Catalyst-free growth of InAs nanowires on Si (111) by CBE

Semiconductor nanowires (NWs) have been extensively studied due to their potential applications in various fields and have become a major component of the technology roadmap for semiconductors [1]. In this respect NWs represent a powerful platform within the 'more than Moore' scenario. The major bottleneck to NW exploitation in practical systems probably remains the integration of the bottom-up techniques for III–V growth with the state-of-the art complementary metal oxide semiconductor (CMOS) technology. Such integration would combine the advantages of the standardized low-cost CMOS process and the superior optical and electronic properties of III–V semiconductors. In view of this, the growth of III–V compounds on Si substrates has long been a key research area for both academia and industry. Challenges such as differences in polarity, lattice and thermal expansion coefficient mismatch, formation of anti-phase domains, and cross-doping have been major barriers for the integration of III–V and Si materials. After decades of research activities, two-dimensional growth of III–Vs on large-scale silicon substrates was achieved with commercial results [2]. However, as dimensionality of the growth technology is reduced to one, many further challenges must be met to integrate III–V NW on Si substrates [3]. On the other hand, nanoscale heteroepitaxy of NWs is very appealing since the NW geometry offers numerous advantages such as prevention of anti-phase domains and dislocation-free strain relaxation.

The vapor–liquid–solid (VLS) growth mechanism assisted by a foreign catalyst metal is well-understood, but the problems related to catalyst contamination in CMOS technology remain severe [4]. In recent years, several groups demonstrated the growth of catalyst-free InAs NWs on Si substrate using molecular beam epitaxy (MBE) [5, 6] and metal-organic vapor phase epitaxy (MOVPE) [7–12]. In parallel to the catalyst-free mechanism, self-catalyzed growth has also been frequently reported in MBE and MOVPE [13–16]. However, a clear understanding of the growth mechanism of InAs NWs on Si substrate is still lacking [15, 17, 18]. Chemical beam epitaxy (CBE) combines the advantages of both MBE and MOVPE techniques along with its own unique and versatile features. The CBE growth kinetics of NWs is expected to be very different from that of MBE and MOVPE and a coherent description of the correlation between growth parameters and morphological characteristics of catalyst-free InAs NWs grown on Si substrates by CBE is not yet available.

In the present work, we investigate the growth mechanism of InAs NWs and demonstrate that InAs NWs can be formed on Si (111) substrates by a catalyst-free procedure (as opposed to self-catalyzed growth, where a In metal droplet on the NW tip drives the axial growth). We present a two-stage growth protocol (low-temperature (LT) nucleation and high-temperature (HT) growth steps) that yields InAs NWs and explore the impact of various growth parameters on their morphology. We show that InAs NWs nucleate from nanoscale islands without forming any In droplets. Then, we investigate how the metal-organic (MO) flow ratio and growth temperature influence the nucleation and growth of NWs to find the optimum parameters for obtaining non-tapered InAs NWs with a high aspect ratio. We develop a theoretical model that yields an expression for the dependence of the NW morphology on the MO flows, growth time and NW diameter. The results obtained from the model describe quantitatively quite well the experimental data obtained for different V/III ratio and growth time series. Thanks to this model, we shall show that it is possible to modulate independently the NW diameter and length, and achieve a good control over the NW morphology. Finally, we present a full mapping of the NW aspect ratio versus the group V and III flows.

InAs NWs were grown in a RIBER C21 CBE reactor on Si (111) substrates. The substrates were covered by a 20 nm silicon oxide layer deposited in-house with a magnetron sputtering unit. The oxide was completely etched with a buffered oxide etch. The hydrogen-terminated substrates were mounted into the ultra-high vacuum load-lock immediately after indium bonding on the molybdenum platen. Parameters for Si(111) substrate preparation such as exposure time to air, HF treatment, surface roughness and sputtering parameters were optimized for high reproducibility of the NW growth. Tertiarybutylarsine (TBAs) and trimethylindium (TMIn) were used as As and In sources, respectively. TBAs was pre-cracked in the injector at 1000 °C since the substrate temperature is not sufficient for its decomposition while TMIn decomposes directly at the surface [19]. The TMIn and TBAs fluxes were changed by controlling the line pressure (P_TMIn and P_TBAs) of the MO sources.

