Record Pure Zincblende Phase in GaAs Nanowires down to 5 nm in

Letter pubs.acs.org/NanoLett

Record Pure Zincblende Phase in GaAs Nanowires down to 5 nm in Radius Evelyne Gil,†,‡,* Vladimir G. Dubrovskii,§,∥,⊥ Geoffrey Avit,†,‡ Yamina André,†,‡ Christine Leroux,#,¶ Kaddour Lekhal,†,‡ Jurij Grecenkov,§ Agnès Trassoudaine,†,‡,□ Dominique Castelluci,†,‡ Guillaume Monier,†,‡ Reda M. Ramdani,†,‡ Christine Robert-Goumet,†,‡ Luc Bideux,†,‡ Jean Christophe Harmand,■ and Frank Glas■ †

Clermont Université, Université Blaise Pascal, Institut Pascal, BP 10448, F-63000 Clermont-Ferrand, France CNRS, UMR 6602, IP, F-63177 Aubière, France § St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia ∥ Ioffe Physical Technical Institute of the Russian Academy of Sciences, Polytekhnicheskaya 26, 194021 St. Petersburg, Russia ⊥ St. Petersburg State University (Physical Faculty), Ulianovskaya Street 3, Petrodvorets, 198504 St. Petersburg, Russia # Université de Toulon, IM2NP, Bât.R, B.P.20132, 83957 La Garde Cedex, France ¶ CNRS, UMR 7334, 83957 La Garde Cedex, France □ Clermont Université, Université d’Auvergne, Institut Pascal, BP 10448, F-63000 Clermont-Ferrand, France ■ CNRS-LPN, Route de Nozay, 91460 Marcoussis, France ‡

ABSTRACT: We report the Au catalyst-assisted synthesis of 20 μm long GaAs nanowires by the vapor−liquid−solid hydride vapor phase epitaxy (HVPE) exhibiting a polytypismfree zincblende phase for record radii lower than 15 nm down to 5 nm. HVPE makes use of GaCl gaseous growth precursors at high mass input of which fast dechlorination at the usual process temperature of 715 °C results in high planar growth rate (standard 30−40 μm/h). When it comes to the vapor− liquid−solid growth of nanowires, fast solidification at a rate higher than 100 μm/h is observed. Nanowire growth by HVPE only proceeds by introduction of precursors in the catalyst droplets from the vapor phase. This promotes almost pure axial growth leading to nanowires with a constant cylinder shape over unusual length. The question of the cubic zincblende structure observed in HVPE-grown GaAs nanowires regardless of their radius is at the heart of the paper. We demonstrate that the vapor− liquid−solid growth in our conditions takes place at high liquid chemical potential that originates from very high influxes of both As and Ga. This yields a Ga concentration systematically higher than 0.62 in the Au−Ga−As droplets. The high Ga concentration decreases the surface energy of the droplets, which disables nucleation at the triple phase line thus preventing the formation of wurtzite structure whatever the nanowire radius is. KEYWORDS: Nanowire, GaAs, HVPE, VLS, crystal structure, chemical potential

T

phase of III−V NWs has been a challenging task for a while.13−16 Indeed, GaAs NWs often feature spontaneous zincblende (ZB)-wurtzite (WZ) polytypism and stacking faults can form between alternating WZ and ZB layers along the ⟨111⟩ axis of the NWs.6,17−20 It is now admitted that the swapping between WZ and ZB sequences is related to surface energy values and crystal-growth conditions. In the Aucatalyzed MOVPE procedures, high V/III ratio and low temperature (T) have been demonstrated to favor predominantly ZB NWs, while low V/III and high T are suitable for

he III−V high carrier mobility and direct bandgap semiconductor nanowires (NWs) have been extensively studied for fundamental physics and nanoscale electronic, photonic, and sensing device applications.1−7 First micro- and nanosized wires were synthesized for Si and III−V materials by the vapor−liquid−solid (VLS) growth.8,9 Continuous efforts have been put forth into catalyst-assisted VLS growth of III-V NWs and most commonly used GaAs NWs for almost 15 years. The processes involved are molecular beam epitaxy (MBE) and metal−organic vapor phase epitaxy (MOVPE), as the most widespread growth techniques for III−V compounds since the 1980s. VLS growth is particularly well mastered nowadays for both of these epitaxial tools and enables growth of complex NW structures.10−12 Whatever the structure device is, high material crystal quality is required. The control of the crystal © 2014 American Chemical Society

