Sb-saturated high-temperature growth of extended, self-catalyzed GaAsSb nanowires on silicon with high quality

Ternary GaAsSb nanowires (NW) are key materials for integrated high-speed photonic applications on silicon (Si), where homogeneous, high aspect-ratio dimensions and high-quality properties for controlled absorption, mode confinement and waveguiding are much desired. Here, we demonstrate a unique high-temperature (high-T >650 °C) molecular beam epitaxial (MBE) approach to realize self-catalyzed GaAsSb NWs site-selectively on Si with high aspect-ratio and non-tapered morphologies under antimony (Sb)-saturated conditions. While hitherto reported low-moderate temperature growth processes result in early growth termination and inhomogeneous morphologies, the non-tapered nature of NWs under high-T growth is independent of the supply rates of relevant growth species. Analysis of dedicated Ga-flux and growth time series, allows us to pinpoint the microscopic mechanisms responsible for the elimination of tapering, namely concurrent vapor–solid, step-flow growth along NW side-facets enabled by enhanced Ga diffusion under the high-T growth. Performing growth in an Sb-saturated regime, leads to high Sb-content in VLS-GaAsSb NW close to 30% that is independent of Ga-flux. This independence enables multi-step growth via sequentially increased Ga-flux to realize uniform and very long (>7 μm) GaAsSb NWs. The excellent properties of these NWs are confirmed by a completely phase-pure, twin-free zincblende (ZB) crystal structure, a homogeneous Sb-content along the VLS-GaAsSb NW growth axis, along with remarkably narrow, single-peak low-temperature photoluminescence linewidth (<15 meV) at wavelengths of ∼1100–1200 nm.


Introduction
Owing to their wide bandgap tunability and various other attractive properties, GaAsSb-based semiconductors and their low-dimensional derivatives, including nanowires (NW), have become promising systems for optoelectronic and photonic applications, such as optical fiber communication systems [1], high-speed photodetectors [2][3][4], infrared light emitting diodes [5] and lasers [6][7][8].Employing these materials in the form of bottom-up NWs is particularly appealing, as this enables direct monolithic integration on silicon (Si) and unprecedented flexibility in heterostructure engineering [9].Naturally, the envisioned photonic applications require excellent control of Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.NW-dimensions, morphological and structural uniformity at the single and array device level.Non-uniformities or limited dimensions can critically impact photonic properties of, e.g.light trapping and photo-absorption, confinement and waveguiding of optical modes within the NW cavity.
To date, both vapor-solid (VS) and vapor-liquid-solid (VLS) growth methods have been employed to realize bottom-up GaAsSb NWs on various substrates using common epitaxial techniques, such as molecular beam epitaxy (MBE) [10][11][12][13][14][15][16] and metal-organic chemical vapor deposition (MOCVD) [17].Vapor-solid processes mediated by selective area epitaxy (SAE), have evidenced very promising control towards extended NW lengths and aspect ratios with remarkable morphological uniformity [10,11].However, such growth enhancement was, so far, only observed at limited Sb incorporation of only few percent.Larger flexibility, on the other hand, has been gained by VLS-type growth, either by Au- [12,17] or self-catalyzed, i.e.Ga-droplet mediated processes [13][14][15][16], where much focus aimed at increasing Sb-content to tune emission wavelength of GaAsSb NWs.Yet, growth at increased Sb-content is notoriously difficult, due to the surfactant nature of Sb that limits Sb incorporation, Ga diffusion and axial growth [13][14][15].Limited Ga-diffusion in the presence of Sb has particularly adverse consequences in self-catalyzed growth, since the Sb surfactant effect [14] reduces the wetting angle of the Ga droplet catalyst over time, thereby decreasing the collection of group-V elements and ultimately terminating growth at relatively early stage [13][14][15].As a result, typical self-catalyzed GaAsSb NWs reported in literature (Sb-contents of ∼15%-40%) [13-16, 18, 19] are, at best, only few μm long.The axial growth complications are further reflected by tapered or inhomogeneous morphologies, self-induced alloy composition gradients along the growth axis [20], and growth termination seen by an early crystallization of Ga droplets [14-16, 18, 19].Unsurprisingly, no coherent light sources, such as NW-lasers, are yet reported from bulk ternary GaAsSb NWs, given the limited growth physics.
In our view, the key challenge lies in addressing the thermodynamic and kinetic limitations at the growth front to develop NWs with untapered, homogeneous morphology in regimes where Sb incorporation is less sensitive to dynamic changes of the catalyst droplet.By introducing a high-temperature MBE growth process, and performing a series of dedicated growth experiments, we provide here new insights into the growth of self-catalyzed GaAsSb NWs in an Sbsaturated regime.In particular, we illustrate the competition between Ga diffusion and step nucleation on the NW sidewall facets that governs the morphology of GaAsSb NWs, and which can be tuned by Ga-flux rates in order to extend NW lengths to unprecedented dimensions of >7 μm, with fully non-tapered morphologies and high Sb-content close to 30%.These findings are supported by rigorous analysis of optical, structural, and compositional properties using correlated micro-photoluminescence (μPL) spectroscopy experiments, modelling of electronic band-structure, and high-resolution scanning transmission electron microscopy (HR-STEM).

Experimental
To best describe the growth dynamics and morphology evolution, unobscured by variations in NW-density, highquality SAE-growth schemes were pursued to realize NWarrays with widely separated, isolated NWs.Hereby, standard Si(111) substrates were employed with a thin (∼20 nm) thermally grown SiO 2 layer on top, which were prepatterned by electron beam lithography (EBL) and wet chemical etching (buffered hydrofluoric acid), to serve as a mask for the SAE-process [21].If not otherwise noted, the pattern pitch was 10 μm, and arranged in periodic hexagonal lattices.The growth of GaAsSb NWs was performed in an all-solid-source Gen-II MBE system equipped with conventional effusion cells for group-III elements (In, Ga, Al) and Veeco valved cracker cells for supply of group-V elements arsenic (As) and antimony (Sb).Supply of As species was provided by uncracked As 4 , while the Sb species were supplied as Sb 2 molecules.All group-V fluxes are given in units of beam equivalent pressure (BEP) or fractional flux ratios of Sb-BEP over As-BEP, i.e.FF Sb .The Ga-flux is given in equivalent growth rate units (Å/s) based on the growth rate of homoepitaxial planar GaAs growth [22].The growth temperature reported here was measured by an optical pyrometer.
