P Rueda-Fonseca

M Orrù

E Bellet-Amalric

E Robin

M Den Hertog

Y Genuist

R André

S Tatarenko

J Cibert

Diffusion-driven growth of nanowires by low-temperature molecular beam epitaxy

Keywords: nanowires, molecular beam epitaxy, electron microscopy, ZnTe, EDX

With ZnTe as an example, we use two different methods to unravel the characteristics of the growth of nanowires by gold-catalyzed molecular beam epitaxy at low temperature. In the first approach, CdTe insertions have been used as markers, and the nanowires have been characterized by scanning transmission electron microscopy, including geometrical phase analysis, and energy dispersive electron spectrometry; the second approach uses scanning electron microscopy and the statistics of the relationship between the length of the tapered nanowires and their base diameter. Axial and radial growth are quantified using a diffusionlimited model adapted to the growth conditions; analytical expressions describe well the relationship between the NW length and the total molecular flux (taking into account the orientation of the effusion cells), and the catalyst-nanowire contact area. A long incubation time is observed. This analysis allows us to assess the evolution of the diffusion lengths on the substrate and along the nanowire sidewalls, as a function of temperature and deviation from stoichiometric flux.

I. INTRODUCTION

The core-shell nanowire (NW) configuration is extremely flexible and virtually any material combination, with any mismatch (up to a critical thickness which can be large) 1 or no mismatch, can be realized. A first, obvious application in semiconductor materials is the fabrication of a shell with a larger bandgap in order to reduce the effect of surface defects on the properties of carriers confined in the core. 2,3 A tapered (cone-shaped) configuration may even be tailored to improve light extraction. 4 A natural extension is a dot embedded in a NW, where the shape of the insertion controls the confinement of the carriers -electrons and holes. Many opportunities are then opened for a precise engineering of the envelope functions, not only through the natural band offsets, but also through a proper design of the built-in strain and the associated piezoelectric field and deformation potential. [5][6][7] In particular, it allows one to engineer the hole states in a semiconductor dot and tailor their orbital and spin states: a flat insertion induces a strain configuration (hence a light-hole heavy-hole splitting) quite similar to that of a dot made of the same materials but grown by the Stranski-Krastanov mechanism, while the configuration is reversed in a core-shell NW 7 or an elongated dot. This opens the opportunity to fully design the photonic properties of the nanostructure, and its magnetic properties if magnetic impurities are added.

To grow a well-controlled core-shell structure, two different strategies can be implemented: (1) start with the a) Electronic mail: joel.cibert@neel.cnrs.fr growth of the core under conditions which favor the diffusion of adatoms on the sidewalls and therefore the axial (or longitudinal) growth, then change the growth conditions in order to enhance the radial growth and form the shell. For instance, the substrate temperature is decreased between the core and shell growth steps. (2) use conditions where a moderate diffusion occurs along the sidewalls, allowing that both axial and radial growth occur simultaneously, resulting in cone-shaped (tapered) structures; this can be achieved using the same, moderately low temperature for the growth of the whole structure.

In the present study we describe the growth mechanisms of ZnTe NWs and CdTe-ZnTe structures by molecular beam epitaxy (MBE). The specific properties of II-VI materials can be fully exploited in such heterostructured NWs, with applications in photonics, photodetectors, 8 single photon emitters, 9 photovoltaics 10 including type-II configurations, various sensors, and magnetic objects. 11 In the case of tellurides, (Zn,Mg)Te shells have been shown to enhance the photoluminescence efficiency by several orders of magnitude with respect to that of bare ZnTe NW. 12 Moreover, previous studies of heterostructured NWs based on tellurides (of Cd, Zn, Mg, Mn) suggest that they offer a great flexibility in their design in order to control the light-hole / heavyhole character of the confined ground state of holes. 7,[11][12][13][START_REF] Artioli | 17th International Conference on II-VI compounds and related materials[END_REF][START_REF] Jeannin | Nanowires Workshop -2015[END_REF] A low growth temperature (350 • C) was chosen to minimize the desorption of adatoms, particularly in view of the insertion of CdTe segments in the ZnTe NWs. We obtain tapered NWs with smooth sidewalls, and a well controlled insertion of CdTe and (Cd,Mn)Te. Characteristic parameters are extracted using the analytical results of a model of diffusion-limited growth; their dependence on growth temperature and stoichiometry, and on the shape of the gold nanoparticle, is discussed.

