Simultaneous Selective-Area and Vapor–Liquid–Solid Growth of InP

Letter pubs.acs.org/NanoLett

Simultaneous Selective-Area and Vapor−Liquid−Solid Growth of InP Nanowire Arrays Qian Gao,*,† Vladimir G. Dubrovskii,*,‡,§,∥ Philippe Caroff,*,† Jennifer Wong-Leung,† Li Li,⊥ Yanan Guo,† Lan Fu,† Hark Hoe Tan,† and Chennupati Jagadish† †

Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia ‡ St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia § Ioffe Physical Technical Institute of the Russian Academy of Sciences, Politekhnicheskaya 26, 194021 St. Petersburg, Russia ∥ ITMO University, Kronverkskiy pr. 49, 197101 St. Petersburg, Russia ⊥ Australian National Fabrication Facility, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia S Supporting Information *

ABSTRACT: Selective-area epitaxy is highly successful in producing application-ready size-homogeneous arrays of III−V nanowires without the need to use metal catalysts. Previous works have demonstrated excellent control of nanowire properties but the growth mechanisms remain rather unclear. Herein, we report a detailed growth study revealing that fundamental growth mechanisms of pure wurtzite InP ⟨111⟩A nanowires can indeed differ significantly from the simple picture of a facet-limited selective-area growth process. A dual growth regime with and without metallic droplet is found to coexist under the same growth conditions for different diameter nanowires. Incubation times and highly nonmonotonous growth rate behaviors are revealed and explained within a dedicated kinetic model. KEYWORDS: III−V nanowires, selective-area epitaxy, vapor−liquid−solid growth, metalorganic vapor phase epitaxy, metal-catalyst, nucleation

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control this process would bring crystal structure tunability23,26 and advantages for ultrasharp axial heterostructures,27,28 both features being practically impossible using a pure SAE growth mechanism. Very importantly, several works have reported that even in the presence of a droplet at the initial stages, NW growth is still possible after consuming the droplet and therefore continues via the pure SAE process, for example, after a long growth interruption under group V flow.20,22 One reason for the controversy about the presence or absence of metal droplet during growth is due to the necessary cooling down stage prior to NW analysis. Indeed, even if the droplet is present during steady-state NW growth, it might easily be transformed to solid III−V material during cool down under group V flow.17,29−31 On the other hand, group III droplets are also able to reappear after the growth interruption.32,33 Therefore, definite conclusions about the pure SAE versus VLS nature of the growth process are far from straightforward and most often rely on indirect evidence. Consequently, here we attempt to clarify the formation mechanisms of SAE-grown III−V NWs by performing detailed growth investigations of MOVPE-grown InP NWs and

ost nanowire (NW) devices require ensembles of position-controlled NWs with the highest spatial homogeneity.1,2 Selective-area epitaxy (SAE), involving a patterned mask substrate that directs one-dimensional growth, has emerged as a natural candidate to provide highly regular arrays of NW with perfect vertical yield.3−5 It is also crucial that SAE-grown NWs are highly compatible with the silicon technology via direct integration without any foreign metal contaminants.6−10 With easily accessible NW arrays over a wide range of growth parameters, it is not surprising that the literature on SAE-grown III−V NWs in the past decade has been dominated by device-oriented studies.4,11,12 Only a few reports have attempted to explain the growth mechanisms involved13−16 and a controversy still exists about the interplay between the pure SAE (i.e., epitaxial growth in openings of a mask layer and NWs grow without any metal droplet) and the self-seeded vapor−liquid−solid (VLS) (i.e., with a group III metal droplet on the NW top) growth during selective-area metalorganic vapor phase epitaxy (MOVPE).17,18 In the case of randomly positioned foreign-metal free growth of NWs on oxide-masked substrates, such as InAs19,20 or InAsSb,21 recent works have already acknowledged the possibility for a self-formed metal droplet to exist under certain growth conditions,22−25 at least at the growth initiation stage. Understanding metal-seeded SAE growth and the ability to © XXXX American Chemical Society