The morphologies of the NWs were investigated using a scanning electron microscope (SEM) (Zeiss Merlin) with images acquired at 45° tilt for length and diameter measurements. The tilt axis was always parallel to both the {111} surface and one {110} Si cleavage plane, in order to increase the reproducibility of the diameter measurements. All diameters indicated here thus correspond to $D=l.\sqrt{3}$ in case of a regular hexagonal cross section, with a hexagon side of length $l.$ For each sample at least 30 (and up to hundreds) NWs were measured, in several, mm-apart, areas of the sample. The average values for length and diameter are the arithmetic averages while the indicated uncertainties correspond to the standard deviation from the average. When several samples were repeated in identical conditions the average of the various samples where within the individual standard deviations. Structural characterization of the NWs was performed using a Zeiss Libra 120 transmission electron microscope (TEM). Samples for TEM observation were prepared by mechanical transfer of the NWs onto copper TEM grids coated with formvar-carbon film.

The growth process employed for growing InAs NWs on Si (111) substrates involves a high temperature annealing under TBAs flux followed by a two-temperature sequence. The latter consists of a LT nucleation and a HT growth steps followed by a rapid cool down under TBAs flux to terminate the growth. The parameters for each step are fully provided in the following. Hydrogen-terminated Si (111) substrates were annealed at 720 ± 10 °C under a TBAs line pressure of 1.00 Torr for 15 min. After annealing, the temperature was ramped down to 385 ± 10 °C. All standard samples were then grown with a 10 min LT nucleation step (P_TMIn = 0.30 Torr, P_TBAs = 3.00 Torr, 385 ± 10 °C), 10 min ramp (P_TMIn = 0.30 Torr, P_TBAs = 3.00 Torr) to the HT growth step (P_TMIn = 0.20 Torr, P_TBAs = 3.00 Torr, 520 ± 10 °C) continuing for 60 min.

We now consider the role of each step in the NW formation. First, the annealing procedure is essential for removing the weakly-bound organic contaminants and transforming the Si surface reconstruction from Si 1 × 1-H to Si 1 × 1-As [20]. The As-passivated substrate is an ideal surface for growing polar semiconductor on non-polar substrate and was successfully implemented for 2D and 1D epitaxial growth of III–Vs on Si (111) [20, 21].

Figure 1 shows the growth sequence along with the corresponding SEM images on different stages of growth, marked by the colored dots in the temperature graph of figure 1(a). The top colored bars indicate when TBAs and TMIn fluxes are switched on and off. Figure 1(b) shows that at the end of the LT step the Si surface appears decorated by InAs islands with a typical size of about 20 nm. No particular anisotropy of the islands is observed at this stage of the growth. At the end of the ramp between the LT nucleation and the HT growth steps (figure 1(c)) some islands start elongating in the direction orthogonal to the Si surface. At the end of the HT step (figure 1(d)) two different types of structures are present: highly anisotropic NWs with hexagonal cross section growing normal to the Si surface and large isotropic islands having the aspect ratio of the order of one. The two types of structures are already distinguishable before the HT growth step (figure 1(c)). Isotropic islands seem to be present independently to our choice of LT and HT temperatures and fluxes, suggesting that the NW and island formation is linked to the substrate preparation protocol.

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We shall show that the LT nucleation step helps to prevent thermal desorption of In from Si (111) substrates (due to a low surface tension of In), while the HT step is required to start anisotropic growth where the axial elongation of NWs dominates over their radial extension, similarly to the case of self-induced GaN NWs on Si substrates [22–25]. Figure 2 shows the results of 20 min constant temperature growth runs with P_TMIn = 0.30 Torr and P_TBAs = 3.00 Torr (corresponding to the fluxes during the LT stage of the two-temperature growth), at three different temperatures. The annealing step was kept as described above for the two-temperature growth. At the lowest temperature (385 ± 10 °C, corresponding to the LT stage of the two-temperature growth), we observe the formation of a high density ensemble of InAs crystals with the aspect ratio of the order of one (figure 2(a)). At the intermediate temperature (450 ± 10 °C, figure 2(b)), the island density was strongly reduced. Further increase of the growth temperature to 480 ± 10 °C (figure 2(c)) resulted in a clean Si surface with no nucleation of InAs islands. It must be noted that this last temperature is still lower than that used for the HT step in the two-temperature growth.

