Structure and Morphology in Diffusion-Driven Growth of Nanowires

Wurtzite ZnTe Nanotrees and Nanowires on Fluorine-Doped Tin Oxide Glass Substrates. Man Suk Song , Seon Bin Choi , and Yong Kim. Nano Letters 2017 17 ...
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Structure and Morphology in Diffusion-Driven Growth of Nanowires: The Case of ZnTe P. Rueda-Fonseca,*,†,‡ E. Bellet-Amalric,‡ R. Vigliaturo,† M. den Hertog,† Y. Genuist,† R. André,† E. Robin,‡ A. Artioli,† P. Stepanov,† D. Ferrand,† K. Kheng,‡ S. Tatarenko,† and J. Cibert† †

Inst. NEEL, Univ. Grenoble Alpes, F-38042 Grenoble, France, and Inst. NEEL, CNRS, F-38042 Grenoble, France INAC, CEA, Univ. de Grenoble, 17 rue des Martyrs, 38054 Grenoble, France

‡

ABSTRACT: Gold-catalyzed ZnTe nanowires were grown at low temperature by molecular beam epitaxy on a ZnTe(111) B buffer layer, under different II/VI flux ratios, including with CdTe insertions. High-resolution electron microscopy and energy-dispersive X-ray spectroscopy (EDX) gave information about the crystal structure, polarity, and growth mechanisms. We observe, under stoichiometric conditions, the simultaneous presence of zinc-blende and wurtzite nanowires spread homogeneously on the same sample. Wurtzite nanowires are cylinder-shaped with a pyramidal-structured base. Zinc-blende nanowires are cone-shaped with a crater at their base. Both nanowires and substrate show a Te-ended polarity. Te-rich conditions favor zinc-blende nanowires, while Zn-rich suppress nanowire growth. Using a diffusion-driven growth model, we present a criterion for the existence of a crater or a pyramid at the base of the nanowires. The difference in nanowire morphology indicates lateral growth only for zinc-blende nanowires. The role of the direct impinging flux on the nanowire’s sidewall is discussed. KEYWORDS: Nanowires, molecular beam epitaxy, electron microscopy, ZnTe, EDX

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NWs with a crater at their base. These NWs have different length distributions and are homogeneously distributed over the same sample. The presence of lateral growth is checked in both cases by imaging a CdTe insertion using energy-dispersive X-ray spectroscopy (EDX). The crystal structure, wurtzite vs zinc-blende, and the polarity are assessed by transmission electron microscopy (TEM). Finally, values of the diffusion length on the substrate and along the NWs are discussed, in the frame of a diffusion-driven model, and their role in the presence of a crater or a pyramid at the base of the NW is identified. The whole growth process took place in an ensemble comprising two chambers connected under ultrahigh vacuum. Details are given elsewhere.5 In the III−V chamber, the (111)B GaAs substrate was deoxidized under As, and a fraction of a monolayer of gold was deposited at room temperature after depositing and smoothing a ZnTe buffer layer in the II−VI chamber. Smoothing of this pseudosubstrate (hereafter called simply substrate) at high temperature (380−420 °C) under Te flux ensured a low roughness: we observed surface reconstructions similar to those observed on (111)B CdTe.6,7 By contrast, any exposure to a Zn flux deteriorates the surface. This suggests that the diffusion on the (111) ZnTe surface is low under Zn excess and large under Te excess, as already

anowires (NWs) have been increasingly studied for the past years, both for fundamental research and for applications. Among the many attractive properties they offer, let us mention the different but prominent role of surfaces due to a high surface/volume and length/radius ratio, the possibility to grow heterostructures (axial or radial), including selective doping, the efficient relaxation of stress on sidewalls but also the easy tailoring of strain in core−shell NWs, various opportunities for quantum confinement, etc. Understanding and controlling the mechanism of NW growth is necessary to develop optimized NW-based structures. In this Letter we present results obtained on the growth of ZnTe NWs by molecular beam epitaxy (MBE). ZnTe NWs with the zinc-blende structure can be grown by various methods from vapor phase transport1 to MBE.2 Beside the specific interest of II−VI NWs for single photon emission3 and for spintronics when they contain diluted magnetic semiconductors,4 these NWs are an ideal system to explore NW growth under different stoichiometric growth conditions. This advantage arises from the congruent nature of the evaporation of tellurides: this allows one to obtain a stoichiometric molecular beam from a Knudsen cell loaded with the compound semiconductor and to precisely tune the cation− anion balance thanks to additional elemental cells. In this study we show that under stoichiometric growth conditions two types of NWs are observed: cylinder-shaped NWs with a pyramid at their base and tapered, cone-shaped © 2014 American Chemical Society