Received: April 8, 2016 Revised: May 24, 2016

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DOI: 10.1021/acs.nanolett.6b01461 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. (a) Average NW length (after 5 min of growth time) as a function of NW diameter for NWs grown under different V/III ratios obtained by varying only group V flow. The error bars represent the standard deviation of lengths and diameters from 12 individual NWs. Panels (b,c) and (d,e) show 30° tilted SEM images of the InP NWs grown with a V/III ratio of 81 and 198, respectively, as indicated in (a). The NW diameters are around 60 nm in (b), 150 nm in (c), 60 nm in (d), and 150 nm in (e). Lines in (a) are theoretical fits by the model. Details of the model will be further discussed in later sections.

above, the length-diameter correlation does not evolve much anymore. The striking difference in NW lengths under varying V/III ratio cannot be understood within the standard view of pure SAE NW growth. Indeed, if the elongation rate is group-III limited, as commonly assumed,13 it may increase for smaller diameters but should not be much affected by the group V flow. On the other hand, in the self-seeded VLS mode the growth rate is simply determined by the group V flow and does not depend on the NW diameter.32 In order to understand this unusual behavior, we have thoroughly studied the NW length evolution as a function of both diameter and growth duration for two different V/III ratios. Figure 2a,b shows the NW length as a function of growth time for a set of different hole diameters and V/III ratios of 81 and 324. Growth times were adjusted for both low and high V/ III regimes to capture the relevant evolutions. Both figures show that the NW length increases almost linearly with time for large diameters of 85 and 150 nm. Conversely, for NWs grown from smaller diameter openings the axial growth rate varies significantly with increasing growth time, making the corresponding curves strongly nonlinear. First of all, smaller opening diameters lead to longer incubation times for NW nucleation. For example, the NWs growing from 40 nm diameter holes nucleate only after 2.7 min while NWs growing from 25 nm diameter holes nucleate after 4 min at V/III = 81. However, these small diameter NWs start growing very rapidly after nucleation and soon overtake the length of thicker NWs. For example, at a V/III ratio of 81 the NW length reaches about 4200 nm in 20 s. The instantaneous growth rate for these NWs is huge, around 210 nm/s, which is 3 orders of magnitude higher than the equivalent two-dimensional growth rate of InP (∼0.1 nm/s under these conditions). It is noteworthy that the incubation time for a given opening diameter consistently increases for higher V/III ratios. Furthermore, NWs emerging from smaller holes grow much longer in 4 min at a V/III ratio of 81 than in 6 min at a V/III ratio of 324. The size of the first stable NW nucleus (i.e., the number of III−V pairs in the critical nucleus) is usually very small and can be estimated at only 3−5 GaAs pairs based on the data of ref 34 for Ga-seeded and ref 35 for Au-seeded GaAs NWs grown by MBE. Assuming similar values for our MOVPE growth process, we can safely neglect the critical size compared to the hole diameter and hence the size of the first stable nucleus emerging in the hole cannot limit the NW nucleation. For the minimum hole

supporting the results by kinetic modeling that combines prior theories of pure SAE and self-seeded VLS growths. The complete trends of the NW length as a function of growth time and opening dimensions are obtained. We reveal a highly surprising nonmonotonic diameter dependence of the NW length and ascribe it to the coexistence of the self-seeded VLS and pure SAE growths under the same nominal growth conditions. Transmission electron microscopy (TEM) studies along with the growth interruption experiments confirm the presence of indium droplets under these conditions. The model fully supports the dual growth mode under nominally identical macroscopic growth parameters and shows how pure SAE is transitioned to self-seeded VLS growth. To grow the InP NW arrays, a thin SiOx layer was first deposited on (111)A InP substrates and patterned using a standard electron beam lithography (EBL) process. Hexagonal arrays of holes with 25−280 nm diameters were etched into the SiOx layer using inductively coupled plasma reactive ion etching (ICP-RIE). The patterned substrates were then placed in a horizontal flow low-pressure MOVPE system using a total flow of 14.5 l/min for growth at 730 °C with trimethylindium (TMIn) and phosphine (PH3) as precursors.5 The TMIn flow rate was fixed to 6.07 × 10−6 mol/min while the PH3 flow rate was varied from 3.57 × 10−4 to 1.96 × 10−3 mol/min, to achieve the V/III flow ratios ranging from 59 to 324. The NW morphology was investigated using a FEI Helios 600 NanoLab scanning electron microscopy (SEM) system. The crystal structure and composition of the NWs were determined using both TEM and scanning transmission electron microscopy (STEM) in a JEOL 2100F TEM equipped with energy dispersive X-ray spectroscopy (EDX). Figure 1a shows the evolution of the NW length as a function of diameter for a fixed pitch of 500 nm with hole opening diameters ranging from 40 to 280 nm and five different PH3 flows. Representative NW array geometries are illustrated in Figure 1b−e. The growth time was 5 min for all these samples. The NW length is found to increase with diameter to a maximum value before decreasing for larger diameters. The measured length-diameter correlations are drastically affected by the V/III ratio. Lower V/III ratios systematically lead to longer length for all diameters and this effect is much more pronounced for smaller diameter NWs. For the smallest V/III ratio investigated here, the maximum NW length is achieved for the hole size of 40 nm. For higher V/III ratios of 198 and B