Received: April 3, 2014 Revised: May 22, 2014 Published: May 29, 2014 3938

dx.doi.org/10.1021/nl501239h | Nano Lett. 2014, 14, 3938−3944

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Figure 1. (a) TEM image of a GaAs nanowire 14 μm long with a constant radius of 15 nm grown by Au-assisted VLS-HVPE at 715 °C. (b) HRTEM image taken along the [011]̅ zone axis.

pure WZ.21,22 Crystal phase engineering involving controlled axial stacking of WZ and ZB segments is now demonstrated for NW radii of several tens of nanometers.23−25 MOVPE and MBE processes produce NWs whose properties are controlled on the lengths up to a few micrometers. A compromise between the V/III ratio and temperature parameters should be carefully chosen so as not to deteriorate the morphology of the NWs subject to tapering. In this paper, we address the synthesis of GaAs NWs by Auassisted VLS growth by the hydride vapor phase epitaxy (HVPE) process. HVPE is known as a near-equilibrium condensation process: one can understand it as reacting almost immediately to an increase of the vapor supersaturation toward return to equilibrium of the deposit reaction.26 This results in a very fast growth upon setting high mass input of growth precursors to overcome very substantial desorption fluxes at high temperatures. This property is due to the use of chloride molecules GaCl as the element III precursor. The salient features of NWs grown by catalyst-assisted HVPE are a high axial growth rate greater than 100 μm/h and a constant untapered morphology.27,28 As a matter of fact, NWs grown by HVPE have shown the highest aspect ratio, ranging from 800 to 1000 for radii ranging from 25 to 70 nm for GaAs. Another property is the crystal phase: GaAs NWs exhibit defect-free and stacking fault-free ZB structure. This result is surprising because it disagrees with what has been demonstrated by MOVPE,16,21,22 as Au-assisted VLS-HVPE growth is carried out at a high-temperature process of 715 °C compared to 400− 500 °C typically used in MOVPE. As for Au-assisted MBE, it is almost impossible to obtain pure ZB GaAs NWs,18 and one should switch to Ga catalyst to achieve that.30,31 The last attribute is the record length of the observed pure crystal phase: from 20 to 100 μm for the growth times (15−30 min) and the growth rates that were tested (100 to 170 μm/h). Here, we focus on the growth and related structural property of NWs with radii lower than 15 nm with two objectives: (i) demonstrate the capability of the HVPE process in growing long pure phase NWs for the smallest radii; (ii) help the nanowire community in comprehending phase control as a function of the growth parameters. As a matter of fact, the HVPE process is carried out under completely different thermodynamic conditions with respect to MBE and MOVPE