Compared to reported data in literature [13][14][15][16][18][19][20], a distinctive difference of our approach is the use of a rather high growth temperature of 660 °C.The motivation for such high temperature is twofold: first, the increased diffusion length of Ga at higher temperature should allow for higher aspect ratio NWs.Indeed, under usual VLS growth conditions, a temperature close to 660 °C resulted in optimized aspect ratios in recent GaAs NW growth experiments [23].Secondly, thermodynamic considerations suggest that the miscibility gap of ternary GaAsSb is decreased for higher temperature [24], a characteristic that has been seen in liquid phase epitaxy (similar to VLS growth) of this material [25].This means that for sufficiently high Sb-content being incorporated in the NW via the liquid Ga droplet, a tendency towards a more homogeneous phase along the NW axis is expected at higher temperature.

General growth aspects
Figure 1(a) illustrates the typical process flow for the growth of self-catalyzed GaAsSb NWs on SiO 2 -templated Si(111) substrates.The growth started with an initial thermal cleaning step at 720 °C, followed by ramping the Ga-cell to a high flux of 2.35 Å s −1 and temperature to 660 °C.A short 2 min Ga prewetting step was then introduced to form Ga droplets as nucleation sites within the SiO 2 -mask openings.By supplying As-BEP = 4 × 10 −6 mbar, a GaAs stem is first grown, during which the Ga-flux was ramped down to the desired rate for subsequent GaAsSb NW growth (e.g.Ga = 0.9 Å s −1 ).Such ramp is necessary to minimize the NW diameter, while maintaining high yield nucleation.In the first set of experiments shown here, the nucleating GaAs was grown for 15 min to induce relatively long (∼1.86 ± 0.03 μm) and thin (60 ± 3 nm) stems (see supplementary material).Growth of such long stems was motivated by the idea to unambiguously study the dynamics of GaAsSb VLS growth in regimes that are isolated from nucleation stages.Later, we also illustrate experiments where the growth of the GaAs stem was reduced to only 3 min (see growth time series).The growth of GaAsSb on top of the GaAs NW stem was then performed for a certain growth time by supplying Sb-flux at fixed BEP, and terminated by simultaneously shuttering all growth species and quenching the substrate temperature.A scanning electron microscopy (SEM) image of a representative array of NWs is shown in figure 1(b), as obtained for a GaAsSb growth time of 60 min and a Sb-BEP of 7.7 × 10 −7 mbar (FF Sb = 19%).We observe high uniformity of NWs with very small wire-towire variation within the array.This is a direct result of the large pitch chosen for our experiments, where competition of growth species amongst neighboring NWs is negligible [26], such that even non-perfect growth yield has no influence on NW dimensions due to their isolated design.
All NWs show the typical hexagonal cross-section with { ̅ 11 0} sidewalls, identical to GaAs NW growth, es evidenced by close-up images on the right (figure 1(c)).On the tip of each NW, a droplet is clearly visible proving the VLS growth behavior.Increasing the supply of Sb, i.e. varying Sb-BEP from 7.7 × 10 −7 mbar (FF Sb = 19%) to 1.6 × 10 −6 mbar (FF Sb = 40%) maintains nicely the same VLS growth characteristics, as the Ga droplet is well preserved.Several other general observations can be made: first, despite the overall well extended NW length (∼5 μm for the GaAsSb segment alone), the axial growth of GaAsSb is smaller than that of GaAs for the same As-BEP [23], and further decreases with increasing Sb-flux.This is interesting insofar, since VLS growth of GaAs-based NWs is group-V limited [22,27] and the total group-V flux is increased by the addition of Sb.Yet, the decrease in NW length with increasing Sb-flux is well observed in literature [14][15][16], and was, so far, explained by a reduced droplet wetting angle ('Sb-poisoning effect') [14,16].Analysis of the droplet wetting angle in our GaAsSb NWs (using SEM side-view images), however, finds no distinct dependence on Sb-BEP, with wetting angles on the order of ∼103 ± 4°.This suggests that another reason is most likely responsible for the suppressed axial growth.PYCALPHAD modeling [28,29] (open-source Python library for designing thermodynamic models) of the vapor pressure of As and Sb species in the liquid Ga-As-Sb alloy droplet was therefore performed (see supplementary).The data provides evidence, that under increased Sb-content in the liquid alloy droplet, not only Sb desorption, but also As desorption increases.This lowers the total group-V supply, thereby reducing the axial growth rate, and explains the reduced NW-length upon increased Sb-BEP.Increasing As-BEP beyond the optimized conditions (>4 × 10 −6 mbar) did not result in gains in aspectratio, because VLS-growth cannot be maintained under these growth conditions, leading to growth termination and VStype growth.
Secondly, another unique observation finds that, despite the variation of Sb-BEP, the NWs exhibit consistently a completely non-tapered morphology along the entire sidewall facets (less than 10 nm variation in diameter over >5 μm length).This is in contrast to previous findings of self-catalyzed GaAsSb NW growth [13,14], and even more surprising, considering that growth of GaAsSb NWs proceeds from a thin GaAs nucleus and extends over time via the interplay of axial and radial growth.Note, compared to the ∼60 nm thin GaAs stem, the radial dimensions of the subsequent GaAsSb growth increased to ∼300 nm, yet, fully homogeneously along the entire length-i.e.not only at the NW tip, as can be anticipated by the obvious size increase of the Ga droplet that determines the diameter during the VLS process (see figure 1(c)), but also at the bottom and in all other regions along the NW.While this is reminiscent of concurrent radial growth via a vapor-solid process, as suggested by the Sb surfactant effect [13], the equilibration towards such highly uniform morphology has been unobserved and is very intriguing.

Morphology and compositional evolution under varying Ga-rate
To shed more insights into the NW morphology, we show in the following results from a dedicated Ga-flux rate series performed under the same conditions as discussed above.It should be noticed that such Ga-flux dependent studies have not been reported yet, and provide therefore valuable new information.In particular, by increasing the Ga-flux during growth, we expect the development of an enlarged Ga-droplet and, thereby, intuitively more control over tapering during the VLS-GaAsSb NW growth.Figure 2 summarizes the morphology characteristics of GaAsSb NWs grown on top of the same GaAs nucleation stem under four different Ga-fluxes of 0.6 Å s −1 , 0.7 Å s −1 , 0.8 Å s −1 , and 0.9 Å s −1 at fixed Sb-BEP of 7.7 × 10 −7 mbar (FF Sb = 19%).Remarkably, despite the changes in Ga-flux throughout the individual growths, the homogeneous, non-tapered nature of the resulting NWs remains persistent.