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related to the formation of holes in the surface oxide layer,39 and the droplets having longer incubation times results in NWs with shorter NW length and smaller NW radius.40 For selfinduced GaN NWs, long incubation times are attributed to difficult nucleation of GaN islands that subsequently transform to NWs.41,42 Similarly, long nucleation stage of Ga droplets on unpatterned SiOx/Si(111) delays the Ga-assisted nucleation of GaAs NWs.43 The relationship between the incubation time and NW diameter will be further discussed in later sections. We have designed special experiments aiming at probing the presence or absence of indium droplets during growth by postgrowth measurements. By cooling down the sample under arsine (AsH3) instead of PH3, we analyze ex situ the properties of InAs segments on the NW tops versus the NW diameter and try to unravel the postulated indium droplet presence and its volume during steady-state growth.44−46 The SEM images show some visible features on the top of each NW linked to growth with different faceting (see Supporting Information, Figure S2). Figure 3a,b shows the EDX images of the compositional maps

Figure 2. Average NW length as a function of growth time for a V/III ratio of (a) 81 and (b) 324. The NWs were grown from the openings with a pitch of 500 nm and diameters of 25, 40, 60, 85, and 150 nm. For 40 nm opening, the incubation time is found to be around 2.7 and 5 min for the NWs grown with the V/III ratio of 81 and 324, respectively. Lines are theoretical fits by the model. The error bars are measured from 12 NWs. When error bars are too small, they are not clearly visible on the graphs.

diameter of 25 nm, we can also ignore the Gibbs−Thomson effect36 on the NW growth rate. Rather, the size-dependent incubation time should be due to a longer waiting time for the first nucleation event in smaller holes37 as will be discussed shortly. On the basis of these data, it is reasonable to assume that at least the initial nucleation step of our selective-area growth has the self-seeded VLS character, as in ref 19 for InAs NWs grown by molecular beam epitaxy (MBE). In this case, lower V/III ratios can lead to and preserve indium droplet formation and the VLS nucleation through this droplet will occur faster because of a less energetic liquid−solid interface compared to the vapor−solid one. Furthermore, because the diffusion flux from the substrate or NW sidewalls to the top increases for smaller diameters,32 the droplet-assisted nucleation and VLS growth are more probable for thinner NWs. On the other hand, higher V/III ratios do not favor the droplet formation and hence the NWs emerge in the pure SAE mode at a lower growth rate. Considering this self-seeded VLS nucleation, Figure 2b demonstrates that the NWs grown from 25 and 40 nm openings have an incubation time of 6 and 5 min, respectively. Hence, the incubation time is affected not only by the V/III ratio, but also increases for smaller openings. This result is in contrast to those in ref 38, where the authors attributed the reduction in the Si NW length for larger diameters to an increase in the time required to fill the droplets to reach the initial supersaturation. They stated that as the initial droplet diameter increases, the volume of silicon required to supersaturate the droplet also increases and adds a delay time before crystallization begins. It has been reported that the spread in nucleation times in self-seeded GaAs NW growth is more likely

Figure 3. (a,b) EDX images of the top parts of InP NWs grown with a V/III ratio of 81 but cooled down under AsH3 instead of PH3. Compositional maps of phosphorus and arsenic are given in red and green color, respectively. (c) The length of InAs segments as a function of NW diameter. The red and black lines show the linear and inverse diameter dependences of the segment height, obtained from the model for the self-seeded VLS and pure SAE growth modes, respectively. (d) Schematic representation of the growth model for InAs segments.