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The growth of InAs NWs on Si substrates is often described by self-catalyzed VLS mechanism [13, 14], where a liquid-In particle at the NW tip enhances the growth rate of the top (111) facet and leads to the formation of highly anisotropic structures. Several other reports suggest that InAs NW growth is a catalyst-free process [6–12, 26] while other report that NW nucleation is catalyst assisted but the growth proceeds without the catalyst droplet because of its consumption in arsenic rich conditions [27, 28]. In the present case much evidence indicates that our NWs grow without any metal droplet on top.

First, post-growth SEM images after the cool-down stage under TBAs flux for 60 s revealed no sign of In droplets. In principle such droplets may be quickly consumed due to the TBAs flux exposure. Hence, we grew some InAs NWs in standard conditions and cooled them down without any As supply. Also in this case the morphological characterization did not show any In droplets on the NW tips. It was previously argued that the residual As species in the chamber could consume In particles even if the TBAs flux is turned off [29]. We therefore carried out additional experiments to further investigate this point.

Growth interruption tests were performed in analogy to previous works [18, 29]. After 30 min of NW growth, the TMIn flux was stopped for 15 min and then resumed for the next 30 min The TBAs flux was kept constant all the way. In self-catalyzed NWs, the interruption of the TMIn supply in presence of TBAs leads to the consumption of the In metal particle at the NW tip, so that the axial growth is inhibited and the NW diameter rapidly increases [30]. In our case, comparison with a standard sample grown for 60 min without interruption does not show any noticeable difference in length or diameter with respect to the NWs grown with an interruption (see figure 3). For NWs grown under standard conditions (one of them is shown in figure 3(a)), the measured length and diameter are (951 ± 143) nm and (52 ± 3) nm, respectively; while NWs obtained with the growth interruption (one is shown in figure 3(b)) showed length and diameter of (900 ± 95) nm and (50 ± 6) nm, respectively. These measurements are averages and standard deviations of NW ensembles (∼50 NWs per sample). This observation supports the catalyst-free character of the growth in our case but is not a sufficient evidence to rule out self-catalyzed growth by itself. It has been already demonstrated that Ga droplet could reform after growth interruption in self-catalyzed growth of GaAs NWs [31].

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Last and most convincing, our NW growth is started and continued under highly As-rich conditions. At the beginning of growth, the TMIn source is opened after a 15 min anneal under the TBAs flux corresponding to P_TBAs = 1.00 Torr. Such an As overpressure is expected to strongly reduce the probability of In droplet formation. In order to demonstrate this, we closely examined the evolution of intentionally pre-deposited In droplets at variable V/III flow ratios. The droplets were formed on top of InAs islands immediately after the standard LT nucleation step using the protocol illustrated in figure 4(a). The TMIn line pressure used for In deposition was 0.30 Torr. Such In deposition yields InAs islands formed in the LT step with an In metal particle on their tips, as clearly visible in the inset of figure 4(a). After In-droplet formation, TBAs and TMIn were again fed into the reactor with different V/III line pressure ratios. After the additional InAs growth, the droplets were still present on the tip of the NWs for V/III ratios smaller than ∼1 (region I in figure 4(b), pink dots). The pink inset of figure 4(b) shows a SEM image of one of the samples at the end of the second InAs growth. The droplets are not present when the V/III ratio is above ∼1 (green triangles in figure 4(b), and SEM image in the green inset). In both the LT and HT stages of samples discussed in the present work, the InAs NWs were grown at very high V/III ratios ≫1 (violet pentagons), far away from the conditions where In droplets can develop or survive. These results are in agreement with the conclusions drawn in a previous work [29] where in situ and ex situ investigation of InAs NWs on Si revealed no droplet formation at V/III ratio >1.