Received: December 16, 2013 Revised: February 18, 2014 Published: February 24, 2014 1877

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known for (111) CdTe.6 Gold dewetting was performed at 350 °C. Scanning electron microscopy (SEM) images reveal gold particles with a diameter in the 10−20 nm range, homogeneous over the sample (not shown), with an ultralow density of 5−10 droplets per μm2. Figure 1 displays SEM images of NW samples grown with different Te/Zn flux ratios. They were grown at 350 °C for 30

The most interesting observation is made on the sample grown under stoichiometric flux: two sorts of wires are seen, homogeneously distributed throughout the same sample (Figure 1c). The majority of the NWs are cone-shaped, like the ones grown under Te rich growth conditions; however, about 20% of the total have a cylinder shape (nontapered). Remarkably, for both types of NWs the gold-particle diameter is in the same range. The cone-shaped NWs in this sample (stoichiometric growth conditions, Figure 1c) are longer than the ones of the sample grown under high Te rich growth conditions (Table 1). However, the base diameter range is quite the same. The cylinder-shaped NWs present an almost constant diameter (with a variation of at most 10 nm from the base to the tip), mainly determined by the diameter of the gold droplets. They present a narrower length dispersion (Table 1). They sit at the top of a pyramid. Note that facets are likely to exists and are observed on the thicker NWs. The two kinds of NWs also coexist in a sample grown with a moderate Te excess (to Te/Zn flux ratio 1.7/1), shown in Figure 1b. When compared to the stoichiometric sample, the percentage of cylinder-shaped NWs is smaller and the base pyramid has a smaller diameter. We now show complementary observations aimed at unraveling the mechanisms involved in such different behaviors: we checked the possible presence of lateral growth using EDX to detect a CdTe marker, and we used highresolution transmission electron microscopy (TEM) to determine the crystal structure (zinc-blende or wurtzite) and finally high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) to reveal the polarity of the two types of NWs. A ZnTe NW sample was grown under the same conditions as the sample of Figure 1c, except for a 2 min interruption at t = 25 min, and the subsequent insertion of CdTe (for 30 s). ZnTe growth was then resumed for an additional 5 min. In photoluminescence such a CdTe insertion acts as a quantum dot.9 The two types of NWs, cylinder-shaped and cone-shaped, are also found to coexist on this sample. NWs were mechanically removed from the as-grown samples and deposited on a holey carbon-coated copper grid. EDX imaging of Te, Zn, Cd, and Au was performed at 30 kV in a Zeiss U55 SEM, using an XF5030 silicon drift detector (127 eV at the Mn Kα line) and the Quantax software from Bruker. The EDX maps for a cone-shaped NW (Figure 2) and a cylinder-shaped NW (Figure 3) are strikingly different. Cd is detected only at the position of the CdTe insertion for the cylinder-shaped NWs, whereas it is detected also along the lower part of the NW up to the CdTe insertion in cone-shaped NWs. A better resolution, of the order of 1 nm, can be obtained with a FEI Tecnai Osiris S/TEM equipped with four silicon drift detectors and operated at 200 kV. TEM samples were prepared either using the cleaving technique10,11 or by conventional mechanical polishing followed by Ar ion milling using a Gatan PIPS. This was used to study thicker cone-shaped

Figure 1. SEM image of ZnTe NWs grown at 350 °C under (a) high Te rich conditions (Te/Zn: 4.1/1), (b) low Te rich conditions (Te/ Zn: 1.7/1), (c) stoichiometric (Te/Zn: 1/1), and (d) Zn rich conditions (Te/Zn: 1/2.3). Samples are tilted at 65°.