The paper is organized as follows: the experimental results are described in section II and used in section III to extract significant parameters of a diffusion-limited model of growth adapted to our findings (presented in the appendix). Section IV discusses the main aspects of the growth and their consequences. • surface reconstruction of smoothed ZnTe layers, 18,19 and formation of a Au-induced 3

√ 3 × 3 √ 3 R30
• surface reconstruction. 18,19 NWs deposited on a holey carbon-coated copper grid were imaged by energy dispersive x-ray (EDX) spectrometry using a FEI Tecnai Osiris scanning transmission electron microscope equipped with four silicon 157 drift detectors, as described in Ref. 20. Other NWs, still standing on the substrate, were imaged by scanning electron microscopy (SEM) using a Zeiss U55 operated at 10 keV, with a spatial resolution around 1 nm. Selected NWs, attached to the substrate in the cleaved sample geometry, 21 were imaged by scanning transmission electron microscopy (STEM) on a probe corrected FEI Titan working at 300 kV, and the lattice spacing in the high resolution images was analyzed by the geometrical phase analysis (GPA) 22 . Scan noise was removed from the images by using the unperturbed ZnTe lattice as a reference. 23

B. Experimental results

Two types of ZnTe NW can be grown: cone-shaped (tapered) NWs, and cylinder-shaped NWs, as indicated by the green and blue arrows, respectively, in the inset of Fig. 1. The main characteristics [START_REF] Rueda-Fonseca | [END_REF] of cone-shaped NWs are the zinc-blende structure with the NW axis parallel to the 111 direction, a significant lateral growth on the sidewalls (formed by 112 facets visible for thick enough NWs) and a crater surrounding the base of the NW. In contrast, cylinder-shaped NWs exhibit the wurtzite structure with the NW axis along the c-axis, no contribution from lateral growth detected and a pyramid at the base of the NW clearly visible in the inset of Fig. 1. The flux on the substrate far away from any NW results in the growth of a two-dimensional layer: its thickness h was determined from the SEM observation of a cleaved edge.

As shown in the plot of Fig. 1, the wurtzite NWs are characterized by a reasonably compact distribution of their length, and of the base diameter (which actually fairly matches the typical gold particle diameter). This is in sharp contrast with the statistics on the zinc-blende NWs: (1) except for the shorter NWs, the base diam-eter increases significantly; (2) we observe a broad distribution of their length, with one order of magnitude between the longest and the shortest NWs; (3) there is a clear trend suggesting a correlation between the base diameter and the NW length.

Such a large dispersion cannot be explained by the distribution of gold particle size (we did not observe any significant difference in the external diameter of the gold particle present at the tip of different NWs), or by the molecular flux. In the following we will (1) use CdTe markers to reveal the presence of an incubation time, (2) analyse the distribution obtained when growing at higher temperature to reveal the role of the shape and size of the gold nanoparticle, and (3) use a model adapted to the present growth conditions, which is amenable to analytical expressions, to examine the role of adatom diffusion.

CdTe markers

In order to obtain precise information on a single NW, we used a marker technique: 24,25 we inserted 10 thin CdTe markers (stoichiometric Cd+Te flux from the CdTe cell) during the growth of a ZnTe NW sample (stoichiometric Zn+Te flux from the ZnTe cell), see Fig. 2a. The EDX image of a NW deposited on a grid (Fig. 2b) clearly reveals 7 regularly spaced CdTe insertions (and another one at the broken end). On such a broken NW, we cannot exclude that the two missing insertions were lost in the harvesting process.