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As for the nucleation mechanism of InAs islands, we believe that it is driven by the lattice mismatch between InAs and Si and that it proceeds via the Volmer–Weber growth mode. Three-dimensional islands are formed because they have a lower elastic energy compared to a 2D layer and may undergo several shape transitions to minimize their free energy before NWs form, as in the case of GaN islands on lattice-mismatched AlN interlayer on Si(111) [22]. Plastic relaxation via the formation of misfit dislocation at the island–substrate interface [22] is not excluded, and after that the transformation to anisotropic growth may be associated with a lower surface energy of hexahedral elongated NWs [23]. However, as mentioned above, the axial growth of InAs NWs necessarily requires the HT growth step and hence kinetic factors strongly influence the surface morphology of InAs nanostructures. Also, our InAs NWs start from the isotropic islands which always remain at the NW base (see figure 5), while the self-induced GaN NWs almost completely suppress the island population at a later growth stage [22–25].

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Using our two-temperature growth protocol, most InAs NWs grow approximately perpendicular to the Si (111) surface, with hexagonal cross-sections. Small deviations from the $\langle 111\rangle$ alignment can be seen in figures 5(a), (b) and are limited to a few degrees at most. We believe they can be associated to strain-induced effects [32]. In order to confirm the NW-substrate epitaxial relationship, InAs NWs were also grown on Si (001) substrates with the same protocol as with Si (111). Figure 5(c) gives the direct indication of the epitaxial relationship: InAs NWs grow in the four equivalent 〈111〉 directions that have an out-of-(100)-plane component. The predominant orientation of the NW side facets were obtained by aligning the samples with the known substrate direction and appear parallel to {112} Si planes.

TEM analysis of InAs NWs confirms non-tapered shape and reveals a defective crystal structure. Bright-field images in ${[2\bar{1}\bar{1}0]}_{{\rm{WZ}}}$ (or ${[110]}_{{\rm{ZB}}})$ zone axis shown in figure 6(b) display a sequence of bright and dark stripes characteristic of a disordered stacking. The wurtzite (WZ) and zincblende (ZB) index in the zone axis notation indicates a hexagonal WZ or a cubic ZB bravais lattice. The corresponding diffraction pattern (figure 6(a)) exhibits a strong streaking parallel to ${\left(0001\right)}_{{\rm{WZ}}}$ (or ${(110)}_{{\rm{ZB}}})$ reciprocal direction, which does not allow the determination of any dominant polytype between the WZ and ZB structures. Thus, our NWs can be considered as a disordered stacking sequence of hexagonal InAs closed-packed layers where the ordered ZB and WZ domains do not exceed few nanometers in length.

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Some considerations on the highly anisotropic growth leading to the catalyst-free InAs NW formation during the HT step are due at this point. First, we note that under the As-rich conditions employed in our experiments, the InAs (111) surface of the NW top facet is likely to exhibit 2 × 2 reconstruction with As trimers on top of the As layer [33–35]. The nucleation barrier to form a critical 2D nucleus on the NW top (${\rm{\Delta }}{G}_{*})$ is proportional to $h,$ the height of the nucleus: ${\rm{\Delta }}{G}_{*}\propto h$ [36, 37]. When modeling the VLS growth of NWs the nucleus height is usually considered as the height of a bilayer [36, 37]. On the contrary, in our case, the arsenic part of the bilayer should form almost instantly and thus the nucleation requires the completion of only the In layer with an $h$ value that is approximately half that of the complete bilayer. This reduces the nucleation barrier to approximately one half of its value on the side facets. Due to a steep exponential dependence of the nucleation rate (and the resulting growth rate V) on the nucleation barrier [37], $V\propto {\rm exp}\left(-{\rm{\Delta }}{G}_{*}/{k}_{B}T\right),$ the axial growth rate will be an order of magnitude higher than the radial one.