Closer quantitative inspection, as described by morphological parameters (NW length, NW diameter and droplet diameter) in figure 2(b), reveals interesting details that further highlight distinctly different behavior known from typical GaAs NWs: first, NW-length, diameter and droplet diameter increase with increasing Ga-flux in GaAsSb NWs.The total diameter increases by ∼65% over the range of investigated fluxes (from ∼200 to ∼300 nm), similar to the Ga-rate, however, the length increases by only ∼20% (4.7 μm at Ga = 0.6 Å s −1 to 5.6 μm at Ga = 0.9 Å s −1 ).In a strictly group-V limited growth, such as in GaAs VLS growth, the length of the NW is almost independent of the Ga-rate [27,30], as long as the droplet is preserved.Typically, only the diameter and the droplet size change when changing the Ga flux.This is rooted in the fact that the amount of As collected by the droplet is proportional to its cross-sectional area and the As required to grow an axial monolayer is proportional to the cross-sectional area of the NW.Due to the similarity of droplet diameter and NW top diameter, a change in droplet diameter does not change the axial growth rate, because the supplied As increases by the same fraction as the As necessary to form a monolayer.
The absence of tapering in GaAsSb NWs, throughout the entire range of Ga-fluxes, is also in striking contrast to VLSgrown GaAs NWs.In GaAs, NWs are commonly also nontapered at low Ga-rates, but become inversely tapered for higher Ga-rates due to the increasing size of the Ga droplet [27,30].The GaAsSb NWs presented here show an increase in droplet diameter with Ga-rate, but clearly the tapering is compensated by radial growth.Further information can be obtained by inspecting the droplet wetting angle, which reflects the local conditions at the NW tip during growth.Surprisingly, the droplet wetting angle gets smaller with Garate, i.e. from ∼120°(Ga = 0.6 Å s −1 ) to ∼100-105°(Ga = 0.9 Å s −1 ) (supplementary material).Ren et al [14] suggest that a reduced droplet wetting angle might be responsible for the reduced axial growth rate in GaAsSb compared to GaAs, due to the reduced collection area of As.This claim is based on the difference in wetting angle and length depending on NW position in a NW array [31].Our experimental results show that this is not the most relevant influence, since in this experiment the GaAsSb NWs with higher Ga-rate have smaller wetting angles but are longer at the same time.
Based on all these results, we can now accurately delineate the underlying growth dynamics by sketching the anticipated internal structure of the resulting non-tapered NWs.As depicted in figure 2(c), the GaAsSb growth must obviously proceed via two different growth regions demarcated by axial VLS and radial VS growth.First, on top of the ∼60 nm thin GaAs NW stem, a long axial segment of GaAsSb grows by VLS mode that increases in width towards the tip of the NW to account for the dynamically changing droplet diameter.This segment, as well as the entire GaAs stem beneath, is in turn covered by a shell of vapor-solid grown GaAsSb, which results in the constant diameter observed by SEM.The indices 'VS' and 'VLS' account for the two respective axial and radial regions, which form an intrinsic heterostructure and which are expected to have different Sb-content due to the different growth mechanisms.
Although not studied on non-tapered NWs, such heterostructure mediated by concurrent VLS core and VS shell growth has, indeed, been observed before by Conesa-Boj, et al [13], who observe a somewhat lower Sb-content in the shell.In the following, we directly elucidate the nature of the individual segments using a fully correlated approach, that combines μPL experiments with modelling of electronic band-gap and composition taking optical transition energies and strain into account.Such approach offers a uniquely noninvasive, and, thereby, rapid method to extract important compositional and strain data from the complex GaAsSb-NW heterostructure, to complement microstructural analysis by HR-STEM and energy-dispersive x-ray spectroscopy (EDXS) measurements further shown below.
Figure 3 summarizes data from m-PL measurements and modelling performed on the entire Ga-flux rate series, with the aim to derive estimates of Sb-content in both the VLSand VS-part of the NW and to further determine the extent by which the Ga-rate (Ga/Sb-ratio) affects Sb-incorporation.Hereby, all m-PL measurements were performed in a He-flow cryostat at 10K, using a mode-locked pulsed Ti:Sa laser (excitation energy 1.59 eV) for excitation and an LN 2 -cooled InGaAs CCD for detection [23].Figure 3(a) shows a typical measurement of a single NW grown with a Ga-rate of 0.9 Å s −1 (as in figure 2(a)) at varying pump fluence.Spectra taken on NWs from all other samples show qualitatively similar characteristics (see supplementary).In general, we observe three main peaks that appear at 1.1 eV, 1.15 eV and 1.25 eV.From the internal structure of the NW as sketched in figure 2(c), we expect, indeed, three PL peaks as described as follows.Two of the peaks can be associated with the GaAsSb sections, and the other with the GaAs NW stem.Intuitively, the two lowest energy peaks (1.1 eV and 1.15 eV) are expected to arise from the GaAsSb sections given the lower bandgap energy than GaAs.Yet, both peaks are very close in energy and merge for higher pump fluence due to band filling.Given previous knowledge from [14], the VLS-GaAsSb and VS-part of the NW are expected to have only marginally different composition, with the VLS-section containing slightly larger Sb-content than the VS-section.Thus, larger Sb-content (i.e.VLS-GaAsSb) refers to lower bandgap energy.On the other hand, the GaAs stem has an unstrained band-gap of 1.52 eV, [32] but due to the thick VS-GaAsSb shell surrounding it, the stem experiences an intense tensile strain, which reduces its bandgap [33].Therefore, we tentatively assign the lowest energy peak (1.1 eV) to the unstrained VLS-GaAsSb, the middle peak (1.15 eV) to VS-GaAsSb and the highest energy peak (1.25 eV) to the GaAs stem.
