# Growth of Self-Catalyzed InAs/InSb Axial Heterostructured Nanowires: Experiment and Theory

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## Abstract

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## 1. Introduction

_{1−x}Sb

_{x}NWs on InAs stems cannot work for x higher than ~0.4 [24]. More Sb-rich alloys prefer to grow on the InAs sidewalls and the NWs finally become nano-discs. Catalyst-free growth of pure InSb in the form of InAs/InSb axial heterostructured NWs is hence extremely challenging. The only remaining way for the Au-free synthesis of InSb NWs on InAs stems should then be the self-catalyzed (or self-assisted) approach [25,26], in which the Au catalyst is replaced by In. To the best of our knowledge, only a few studies have been reported on self-catalyzed InAs/InSb NWs [7,27,28] and a detailed description of the growth mechanisms is still lacking. Consequently, here we present the first systematic analysis of the self-catalyzed growth of InAs/InSb axial heterostructured NWs on silicon substrates by Chemical Beam Epitaxy (CBE). Our investigation shed new light on some general features of the growth mechanisms and the resulting properties of NWs, including the evolution of the InSb morphology, crystal phase and the role of In droplets in forming InAs/InSb axial heterostructured NWs. Most importantly, this understanding allows for the realization of Au-free and CMOS-compatible InAs/InSb heterostructured nanostructures with well controlled properties.

## 2. Methods

_{In}) and TDMASb (F

_{Sb}) line pressures and time durations were investigated at a fixed growth temperature of 430 ± 10 °C. At the end of growth, the TMIn flux was stopped and the sample was cooled down to 150 °C in 3 min, linearly decreasing the TDMASb line pressure to 0 Torr. The NW morphology was characterized by scanning electron microscopy (SEM) in a Merlin field emission microscope (Zeiss, Jena, Germany) operated at 5 KeV. For imaging the NWs were mechanically transferred from the as-grown substrates onto a Si substrate, in order to measure the geometrical parameters (nanoparticle (NP) height and base radius, InSb segment length and diameter) from a 90° projection. Crystal structure and chemical composition of the NWs were measured by transmission electron microscopy (TEM) using a JEM-2200FS microscope (JEOL, Tokyo, Japan) operated at 200 keV, equipped with an in-column Ω filter and a detector for X-ray energy dispersive spectroscopy (EDX). Imaging was performed in high resolution (HR) TEM mode combined with zero-loss energy filtering. For TEM characterization, the NWs were mechanically transferred to carbon-coated copper grids.

## 3. Results and Discussion

_{In}and F

_{Sb}were fixed at 0.2 Torr and 0.35 Torr, respectively, while the growth times of InSb were varied (t = 10, 15, 20, 30, 45, 60, 120 and 180 min). SEM images of one representative NW from each sample are shown in Figure 1a. The InAs/InSb interface is always well visible thanks to a larger diameter of the InSb segment. We performed EDX analysis of the longest NWs (with t = 180 min). We did not find any Sb signal around the InAs stem and the InAs/InSb axial interface was quite sharp, corresponding to the position at which the NW diameter started to increase. Therefore, the InSb segment length can be measured directly from the SEM images as the distance from the InAs/InSb interface to the InSb/NP interface. A frozen In droplet (the NP) is always visible on top of InSb segment, clearly revealing the self-catalyzed VLS growth mechanism for InSb section. Accumulation of In on the NW top must be due to In-rich conditions during growth of InSb, as in Ref. [18,29], for In and Ga catalyzed InAs and GaAs NWs.

_{d}and the height H of the NP, as described in panel (b) of Figure 1. All the average quantities with the standard deviation, for all the series of samples, are reported in the Supplementary material file. The time evolution of the NP shape under these growth conditions shows that it first appears smaller than the maximum InSb diameter due to tapering of the top NW section (after 10 min of InSb growth), but soon is pinned at the corners of vertical NW, with the aspect ratio (H/R

_{d}) increasing toward longer times. The InSb segment length L and diameter D versus time t are shown in panel (c). We can see that both quantities increase with the growth time, but the InSb length increases faster than the diameter. Both length and diameter are approximately linear in time. Assuming spherical cap shape of the NP resting on the NW top facet, the contact angle $\beta $ can be obtained using the known expression tan(β/2) = H/R

_{d}[30]. This is a standard method of measuring the contact angle [31]. In order to verify that the droplet geometrical parameters measured ex-situ are representative of the actual droplet shape during growth, we carried out some cooling experiments with and without TDMASb flux (see the Supplementary Material for the details). The results confirm that the cooling down step does not affect the NW and droplet geometry, so the ex-situ measurements well reproduce the real shape and can safely be used for the β calculation. The plot of the contact angle versus time is shown in Figure 1d. It is seen that the contact angle increases quite rapidly at the beginning but then saturates at 102° ± 2°.