in terms of temperature and precursors with a particular H2/ chlorine ambient pressure. It appears interesting to follow the evolution of the morphology and crystalline phase of NWs grown under these experimental conditions and especially for this peculiar radii range (5−15 nm) where uncontrolled polytypism and conversion to WZ should take place. To date, the thinnest GaAs NWs have been synthesized by VLSMBE; NWs with radii of 5 and 6.5 nm exhibited a WZ structure over length of 5 μm with negligible intermixing of ZB stacking.29 In this paper, we show that Au-catalyzed HVPE process yields polytypism-free ZB GaAs NWs for radii below 15 nm on more than 10 μm length, which to our knowledge has never been achieved for whatever growth technique. Thorough theoretical investigations of catalyst-assisted growth in the MBE and MOVPE processes have shown that suppression of nucleation at the triple phase line (TPL) (where the vapor, liquid, and solid phases meet) helps to avoid ZB-WZ polytypism under optimized growth conditions.18 This model was supported by experimental data provided by the VLS-MBE process with the Ga-catalyzed growth of GaAs NWs.30 As a matter of fact, several groups confirmed that self-catalyzed III− V NWs adopted the ZB phase much more often than Aucatalyzed one.30−33 We propose here to test the robustness of the model with the supersaturation conditions encountered in the HVPE environment. GaAs VLS-HVPE growth was carried out on Au-coated 4° misoriented vicinal {100} GaAs substrates in a hot wall horizontal reactor kept at atmospheric pressure. Au droplets with diameters ranging from 50 to 10 nm were formed after annealing at 715 °C in the HVPE reactor of the Au/GaAs substrates (for a nominal deposited amount of Au equivalent to 0,1 monolayer). HVPE involves gaseous GaCl molecules synthesized inside the quartz reactor in an upstream zone by the use of HCl flow reacting with a Ga liquid source. The reaction is carried out at temperature greater than 750 °C, so that the HVPE reactor is fully heated. Element V is transported as arsine (AsH3) that is completely decomposed into As2 and As4 molecules considered to be at equilibrium by entering the hot wall reactor.34 GaAs growth was carried out at 715 °C for 30 min with a partial pressure of GaCl of 300 Pa, a partial pressure of As4 of 71 Pa and with a H2 vector flow of 3000 SCCM including additional HCl flow (at 50 Pa) used to tune 3939


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the supersaturation of the vapor phase.35−37 These experimental parameters yield a GaAs 2D planar growth rate of 38 μm/h and 20 μm/h on vicinal (001) and (111)B GaAs substrates, respectively. Scanning electron microscopy (SEM) was used for postgrowth measurements of the tens of micrometers-length of NWs. Transmission electron microscopy (TEM), electron diffraction, and energy dispersive spectroscopy (EDS) were performed on several NWs for the atomic level examination of the morphology and crystal structure (Tecnai G2 ST operated at 200 kV, 0.25 nm point-to-point resolution). For highresolution TEM (HRTEM) measurements, the electron beam was aligned along the ⟨11̅0⟩ direction for an accurate assessment of stacking faults. Figure 1 shows the TEM and HRTEM images of a GaAs NW 14 μm long with a constant radius of 15 nm grown by VLS-HVPE. For the observation of individual NWs, GaAs samples were put in ethanol and sonicated for several minutes to separate the wires from the substrates. The preparation method yields broken NWs, especially for the thinnest ones. A rodlike shape with a constant radius was observed over lengths higher than 10 μm for the detached NWs, which is in agreement with what was shown earlier for NWs grown by VLS-HVPE with a radius of 50 nm.27 Figure 2a,b displays the HRTEM images of NWs with radii of 11 nm and 5−6 nm, respectively. The NWs were all indexed in the cubic ZB structure (see the fast Fourier transform (FFT) image in Figure 2). FFT on the carbon film indicated that the HRTEM images were taken near the Scherzer defocus. HRTEM images of the cubic ZB structure were simulated using the software JEMS for different thicknesses (from 4 to 24 nm) at the near-Scherzer defoci. Simulated HRTEM images are the same for different thicknesses except at 15−17 nm where the (111) and (11̅1̅) planes have a very weak contrast. For a NW 11 nm in radius (Figure 2a), this critical thickness value is reached for different distances from the edge of the NW, compatible with a mixture of (211) and (110) facets along the growth direction. For a NW 5 nm in radius (Figure 2b), the thickness remains less than 15−17 nm, thus no contrast variation is observed. As a summary, NWs with very small radii were grown in the ⟨111⟩ direction, exhibiting stacking-fault free pure ZB phase over the lengths that could be observed on individual NWs, that is, up to 20 μm. Contrary to the NWs with radii of 25 nm or above, which were found hexagonal with (211) facets,27 thinner NWs have a more complex faceting. The prevalence of (211) ZB facets makes the observed crystal phase purity even more surprising, because it is known from different calculations38−40 that these facets have a higher surface energy than (110) and therefore the formation of ZB structure is more energetically costly in this case. The defect-free area excludes a very narrow zone just beneath the droplet where structural instabilities take place. This is due to unsteady conditions in the droplet upon stopping precursors at the end of growth, resulting in progressive decreasing Ga liquid supersaturation after consumption upon crystallization. This is consistent with the observations related to NWs with radii of 50 nm.27 The unexpected ZB phase for GaAs NWs of 5−15 nm radii calls for discussion. The radius-dependent polytypism in GaAs NWs was calculated from equilibrium formation energies; it is predicted that pure WZ phase should form for a radius of the order of 10 nm regardless of the growth conditions.40,41 In addition to these considerations related to intrinsic energetic morphological stability, crystal growth conditions play a major