This simple argument applies to the nucleation-mediated growth rate. On the other hand, a much faster growth on the NW top with respect to the side facets requires efficient diffusion transport of In adatoms to the top. Indium will migrate to the top only if there the chemical potential is lower than at the NW sidewalls [38]. This property is ensured by the fact that the top facet is a more efficient sink of In adatoms relative to the side facets and therefore the In concentration on the NW top is the lowest. As in the case of catalyst free GaN NWs [25] or selective area III–V NWs [39], the nucleation probability at the top facet is higher than on the sidewalls and therefore it acts as a sink for In adatoms migrating to the NW top. The concentration gradient gives rise to a diffusion flux to the top. In this sense, the top facet acts as a material collector for In adatoms. Under As-rich conditions, catalyst-free growth of InAs NWs is expected to be limited by surface diffusion of In, similarly to the case of self-induced GaN nanowires under high nitrogen flux [25].

7.1. Influence of the growth temperature

Figure 7(a) shows the growth-temperature dependence of InAs NW length and diameter, with the typical SEM images presented in panels (b)–(d). All these NWs were grown with the same LT nucleation step (P_TBAs = 3.00 Torr, P_TMIn = 0.30 Torr, and at 385 ± 10 °C) while in the HT stage the growth temperatures were varied from 480 ± 10 °C to 540 ± 10 °C under P_TBAs of 3.00 Torr and P_TMIn of 0.20 Torr, with 60 min growth time.

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The NW length first increases with increasing growth temperature, due to an enhanced thermally-activated diffusion of In adatoms at higher temperatures [40]. When the diffusion length increases, the sidewall incorporation of In adatoms becomes less pronounced and consequently the NW diameter decreases [40]. At 520 ± 10 °C, the NW length reaches its maximum of (955 ± 116) nm while the diameter reaches the minimum at (49 ± 4) nm, yielding the highest aspect ratio observed (about 20). Decrease of the NW length at temperatures higher than 520 ± 10 °C and a corresponding increase of the diameter are likely caused by the enhanced thermal decomposition of InAs along the $\langle 111\rangle$ direction, as shown by In desorption experiments [41]. When the adatom sink at the NW top decreases its efficiency due to this thermal decomposition, the diffusion flux to the top decreases and thus the NW diameter increases [25].

7.2. Length–diameter dependence

We mentioned earlier that anisotropic catalyst-free growth of InAs NWs necessarily requires a positive diffusion flux of In adatoms from the NW sidewalls to the top. Diffusion-induced growth of NWs with a time-independent diameter is characterized by a decreasing length–diameter [$L(D)]$ correlation at a given time [42, 43]. For a hexahedral NW with a flat top facet, the simplest equation for the axial growth rate ${\rm{d}}L/{\rm{d}}t$ can be expressed as [43]

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{d}}L}{{\rm{d}}t}=W\left[1+\displaystyle \frac{3\sqrt{3}}{8}\displaystyle \frac{\lambda {\rm tan}\alpha }{D}\right].\end{eqnarray} \tag{ 1 }$$

Here, the first term describes the direct impingement of TMIn beam, with $W$ the effective deposition rate of In accounting for the incorporation efficiency of TMIn that can depend on both P_TBAs and P_TMIn. The second term accounts for the diffusion flux of In adatoms from the NW sidewalls to the top, with $\lambda$ the effective diffusion length of In and $\alpha \;=$ 38° the incident angle of TMIn beam. $\lambda$ accounts for the pyrolysis efficiency of TMIn at the sidewalls.

Now, we introduce the two specific features of our self-induced mechanism of NW formation into the standard scenario of the diffusion-induced growth. First, our InAs NWs not only grow axially but also extend radially. The measured time dependence of the NW diameters is well fit by the linear law $D={D}_{0}+vt,$ with ${D}_{0}$ initial diameter and $v$ the radial growth rate which depends on the V/III flow ratio $F={P}_{{\rm{TBAs}}}/{P}_{{\rm{TMIn}}}.$ The linear fit of the data obtained for a time series of samples with $F=15$ is shown in figure 8 and yields $v\;=$ 0.3 nm min⁻¹. The zero growth time data point corresponds to the NWs formed after the LT step and ramp. Each point is the average of many NWs measured on one sample. Second, self-induced NWs grow from NW seeds that also have some height-diameter dependence at $t=0.$ NWs formed after the LT step and ramp data are plotted in figure 9 as blue inverted triangles and are fitted by a linear dependence: $H({D}_{0})={H}_{0}-{H}_{1}\cdot {D}_{0},$ with ${H}_{0}\;=$ 363 nm and ${H}_{1}\;=$ 8.23. Considering an individual NW with a length L and a diameter D measured after a HT growth time t, and combining the two linear relations above, it is possible to derive the length $H\left({D}_{0}\right)$ that one such NW has at the end of the LT stage: $H({D}_{0})=H(D-vt)={H}_{0}-{H}_{1}(D-vt).$ This, in turn, allows us to integrate equation (1) for each individual NW, obtaining the NW length (including the initial island height) in the form