_{Sb}value from 0.35 Torr to 0.7 Torr and keeping the same F

_{In}of 0.2 Torr. We grew three samples with t = 30, 45 and 60 min, for which the representative SEM images are shown in Figure 1e. Figure 1f shows the measured diameter and length of InSb segments as a function of the growth time. It is seen that the droplet is always smaller than the maximum NW diameter due to tapering of the NW top. Furthermore, the droplet diameter stays almost constant during growth, while the maximum InSb diameter increases linearly with time according to Figure 1f. By measuring the aspect ratio of the NPs, we deduced their contact angle plotted in Figure 1g. It is seen that for these growth conditions, the contact angle saturates at approximately 79°.

_{Sb}and F

_{In}separately, we studied the effect of the In/Sb line pressure ratio on the morphology of InSb segments. Figure 2a shows the representative SEM images of a series of InAs/InSb NWs as a function of F

_{Sb}, obtained by keeping F

_{In}at 0.2 Torr and varying F

_{Sb}from 0.35 Torr to 0.80 Torr. The InSb growth time was 60 min for all samples. It is clearly seen that the size of In droplets decreases and the length of InSb segment increases with increasing the TDMASb line pressure. For lower TDMASb pressures (F

_{Sb}< 0.55 Torr), the droplet covers the whole top facet of InSb NW, while for higher TDMASb line pressures it becomes smaller than the facet. The maximum F

_{Sb}at which the In droplet is preserved on the NW top equals 0.8 Torr. Higher TDMASb line pressure leads to a transition from the VLS growth to the catalyst-free vapor-solid (VS) mode, where no axial growth of InSb is observed. Instead, InSb starts forming a shell around the InAs stem (see the Supplementary material). We can thus conclude that axial growth of InSb on InAs can only proceed in the presence of an In droplet through the VLS growth mode, while no axial growth occurs in the catalyst-free VS regime, as observed earlier in [14,15]. Figure 2b shows the diameter and length of InSb segment as a function of F

_{Sb}. It is seen that, while the In droplet size gradually decreases with increasing the TDMASb line pressure, the diameter of InSb segment remains constant. It clearly demonstrates that radial growth of InSb depends neither on the TDMASb line pressure nor on the In droplet size. Furthermore, the radial growth rate remains the same regardless of NW tapering at the top. Hence, radial growth should proceed independently of the VLS process occurring on the NW top. The length of InSb segment increases almost linearly with F

_{Sb}, as usually observed in self-catalyzed III-V NWs [25,29,32]. By applying the same method as above, we deduced the droplet contact angle as a function of F

_{Sb}, shown in Figure 2c. The contact angle gradually decreases with increasing the TDMASb line pressure. For lower pressures (F

_{Sb}< 0.4 Torr), it remains larger than 90°, while for higher pressures (above ~0.65 Torr) it saturates at ~79°. The droplet volume further decreases by shrinking its base diameter smaller than the facet.

_{In}from 0.2 Torr to 0.65 Torr at a fixed F

_{Sb}of 0.35 Torr. The InSb growth time was fixed to 60 min for all samples. Clearly, all these growths proceed under highly In-rich conditions, where the volume of the In droplet gradually increases with increasing F

_{In}. The In droplets cover the whole NW top facets in all cases. Figure 3b shows the InSb diameter and length versus F

_{In}. The diameter increases linearly with F

_{In}, while the length is independent of F

_{In}. We can thus conclude that the axial growth rate of InSb segment is independent of F

_{In}, while the radial growth rate is proportional to F

_{In}. Figure 3c quantifies the droplet contact angle as a function of F

_{In}, showing a rapid increase at the beginning but then showing a tendency for saturating at around 125°. Further increase of the In droplet volume occurs by increasing the base radius.

_{In}= 0.2 Torr and F

_{Sb}= 0.7 Torr (additional TEM images of a sample grown using different growth conditions are provided in the Supplementary Material). Panel (a) shows the EDX map of a NW, while panel (b) is a HR-TEM image of another NW. Panels (c) and (d) are the magnified views of the selected portions of the NW framed by the colored squares in (b), with the insets showing the Fast Fourier Transforms (FFT) of the InSb lattice. In all the NWs analyzed, we found that the catalyst nanoparticles contain only In. The Sb concentration is always lower than 1%, regardless of the In/Sb precursor ratios used. From the HR-TEM and the FFT analyses, we found that the InAs stems have a mixed wurtzite/zincblende (WZ/ZB) crystal structure, while the InSb segments have the ZB structure with a few stacking faults, often followed by a thin WZ insertion at the NW top (close to the NW/NP interface). The TEM results confirm the self-catalyzed growth mechanism with pure In droplet on the NW top, as reported earlier in Refs. [12] and [24], and the good stability of the ZB crystal phase in InSb NWs regardless of the growth parameters employed. A more detailed discussion of this stability based on the surface energy considerations is given in the Supplementary material.