Figure 2. HRTEM images taken along the [011̅] zone axis of GaAs NWs grown by Au-assisted VLS-HVPE at 715 °C with radii of 11 nm (a) and 5−6 nm (b). FFT shown in the insets are indexed in the cubic ZB structure.

role through supersaturation state in the catalyst droplet that drives the nucleation path. In fact, the competition between the ZB and WZ structures is driven by the difference in the corresponding nucleation barriers rather than equilibrium energies of fully formed NWs. This increases the actual critical radius for the ZB-to-WZ transition to the value of the order of several tens of nanometers depending on the growth conditions.38 Indeed, this was in agreement with up to date MBE experimental results for such a radius.18,29 VLS-HVPE yields NW axial growth rate of 100 μm/h or higher, as measured on the longest NWs grown during the 30 min process (we note that the NWs start growing at different moments of time due to random nucleation). VLS-HVPE for GaAs is carried out at high temperature above 700 °C (while it is usually lower than 600 °C for Au-catalyzed MBE),15,18 which ensures a liquid phase for the Au−Ga−As droplet with an original high percentage of Ga (higher than 30% if the droplets were pure binary Au−Ga alloys).42 The NW growth is supposed to occur preferentially via the adsorption of As and 3940


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where v05 depends only on temperature. Using this in eq 1, we are able to express the μl5 through the impinging As flux and the NW elongation rate.43 Substitution of the result into the general expression for the liquid chemical potential of GaAs in an Au−Ga−As droplet with respect to the stoichiometric ZB solid (Δμ = μl3 + μl5 − μs35, with μl3 as the chemical potential of Ga atoms in the liquid state and μs35 as the chemical potential of a GaAs pair in the solid state) leads to46

GaCl species on fully liquid Au−Ga−As droplets, followed by fast decomposition and desorption of the Cl atoms in the H2 ambient atmosphere through gaseous HCl. Continuous high amounts of Ga atoms enter the droplets and quickly diffuse toward the liquid−solid interface with the NWs where solidification takes place at a high rate. High growth temperatures used allow one to eliminate any diffusion of growth precursors from the substrate surface and/or sidewalls, which is consistent with the hypothesis of preferential supply of matter through the catalyst droplets. Therefore, in our modeling we assume that the NW elongation rate, dL/dt, is determined by the direct and desorption fluxes of Ga (under As-rich conditions) arriving at and leaving from the droplet at a given vapor composition. The observed ∼3 times increase of the NW elongation rate with respect to the planar one is well explained by the magnifying effect of the catalyst droplet having the contact angle β (since 2/(1 + cos β) = 3 at β 110°). Consequently, the model treats only a supersaturated Au−Ga−As droplet and is not limited to a particular choice of vicinal GaAs(100) substrates, working the same way for other substrates such as Si or glass provided that growth is catalyzed by Au, NWs are straight and elongate in ⟨111⟩ direction. Under steady-state conditions, the NW elongation rate can also be obtained from the kinetics of As atoms arriving to and leaving from an Au−Ga−As droplet43 dL 2 = (v5 − v5des) dt (1 + cos β)