min, one after another on the same day, and adding a Zn or Te flux to the stoichiometric flux from the ZnTe cell. Flux ratios (atoms cm−2 s−1) were calculated from beam equivalent pressures8 (BEP): (a) strongly Te rich (Te/Zn: 4/1), (b) Te rich (Te/Zn: 1.7/1), (c) stoichiometric (Te/Zn: 1/1), and (d) Zn rich (Te/Zn: 1/2.3). At such temperature a 2D layer is also formed, and it can be observed by SEM, with a thickness around 200 nm under stoichiometric conditions. Typical sizes of the NWs above the 2D layer are given in Table 1. Under a strong Zn excess (Figure 1d), the growth of NWs is totally inhibited. Even when the zinc excess is significantly reduced (1/1.2), the conditions for catalyzed NW growth are not fulfilled (not shown here). In contrast, under strongly Te rich conditions (Figure 1a), the growth of NWs is highly enhanced. The NW density, about 7 NW/μm2, corresponds to the gold-droplet density. Most of the NWs are vertical. They are cone-shaped (tapered): the diameter at the tip matches that of the gold particles, 17 ± 2 nm on this sample, while the base diameter is larger. The NW length distribution is broad. A general trend is that the base diameter increases with the NW length. However, we observed several NWs with a quite high difference in length, up to 500 nm, and the same base diameter. Another characteristic of these cone-shaped NWs is the presence of a crater around the NW base, with a diameter smaller than the average distance between the NWs.

Table 1. Size Statistics of the NWs Shown in Figure 1 (Average Values ± Standard Deviations)

height (nm) base diameter (nm) Au diameter (nm)

Figure 1a (Te/Zn: 4.1/1)

Figure 1b (Te/Zn: 1.7/1)

Figure 1c (Te/Zn: 1/1) cone

Figure 1c (Te/Zn: 1/1) cylinder

410 ± 170 46 ± 8 17 ± 2

600 ± 230 49 ± 6 18 ± 2

820 ± 300 47 ± 6 17 ± 3

460 ± 50 17 ± 2 16 ± 3

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Figure 4. Energy-dispersive-X-ray spectroscopy image showing the Cd, Te, and Au content of a cone-shaped ZnTe NW with a CdTe insertion.

CdTe below the insertion, in the form of an inner shell, and also of a ZnTe outer shell) demonstrate that lateral growth of CdTe and ZnTe takes place on the cone-shaped NWs, while it is not the case on the cylinder-shaped NWs. High-resolution TEM (HRTEM) images were realized on a Philips CM300 TEM equipped with a CCD camera and STEM images on a probe corrected FEI Titan, both operated at 300 kV. ZnTe NWs are prone to beam damage, especially the cylinder type due to their very small diameter, and can easily move under the beam due to charging effects. In spite of these difficulties, more than 10 NWs of each type were observed. Cone-shaped NWs have a cubic zinc-blende structure (Figure 5), and the majority of them are oriented along the

Figure 2. Energy-dispersive-X-ray spectroscopy map of a cone-shaped ZnTe NW with a CdTe insertion. The Te, Zn, Cd, and Au distributions are obtained from the intensity of the Lα or Kα lines as indicated.

Figure 3. Energy-dispersive-X-ray spectroscopy map of a cylindershaped ZnTe NW with a CdTe insertion. The Te, Zn, Cd, and Au distributions are obtained from the intensity of the Lα or Kα lines as indicated.

Figure 5. (a) Low-magnification and (b) high-resolution TEM image of a cone-shaped ZnTe NW grown for 30 min under stoichiometric growth conditions. The crystal structure is zinc-blende. A pair of twins along the (−1−11) plane (diagonal plane to the growth axis) is clearly visible. (c) Fourier transform of (b).