Figure 3(b) shows the dependence of the distinct PL peak energies as a function of Ga-rate for each of the three NWsections.The data give average values as obtained by measurements of three NWs per sample.Comparing the lowest energy peak associated with the VLS-GaAsSb, no clear trend as a function of the Ga-rate is evident.Both the lowest and highest Ga-rate show higher emission energy than the other two Ga-rates, which is associated with a lower Sb-content.Assuming that the lowest energy peak corresponds to the strain-free emission of GaAsSb, we determine an Sb-content from the known dependence of the bandgap as a function of the Sb-content from [34].The resulting Sb-content is in the range of 26%-30% without any systematic trend with Ga-rate and shown in (d) as black data points.In this assessment and all following analysis, we assume that the crystal phase of the NW is pure ZB, which is further validated in figure 7 below.
In contrast, the high energy peak in figure 3(b), associated with the GaAs stem, decreases continuously in energy with increasing Ga-rate.This shift can be ascribed to the increased strain in the GaAs stem due to changes in dimensional parameters with Ga-rate.For a higher Ga-rate, the shell thickness increases from ∼50 nm at 0.6 Å s −1 to ∼110 nm at 0.9 Å s −1 , which increases the tensile strain in the stem, even for a constant Sb-content in the shell.In order to differentiate between the contribution of a thicker shell and a changing Sbcontent of the VS-GaAsSb shell, nextnano-3 simulations were employed, using similar approaches as reported in our recent work [23].Hereby, a 2D-simulation of the strain state close to the bottom of the NW was performed and its influence on the bandgap of the GaAs stem and VS-GaAsSb shell evaluated.From the morphological analysis, the shell thickness is known for each sample and the stem diameter is considered constant (60 nm).The only unknown quantity of the system is the Sbcontent of the GaAsSb shell on the GaAs stem.Thus, a range of simulations was performed at different Sb-content, which is shown in figure 3(c).Each Ga-rate corresponds to one curve of the core bandgap as a function of Sb-content, and the simulations differ only by the thickness of the VS-GaAsSb shell.For Ga-rates 0.7-0.9Å s −1 the simulation results barely differ.The reason for this is the saturation of the strain in the core, as soon as the shell thickness is much larger than the core radius.When this is the case, the core is fully strained and the shell strain-free [23].Further increasing the shell thickness does not change the strain either.Similarly, in this regime small changes in core diameter do not significantly alter the strain, hence changes due to the initial stem diameter can be neglected.For the lowest Ga-rate, however, the stem diameter (60 nm) is comparable to the shell thickness (50 nm), thus, both are strained and the bandgap energy depends on shell thickness.
The average bandgap energy of the strained GaAs stem is defined by the energy of the high energy peak of the PL measurement, which is shown by the red data points in figure 3(c).By identifying their position with respect to the simulated data, we can provide an estimate of the Sb-content of the VS-GaAsSb shell on the bottom of the NW that is shown as blue lines in figure 3(d).The Sb-content increases with Ga-rate from 22% (Ga = 0.6 Å s −1 ) to 27% (Ga = 0.9 Å s −1 ).This directly shows that the increased thickness of the shell is not sufficient to explain the shift of the high energy peak, but that simultaneously the Sb-content of VS-GaAsSb increases.In fact, this is expected based on the well-known growth rate dependencies of Sb-incorporation in GaAsSb layers.Zhang et al [35] modelled the composition of VS-grown GaAsSb layers on GaAs and found that at higher growth rate, the Sb-content is increased because the As-for-Sb exchange reaction, which occurs on the surface of the layer, has less time to proceed until the next layer is grown.In our case, a higher Ga-rate increases the VS growth rate on the sidewalls, which, in agreement with these effects, increases the Sb-content.
So far, the Sb-content in the VS-GaAsSb was only indirectly estimated from the strain it exerts on the GaAs core.The same material should also directly lead to an emission peak in the PL spectrum.Accordingly, the average bandgap values of the VS-GaAsSb shell were extracted from the same simulations as in figure 3(c), with the Sb-content determined from the high energy peak positions, and plotted as a green bar in figure 3(b).Uncertainties associated with the simulation are due to the derived PL peak positions, given the number of NWs measured per sample.Over the entire range of Ga-rates, the simulated bandgap of the VS-GaAsSb shell agrees quite well with the measured GaAsSb PL peaks, confirming the validity of our approach (only at highest Ga-rate (0.9 Å s −1 ) slight deviation is observed, likely due to the broadened PL peak nature seen in the supplementary).In summary, we conclude that both VLS-and VS-sections of the GaAsSb NW exhibit distinct PL peak features, with estimated Sb-contents being ∼4%-5% higher in the VLS-part.This difference in Sb-content is directly confirmed by HR-STEM-EDXS data shown in figure 7.More strikingly, VLS-growth of GaAsSb along the NW axis shows no dependence of the solid Sbcontent on the Ga-rate.This insensitivity implies that under our high-temperature conditions the growth of VLS-GaAsSb NWs proceeds in an Sb-saturated regime, since obvious changes in Ga/Sb ratio do not affect Sb incorporation.We hypothesize that the Sb-saturated regime is mainly established by the Sb desorption from the liquid alloy droplet counteracting an increasing liquid Sb-content upon variations in Ga/Sb ratio, as shown in the supplementary.

Ga diffusion limited growth and facet structure
From the previous observations it became clear that GaAsSb NWs with high Sb-content (close to 30%) can be realized over fairly extended lengths (>5 μm) in a fully non-tapered morphology (figure 2(b)), thanks to the simultaneous VLS and VS growth mechanism.Such extended lengths have not been reported before in single-step self-catalyzed GaAsSb NWs, under similarly high Sb-content, as growth has terminated by the loss of the Ga droplet catalyst at lengths much below ∼4 μm [14,15,18,19].This raises the natural question whether the VLS growth under our high-temperature conditions offers intrinsically improved growth kinetics and scope for much longer NWs without facing previously observed limitations.
To examine this, we performed a specific growth time series, using optimized conditions under highest possible Sbflux, i.e.Ga-rate = 0.9 Å s −1 , As-BEP = 4 × 10 −6 mbar, Sb-BEP 1.6 × 10 −6 mbar (FF Sb = 40%).In this series, the initial GaAs stem growth was shortened to 3 min (length ∼350 nm), which makes its contribution almost irrelevant for the final NW dimensions.Figure 4 shows SEM images and resulting morphological parameters of the obtained NWs, for growth times ranging from 30 min to 120 min.It can be clearly seen that both length and diameter increase approximately linear with time from 30-90 min.After 120 min, the length still increased linearly, but the diameter increased much more than is expected by the incremental 30 min growth time.Additionally, the tip region of the NW drastically changes.As further visible in figure 5, which shows a top and side-view of the tip, the tip is strongly tapered and presents different crystal facets than the standard { ̅ 11 0} sidewalls, and the droplet is absent.The absence of the droplet is most likely caused by the reduction of the incoming Ga flux into the droplet, as further discussed below.This disappearance does not occur in GaAs VLS growth for extended growth duration, where the length is only limited by growth time.