In order to rule out any effect of harvesting, as-grown NWs from the same sample, still on the substrate, have been visualized by TEM, and two cone-shaped NWs very different in length (520 and 70 nm respectively) have been analyzed by GPA. The zinc-blende structure was confirmed for both NWs.

The topmost half of the longer NW (NW1 in Fig. 2c-f) could not be analyzed due to vibrations and charging effects. In the lower half, four CdTe insertions are clearly identified (Fig. 2f). The period is 68 nm, with 64 nm for the ZnTe spacers and 4 nm for the CdTe insertions: this ratio is in good agreement with the ratio of integrated lateral flux, which was ZnTe:CdTe∼15, suggesting that the growth of this part of the NW is mainly governed by the adatoms resulting from the flux to the sidewalls and diffusing to the gold nanoparticle. This preponderant role of the lateral flux is confirmed by the plot of the length of CdTe and ZnTe components of various heterostructured NWs grown using molecular beams with very different angles of incidence (Fig. 3a).

On the shorter NW (NW2 in Fig. 2g,h), only one CdTe insertion is identified, suggesting a long incubation time.

The visible length of the nanowire, L, the radius of the NW, the radius of the gold nanoparticle, and the radius of the gold-tip contact are available from the HAADF images in Fig. 2 (see also Fig. 4); the distance of several CdTe insertions from the tip, d n , are measured on the GPA images. Figure 3b describes the growth of a NW we plot (squares) Ln vs. hn (as defined in (b), and marked here by the red arrows) at the time of insertion of CdTe, and L at the end of the growth, vs. h. NW3 is the longest NW observed by SEM on the same sample. The hatched triangle represents the masking by the 2D layer (i.e., the thickness (h -hn) remaining to grow after the formation of the CdTe insertion). The solid lines are the fit with Eq. A6, with the same values of the diffusion length λs = 18 nm on the substrate and λNW = 78 nm on the sidewall facets, and different incubation times. We assumed that the gold nanoparticle was close to a full sphere from the beginning of the growth, with the contact diameter 7.7 nm (NW1) and 7.9 nm (NW2), as measured on the HAADF image, and assuming 7.3 nm for NW3. An additional constraint (not shown) is that the diameter of the crystalline core at the base of the NW agrees with Eq. A9. With these values of the parameters, we deduce an incubation time for NW1 and NW2, and an immediate start for NW3.

with a CdTe insertion, with the characteristic lengths involved. The length L is the visible length of the NW, a part of the NW being hidden by the parasitic growth of the 2D layer. The visible length L n at the moment of the growth of the CdTe insertion is obtained as

L n = L + h -d n -h n ,
where the total thickness of the parasitic 2D layer, h ∼ 120 nm, was measured on a cleavage plane, and its thickness at the moment of the growth of the CdTe insertion, h n , is deduced from the growth sequence. Fig. 3c plots L(h) and L n (h n ) for the two NWs of Fig. 2. Even without the lines which show the fit described in section III below, it appears that the NWs started to grow after a significant incubation time. This will be addressed more quantitatively in the remainder of the paper, and possible reasons will be discussed in Section IV. Note that the existence of this incubation time was confirmed by exposing a series of samples, prepared under the same conditions, to the Zn+Te flux for 2, 10 or 30 min.: the number of nanoparticles having catalyzed the growth of NWs was found to increase. Full details are given in Ref.19.

Gold particle

Figure 4a shows the gold catalyst on a NW with the wurtzite crystal structure. The NW was long enough that it vibrates under the electron beam near the tip, so that only (0002) planes are visible in the NW; yet the wurtzite structure was clearly observed closer to the NW base, as shown in the inset of Fig. 4a. The NW exhibits a flat tip, and the shape of the gold particle is close to a half sphere with a diameter matching the NW diameter. This is close to the shape assumed by the gold particles sitting at the surface of the buffer layer before opening the shutter to start the growth of the NWs. 18,19 This configuration is well known for III-V NWs with the wurtzite structure, and it is associated to a nucleation at the edge of the < 0001 > facet forming the top of the NW. 26 An extensive, statistically significant study of the interface is however out of the scope of the present paper.

