal vapor ﬂux successfully enhances the
VLS nanowire growths of both SnO2 and ZnO even at thelower growth temperature, 400 °C, and these results highlightthe universality of the present strategy for VLS nanowire
growth of various metal oxide materials. Figure 6 shows the
microstructures, optical and electrical properties of SnO2
nanowires fabricated at both relatively high (750 °C) and low(500 °C) temperatures. Figure 6a shows the transmission
electron microscopy (TEM) images of SnO2 nanowires. The
smooth surfaces of nanowires can be seen in both samples. In
addition, the single crystallinity of SnO2 nanowires with thegrowth direction perpendicular to [011] orientation wascommonly observed in the high-resolution TEM (HRTEM)
images and the selective area electron diﬀraction (SAED)
pattern. Figure 6b shows the electron energy loss spectroscopy(EELS) of SnO2 nanowires at Sn−M4,5 edge and O−K edge.

Figure 5. (a) SEM images of SnO2 nanowires formed via a VLS route
when varying the growth temperature and the Sn metal vapor ﬂux. (b)SEM images of ZnO nanowires formed via a VLS route when varying
the growth temperature and the Zn metal vapor ﬂux.

The reference data of SnO2 and SnO bulks are also shown forcomparison.27 Since the EELS peaks at Sn−M4,5 edge are notclear, the O−K edge peaks are used for the discussion. The O−
K edge peaks indicate that the valence state of 750 °C sample
and 500 °C sample are similar to SnO2 bulk and the signiﬁcantdiﬀerence between the two spectra cannot be seen, indicating
the similar defect density in both samples. Next we performed
the photoluminescence (PL) spectroscopy as shown in Figure
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Nano Lettersshould be higher than 500 °C sample. To directly compare thenanowire property, we performed the electrical conduction
measurement using single nanowire device.31 Figure 6d shows
the current−voltage (I−V) characteristics of single SnO2
nanowire measured at room temperature in vacuum condition(10−3 Pa). The nanowire diameters of 750 °C sample and 500°C sample are 25 and 13 nm, respectively. The SEM image ofthe single SnO2 nanowire device and the resistivity data areshown as the insets in Figure 6d. The resistivity of 750 °C
sample and 500 °C sample are 15.2 × 103 Ωcm and 5.0 × 103
Ωcm, respectively. These resistivity values are much higher thanthat of previous work.32 Since the electrical conduction of SnO2
is associated with the defect density,33 these results imply the
low defect density of our SnO2 nanowires. Comparing the two
growth temperature conditions, the resistivity value of 500 °C
sample is slightly lower than that of 750 °C sample. This
indicates the higher defect density of 500 °C sample.
Presumably, this might be related to the surface defect rather
than the defect density within nanowires since the surface-tovolume ratio of 500 °C sample is almost twice of 750 °C
sample. Thus, these results of measured physical properties
highlight that we can fabricate relatively high quality metaloxide nanowires even at low temperature by utilizing thepresent temperature dependent “material ﬂux window”
principle.
Finally, we apply the present concept to VLS nanowire
growths of metal oxides onto various substrates, which require
relatively low growth temperatures due to their thermal
stability. Figure 7 shows the photo shots and SEM images of

Figure 6. Characterization of SnO2 nanowires grown at hightemperature (750 °C) and low temperature (500 °C). (a) TEM
images (upper), HRTEM images (middle), and SAED patterns(lower). EELS spectra at (b) Sn-M4,5 edge (left) and (c) O−K edge(right). Reference data of SnO2 and SnO from ref 27 is also shown.
(d) PL spectra measured at room temperature. (e) Current−voltage(I−V) curves of single SnO2 nanowire device measured at room
temperature in vacuum condition (10−3 Pa). The upper inset shows
the SEM image of single nanowire device. The nanowire diameters are
25 nm for 750 °C sample and 13 nm for 500 °C sample, respectively.
The resistivity values are shown as lower inset.

Figure 7. Photo shots and SEM images of SnO2 and ZnO nanowires
grown on ITO glass and PI substrates by utilizing the present method,(a) SnO2 nanowires grown on ITO glass substrate at the Sn metal ﬂux
of 6.0 × 1017 cm−2s−1 and oxygen partial pressure of 10−3 Pa at 500 °C,(b) ZnO nanowires grown on PI substrate at the Zn metal ﬂux of 4.2
× 1017 cm−2s−1 and oxygen partial pressure of 1 Pa at 400 °C. The
typical growth time is 1 h.