NWs from a sample grown under Te rich conditions (same growth temperature and growth time). The EDX image of a typical NW of this new sample is shown in Figure 4. It is mainly cone-shaped with a kink: most of the NWs of this sample (but not all) present such a kink located at 150−300 nm from the tip. The composition map clearly reveals the CdTe insertion and a Cd-rich inner shell below it. Note that the change in growth direction takes place just after the CdTe insertion. A possible relationship between the insertion of a different material and the formation of a kink is not fully understood.12 Some authors have also reported kinking in Si NWs grown by chemical vapor deposition, induced by changes of the growth conditions, such as a temperature gradient13 or a change in the total pressure.14,15 The EDX images (showing the presence of

⟨111⟩ axis. Some cone-shaped NWs are defect-free, but most of them feature twins, as frequently observed in ⟨111⟩ oriented NWs. Many of these twins are perpendicular to the ⟨111⟩ NW axis, but some are on {111} diagonal planes as shown in Figure 5b. Very few cone-shaped NWs have a short WZ section embedded in the ZB phase. In contrast, cylinder-shaped NWs have a homogeneous hexagonal wurtzite crystal structure (Figure 6). These NWs are mostly defect-free or with a very small number of stacking faults. HAADF STEM measurements were performed to determine the polarity of both types of ZnTe NWs. The more heavy element (Te) scatters more electrons on the annular HAADF detector and appears therefore brighter in the HAADF STEM 1879

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Figure 6. (a) SEM and (b) bright field (BF) STEM image of a cylinder-shaped ZnTe NW grown under stoichiometric flux conditions. The crystal structure is wurtzite, and we observed no stacking faults. (c) Fourier transform of (b).

image than the lighter (Zn) element, providing a chemical contrast that allows identification of Te and Zn columns, respectively, in the HAADF STEM image. The results are shown in Figure 7 for a cylinder-shaped NW (including its pyramid and the substrate) and in Figure 8 for a cone-shaped NW (and substrate). All presented STEM images are raw data, and no filtering or image processing was done. Figure 7 shows the results for a cylinder-shaped NW. The central image, Figure 7a, is a bright-field STEM image where the pyramidal base is clearly visible. Figure 7b is a zoom of the area marked in red, which contains the base of the NW and the top of the pyramid. Figure 7c,d is a closer zoom of the Zn−Te lattice where we can clearly distinguish both Zn and Te columns in the zone marked in green, both in gray and in color scale. These HAADF STEM images show that the polarity is Te-ended along the growth axis and that it does not change at the intersection between the pyramid and the NW. The polarity is the same for the (pseudo) substrate, the pyramid, and the cylinder-shaped NW (Figure 7e−g). An HAADF STEM intensity profile shown in Figure 7h confirms our results: substrate, pyramids, and cylinder-shaped NW are Te-polar (Te facing the growth direction, which is the [−1−1−1] axis of the substrate). The polarity of the cone-shaped NWs remains Te polar (Figure 8). Again, a zoom of the ZnTe lattice is presented in Figure 8b along with its corresponding HAADF intensity profile in Figure 8c. Clearly there is no polarity inversion for ZnTe NWs. Whatever the crystal structure, both NWs and substrate are Tepolar. These results agree with those previously observed16 on ZnTe NWs. They completely differ from cylinder-shaped ZnO NWs grown by metal−organic vapor phase epitaxy over Opolar ZnO substrates. Like the present ZnTe NWS, these ZnO NWs have the wurtzite structure and feature a pyramid at their base. In that case, however, the pyramids are O-polar whereas the NWs are Zn-polar.17 To summarize, we observe two types of ZnTe NWs, homogeneously distributed on the same sample grown under

Figure 7. STEM images of the a cylinder-shaped NW. (a) BF STEM of the (pseudo) substrate, the pyramid, and the lower part of a cylinder-shaped NW. (b) HAADF STEM zoom on the region marked with a red rectangle in (a). The inset identifies the atoms in the image. (c) Zoom on the marked region in (b) in gray scale and (d) in color scale with the indicated atomic structure. We have illustrated the Zn (in green) and Te (in blue) atomic columns. (e) HAADF STEM zoom on the region marked with the orange rectangle in (a). (f) Zoom on the marked region in e in gray scale with the indicated atomic structure and (g) in color scale. (h) Intensity profile along the marked box in (f). The inset identifies the atoms in the image. 1880