All tapered nanowires which have been observed by TEM have the zinc-blende structure. Long tapered NWs show a gold particle with a shape closer to a full sphere, as shown in Fig. 4b. This is expected if the nucleation takes place on an inclined facet. 27 Indeed, the interface is far from being flat, and a meniscus (or incompletely formed facet) is clearly apparent. Hemispherical gold nanoparticles are also observed by SEM at the tip of tapered NWs, particularly at the tip of the shorter ones. Note that a change of shape -and of facet morphology -has been observed on III-V NWs, and may even take place regularly during the growth of the NW. 27 In addition, several facets (3 in the simplest case) may form, not necessarily at the same time. For such full-sphere nanoparticles, three characteristic diameters may be considered: the measured diameter of the full sphere, 2R f ull , the diameter of the initial particle which is approximately half-sphere, 18,19 2R half , and the diameter of the contact area between the particle and the NW tip, 2R tip . If the shape change from half sphere to full sphere takes place at constant volume, the droplet diameter is slightly reduced, from 2R half to 2R f ull = 2R half /2 1/3 , i.e., by 25%. More significant is the fact that the diameter at the interface between the gold particle and the NWthe contact diameter 2R tip -is definitely smaller. It is this diameter which defines the diameter of the growing NW (hence the lateral size of a quantum dot embedded in the NW, but also partly the growth rate, as recalled later on). Typical values of the diameter of the gold particle are 20 nm. The diameter of the NW neck below the spherical gold particle is more difficult to measure; typical values measured by SEM are around 15-20 nm but this includes an amorphous or ill-crystallized surface layer, which is due either to some oxidation of the NW, or to post-growth deposition; the crystalline core imaged by TEM is thinner, 6 to 10 nm (see Fig 4,

The role of the gold particle shape and size

With the previous samples, we have explored the growth at a temperature (T growth = 350 • C) where the distribution of gold nanoparticles is relatively narrow. Figure 5a shows a SEM image of a sample obtained by first dewetting the gold nanoparticles at 350 • C, and rapidly increasing the temperature to 375 • C to start the growth with an additional Te flux. It displays cylindershaped NWs (blue arrows), and cone-shaped NWs (green arrows) -quite similar to samples grown under stoichiometric conditions at 350 • C. This indicates that the increase of the sample temperature and the presence of a higher Te flux compensate each other, a hint that the evaporation of Te atoms is probably the limiting mechanism. Also visible are aborted or badly formed NWs (yellow arrows) and thick, inclined NWs (bottom right corner).

Fig. 5b plots the volume of the gold nanoparticle, vs the NW length. As observed previously in Fig. 4, the nanoparticles assume two different shapes (close to halfsphere and close to full sphere), which are identified in Fig. 5 by different symbols. Again one observes a stronger dispersion in the NW length for the cone-shaped NWs than for the cylinder-shaped ones. But also one observes (1) a significant dispersion in the nanoparticle size, which is due to an evolution of the nanoparticles during the ramp to the higher growth temperature, and (2) a correlation between the shape of the gold particle at the tip (half-sphere or full-sphere) and the length of the coneshaped NWs: the two sets of NWs occupy two different areas, delineated by the grey lines.

As a result of the dispersion in the nanoparticle size, the trend between the base diameter and the NW length (Fig. 5c) appears as partially blurred when compared to Fig. 1. To cope with this dispersion, in Fig. 5d we plot the ratio of the base diameter to the size of the gold nanoparticle, R/R half where R half is the radius of the half-sphere with the same volume (see Fig. 5b). This plot will be used in the following section, in the frame of a growth mechanism taking into account the diffusion of adatoms and the incubation time mentioned previously, but also the effect of the nanoparticle size and shape: the results of this model are summarized by the lines in Fig. 5d,e, to be discussed in section III.