Δμ =

and

v50 =

(

(1 + cos β) 2 0 v5

)

dL dt

⎤ ⎥ s ⎥ − μ35 ⎥⎦

(3)

Δμ > max{ΔμTPL ; ΔμC }

(1)

ΔμTPL =

ψWZ − ZB 1−

2

( ) ΓWZ ΓZB

;

ΔμC =

ψWZ − ZB 1−

2

( ) ΓWZ γsl

(4)

with ψWZ−ZB being the bulk energy difference between the WZ and ZB structures. The effective surface energies of nuclei at the TPL positions are given by18 ΓZB = (γZB − γlv sin β) x + γsl(1 − x); ΓWZ = (γWZ − γlv sin β)x + γsl(1 − x). The γZB, γWZ are the surface energies of relevant ZB and WZ NW sidewall facets, γlv is the liquid−vapor surface energy of the droplet, γsl is the surface energy of the lateral solid−liquid interface of a twodimensional island, and x is the fraction of the island perimeter at the TPL. The critical curve max{ΔμTPL; ΔμC} is shown in Figure 3 for the following parameters of Au-catalyzed VLS GaAs NWs: ψWZ−ZB = 24 meV/pair,48 γWZ = 1.30 J/m2 for the lowest energy (11̅00) WZ side facets, γZB = 1.543 J/m2 for the lowest energy (110) ZB side facets, and γZB = 1.79 J/m2 for the more energetic (211) side facets,38 β = 110°, and a triangle island (x = 1/3). The γlv(c3) dependence is taken as the linear approximation between pure liquid (γGa = 0.663 J/m2 and γAu = 1.215 J/m2 at 715 °C).49 The γsl(c3) is the linear approximation between 1.0 J/m2 at c3 = 0.218 and 0.123 J/m2 for a pure Ga droplet (at c3 = 1).45 It is seen that the critical chemical potential is limited by the ΔμTPL for the Ga concentrations lower than 0.36−0.51, depending on the ZB facet type, while for higher c3 it is given by the Δμc, that is, by the competition of the WZ TPL and the ZB C nucleation scenarios. Above c3 ≅ 0.65, the WZ phase formation is completely suppressed on surface energetic grounds due to a low surface energy of a Ga-rich droplet, as in the case of pure Ga catalyst.30 Hence, the WZ phase should be observed for high chemical potentials and low Ga concentrations in the topleft corner, while the ZB phase dominates below the critical curves. Very importantly, the ZB phase should form for all c3 >

0 Ω35nP5(4)

2πm5(4)kBT

⎡ kBT ⎢ v5 − ln⎢ + 4 ⎢⎣

Because of the known low solubility of As in liquid Au, the μl3 should be controlled primarily by the surface temperature T and the Ga concentration in the liquid droplet (c3). Conversely, the second and the third terms in eq 3 do not contain any dependence on the droplet composition. According to refs 18 and 47, the prevalence of the WZ phase over ZB in VLS NWs requires that the Δμ value is larger than the two critical chemical potentials. The first one corresponds to the equality of the nucleation barriers for the critical WZ and ZB nuclei at the TPL and the second to the equality of the nucleation barrier for the WZ nucleus at the TPL and the ZB nucleus in the center (C) of the liquid−solid interface under the droplet. Consequently, the WZ structure forms when