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Figure 8. HAADF STEM images of a cone-shaped NW. (a) HAADF STEM of a cone-shaped NW. Twins perpendicular to the ⟨111⟩ direction are visible. (b) Zoom on the marked region in (a). The inset identifies the atoms in the image. (c) Intensity profile along the marked box in (b).

dependence on growth temperature and flux ratio (including a possible change of phase, liquid or solid, of the droplet) would bring information on these aspects. This is out of the scope of the present study. In the diffusion model which is known to apply to a wide range of growth conditions of III−V and Si NWs22 and even CdTe NWs,23 the length and shape of the NWs are directly related to different values of the diffusion length on the substrate and along the NW sidewalls. Several assumptions can be made in the present case.5 (1) The density of gold droplets (and hence the density of NWs on the substrate) is low enough that we can consider a single NW. (2) The NW is perpendicular to the substrate surface. (3) The temperature is low enough that re-evaporation is negligible: that implies that the diffusion length is defined by the incorporation of adatoms on the substrate or on the NW facets. (4) We observe a NW growth rate enhanced by more than 1 order of magnitude with respect to that of the 2D layer; hence, we neglect the effect of the direct flux on the gold droplet. As we observe no saturation effect if we double the growth time,24 as we would expect in the presence of a significant Gibbs−Thomson effect,22 we assume that the gold droplet acts as a perfect sink, as reported for the growth of thick CdTe NWs.23 An evaluation of the chemical potentials for II−VI semiconductors (as it was done for III− Vs25) would be helpful to decide whether this remains valid in the case of NWs as thin as the present ones. In this model, the flux onto the substrate induces the presence of adatoms and results in the growth of a quasi-2D layer on the substrate, with a local height h(r) increasing as dh(r)/dt = Ω0ns(r)/τs, where ns(r) is the local adatom density, Ω0 is the volume occupied by an atom in the crystal, and 1/τs is the rate of incorporation of the adatoms. Far from the NW, the value of the uniform adatom density is n0s = τsJ, where J is the incident flux. In our MBE machine, the flux from the ZnTe cell makes an angle of α = 25° with respect to the substrate normal. Hence, for a NW perpendicular to the substrate, there is also a direct flux incident on the NW facets, J tan(α)/π (the factor π taking into account averaging due to the rotation of the substrate): for an infinitely long NW, this flux would give rise to a uniform lateral growth rate and a uniform adatom density on the facets equal to n0f = τf J tan(α)/π. The actual adatom density on the substrate close to the NW, and on the NW, are solutions of the diffusion equation (with a diffusion length λs = (Dτs)1/2 on the substrate and λf = (Dτf)1/2 on the facets; we assume identical values of the diffusion coefficients D), which obey

stoichiometric ZnTe flux: (1) cone-shaped NWs, with the zincblende structure, with the presence of a crater at the base, and the occurrence of lateral growth as confirmed using a CdTe insertion; (2) cylinder-shaped NWs, with the wurtzite structure, with a pyramid at the base, and no lateral growth detected. In both cases the polarity is identical to that of the (111)B buffer layer. Finally, increasing Te/Zn flux ratio progressively suppresses the formation of cylinder-shaped NWs. Different crystallographic structures have been reported for both III−V and II−VI semiconductor NWs, and relations between the NW crystal structure and other growth parameters have been proposed. A connection between the NW diameter and the crystal phase was shown for GaAs and InAs NWs.18,19 In these studies, the NW diameter is determined by the diameter of the gold droplet. In general, NWs with a large diameter have the zinc-blende structures, as in bulk, albeit with twins or even wurtzite inclusions, whereas those with a small diameter tend to have the wurtzite structure. The contribution from the lateral surface energy to the total free energy can determine the crystal phase: in narrow NWs, the low energy of the facets in the wurtzite structure can compensate for a higher bulk energy.20 Nucleation models have been proposed which take into account the influence of the sidewall surface reconstruction on the NW crystal phase20 or relate the crystallographic phase of the NWs to the interface energies involved in the formation of 2D nuclei at the vapor−liquid− solid triple phase line.21 In the present case, the size of the gold droplet, and hence the NW diameter in the initial stage of growth, spans a rather narrow range on each sample, identical for all samples described here. The diameter of the catalyst particle appears to be the same before and after the growth of the NWs. We never observed a bimodal distribution of these diameters, and both cone-shaped and cylinder-shaped NWs are found over the whole range of gold droplets diameters. Hence, the growth conditions of Figure 1clow growth temperature and stoichiometric fluxare those for which the two growth modes coexist for this range of droplet diameters. Nevertheless, surface energies may play a role in favoring the formation of only zinc-blende NWs under a strong Te excess. A similar trend was observed in arsenide NWs grown under As excess.20 The nucleation mechanism involves the supersaturation in the gold droplet: the supersaturation in Zn and Te is governed by the diffusion rate of each species on the substrate and on the sidewalls. A comprehensive study of the 1881