III. DIFFUSION-LIMITED MODEL

The growth of nanowires is strongly influenced by two parameters: the nucleation at the Au catalyst particle, and the diffusion of species on the surfaces. On one hand, complex models based on growth kinetics, involving the interaction of atoms in various thermodynamic states at the Au-NW interface, have been proposed for the VLS growth of III-V NWs. 28 These models rely on transition state kinetics driven by the minimization of the free energy of the total system. On the other hand, diffusion- dependent nanowire growth models have also been developed . 29 In these type of models, the morphology (length and shape) of the nanowires is directly related to different values of the diffusion length on the substrate and along the NW sidewalls. These models are also known to apply to a wide range of growth conditions of III-V and Si NWs 30 and even to CdTe NWs. 31 In this section we focus on the role of adatom diffusion on the growth of ZnTe NWs by MBE at low temperature: any possible effect of the nucleation at the gold particle / NW tip is ignored. We obtain analytical expressions which we can readily exploit to extract quantitative parameters (diffusion lengths, incubation times) from the plots in Fig. 1, 3, 5.

A. Axial and lateral growth rates in the diffusion-limited model

The description is made simpler if we keep in mind that:

• The density of Au droplets (and even more the den-sity of NWs) on the substrate is low enough that we can consider a single, isolated NW.

• The NW is perpendicular to the substrate surface.

• The temperature is low enough that re-evaporation is negligible: the diffusion length is defined by the incorporation of adatoms on the substrate or on the NW facets.

• We observe a NW growth rate significantly larger than that of the 2D layer; hence we calculate only the contribution of adatoms diffusing from the substrate and the NW sidewalls to the gold particle. Indeed, the contribution of the direct flux onto the Au droplet is not too different from the contribution to the 2D layer away from the NW (they are equal for a half-sphere droplet and complete sticking); hence the length we calculate is close to the length visible above the 2D layer.

The diffusion-based NW growth model adapted to these conditions is described in Appendix A. It involves the general solution of the diffusion equations of adatoms on the NW sidewalls in 1D, and on the substrate surface in 2D with a circular symmetry. It assumes complete trapping at the tip of the NW (catalyst acting as a perfect sink). 29 It results in simple analytical relationships between the length L of the NW (axial growth) and the thickness h of the 2D layer far from the NW (growth in the absence of catalyst), on one hand, and between L and the radius R at the NW basis (lateral growth), on the other hand. These relationships are derived from Eq. A6 and A9 in Appendix A where we set all sticking coefficients to unity (this is a reasonable approximation for the ZnTe surfaces at 350 • C):

h R 0 = 1 2 π tan α ln 1 + tan α π λNW λs 2 cosh( L+ λs λNW ) -1 1 + tan α π λNW λs 2 cosh( λs λNW ) -1 (1) and R -R(0) R 0 = 1 2 π tan α λ s λ N W 2 × ln 1 + tan α π λNW λs 2 cosh( L+ λs λNW ) -1 1 + tan α π λNW λs 2 cosh( λs λNW ) -1 (2)
where λ s and λ N W are the diffusion length on the substrate and along the NW sidewalls, respectively, R 0 is the radius of the contact area between the gold catalyst and the NW tip, R(0) is the initial radius of the gold nanoparticle. We have replaced the ratio of lateral to substrate flux by its value, tan α π , and we have defined an effective diffusion length λs , which is small with respect to λ N W and kept constant in the calculation, as discussed in Appendix A.

Examples of Eq. 1 are displayed in Fig. A2a: the initial growth rate (for L ≪ λ N W ) is governed by the diffusion on the substrate; for most of the NWs described here, the final length L ≫ λ N W so that the growth rate during most of the growth is the asymptotic growth rate due to the lateral flux, given by dL dh ≈ 2 tan α π λNW R0 . The lateral growth at the basis of the NW (Eq. 2) reflects the fact that the adatom density on the sidewalls at the basis of the NW is linked to the adatom density on the substrate, so that the difference in the incorporation rates leads to dR dh ≃ λs λNW 2

. Figure A2b shows that this for most of the growth, with a small correction due to the lateral flux, and except for the initial step where both the NW length and the lateral growth are small. We will use Eq. 2 in the analysis of experimental data, but the asymptotic form suggests that the diameter of the NW at its basis is a rather good measure of the time between the actual start of the NW growth and its end.