6c. The emission peaks were commonly observed at around
635 nm, which are associated with the bridging oxygen
vacancies at SnO2 nanowire surface.28−30 The peak intensityof 750 °C sample is higher than that of 500 °C sample,
however, we cannot simply interpret this results in terms of thehigher defect density of 750 °C sample since the peak intensity
can be varied by the volume fraction of SnO2 nanowires. Since
the nanowire density grown at 750 °C is higher than that at 500°C as shown in Figure 5, the PL intensity of 750 °C sample

VLS nanowires of both SnO2 and ZnO grown on tin-doped
indium oxide (ITO) glass and polyimide (PI) substrates.34,35
The lowest growth temperature of SnO2 and ZnO nanowires
was 350 °C which was achieved by controlling the vapor ﬂux.
Successful formations of nanowires on these substrates can beclearly seen. Thus, the present strategy based on thetemperature dependent “material ﬂux window” concept would
expand the application range of VLS nanowire growth of
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Nano Lettersmake the nanowire-electrode contact, followed by Ti 1 nm/Pt
100 nm electrode deposition using RF sputtering (50 W, Ar 0.3
Pa). The electrical conduction measurement was carried out
using 4-probe method at room temperature in vacuum
condition (10−3 Pa).
Molecular Dynamics (MD) Simulation. The molecular
dynamics simulation can express time-evolution of motion(position and translation speed) for each particles whichinteract each other through short-range Lenard-Jones (L-J)
potential.41 In this simulation system, three types of particles(A, B, and C) were utilized to model the vapor−liquid−solid(VLS) growth process. Here, A and C can make AC compoundin solid phase expressing oxide formation, and B is always
assigned as solvent liquid.
Following L-J type potential was used as 2-body interaction
potential except the interaction between A−A and C−C.

functional metal oxides, where existing VLS process has notbeen applicable due to the temperature limitation.
In summary, we proposed a rational concept to reduce thegrowth temperature of the VLS nanowire growth of various
metal oxides. MD simulations theoretically predicted thepossibility to reduce the growth temperature of VLS nanowire
growth by precisely controlling the vapor ﬂux. This concept isbased on the temperature dependent “material ﬂux window”
that the appropriate vapor ﬂux for VLS nanowire growthdecreases with decreasing the growth temperature. Experimentally, we found the applicability of this concept for
reducing the growth temperature of VLS processes for various
metal oxides including MgO, SnO2, and ZnO. In addition, we
showed the successful applications of this concept to ITO glass
and PI substrates.
Methods. Nanowire Growths. Pulsed laser deposition(PLD, ArF excimer laser, λ = 193 nm, repetition rate =10Hz) method was utilized to grow metal oxide nanowires, as
described previously.36−38 SnO2 and ZnO nanowires weregrown on a sapphire Al2O3 (110) substrate, and MgO
nanowires were grown on a MgO (100) substrate (Crystal
Base Co. Ltd.). As the metal catalysts, Au thin layer (∼1 nm)
was deposited onto the substrates by direct current (dc)sputtering. The vapors of material species were supplied byablating metal tablets or metal oxide tablets (purity over
99.99%; Koujundo Chemicals Co. Ltd.). MgO, SnO2 and Zn
targets were used for MgO, SnO2, and ZnO nanowire growths,
respectively. The materials ﬂux was controlled by changing thelaser energy from 40 to 80 mJ. Oxygen and argon gases wereintroduced into the vacuum chamber with the total pressure of
10 Pa. The oxygen partial pressure was altered from 10−3 to 1
Pa. The temperature of substrate was varied from 250 to 850°C, and the typical growth time was 30 min. After nanowire
growth, the substrate was cooled down to room temperature in
the chamber within 30 min.
Characterizations. Fabricated nanowires were characterized
by ﬁeld emission scanning electron microscope (FESEM, JEOL
JSM-7610F) at an accelerating voltage of 15 kV. The materials
ﬂux was estimated from the thickness of oxide ﬁlms depositedin pure oxygen ambient (10 Pa) and at room temperature,
because the evaporation rate on the substrate is negligible atsuch low temperature.39,40 The thickness of ﬁlm was measured
by surface proﬁler (Alpha-Step IQ). Nanowire density was
extracted by counting the number of nanowires per unit areas(1 μm) in the top view SEM images. Ten unit areas wererandomly selected to ensure the accuracy and the reliability.
The crystallinity and the growth direction of fabricatednanowires were characterized by scanning transmission electron
microscopy (STEM, JEOL JEM-ARM200F) at an accelerating
voltage of 200 kV. Electron energy loss spectroscopy (EELS)
equipped with TEM and photoluminescence (PL, JASCO FP8500) spectroscopy was utilized to evaluate the valence state
and the crystal defects of fabricated nanowires. The PL
measurement was performed at room temperature. The
electrical conduction measurement was performed in theform of single nanowire device.31 The single nanowire device
was constructed onto 100 nm SiO2 coated Si (100) substrate by
the electron beam (EB) lithography at an accelerating voltageof 30 kV. Brieﬂy, the fabricated oxide nanowires were ﬁrst
dispersed into 2-propanol by applying the sonication with 28
kHz for 5 min. Then the nanowire suspension was dropped
onto the substrate where the contact electrodes areprepatterned. Then the EB lithography was performed to⎡⎛ ⎞12 ⎛ ⎞6 ⎤σij
σij
ϕ(rij) = 4ε⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + ϕcorr (rij)r⎝ rij ⎠ ⎦⎣⎝ ij ⎠