Discussing first the regime of shorter growth times (30-90 min), where clear VLS-growth prevails, not only NWlength and diameter, but also the droplet diameter increases linearly with growth time.This indicates that at all times the incoming Ga flux at the droplet growth front is higher than the outgoing flux due to desorption and incorporation.However, over the entire regime, and even up to 90 min of growth, tapering is never observed in these NWs.This is due to the concurrent VS-GaAsSb shell growth as mentioned before, but the mechanism by which the non-tapered morphology actually forms remains to be resolved.We suggest that it can be described by the competition between step-nucleation, stepflow growth and Ga diffusion limited growth on the NWsidewall surfaces, as explained in the following.Here, we need to first consider that the VLS growth induces, by itself, an inversely tapered form (see figure 2(c)).For Ga adatoms on such an inversely tapered sidewall the conditions are similar to those during growth on vicinal surfaces, where the substrate is slightly misoriented (few degrees) from a lowindex plane creating steps with single or few-layer atomic terraces.Hence, a tapered NW can be well approximated by an arrangement of steps on the { ̅ 11 0} sidewall, as found in recent scanning tunneling microscopy (STM) [36].Generally, the Ga diffusion length during VLS growth is large, especially in the early growth stages it can be assumed that it is longer than the NW length.In particular, it is much longer than the distance between steps on the { ̅ 11 0} sidewall.Thus, the conditions on such NW sidewalls are very similar to those that induce step flow growth [37].For a Ga adatom moving along such step-terrace surface, incorporation can either proceed at a pre-existing step or as nucleation of a new layer.As in step flow growth, if the distance between individual steps is small, incorporation at a step is more likely compared to nucleation of a new layer, since no additional surface energy is required [37,38].This implies that the radial growth rate is faster on a tapered sidewall (due to the presence of steps) than on a non-tapered sidewall (nucleation necessary).
Whether the NW will show tapering after growth depends then on the probability of the individual processes, i.e. diffusion and incorporation at a step edge versus incorporation via the Ga-droplet.In GaAsSb NWs, we assume that the incorporation at steps has a faster speed than the diffusion/incorporation at the droplet.The microscopic reason for this could be a lowering of the energy barrier for incorporation due to the presence of Sb (Sb-surfactant effect) [35].If that is the case and a step is present on the sidewall, Ga adatoms will more likely complete a monolayer via step flow growth than diffuse to the droplet.This can be pictured, for example, by a step nucleated at the tip of the NW (due to the increasing droplet size), which then quickly moves downwards towards the bottom of the NW.This is a self-limiting process, because at some point the step reaches the very bottom of the NW and disappears until no steps are present anymore (i.e.no tapering).Ultimately, this explains the absence of tapering over such a large range of growth conditions for GaAsSb NWs.However, once the NW length surpasses the Ga diffusion length on the sidewalls the growth dynamics change, because Ga adatoms at the bottom of the NW can no longer reach the droplet.Thus, they have a higher probability to nucleate a new layer on the sidewall, and thereby create a new step on the side-facet.In GaAs NWs, this usually leads to tapering of the NW due to an increased diameter at the bottom of the nanowire for long growth time [30], but is not observed for the GaAsSb NWs here.Such nucleation of a step of the NW will again lead to a step flow growth from the nucleation site to the tip and base of the NW, eliminating tapering.Since the layer grows along the entire NW length (as opposed to only on the bottom as seen in GaAs VLS growth), it competes with diffusion to the droplet and reduces the effective flux of Ga into the droplet and finally causes its disappearance.Obviously, this effect is suppressed if the length remains below the Ga diffusion length because then the initial nucleation is less likely, which explains the reduced radial growth rate for 30-90 min (see figure 4(b)).
This explanation relies on the single assumption that in GaAsSb growth steps on the { ̅ 11 0} facets grow fast or, in another perspective, that tapered { ̅ 11 0} facets (i.e.{ ̅ 11 0} facets with steps) are energetically unfavorable, while nontapered { ̅ 11 0} facets are the energetically most favorable configuration.This hypothesis is directly supported by the NW morphology after 120 min growth time, where a complex facet structure at the tip of the NWs is visible.Figures 5(a),  (c) show the tip of a NW from the growth array obtained at a pitch of 10 μm.The hexagon on the bottom of the NW (seen in figure 5(a)) has the same orientation as all investigated NWs with { ̅ 11 0} side facets without tapering up to the tip region.On the top however, the NW is almost triangular.To identify these facets, the NW was measured by SEM from the side (〈 ̅ 11 0〉 zone axis) as it is standing on the native growth substrate (figure 5(c), image rotated for better view).The tip shows two different sides, the top side in (c) being imaged parallel to one of the triangular facets (left side in (a)), while the bottom side images the projection of the edge between the two other facets (right side in (a)).The NW shape of the facet (top side in (c)) consists of the alternation of facets with welldefined angles α, which are measured with respect to the NW axis ([ ̅ 111] direction) and evaluated for several NWs.Two angles are prevalent on all NWs, namely (22 ± 2)°and (5 ± 1)°, each being visible on several facets of different length.
The first angle can be assigned to a {11 ̅ 1} facet, which has an angle of 19.5°.There are only three different {11 ̅ 1} facets which are angled towards the center of the NW, which can explain the pyramidal shape at the tip of the NW.For the most dominant 5°facet, no fitting low-index facet was found.Only higher order facets, such as { ̅ 322} (8°) or { ̅ 533} (5°) reproduce the observed angle, but the observed angle could also be caused by other alternating facets, which are too small to be resolved by SEM.However, a random alternation is unlikely because the same angle (5°) is observed on several NWs.At the very tip of the NW, the angles (59 ± 3°and 73 ± 2°) fit very well to {110} top facets (expected 54.7°and 70.5°).Furthermore, short { ̅ 11 0} facets are visible in figure 5(a) (marked by red arrows), which coincide with the corner of the triangle.Here, the { ̅ 11 0} facets are very small and are not homogeneously tapered but show clear steps, which are visible in the top view of figure 5(a) as alternating dark and bright lines in the right corner of the triangle.We interpret this appearance of the higher-order and { ̅ 11 1} facets as a way for the crystal to minimize its energy under tapering, which confirms that tapered { ̅ 11 0} facets are energetically unfavorable.