B. The model applied to experimental data 1. The markers technique

The most complete data are those obtained on single NWs with CdTe insertions, Fig. 3. A reasonable fit (black solid lines) is obtained with the same values of the diffusion lengths for both NWs (λ s =18 nm and λ N W =78 nm), assuming that the growth of the NW does not start immediately after the opening of the cell. A further criterion for the fit (not shown) is that the measured and calculated values of the base diameter coincide. The shape of the gold particle at the tip of NW1 and NW2 is close to a full sphere: the fit in Fig. 3 assumes that the nanoparticles turned very rapidly to a full-sphere; hence in Eq. A9 the initial diameter, 2R(0), and the contact diameter during the growth, 2R 0 , are both taken equal to 2R tip . Moreover, we have assigned to 2R tip the diameter of the crystalline core of the NWs measured by TEM, ≃ 7.7nm for NW1 and 7.9 nm for NW2. The length measured for NW3 is well fitted assuming the same values of diffusion lengths, and 2R tip = 7.3 nm. Actually, there is a 2.5 nm thick amorphous layer around the NW, which can be due to the oxidation of the NW or to a post-growth deposition. If we take the external diameter instead of that of the crystalline core in Eq. A9, an as-good fit is obtained with λ N W unchanged and λ s increased by 15 to 20% (not shown).

The main conclusion here is that the broad range of length values observed involves a significant incubation time: the 2D layer thickness was already 30 nm when NW1 started, and 100 nm for NW2. This delayed growth is the main reason for the length dispersion of the 3 NWs shown in Fig. 3.

It will be further confirmed now using a complementary approach: indeed a similar information can be deduced from the observation of an ensemble of NWs (without markers) and the statistics on the length / base diameter relationship.

Axial vs. radial growth

We start with the results shown in Fig. 5. Keeping in mind the two possible shapes of the gold nanoparticle, close to half-sphere or close to full sphere, we may expect three typical behaviors: NWs driven by a nanoparticle staying half-sphere up to the end of growth (case 1 below), NWs driven by a nanoparticle turning to full sphere from the beginning (case 2), and nanoparticle turning from half-sphere to full sphere shortly after the growth start (case 3). As the growth rate is expected to increase as the contact diameter decreases, the full-sphere-NWs are expected to grow faster than the half-sphere-NWs in spite of a larger nanoparticle volume: the relevant diameter is 2R tip ∼6 to 8 nm in the first case, against 2R half ∼15 to 18 nm in the second case.

• (1) One clearly identifies in Fig. 5d a series of half-sphere NWs with a large base diameter and small length, which we tentatively ascribe to the extreme case of full-time half-sphere NWs. Assuming 2R(0) = 2R 0 = 2R half in Eq. A9, with the additional assumption that the longest NW of the series started to grow immediately, a reasonable fit is obtained as shown by the solid line, with λ s =38 nm and λ N W =126 nm. The different values of the NW length, from the shortest to the longest, correspond to (i) increasing values of the growth duration, with the shortest NW starting on a 2D layer of thickness ∼ 75 nm (40 nm still to go) up to the full h = 115 nm for the longest one (immediate start), (ii) a decreasing nanoparticle size measured within this series of half-sphere NWs (green crosses in Fig. 5e). Taking both effects into account, and using a purely heuristic dependence between the contact area and the final length (dashed line in Fig. 5e), we obtain the green solid line in Fig. 5e.

• (2) For the opposite extreme, the case of a full sphere since the beginning, we keep the same values of the diffusion lengths and decrease the value of 2R(0) = 2R 0 = 2R tip to 7.3 nm to obtain the largest length observed: we then obtain the lowest red dashed line in Fig. 5d; note that the previous dashed and solid lines in Fig. 5e satisfactorily account for this experimental point.