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Figure 9. NW growth scheme in the presence of an oblique flux (green arrows), for the three cases described in the text. (a) Early stage of growth, growth is due to adatoms diffusing (red arrow) from the substrate to the gold droplet. (b) Cylinder-shaped NWs; the diffusion length along the NWs is larger than their length; the flux on the top half of the NW contributes to the axial growth while the flux on the lower half outbalances the flux from the substrate to the NW, so that a pyramid forms. (c) Conic-shaped NWs, the diffusion length along the NW facets is smaller than the NW length; axial growth is due to the flux onto the facets of the top part of the NW; the flux from the substrate to the NW is smaller than the opposite flux, and the crater is maintained.

significant before the end of growth (case 3 above) and is consistent with the persistence of a crater at the base. The wurtzite NWs keep a cylinder shape and a pyramid is formed at the base: this is consistent with a diffusion length comparable to or larger than the final length (second case above). The presence of pyramids was reported at the base of InAs NWs27 under growth conditions such that the adatom flux was directed from the NWs to the substrate. Even if the link was not discussed, this observation suggests that the proposed criterion for the formation of pyramids was fulfilled also in that case. In Figure 1c and Table 1, the cylinder-shaped NWs are slightly shorter than the cone-shaped ones. One reason could be a different incorporation rate at the tip of the NW, which would appear for a different polarity. However, the same polarity (Te exposed at the surface) was observed on all NWs and on the pyramids, and it is the same as the polarity of the substrate. Hence, we can rule out that a different polarity is at the origin of a strongly different axial growth rate which would favor one type of structure. A complete study over a wide range of droplet diameters could decide whether the change of crystal structure can induce a significant change of the nucleation dynamics at the tip of the NWs and affect the final length of the NWs. That would also allow us to determine the values of the diffusion lengths λf and λs. In the absence of nucleation effects, within the frame of pure diffusion-limited growth, the difference in length suggests a different contribution due to diffusion of adatoms from the substrate, i.e., a smaller diffusion length λs on the substrate around the cylinder-shaped NWs than around the cone-shaped ones. On the (111)B ZnTe surface (as on the CdTe one,6,7 albeit with a shift in temperature), a large temperature range exists where two surface reconstructions, c(8 × 4) and (2√3 × 2√3)R30 °C, are observed simultaneously. These reconstructions were ascribed6 to the presence of Te on the surface, forming tetraedra inverted with respect to those of the zinc-blende structure, and this has been confirmed recently by scanning tunneling microscopy.7 The coexistence of different surface domains on the ZnTe (111)B surface could change the local diffusion length λs and also modify the formation of the gold droplets or details of the vapor−liquid− solid triple phase line involved in the nucleation at the beginning of the NW growth. Note that the behaviors of Te and Zn are probably different. Besides, the local surface symmetry may play a role in the formation of nuclei with different crystal structures. Finally, growth is completely inhibited under a small Zn excess (Te/Zn: 1/1.2), and only zinc-blende NWs subsist, but with a reduced growth rate, at a strong Te excess (Te/Zn: 4/1).