Here, rij means a distance between the interacted twoparticles (center−center distance), σij is sum of the respective
particles’ radii and ε expresses the bonding energy constantdeﬁned for respective particle combinations, εBB, εAB, εCB, andεAC independently. To accelerate the calculation speed, a longrange interaction was neglected in this program code by
inducing cutoﬀ distance, Rc, and ϕ(rij) was set to be zero forrij>Rc. The correction term ϕcorr was set to satisfy the continuityof ϕ and dϕ/dr at rji = Rc.25
For the potential between A−A and C−C, other modiﬁed LJ potential was used.
12⎡⎛⎛ σ ⎞6 ⎤σij ⎞⎟⎟ − ⎜⎜ ij ⎟⎟ ⎥ + ϕ (rij − l )ϕ(rij) = 4ε⎢⎢⎜⎜
corr
0
⎥
r
⎝ rij − l0 ⎠ ⎦⎣⎝ ij − l0 ⎠where, l0 is oﬀset distance and εAA (=εCC) is energy constant.
Potential (2) and l0 were introduced to stabilize the rock-salt
structure of AC solid phase. l0 was set to be l0  la(√2−1),
where la is the lattice constant of AC rock-salt crystal.
The simulation box was set to be L × L × αL, where αL isthe system height (set α = 2 in this article). Here the typicalsystem size was set to be L = 32la. Initially, the substrate witheight layer-thick solid consisting of A and C particles with rocksalt order was ﬁxed on the bottom wall. A ﬂat layer of B-particle
solvent was placed on the substrate for the simulation of the
VLS process, while no solvent was added or the VS process.
The sidewalls have a periodic boundary condition. The
temperature of the system was controlled on the top andbottom walls. The particle bath densities of A particles ρsupA andof C particles ρsup
C were set independently, and each species was
suppled from the top wall.25
All physical parameters used in this program are normalized
by εAC, σA, and the particle mass m. This normalization leads todimensionless temperature and time parameters of kBT/εACand t εAC/m /σA , respectively.

■

AUTHOR INFORMATION

Corresponding Author*E-mail: yanagida@cm.kyushu-u.ac.jp.
ORCID

Gang Meng: 0000-0003-3786-5692
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Takeshi Yanagida: 0000-0003-4837-5701
Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS
This work was supported by CREST of Japan Science andTechnology Corporation (JST). M.B was supported by
ImPACT. K.N, H.Y., and F.Z were supported by KAKENHI
Grant Numbers (No.26706005, No.16H00969, No.15K13288,
No.15H03528, No.26220908). This work was performed under
the Cooperative Research Program of “Network Joint ResearchCenter for Materials and Devices” and the MEXT Project of“Integrated Research Consortium on Chemical Sciences”.

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