of phosphorus and arsenic from a NW. These data indicate that the length of InAs segment is around 12 and 23 nm for NW with a diameter of 35 and 65 nm, respectively. Knowing that the As/P exchange is a surface effect that can only form a few monolayer-thick InAs layers,47 it is unlikely that much thicker segments (>20 nm) can grow on top of InP NWs by this effect alone. However, because nucleation may be more favorable on the top {0001} facet than on the side {1̅100} facets, surface migration of indium atoms from the NW sidewalls cannot be excluded immediately. Indeed, if indium is released by phosphorus desorption while the arsenic supply does not lead to instantaneous nucleation on the NW sidewalls, the top facet could eventually become indium-rich via adatom diffusion. Such an indium migration fueled by the presence of unfavorable nucleation sites has been shown to occur in another low dimensional system, during planarization of partially buried InAs/InP Stranski−Krastanow quantum dots.48,49 Therefore, the two main reasons for forming thick InAs segments on the top of the NWs are the following: (i) indium droplets that have been present during growth and then transformed to solid InAs during cooling down, as illustrated in Figure 3d; C

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Nano Letters (ii) indium diffusion from the NW sidewalls to the top with subsequent transformation to solid InAs under the arsenic flow. In both cases, the length of InAs segment, ΔL is determined by the available number of indium atoms on the top of the NWs. If indium is present in a liquid droplet, we have (πR2ΔL)/Ω35 = [cf(β)πR3]/(3Ω3). Here, R is the radius of cylindrical NW, Ω35 and Ω3 are the elementary volumes per InAs pair in solid and indium atom in liquid (here and below, indium is labeled “3” and group V elements are labeled “5”), f(β) = (1−cos β)(2 + cos β)/[(1 + cos β)sin β] is the geometrical function relating the volume of spherical cap to the cube of its base through the contact angle of the droplet β and c < 1 is a percentage of indium atoms that crystallizes at the liquid−solid interface. Assuming β = β0 as radius-independent, we obtain a linear increase of the segment length with NW radius, that is, ΔL ∝ R. On the other hand, if the main source of the indium supply is sidewall diffusion, we have (πR2ΔL)/Ω35 = 2πRλ3n3 with λ3 as the diffusion length of indium atoms and n3 as their residual surface concentration. Taking n3 = I3τ3, where I3 is the indium vapor flux and τ3 is the characteristic lifetime of indium atoms on the sidewalls, we obtain ΔL = (2λ3ν3τ3)/R (with ν3 = I3Ω35 as the indium deposition rate in nm/s), that is, the inverse correlation ΔL ∝1/R. The fits shown in Figure 3c are obtained with β0 = 125°, Ω35/Ω3 = 2.26 (refs 32, 34, and 50), c = 0.135, λ3 = 2500 nm, ν = 0.13 nm/s (these values will be justified shortly) and at a plausible τ3 = 1.2 s. Therefore, we can conclude that NWs thinner than ∼80 nm had indium droplets on top while NWs thicker than ∼100 nm most probably grew in the pure SAE mode. The presence of an indium droplet implies that a growth interrupt by removing TMIn should have a strong influence on the NW growth.17,22,23 If the interruption time is long enough, the droplet can be totally consumed, which means the NW axial growth rate should be strongly reduced in the self-seeded VLS growth mode while it remains the same in pure SAE after such an interrupt.23 This picture does not fully apply if the droplet is able to reform, as observed in Ga-assisted MBE growth of GaAs NW growth.22,32,33 However, in our relatively high group V-rich environment this is unlikely to happen. Consequently, we grew InP NWs for 2.5 min followed by a TMIn interrupt of 5 min and further continuing growth for another 2.5 min, with a V/III ratio of 81. Another two samples were grown for comparison without any interrupt for 2.5 and 5 min, respectively. These three samples were patterned and grown consecutively one after another. The obtained length-diameter correlations are shown in Figure 4a, along with the representative SEM images in Figure 4b−g. It is seen that the NW lengths in the interrupted recipe are similar to those grown for 5 min without interrupt for the diameter larger than ∼125 nm. On the other hand, for diameters smaller than 125 nm the lengths of the NWs grown with an interrupt lie between the lengths in 2.5 and 5 min samples, implying the interrupt significantly reduces the growth rate. This confirms again our argument for the presence and role of indium droplets on the top of thinner NWs and their absence on thicker NWs. We have found some indium droplets in our postgrowth SEM and TEM imaging. As shown in the Supporting Information (Figures S3 and S4), the indium droplets are formed on small diameter NWs but no droplets are found on larger diameter NWs. Beneath the indium droplets, a small ZB InP segment is formed on top of pure wurtzite (WZ) InP for the rest of the NW. We also note that in all cases a pure WZ