$$\begin{eqnarray}&&L=Wt+\displaystyle \frac{W}{v}\displaystyle \frac{3\sqrt{3}}{8}\lambda {\rm tan}\alpha {\rm ln}\left(\displaystyle \frac{D}{{D}_{0}}\right)+H({D}_{0}).\end{eqnarray} \tag{ 2 }$$

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Figure 9 shows the measured length–diameter correlations after different growth times. The experimental points correspond to measurements of individual NWs on SEM images of the as-grown samples. The uncertainty associated to nanowire diameter measurement is ±2 pixel (with a pixel size of 2.7 nm). The uncertainty in the lengths are due to the pixel size, to the non-perfect alignment of the NWs to the $\langle 111\rangle$ substrate direction, and to the possible error in the determination of the length due to the projection of the diameter on the tilted image plane. The curves are a simultaneous fit of all datasets obtained from equation (2) with $\lambda \cong$400 nm and $W\cong$ 1.6 nm min⁻¹; the only parameter changed from one curve to another is t (affecting in turn ${D}_{0}$ and $H({D}_{0})$ for each growth time). In spite of the relative simplicity of the model and the limited number of parameters used, the overall agreement of the fit with the experimental data is very good.

7.3. Influence of MO line pressures

In order to understand the influence of MO flow rates on the effective deposition rate W, we investigated the total volume of NWs ${\rm{\Omega }}$ (excluding the volume of the initial islands) versus P_TBAs and P_TMIn. It turns out that this dependence is well fitted by power-law dependence ${\rm{\Omega }}\propto {P}_{{\rm{TMIn}}}^{1.75}/{P}_{{\rm{TBAs}}}^{0.75}={P}_{{\rm{TMIn}}}{F}^{-\mathrm{3/4}}$ for a variety of samples, as shown in figure 10. In the As-rich conditions used for the growth, the NW volume should be proportional to the available In: ${\rm{\Omega }}\propto \chi {P}_{{\rm{TMIn}}}.$ Thus $\chi ,$ the pyrolysis efficiency of TMIn, scales with the V/III flow ratio approximately as $\chi \propto {F}^{-\mathrm{3/4}}.$ Although a detailed understanding of this dependence is missing, a decrease of the effective deposition rate with increasing V/III flow ratio was previously reported for Au-catalyzed InP NWs [40], and GaAs NWs [44]. This effect could be explained by a reduced adsorption of In which is suppressed by an increasing density of As trimers [33].

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In the absence of an In-rich droplet (which would serve as a reservoir of indium), the axial growth rate on the NW top facet is expected to be proportional to $\chi {({P}_{{\rm{TMIn}}}{P}_{{\rm{TBAs}}})}^{\mathrm{1/2}}$ so that at a fixed $\chi ,$ an increase of both fluxes by a factor 2 leads to a twice as fast growth rate. These simple considerations yield to $W=A{({P}_{{\rm{TMIn}}}/{P}_{{\rm{TBAs}}})}^{\mathrm{3/4}}{({P}_{{\rm{TMIn}}}{P}_{{\rm{TBAs}}})}^{\mathrm{1/2}},$ where $A$ is a uniform normalization factor. Combining this with equation (2), we obtain the following model equation for the average NW length $\langle L\rangle$ as a function of the growth time, MO line pressures and the average NW diameter $\langle D\rangle$:

$$\begin{eqnarray}&&\langle L\rangle =A{\left(\displaystyle \frac{{P}_{{\rm{TMIn}}}}{{P}_{{\rm{TBAs}}}}\right)}^{\displaystyle \frac{3}{4}}{\left({P}_{{\rm{TMIn}}}{P}_{{\rm{TBAs}}}\right)}^{\displaystyle \frac{1}{2}}\left[t+\displaystyle \frac{3\sqrt{3}}{8}\displaystyle \frac{\lambda {\rm tan}\alpha }{v}{\rm ln}\right.\\ &&\quad \;\;\;\;\;\;\;\;\;\;\times \left.\left(\displaystyle \frac{\langle D\rangle }{\langle {D}_{0}\rangle }\right)\right]+\langle H({D}_{0})\rangle .\end{eqnarray} \tag{ 3 }$$

Here, $\langle {D}_{0}\rangle$ and $\langle H({D}_{0})\rangle$ are the average diameter and height of the initial InAs islands, respectively. Since $v,$ $\langle {D}_{0}\rangle ,$ and $\langle H({D}_{0})\rangle$ can be directly derived for each sample as shown before, equation (3) contains only two adjustable parameters: the effective diffusion length of In adatoms, $\lambda$ and the normalization constant $A.$ Figure 11 shows very good consistency between the measured data and calculated $\langle L\rangle$ for the NWs grown in different conditions in the HT stage. The computed $\langle L\rangle$ values in figure 11 were all obtained with the same values of the fitting parameters $\lambda =400{\rm nm}$ and $A=$18 nm × Torr⁻¹ × min⁻¹.

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Although λ in principle has a non-trivial dependence on precursor fluxes and ratio, we have decided to use the constant value determined from the fit with equation (2) of the growth time series of figure 9. This leaves only one fitting parameter, A. The overall linearity of the heterogeneous data shown in figure 11, considered the single free parameter for the fit, confirms the soundness of our assumptions and the validity of the model.

With this understanding, we have systematized the InAs NW aspect ratios as a function of the MO line pressures. The overall results are summarized in the map of figure 12(a) for samples grown 60 min at 520 ± 10 °C in the HT step. The diameter of the NWs formed after the LT step and ramp for all the growths shown on the map is 28 ± 4 nm. Based on this map, we are able to carefully modulate the InAs NW aspect ratio by changing the MO line pressures during the HT growth steps. In particular, figure 12(b) shows the SEM images of the InAs NWs with the highest aspect ratio of 20, obtained with P_TMIn = 0.20 Torr and P_TBAs = 3.00 Torr, (F = 15), while figure 12(c) displays the InAs NWs with the lowest aspect ratio of 8.5, obtained with P_TMIn = 0.20 Torr and P_TBAs = 1.00 Torr (F = 5). InAs NWs with any desired aspect ratio between these values can be obtained by the appropriate choice of the MO line pressures.

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In summary, we demonstrated catalyst-free growth of InAs NWs on Si (111) substrates using the CBE technique. We presented a two-temperature growth protocol that yields InAs NWs with controlled morphology. Self-induced InAs NWs were shown to nucleate from isotropic islands that are formed during the LT nucleation step. Growth begins and proceeds during the HT step without any metal catalyst at the NW tip thanks to the lower nucleation barrier on the top (111) NW facet with respect to its side facets. The resulting NWs have a mixed WZ/ZB crystal structure and predominantly grow normal to the Si {111} surface plane. We analyzed the influence of the growth parameters on the NW morphology. In particular, the optimum temperature to obtain NWs with the highest aspect ratio was shown. The impact of the TBAs and TMIn line pressures on the NW growth rate and morphology was also investigated and modeled. Our model yielded good agreement with the experimental results for the whole set of deposition conditions and growth durations. Based on this understanding, non-tapered InAs NWs with a tunable aspect ratio were shown. We believe these results can be useful for the development of catalyst-free methods to fabricate III–V NWs on Si with the desired morphology.

We gratefully acknowledge the bilateral project CNR/RFBR. N V S and V G D acknowledge the financial support received from the Russian Foundation for Basic Research under grant No. 15-52-78057 and 15-02-06525.