Finally, it was assumed that the non-tapered { ̅ 11 0} and {110} facets are energetically most favorable.Indeed, the triangular tip structure discussed previously was only temporary.If the growth continues, the most typical facet structure is restored with six { ̅ 11 0} side-and three inclined {110} top-facets, as common in vapor-solid growth of III-V NWs [39].The beginning of the formation of this tip is already weakly visible in figure 5(c), where the very tip consists of three such inclined {110} facets.For the same growth time, on a 1 μm pitch array, the disappearance of the droplet is already further progressed, because at such reduced pitch, NWs compete for material and, thus, the Ga droplet is consumed earlier.Here, one can clearly see the inclined {110} top facets and disappearance of tapering in 45°tilted-and topview (figure 5(b)).A similar facet configuration has been observed by Koivusalo et al [18].By reducing the growth temperature of GaAsSb NWs from 640 °C to 620 °C and 600 °C, and increasing Sb-flux to achieve higher Sb incorporation, they observe NWs without droplet and either triangular tip or {110} top facets.From this, they conclude that the entire growth proceeds as completely droplet-free VS growth.However, the results presented here show that it is more likely that the reduction in temperature or increase in Sb-flux reduced the Ga diffusion length.As such, offering high growth temperature, allows us to keep up the VLS growth for much longer time, thanks to the enhanced Ga diffusion, resulting in VLS-GaAsSb NWs with lengths exceeding well beyond 6 μm as shown in figure 4.
The remaining question is whether the disappearance of the Ga-droplet can be averted to realize even higher aspectratio GaAsSb NWs, e.g. by further increasing Ga diffusion length, or modifying other growth parameters.From the growth time series performed here, it becomes obvious that simply increasing growth time under fixed growth parameters is insufficient, as this also increases NW-diameter, without desired gains in aspect ratio.In the following, we describe alternative routes to achieve NWs with not only further improved aspect ratio, but simultaneously remarkable morphological, structural, and compositional uniformity along the entire growth axis.

Multi-step growth of GaAsSb NWs with high-quality properties
A suitable way to enhance the aspect ratio of GaAsSb NWs is to minimize radial growth throughout the entire growth process.In this regard, important lessons can be learnt from the data of figure 2, where changes in Ga-rate have obvious implications on the final aspect ratio of GaAsSb NWs.For example, at lowest investigated Ga-rate of 0.6 Å s −1 the aspect ratio of the axial GaAsSb segment is found to be ∼30, while it decreases with increasing Ga-rate to ∼20 (Ga-rate of 0.9 Å s −1 ).Despite the better aspect ratio, growth at low Garate yields lower Ga-droplet diameter, which bears the risk for early shrinkage and disappearance at extended growth times.To compensate for this, Ahmad, et al [19] employed a two-step process, by increasing the Ga-supply by ∼15%-30% during the growth to prevent the droplet consumption.Although this showed improved NW-lengths, the growth was not yet optimized, leaving a growth termination with significantly consumed Ga-droplet at the end, and aspect ratios of only ∼10-15.
Taking this a step further, we propose in the following, a multi-step growth process by which we sequentially increase the Ga-rate in several consecutive steps.This way we keep radial growth at a minimum, by limiting the increase of the droplet size during growth while maintaining sufficient diffusive flux, that compensates continually incorporated Ga by VLS growth.Given the large insensitivity of the Sb-content on the Ga-rate (Sb-saturated regime as seen in figure 3), we thereby also expect to achieve constant Sb-incorporation throughout the entire VLS-growth process.In order to optimize the conditions for such growth, we first identified the lowest possible Ga-rate that still maintains VLS growth.These experiments, as shown in the supplementary, were performed under the same parameters, as in the previous section, i.e.Sb-BEP = 1.6 × 10 −6 mbar (FF Sb = 40%), 3 min GaAs stem growth, and a growth time of 30 min.It was found that by reducing the Ga-rate from 0.9 to 0.4 Å s −1 the NWlength decreased only slightly, but the diameter was significantly reduced.A Ga-rate of 0.4 Å s −1 defined the lowest bound for VLS-growth under these conditions, while further reduced rate of 0.3 Å s −1 resulted in early growth termination and transition to VS-growth.
Using the lower-bound Ga-rate of 0.4 Å s −1 , we then optimized the growth time to identify the maximum possible length for VLS-growth.VLS-growth was preserved well beyond 30 min, however, increased growth time led to growth termination and transition to VS-type growth.Based on this finding, we adjusted the growth by introducing incremental increases in Ga-rate (in steps of 0.2 Å s −1 ), in growth intervals of 30 min, i.e. raising Ga-rate from 0.4 to 0.6 Å s −1 (2-step growth), and further to 0.8 Å s −1 (3-step growth), and 1 Å s −1 (4-step growth).The total growth times for these optimization runs were 60 min, 90 min, and 120 min growth, respectively.As shown in the Supplementary, the 120 min long 4-step process resulted in nearly 8 μm long GaAsSb NWs, with a diameter of ∼420 nm.However, the growth front exhibits a tapered end (similar to figure 5(c)) with a shrinking Ga-droplet at its end.To prevent the termination of VLS-growth and produce a fully intact growth front, the growth interval of the last step in the 4-step process was reduced to 15 min.Figure 6(a) shows the resulting NWs, exhibiting a NW-length of ∼7.5 μm, a diameter of ∼315 nm (aspect ratio ∼24).The NWs further represent an excellent homogeneity without any tapering, both at the single NW as well as at the periodic array level.The excellent quality of these NWs is further confirmed by μ-PL spectra recorded on a single NW at 10 K.As shown in figure 6(b), intense luminescence at ∼1.03 eV (∼1200 nm) is observed with remarkably low linewidth (full width at half maximum, FWHM ∼11-15 meV, depending on pump fluence).Increasing pump fluence induces a blue-shift and peak broadening, which is ascribed to band-filling effects.Such narrow linewidth emission implies a structure with quite homogeneous Sb-content along the growth axis.This is not necessarily guaranteed in such multi-step process, but was anticipated from the insensitivity of Sb-content on Ga-rate, as VLS-growth proceeds in the aforementioned Sb-saturated regime at the high temperature.