Figure 4. (a) NW length as a function of diameter for NWs grown for different times with and without the indium flow interrupt. (b,c), (d,e), and (f,g) are the 30° tilted SEM images of NWs grown for 2.5 min, 5 min with 5 min TMIn supply interrupt after the first 2.5 min, and 5 min without interrupt, respectively. The diameters of NWs shown in (b,d,f,) and (c,e,g) are around 45 and 170 nm, respectively, with the corresponding lengths indicated in (a). Lines in (a) are theoretical fits by the model.

NW growth is maintained except for the very top due to transient cooling down steps. Because of the sensitivity of the growth to small variations in the growth processes and to the reactor history or conditions over time of this study, the droplets have not been observed in subsequent runs, which could be linked to the strong dynamics of indium as claimed in ref 17. Overall, the observed growth behavior poses a puzzle. We have presented several results with strong evidence of a competition between the pure SAE and self-seeded VLS growth modes of InP NWs with the indium droplets appearing at lower V/III ratios and on smaller diameter NWs. This can be well understood through the diffusion of indium atoms which is faster for small diameters and for lower PH3 flows. However, because no indium droplets are initially present the group Vlimited self-seeded VLS growth can occur only when the total indium influx is larger than that of phosphorus and then the axial growth rate should decrease and become diameterindependent.32,34,43,50 This is not what we observe experimentally, for example, in Figure 1a. To understand this complex growth process and in particular the interplay between the pure SAE and self-seeded VLS modes, we have established a model that combines the major features of both growth mechanisms. The main idea of our approach is to define the boundary values of the growth parameters and NW dimensions at which pure SAE growth transforms to the self-seeded VLS to access variable droplet volume and its influence on the resulting axial growth rates of NWs under different conditions. We use standard theories for the diffusion-induced NW growth in group III limited regime, the group V limited VLS growth rate and then unify them by allowing the indium droplet to appear and swell on the NW top under the excessive indium influx. We start with the NW axial growth rate in the pure SAE mode in the form of v dL = v3(gdiff + 1), gdiff + 1 < F53 ≡ 5 dt v3 (1) with gdiff as the dimensionless diffusion flux of indium atoms to the NW top which increases with smaller R and may depend on the NW length L. Such expression is standard for pure SAE III−V NWs13 or self-induced GaN NWs41 under group V-rich conditions, that is, when the total indium influx including its surface diffusion is smaller than the phosphorus vapor influx ν5. D

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Figure 5. (a) Axial growth rate versus dimensionless length for 40, 85, 130, and 160 nm diameter NWs, obtained from eq 7. Dotted line corresponds to a V/III flux ratio of 81. Smaller diameter NWs grow in the self-seeded VLS mode with indium droplets on top. NWs with a diameter of 130 nm evolve in a combined VLS-SAE mode with indium droplet appearing and disappearing in the course of growth, while 160 nm diameter NWs grow in the pure SAE mode regardless of their lengths. (b) Droplet contact angle versus dimensionless length for the same parameters as in (a). Forty nanometers diameter NWs reach an equilibrium droplet angle of 125° at a certain stage and extend radially.