_{Sb}, as demonstrated in Figure 2b. This is standard for self-catalyzed VLS growth [25,32,33,34,35] and occurs because the catalyst droplet serves as a reservoir of group III atoms (In in our case) and the VLS growth conditions are always group V limited. Including the re-emitted flux of group V atoms scattered from the substrate surface or the neighboring NWs [32] does not change the linear scaling of the axial growth rate with group V flux. On the other hand, group V species are not diffusive on the NW sidewalls [32,33,34]. Conversely, VS growth on the NW sidewalls is usually group III limited [15,26,33,36] and may involve surface diffusion of In adatoms. This would not change the linear scaling of the average NW diameter with group III flux, clearly demonstrated in Figure 3b. Diffusivity of In on Si(111) surface might be high, but we consider growth of InSb on InAs at a distance ~500 nm from the substrate. Surface diffusion of In is known to not strongly affect even the Au-catalyzed CBE growth of InAs NWs, which is evidenced by their Poissonian length distributions [37]. When the VLS growth is driven by surface diffusion, the NW length distributions become much broader, with the variance scaling as the squared mean length [38] (against the linear scaling in the Poissonian case [37]). Finally, we are dealing only with the average values of the InSb segment length, diameter, and In droplet angle. In this case, it seems reasonable to assume a linear scaling of the growth rates with the corresponding fluxes, leaving aside more delicate effects of re-emission, surface diffusion and random nucleation of NWs on the surface [37]. Deviations from the linear fits, seen in Figure 1c, Figure 2b and Figure 3b, might be due to the effects listed above.

_{In}/F

_{Sb}= 0.2/0.9. The two typical geometries are illustrated in Figure 5 and can be understood on surface energetic grounds similarly to other III-V NWs.

_{In}dependences of the In-limited radial growth rates of InSb, shown in Figure 1c,f and Figure 3b, respectively, yield:

_{In}= 0.2 Torr. Integration gives $R={R}_{0}+{a}_{In}{F}_{In}t$, with R

_{0}≈ 30 ± 5 nm as the initial radius of InAs stems. This matches exactly the horizontal line in Figure 2b at t = 60 min. Therefore, radial growth of InSb segments proceeds in the VS mode and has nothing to do with the droplet size evolution, in sharp contrast with Refs. [29], [34], and [39].

_{Sb}in the general case (measured in nm/min × Torr). After the contact angle saturates to a certain β

_{c}, as in Figure 1d, the axial growth rate becomes independent of β and hence on the In flux. In particular, from the linear fits shown in Figure 1c,f, the axial growth rate is almost precisely doubled (4.5 ± 0.2 nm/min against 2.4 ± 0.12 nm/min) by increasing F

_{Sb}from 0.35 Torr to 0.7 Torr.

^{3}is the elementary volume of InSb pair in ZB InSb [36]. Since the droplet contains only In atoms, we can write the corresponding change in the droplet volume, which equals ${\mathsf{\Omega}}_{In}{N}_{In}$ (where ${\mathsf{\Omega}}_{In}=$ 0.0261 nm

^{3}is the elementary volume of liquid In) [36]. At a fixed $R$, we can present the volume change solely through $d\beta $ according to $d{N}_{In}/dt=(\pi {R}^{3}/{\Omega}_{In}){(1+cos\beta )}^{-2}{(d\beta /dt)}_{2}$ [41].

_{c}is obtained from:

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Series of SEM images of InAs/InSb axial heterostructured NWs with In droplets on top, obtained with the line pressures F

_{In}= 0.2 Torr and F

_{Sb}= 0.35 Torr for different InSb growth times as indicated in each panel. The In droplet nucleates smaller than the NW facet, but then extends its base to cover the whole NW already after 15 min of InSb growth. (

**b**) Schematic view of the measured geometrical parameters. (

**c**) Time evolution of the diameter and length of InSb segments (symbols) and (

**d**) time evolution of the contact angle of In droplets on top of InSb segments (symbols) of the sample series shown in (

**a**). (

**e**) Series of SEM images of InAs/InSb axial heterostructured NWs with In droplets on top, obtained under F

_{In}= 0.2 Torr and F

_{Sb}= 0.7 Torr for 30, 45, and 60 min of InSb growth time. The droplet diameter appears systematically smaller than the NW diameter. (

**f**) Time evolution of the diameter and length of InSb segments (symbols) and (

**g**) time evolution of the contact angle of In droplets on top of InSb segments (symbols) of the sample series shown in (