in which v5 = I5Ω35, I5 is the direct atomic flux of As (per unit area per unit time), Ω35 = 0.0452 nm3 is the volume of a GaAs des des pair in the solid state, vdes 5 = Ω35I5 and I5 is the As desorption flux from the droplet. Here and below, label “5” represents As, “3” is for Ga, and “35” is for a GaAs pair. We neglect the surface diffusion of As (as we did for Ga), which is commonly accepted even for much lower growth temperatures during MBE (∼600 °C).44,45 As in ref 45, the vdes is expressed through the chemical 5 potential of As atoms in a liquid Au−Ga−As droplet (μl5) by equating the As activities in the liquid droplet with this μl5 and in the corresponding equilibrium vapor of As4: μv5(4) = 4 μl5 at the surface temperature T. The subscript “n” in the chemical potential μv5(n) and elsewhere relates to the densest Asn vapor in a gaseous environment. In HVPE, the As4 pressure is by far the highest one: it equals 71 Pa versus only 0.5 Pa for As2 vapor. One can argue however that arsenic desorbs from the droplet in the form of As2 molecules that only subsequently agglomerate into As4. In this case, the “imaginary” equilibrium vapor is As2 and the corresponding equilibrium condition would rewrite as μv5(2) = 2 μl5. However, it can be shown that this difference does not considerably affect the μl5 value. We then use the perfect gas equation for the vapor chemical potential: μv5(4) = kBT ln(P5(4)/ P05(4)), with P5(4) as the partial pressure of As4 vapor and P05(4) as a certain temperature-dependent value. After that, we imply the known expression for the vapor flux, I 5des = (4P 5 )/ (2πm5(4)kBT)1/2 with m5(4) as the mass of an As4 molecule and kB as the Boltzmann constant. The equilibrium vapor flux onto the droplet should equal the desorption flux from the droplet. This yields43,45 ⎛ 4μ l ⎞ v5des = v50exp⎜⎜ 5 ⎟⎟ ⎝ kBT ⎠

μ3l

(2) 3941


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near 600 °C.45 Also, in eq 5 for the nucleation barrier we use the solid−liquid surface energy of the island because the NWs are ZB and thus should form by the C nucleation mechanism. The nucleation rates obtained from eq 5 at 715 °C and A = 7 nm−2 s−1 are shown by the red lines in Figure 4 for different

Figure 3. Chemical potentials of GaAs in a liquid Au−Ga−As droplet during Au-catalyzed VLS-HVPE of GaAs NWs at temperatures between 700 and 740 °C (red lines) as functions of the Ga concentration, compared to the critical chemical potentials ΔμTPL and ΔμC for the WZ phase formation. The ΔμTPL is lower for (211) than for (110) ZB facets. The WZ phase should be prevalent in the top-left corner, while the ZB structure forms below the two critical curves. Figure 4. Nucleation-mediated NW elongation rates at 715 °C for different R, obtained from eqs 5 at 715 °C and A = 7 nm−2 s−1, compared to the minimum experimental elongation rate of 28 nm/s (horizontal line). The blue lines show the same growth rates for A = 7 × 104 nm−2 s−1.

0.65 actually regardless of the NW radius. This feature does not depend on the ZB facet type [i.e., (211) or (110)], because the nuclei are entirely surrounded by the liquid phase and do not feel the sidewalls. The red lines in Figure 3 show the calculated chemical potential of GaAs NWs, obtained from eq 3 at T = 700 to 740 °C, dL/dt = 28 nm/s, n = 4, v5 = 6.2 × 104 nm/s (estimated from the partial pressure of As4 of 71 Pa), and v05(T) obtained from the data of ref 50 for As4 vapor (in particular, v05 = 2.6 × 1014 nm/s at 715 °C). The chemical potentials of the liquid Ga were computed from the Glas model.46 It is seen that these chemical potentials enter the WZ corner for the Ga concentrations approximately between 0.12 and 0.62, while the ZB structure should be dominant outside this range. The corresponding values of the As concentrations in the droplet (yielding the elongation rate dL/dt = 28 nm/s as discussed below) were estimated at 0.052, 0.049, 0.047, 0.046, 0.043, and 0.039 at 700, 710, 715, 720, 730, and 740 °C, respectively. Therefore, the absolutely defect-free ZB phase of HVPEgrown GaAs NWs would be confirmed if we show that the Ga concentration in the droplets during growth is above 0.62 for all NWs. As in refs 43 and 45, the actual Ga concentration during growth can be estimated by equating the observed elongation rate (with the minimum of 100 μm/h, or 28 nm/s) to the nucleation-mediated NW growth rate