This can be reformulated in terms of the V/III ratio F53. On the other hand, in the self-seeded VLS growth, we have30,32,34,50 2χ5 v5 dL = , dt 1 + cos β

gdiff + 1 > F53

adsorption at the droplet surface is much faster than at the solid InP surface. Of course, the droplet contact angle and consequently the droplet volume cannot grow infinitely. Rather, it will increase to a certain equilibrium value β0 given by the surface energy balance32 and then the stationary configuration of the VLS system will be reached by increasing the NW radius to an equilibrium radius R* given by

(2)

meaning that the axial growth rate is simply proportional to the phosphorus vapor influx. The collection efficiency of phosphorus in the pure SAE case is enhanced by (i) larger surface area of the droplet with the contact angle β and (ii) by its better adsorption at the liquid surface, described by the factor χ5. Most importantly for what follows, the self-seeded VLS regime necessarily requires the condition gdiff + 1 > F53 at which the indium influx to the flat NW top is larger than that of phosphorus. Only in this case the indium droplet will appear and then swell due to an excessive indium flux according to dN3 2 ∝ v3gdiff + (χ v3 − χ5 v5) dt 1 + cos β 3

2 gdiff (R ) = (χ F53 − χ3 ), * 1 + cos β0 5

gdiff + 1 > F53

This corresponds to the regime of radial NW growth, as in refs 32 and 43, and explains why the diameter of the smallest NWs increases with time (see Supporting Information, Figure S1). To quantify our findings, we use an expression for the indium diffusion flux to the NW top in the form similar to that of ref 51 (see Supporting Information for the details)

(3)

2

gdiff

gdiff + 1 > F53

(R )

0 −1 ⎛L⎞ 2λ3 R tanh⎜ ⎟ + = L R ⎝ λ3 ⎠ cosh λ

() 3

(7)

Here, the first term stands for the sidewall diffusion flux and the second describes the contribution from the surface atoms that are collected from the feeding zone of radius R0 (a value of the order of the array pitch of 500 nm). At L/λ3 ≫ 1, this diffusion flux becomes 2λ3/R. In Figure 4a, we can see the distinct transition from the pure SAE to VLS regime at 2Rc = 125 nm and, assuming F35 ≅ V/III = 81, we obtain λ3 ≅ 2500 nm. Taking R0 = 500 nm, Figure 5a shows the normalized axial growth rate in units of ν3 versus the dimensionless length L/λ for differently sized NWs. It is seen that the values of gdiff + 1 are always greater than F53 for 40 and 85 nm diameter NWs and hence they grow in the self-seeded VLS mode with the corresponding droplet contact angles shown in Figure 5b. At 130 nm diameter, NWs start in the SAE mode. After that, the indium droplets appear on the top of NWs but then disappear again as the indium diffusion flux decreases. At 160 nm diameter, all NWs grow in the pure SAE mode regardless of their length. This picture shows a complex growth process switching between the pure SAE and self-seeded VLS modes depending on the growth parameters such as NW diameter, length, and V/III ratio.

(4)

Therefore, the contact angle increases for smaller diameter NWs and decreases for higher V/III flux ratios. Using eq 4 in eq 2, we obtain χ5 F53 dL = v3 g , dt χ5 F53 − χ3 diff

2 (χ F53 − χ3 ) 1 + cos β0 5

(6)

The N3 value on the left-hand side is the total number of indium atoms in the droplet that increases due to a positive III/ V influx imbalance, with χ3 on the right-hand side as the adsorption coefficient of the group III species at the droplet surface with respect to solid InP. This equation has the same meaning as in ref 32; however, in selective-area growth the droplet shape is nonstationary and the contact angle β can be adjusted to reach the stationary configuration corresponding to dN3/dt = 0 ⎡ 2(χ F − χ ) ⎤ 53 3 − 1⎥ , β = arccos⎢ 5 gdiff ⎢⎣ ⎦⎥

gdiff (R ) >

(5)

showing that the axial growth rate is radius-dependent even in group III-rich conditions. At gdiff + 1 = F53, there is a discontinuous change in the growth rate from ν3F53 for larger R to αν3(F53 − 1) ≅ αF53 for smaller R. The magnifying factor α = χ5F53/(χ5F53 − χ3) > 1 can be noticeably larger than one even for F53 ≫ 1 at large enough χ3, that is, when the phosphorus E

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depending on the indium supply to the top of the NW. Overall, our main conclusion is that selective-area growth of NW growth does not necessarily lead to the pure SAE regime. There is a competing process between a pure SAE and a pure VLS growth mechanism, depending on the growth conditions and mask opening. In many cases, there are indium droplets on the top of the NWs and this can be used for fine-tuning of the NW properties. This fundamental study therefore broadens the scope of possibilities in growth engineering, which is promising for application in optoelectronic devices, such as NW solar cells, photodetectors, and light-emitting diodes.