To verify these characteristics, HR-STEM-HAADF (high angle annular dark field) imaging and associated EDXS analysis was performed on NWs from this sample using a FEI Titan Themis TEM operating at 300 kV.Hereby, NWs were probed as-transferred onto carbon-coated copper grids for full-image characterization of elemental Sb distribution and microstructure (crystal phase) along the NW-axis, as well as by cross-sectional analysis using FIB-cut (focused ion beam) lamellas.Figure 7(a) depicts a STEM-EDXS map of the elemental Sb distribution over the entire NW without any further preparation, and with the growth direction pointing upwards.The growth direction, which is commonly aligned along the (111)B orientation in III-V NWs [21,40], was also confirmed by the group-V/-III dumbbell bilayer structure in HR-STEM images (see supplementary).The EDXS map directly confirms the anticipated internal structure, as proposed in figure 2(c).It illustrates an Sb-rich GaAsSb core (bright contrast), which gradually extends in width from the bottom towards the top of the NW, and a GaAsSb shell around it with a lower Sb-content.The very short, nucleating GaAs stem at the bottom (<400 nm) is not visualized here, since the NWs broke off above the stem during transfer.The observation of an inversely tapered Sb-rich VLS-GaAsSb core is fully consistent with the proposed growth mechanism, whereby the incremental increase of the Ga-rate during the 4-step process replenishes the Ga-droplet, and maintains VLS growth.The VS-grown shell surrounding the inversely tapered core compensates the tapering by a gradually increased shell layer thickness towards the bottom of the NW, thus, resulting in a completely uniform, non-tapered appearance of the outer sidewall facets.
The dynamic variation of shell thickness and NW-core diameter along the NW growth axis is further substantiated by cross-sectional EDXS compositional maps, shown on the right of figure 7(a).The two maps originate from a FIB-cut performed on different sections of two adjacent NWs, i.e. top image corresponding to a section from the top third of a NW, and bottom image from the bottom half of another NW, respectively.From the Sb versus As distribution, we clearly recognize again the Sb-rich core and Sb-deficient shell, and the much wider GaAsSb core/narrower shell towards the NW top.Quantitative analysis from both elemental maps, as well as line scans recorded over the NW cross-section (see supplementary), yield an Sb-content in the VLS-core of ∼26% and ∼20% in the VS-shell, respectively (5% accuracy of EDXS analysis).Such distribution of lower Sb-content in the VS-shell and higher Sb-content in the VLS-core of self-catalyzed GaAsSb NWs was also observed by Conesa-Boj et al [13].Note also, the values for both core and shell, as measured by EDXS here, are very close (within experimental error) to those derived by the modeling of the PL data, confirming the validity of the approaches presented in figure 3.In addition, we found enrichment of As in the six equivalent { ̅ 112} corner facets of the VS-GaAsSb shell, yielding about a factor of 2 lower Sbcontent (i.e.∼10%) in those regions compared to the rest of the shell.Such spontaneous alloy composition ordering with Sbdeficient { ̅ 112} facets can be directly understood by the curvature-induced capillarity and associated differences in diffusion and bonding mechanism of the respective growth species at these nanofacets [41][42][43], as noted previously also in GaAsSb NWs [13] and other III-As-Sb NWs [21].
Most importantly though, the Sb-contents in VLS-core and VS-shell are quantitatively the same in both EDXS maps, recorded in the top and bottom parts of the NW (see supplementary).This verifies the compositional uniformity of the core-shell GaAsSb heterostructure along the NW-axis, as suggested earlier by the Ga-rate dependent growth studies.Line scans performed along the growth axis of the NW further reflect this characteristic, as displayed in the center image of figure 7(a).The data from a scan recorded through the center of the axis (measuring the global Sb-content of both core and shell in projection through the total NW diameter), shows an overall rather constant Sb-and As-content along the NW length.Only towards the bottom of the NW the apparent Sbcontent is slightly decreased (i.e. from ∼25% to 23%), which is expected due the relative increase in VS-GaAsSb shell thickness that contributes to the global Sb-content.
Finally, microstructural analysis was performed on the same NW (as depicted on the left of figure 7(a)), by employing both high-resolution STEM imaging and selected area electron diffraction (SAED).Images and diffraction patterns were recorded in a < ̅ 11 0> zone axis corresponding to the side facets of the NWs.For the analysis, the size of the SAED aperture was adjusted to the full length of the NW to gain representative diffraction pattern information of the whole NW.The SAED pattern (figure 7(b), top left) shows pure zinc-blende (ZB) crystal phase, evidenced by the distinctly periodic diffraction spots with a separation reflecting the lattice parameter of ZB-phase GaAsSb of Sb-content of ∼20%.The pattern shows no sign for inclusions of other phases nor any rotational twin defects, which would induce other intermittent diffraction spots or splitting of spots into twin-pairs (as in the case of rotational twins) [21].In correspondence with the SAED pattern, the HR-STEM images recorded in HAADF mode, as shown in figure 7(b) for two different resolutions, nicely confirm the phase-purity of the NW.The images directly reveal the ZB-type 'ABCABC' stacking throughout the NW.Since the phase-pure ZB structure is observed irrespective of the position along and across the NW, we can assume that the crystal structure is defined during the VLS-core growth and further replicated by the concurrent VSshell surrounding it.Such crystal structure transfer is not surprising, and has been readily observed in III-V or even III-V/ group-IV core-shell systems [41][42][43][44][45].Moreover, the phase-pure crystal structure observed here agrees also well with other reports [13,14,17,46], stating that GaAsSb NWs with Sbcontent in excess of ∼15%-20% eliminate all twin domains and establish completely pure ZB-phase, irrespective of growth method.This is mainly attributed to the much smaller ionic bonds (lower crystal ionicity) of III-Sb based materials compared to Sb-free III-V NWs [47,48], where the latter are more prone to polytype intermixing.