NW radii from 5 to 50 nm. It is seen that crossing points of these curves with the minimum experimental elongation rate of 28 nm/s correspond to the values of c3 that are systematically higher than 0.7. Of course, this analysis is sensitive to the unknown prefactor A. However, even if we increase its value by a huge factor of 104 (which could partly be due to enhanced diffusivity of As at 715 °C compared to 600 °C), the Ga concentration would still remain higher than 0.62, as shown by the blue lines in Figure 4. In other words, our exceptional elongation rate necessarily requires the droplet to be Ga-rich, which yields the pure ZB phase due to the suppression of the TPL nucleation on surface energetic grounds. This conclusion is robust with respect to variations in temperature (700−740 °C) and in the generally unknown pre-exponential factor A. If we estimate the critical size of classical nucleation theory18 from the nucleation barrier at these high values of the liquid chemical potential, it would correspond to only one GaAs pair (and to only two GaAs pairs in the case of Ga-catalyzed GaAs NWs grown by MBE at 600 °C according to the data of ref 45). Therefore, we actually reach the limit of macroscopic models for the island formation energy, calling for some microscopic generalizations as in the case of irreversible growth.51 On the other hand, if the conditions are such that incorporation of just a single atom pair becomes stable, the nucleation at the TPL becomes statistically very unlikely. Then our main result showing the preferred formation of ZB structure is confirmed. In conclusion, the occurrence of the defect-free cubic ZB phase in Au-catalyzed GaAs nanowires of radius down to 5 nm was demonstrated here for the first time. The NWs were synthesized by Au-assisted VLS-HVPE growth at 715 °C at a minimum axial rate of 100 μm/h from vapor phase with high mass inputs of GaCl and As4 precursors. Theoretical modeling was proposed to elucidate the unexpected ZB structure and its

⎛ Δμ ⎞1/2 ⎛ ΔG ⎞ dL 3 3 2 = R hAc5⎜ ⎟ exp⎜ − * ⎟ dt 2 ⎝ kBT ⎠ ⎝ kBT ⎠

ΔG = *

3 3 Ω35hγsl2 Δμ

(5)

Here, ΔG* is the nucleation barrier for triangular twodimensional nuclei of a monolayer height (h = 0.326 nm), c5 is the As concentration in the droplet and A is a certain (generally unknown) prefactor in the Zeldovich nucleation rate. Recently, Glas et al. obtained the recommended value of A = 7 nm−2 s−1 in the case of Ga-catalyzed GaAs NW at temperatures 3942


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purity for such small dimensions. We show that high Ga concentration in the droplets increases chemical potential but dramatically decreases the surface energy. This effectively suppresses the formation of WZ structure regardless of the NW radius. Our results suggest a simple way for avoiding crystal phase mixing in Au-catalyzed GaAs NWs: growth at a high Ga concentration in the Au−Ga−As alloy, yielding the exceptional elongation rate and the defect-free crystal capability simultaneously. This method should work for other deposition techniques and material systems in which these high material fluxes are achievable and provides an interesting tool to control the phase perfection in NWs.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 33 4 73 40 73 44. Fax: 33 4 73 40 73 40. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by FP7 projects NANOEMBRACE (Grant Agreement 316751) and FUNPROB (Grant Agreement 269169), grants of the Russian Foundation for Basic Research, and by Région Auvergne and European FEDER grants (CPER 2007-2013).

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REFERENCES

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Record Pure Zincblende Phase in GaAs Nanowires down to 5 nm in

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