The growth equations given by eqs 1 and 5 can be integrated uniformly when gdiff + 1 ≅ gdiff, that is, when the diffusion flux constitutes the main source of the indium supply to the NW top. Only in such regime the NW growth rates can be much higher than the equivalent two-dimensional growth rate, as observed experimentally. An important aspect is the different incubation times needed for NWs nucleating from different size openings and different V/III ratios. Consequently, in the mononuclear regime34,52,53 we assign a term t0 to the waiting time for nucleation of the very first NW monolayer. This is given by t0 = 1/(πR2J) with J as the corresponding nucleation rate. The latter is expected to be smaller for pure SAE nucleation compared to the self-seeded VLS growth mode because of the lower surface energy of the nuclei in the VLS case. This explains why thinner NWs nucleate later for a given V/III ratio and the same diameter NWs nucleate later for higher V/III ratios. Therefore, we use the following expression for the NW lengths versus time and diameter ⎡ R2 ⎤ 2 2 L = λ3arsh⎢ 0 (e(2αv3/ R)(t − A / R ) − 1)⎥ ⎣ 2λ3R ⎦

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b01461. Patterning of substrates, growth time study, Cooling down under AsH3 protection instead of PH3, NWs grown on substrates patterned by focused ion beam, spacing study, and model for diffusion flux and NW length.(PDF)

(8)

with A = 1/(πJk) for k = VLS or SAE as the delay factors and α as the multiplying factor which is equal to one for the pure SAE growth mode. Equation 8 gives very reasonable fits to all the data, shown by lines in Figures 1a, 2a,b, and 4a. We use the value ν3 = 0.13 nm/s for the indium flux and other parameters used are summarized in Table 1. As expected, the indium diffusion 2

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substrate collection radius R0 (nm)

indium diffusion length λ3 (nm)

magnifying factor for VLS growth α

delay factors A (nm2 × s)

324 198 133 81 59

540 470 520 550 530

2400 2300 2550 2600 2500

1 1.077 1.10 1.30 1.153

1350 1250 895 640 530

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]ffe.ru. *E-mail: philippe.caroff@anu.edu.au. Notes

Table 1. Fitting Parameters for InP NWs Growing in Different Regimes V/III ratio

ASSOCIATED CONTENT

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Australian Research Council is acknowledged for financial support. Access to facilities used in this work was made possible through the Australian National Fabrication Facility, ACT Node, and Australian Microscopy and Microanalysis Research Facility (Centre for Advanced Microscopy). V.G.D. gratefully acknowledges financial support received from the Russian Science Foundation under the Grant 14-22-00018.

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length is close to 2500 nm in all cases and not significantly influenced by the V/III ratio, while the fitting values of R0 are close to 500 nm. The multiplying factor increases with lower V/III ratio, which shows a transition from the pure SAE to more and more pronounced VLS growth with lower V/III ratio. The decrease in the multiplying factor observed for V/III = 59 is due to the higher radial growth in thinner NWs. This is not taken into account in eq 8. In Figure 4a, a reasonable fit for the 2.5 + 2.5 min growth recipe is obtained by taking the average for the multiplying factor between the pure SAE and selfseeded VLS regimes. Finally, the delay factor increases toward higher V/III ratios because of the difficulty for NWs to nucleate without indium droplets in a group III-deprived environment. In summary, we have demonstrated the coexistence of pure SAE and self-seeded VLS growths of selective-area InP NWs as well as the transition between the two modes depending on the opening diameter and/or the V/III ratio. Highly nonmonotonic growth rates and long incubation times are revealed and explained within a theoretical model. We have shown that the NW length is controlled by the indium diffusion flux even under group III-rich conditions due to the changing shape of the droplet which collects more or less growth species

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DOI: 10.1021/acs.nanolett.6b01461 Nano Lett. XXXX, XXX, XXX−XXX