Conclusions
We developed an advanced growth process, and detailed understanding of underlying thermodynamic and kinetic mechanisms, for the realization of extended, self-catalyzed GaAsSb NWs on Si with remarkably pure and homogeneous properties.By performing MBE growth at comparably hightemperature (660 °C), growth is brought to an Sb-saturated regime, where the concurrent Sb-and As-desorption from the liquid catalyst-droplet at increased Sb-vapor pressure, or variable Ga/Sb-ratios, lead to a characteristic insensitivity of Sb-incorporation on changes in group-III elemental supply during the VLS growth process.Yet, the dimensions of asgrown GaAsSb NWs depended strongly on group-V or group-III supply, whereas the morphology of all NWs presented here exhibited a surprisingly uniform, non-tapered nature over the entire NW length-independent of the supply rates of the growth species.The unique, non-tapered morphology was found to result from the equilibration of an original, inversely tapered VLS-NW morphology by a concurrent VS-grown shell, that is simply determined by the competition between step-nucleation, step-flow growth and Ga-diffusion limited growth on the NW-sidewall surfaces.From specific growth time series, we have shown that under sufficiently high Ga-diffusion the formation of a non-tapered morphology is mediated by step-flow growth of the VS-shell, which is a self-terminating process.
The intrinsic core-shell structure, consisting of a VLS-GaAsSb core and VS-GaAsSb shell, was further examined by a fully correlated and non-destructive approach that combined μ-PL experiments, and modelling of electronic bandgap and Sb-content based on optical transition energies and strain.The data was directly compared with high-resolution STEM-EDXS analysis, showing consistently slightly larger Sb-content in the VLS-core (lower bandgap energy) compared to the VS-shell.The STEM analysis and correlated electron diffraction further highlighted a completely phase-pure ZB crystal structure throughout the entire NW, without the formation of any twin defects.Given the extraordinary independence of Sb-content with group-III elemental supply, we ultimately developed multi-step growth procedures, i.e. 4-step processes, by which the Ga-rate was incrementally increased to maintain VLS growth up to very long NW-length while minimizing -diameter.We demonstrated up to ∼7.5 μm long, phase-pure GaAsSb NWs with Sb-content of around 26%, with very uniform, fully non-tapered morphology and complete absence of compositional gradients along the entire NW-axis.Such high-quality NWs were shown to exhibit sharp and intense, long-wavelength PL emission at ∼1200 nm with remarkably narrow linewidth (FWHM < 15 meV).As will be shown in a forthcoming paper [49], the combination of GaAsSb NWs with such excellent uniformity control over extended lengths and further integration of surface-passivating layers, enables, for the first time, direct observation of coherent light sources and lasing action from bulk ternary GaAsSb gain material.

Figure 2 .
Figure 2. (a) SEM images (45°tilt) of typical NWs for a Ga-rate of 0.6-0.9Å s −1 (the scale bar is valid for all images); (b) corresponding quantitative analysis of relevant morphology parameters NW-length (black), NW-diameter at bottom (green) and top (orange), and Gadroplet diameter (blue); (c) anticipated internal growth structure, consisting of a ∼2 μm long/60 nm wide GaAs stem, an extended VLS-GaAsSb NW section on top, where the resulting NW-diameter at the tip is defined by the Ga-droplet diameter, and a VS-GaAsSb shell surrounding the NW leading to an equilibrated total diameter.

Figure 3 .
Figure 3. (a) μ-PL spectra at 10 K of a single NW with Ga-rate of 0.9 Å s −1 at different pump fluence; (b) average PL peak energies as a function of the Ga-rate.The high energy peak is associated with the GaAs stem and the low energy peaks to the GaAsSb segments (GaAsSb 1 corresponds to VLS-GaAsSb, and GaAsSb 2 to VS-GaAsSb shell); (c) simulated bandgap of the GaAs stem as a function of the Sb-content of the VS-GaAsSb shell for the different samples (i.e.different thicknesses of the VS-GaAsSb shell on the GaAs stem).The red data points are the measured PL peak energies of the GaAs stem (orange in (b)), which lie on the curve of the respective sample and, thus, allow estimates of the Sb-content of the VS-GaAsSb shell; (d) Sb-content as a function of Ga-rate.Blue: Sb-content of VS-GaAsSb as estimated from (c); black: Sb-content directly determined from the low energy PL peak position (black data in (b)) and the relationship between bandgap and composition from [34].

Figure 4 .
Figure 4. (a) SEM images (45°tilt) of typical GaAsSb NWs as obtained for a growth time of 30-120 min.The scale bar is valid for all images; (b) corresponding morphological parameters, such as NW-length, -diameter (at bottom and top) as well as -droplet diameter, as a function of growth time.

Figure 5 .
Figure 5. SEM images of GaAsSb NWs obtained after 120 min of growth; (a) top-view of NW-tip (10 μm pitch), (b) 45°tilted-and top-view at smaller pitch of 1 μm; (c) Side-view of the NW tip at 10 μm pitch (measured in 〈 ̅ 110〉 zone axis).The angle α gives the inclination of facets on the sidewall and tip region with respect to the surface normal along the NW-axis.

Figure 6 .
Figure 6.(a) SEM images (45°tilt) of GaAsSb NWs grown by 4-step process with incrementally increasing Ga-rate of 0.4 Å s −1 , 0.6 Å s −1 , 0.8 Å s −1 and 1 Å s −1 with total growth time of 105 min; (b) μ-PL spectra of a single NW from the same sample measured at 10 K and different pump fluences.

Figure 7 .
Figure 7. (a) STEM-EDXS map of the Sb-distribution over the entire GaAsSb NW (left) and corresponding position dependence (center) of both elemental Sb and As, as obtained by an EDXS line-scan performed along the very center of the same NW (marked by arrows); (right) Cross-sectional EDXS maps from a region near the top (upper image) and bottom (lower image) of different NWs, illustrating the core-shell NW heterostructure consisting of a VLS-GaAsSb core (higher Sb-content) and VS-GaAsSb shell (lower Sb content), as well as Sb-deficient { ̅ 112} corner facets; (b) microstructural analysis evidencing phase-pure ZB crystal structure, as confirmed by the SAED pattern (top left) and high-resolution structure imaging of arbitrary regions probed along the NW sidewalls.Clear 'ABCABC ZB-phase stacking sequences are observed without any twin defects.Images and diffraction patterns are taken in a < ̅ 110> zone axis corresponding to the side facets of the NW; the [111B] growth direction is further marked by the white arrow.