**e**). The lines in (

**c**,

**d**,

**f**,

**g**) are theoretical fits discussed in the modeling section.

**Figure 2.**(

**a**) Series of SEM images of InAs/InSb NWs, obtained after 60 min of InSb growth at a fixed F

_{In}of 0.2 Torr and different F

_{Sb}, yielding different In/Sb line pressure ratios as indicated in each panel. The droplets become smaller than the NW facet for higher F

_{Sb}. (

**b**) Diameter and length of InSb segment versus the F

_{Sb}(symbols). (

**c**) Contact angle of In droplets on top of InSb segments versus F

_{Sb}(symbols). The lines in (

**b**,

**c**) are theoretical fits discussed in the modeling part. The change of the slope in the model fit comes from the minimum stable contact angle of 79°.

**Figure 3.**(

**a**) Series of SEM images of InAs/InSb axial heterostructured NWs with In droplets on top, obtained after 60 min of InSb growth at a fixed F

_{Sb}of 0.35 Torr and different F

_{In}, yielding different Sb/In line pressure ratios indicated in each panel. Under these highly In-rich conditions, the In droplets always cover the whole NW facet. (

**b**) Diameter and length of InSb segments versus the F

_{In}(symbols). (

**c**) Contact angle of In droplets on top of InSb segments versus F

_{In}(symbols). The lines in (

**b**,

**c**) are theoretical fits discussed in the modeling section.

**Figure 4.**TEM analyses of the InAs/InSb NWs grown with F

_{In}= 0.2 Torr and F

_{Sb}= 0.7 Torr for 60 min. (

**a**) EDX compositional map of a NW in which is visible the InAs stem in pink color, the InSb segment in green color and the In NP in blue. (

**b**–

**d**) show HR-TEM images of another NW with the FFTs of the selected portions (insets).

**Figure 5.**Illustration of (

**a**) vertical (for β > β

_{min}) or (

**b**) tapered (at β = β

_{min}) NW geometry, with β

_{min}≅ 79° as the small stable angle determined by the surface energetics.

**Table 1.**Parameters describing the morphological evolution of InAs/InSb NWs and In droplets under F

_{In}= 0.2 Torr and F

_{Sb}= 0.35 Torr.

${\mathit{\beta}}_{\ast}$ | ${\mathit{F}}_{\mathit{I}\mathit{n}}^{\ast}$ | ${\mathit{F}}_{\mathit{S}\mathit{b}}^{\ast}$ | ${\mathit{a}}_{\mathit{I}\mathit{n}}{\mathit{F}}_{\mathit{I}\mathit{n}}^{\ast}$ | ${\mathit{b}}_{\mathit{S}\mathit{b}}({\mathit{\beta}}_{\ast}){\mathit{F}}_{\mathit{S}\mathit{b}}^{\ast}$ | ${\mathit{b}}_{\mathit{I}\mathit{n}}({\mathit{\beta}}_{\ast}){\mathit{F}}_{\mathit{I}\mathit{n}}^{\ast}$ | ${\mathsf{\Omega}}_{\mathit{I}\mathit{n}}/{\mathsf{\Omega}}_{\mathit{I}\mathit{n}\mathit{S}\mathit{b}}$ | $\mathit{A}$ |
---|---|---|---|---|---|---|---|

Degree | Torr | Torr | nm/min | nm/min | nm/min | ||

102 ± 2 | 0.2 | 0.35 | 0.57 ± 0.07 | 2.4 ± 0.12 | 6.18 ± 0.05 | 0.384 | 0.534 |

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**MDPI and ACS Style**

Arif, O.; Zannier, V.; Dubrovskii, V.G.; Shtrom, I.V.; Rossi, F.; Beltram, F.; Sorba, L.
Growth of Self-Catalyzed InAs/InSb Axial Heterostructured Nanowires: Experiment and Theory. *Nanomaterials* **2020**, *10*, 494.
https://doi.org/10.3390/nano10030494

**AMA Style**

Arif O, Zannier V, Dubrovskii VG, Shtrom IV, Rossi F, Beltram F, Sorba L.
Growth of Self-Catalyzed InAs/InSb Axial Heterostructured Nanowires: Experiment and Theory. *Nanomaterials*. 2020; 10(3):494.
https://doi.org/10.3390/nano10030494

**Chicago/Turabian Style**

Arif, Omer, Valentina Zannier, Vladimir G. Dubrovskii, Igor V. Shtrom, Francesca Rossi, Fabio Beltram, and Lucia Sorba.
2020. "Growth of Self-Catalyzed InAs/InSb Axial Heterostructured Nanowires: Experiment and Theory" *Nanomaterials* 10, no. 3: 494.
https://doi.org/10.3390/nano10030494