boundary conditions at the tip (vanishing adatom density since the gold droplet is a perfect sink) and at the base of the NW (conservation of the adatom currents). This model was applied to the present data.5 Qualitatively, it can be schematized as follows (Figure 9): • Case 1 (Figure 9a): for short NWs, the contribution from the flux on the facet is negligible, and the growth is due to adatoms diffusing from the substrate to the gold droplet through the NW sidewalls. The adatom density on the facets is vanishingly small (hence, no lateral growth), and there is a depletion of substrate adatoms around the NW: this depletion corresponds to the flux to the NW, and it induces the formation of a crater. • Case 2 (Figure 9b): for long enough NWs, the lateral flux becomes significant. If the diffusion length along the NW facets λf stays long with respect to the NW length L, the adatom density on the facets vanishes at the top and matches the substrate adatom density Jτs at the base, and the corresponding adatom current is proportional to the average gradient over the NW length: js ≃ Jλs2/L. The lateral flux gives rise to a current jf ≃ [J tan(α)/π](L/2) from the NW facets to the gold droplet, and an opposite current − jf from the NW facets to the substrate. Thus, the substrate and facet fluxes add to contribute to the NW growth, and they compete to form either a crater or a pyramid at the base of the NW. The two contributions are balanced when L = λs[2π/tan(α)]1/2. Integrating over the entire NW growth predicts5 that the crater is filled, and the pyramid is visible, if L > 0.23λs[2π/tan(α)]1/2. • Case 3 (Figure 9c): if the NW length L ≫ λf, then the current from the substrate to the NW is js ≃ Jλs2/λf, which contributes to form a crater but does not reach the tip: it is lost in lateral growth.26 The lateral flux gives rise to two currents, jf ≃ [J tan(α)/π]λf from the NW to the tip (ensuring the NW growth) and −jf (filling the crater). The formation of a pyramid is delayed since L is replaced by λf. This diffusion model thus proposes a link between the shape of the NWs, and the formation of a pyramid or a crater, due to the different values of the diffusion lengths. A quantitative analysis is beyond the scope of this paper, but we can extract some information for the NWs of Figure 1c, grown under stoichiometric flux. The cone shape of the NWs with the zincblende structure indicates that the diffusion length λf on the facets is significantly smaller than the final NW length. That implies that the contribution from the lateral flux becomes 1882

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Nano Letters

Letter

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Within the diffusion model, these observations imply that the effective diffusion length λs is too small under Zn excess and reduced under Te excess if compared to the stoichiometric case. This effective diffusion length is a heuristic average between that of Zn and that of Te: indeed, we can expect a decrease of this average diffusion length if the Zn/Te flux ratio is strongly unbalanced (diffusion of Te adatoms blocked under strong Zn excess, and vice versa). An optimum around the stoichiometric conditions would then correspond to a sufficient diffusion of both species. To sum up, ZnTe NWs have been grown by molecular beam epitaxy at low temperature on a (111)B ZnTe layer. The coexistence of NWs with the zinc-blende structure and NWs with the wurtzite structure, homogeneously distributed on the whole wafer, is observed under stoichiometric conditions. All structures have the same Te-terminated polarity as the substrate. NWs with the wurtzite structure assume a cylinder shape, resulting from a diffusion length along the NW larger than the NW length; this favors the formation of a pyramid around the base of each NW in the presence of a flux on the NW sidewalls. NWs with the zinc-blende structure assume a cone shape due to a lower diffusion length on the sidewalls, which reduces the axial growth rate; it also allows a crater to subsist at the NW base. A criterion has been proposed for the existence of a crater or a pyramid at the base of the NWs at the end of their growth, two features which are often observed around the base of NWs made of other semiconductors, but rarely discussed. Within the model of diffusion-limited growth, the diffusion on the substrate surface, needed for the growth of the NWs, appears to be different for the two types of NWs. An additional Te flux suppresses the growth of wurtzite NWs, leaving only zinc-blende NWs, whereas an excess of Zn totally inhibits the growth.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (P.R-F.). Present Address

R.V.: Earth Sciences Department, University of Torino, Via Valperga Caluso 35, I-10125 Torino, Italy. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Most of this work has been done within the CEA-CNRS joint team “Nanophysique & Semiconducteurs”. We thank Catherine Bougerol for many illuminating discussions. This work was supported by the French National Research Agency (ANR project Magwires ANR-11-BS10-013).

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dx.doi.org/10.1021/nl4046476 | Nano Lett. 2014, 14, 1877−1883