• (3) The second red dashed line in Fig. 5d is obtained using 2R(0) = 2R half and 2R 0 = 2R tip =7.3 nm in Eq. A9, i.e., starting the growth with a half-sphere and rapidly turning to a full sphere.

Intermediate data -in particular half-sphere data below the full line, or full-sphere data between the two dashed lines -can be ascribed to NWs with a non-circular shape of the nanoparticle, or a shape which evolves during the growth. Finally, the green solid line in Fig. 5e separates the half-sphere NWs from the full-sphere NWs, it also constitutes a good average fit of the base-diameter / length dependence.

A good overall fit is also obtained using the same procedure for the other sets of data. For instance, in Fig. 1, we had to assume a diameter decreasing from 2R half =20nm to 2R tip =6 nm, and diffusion lengths λ N W =78 nm and λ s =23 nm, close to those of the sample in Fig. 3, as expected since the growth conditions are the same (the slight difference is at least partly explained that we used diameter values obtained either for the crystalline core observed by TEM or the overall NW imaged by SEM). For a sample grown under Te excess (not shown 19 ), slightly lower values of the diffusion lengths, λ N W =57 nm and λ s =18 nm, are obtained, assuming a similar distribution of the gold nanoparticle size. All values are gathered in Table I below.

IV. DISCUSSION AND CONCLUSION

In summary, the large dispersion in the length of the zinc-blende ZnTe NWs is ascribed to the presence of two steps in the growth catalyzed by gold nanoparticles, which initially feature a half-sphere shape: the start of the NW growth, and the evolution of shape of the gold nanoparticle from half-sphere to almost full sphere. The longest NWs have started immediately with a nanoparticle rapidly turning to full-sphere, hence a small contact radius, with facets or a meniscus at the interface. The shortest NWs started with a delay and with a nanoparticle staying with a half-sphere shape on top of the 2D layer and the NW tip. Some nanoparticles never give rise to a NW or even are buried into the 2D layer. The direct effect of the particle size on the growth rate exists but it is mostly hidden by the existence of the incubation delay.

Within this scheme, the characteristics of the NWs are well accounted for using a simple diffusion-limited model, with two diffusion lengths, λ N W on the NW sidewalls and λ s on the substrate. Table I shows the values used to fit our data: the decrease induced by adding a Te flux suggests that the limiting process under these conditions is the diffusion of Zn (the diffusion length of Zn is reduced if the density of Te adatoms increases). Increasing the temperature increases the diffusion length under Te excess, presumably due to an activation of Te desorption.

Growth λNW (nm) λs (nm) Fig. With such values of the diffusion length λ N W on the NW sidewalls, the growth rate at the tip of a NW with a length of several 100 nm is mainly due to the lateral flux, J N W , and dL dh ≃ 2 tan α π λNW R0 . This is important as it determines the length of a quantum dot inserted in the NW, but also its composition if the material is an alloy, for instance a diluted magnetic semiconductor. The diameter of the quantum dot is determined by the contact diameter (2R 0 ).

Our uncertainty on the value of R 0 (crystalline core or the whole NW including the amorphous shell), and that on the value of h, have a straightforward impact on the value of λ N W . In addition, sticking coefficients lower than unity will change the value of λ N W , by a factor αs αNW (see Eq. A4).

The value of λ s , the diffusion length on the substrate, is mainly deduced from the measure of the lateral growth at the basis of the NW. Figure A2 suggests that for the present values of the parameters, both the effect of the depletion of adatoms around the NW basis and the contribution of the lateral flux are small, and moreover they partially compensate each other. Here again, sticking coefficients lower than unity will affect the absolute value of λ s , as we actually determine ( λs λNW ) 2 αNW αs . Note that our values of λ s are quite small, but they are of the same order as the size of the structures observed at the bottom of the NWs: a crater or a zone with no growth in the case of zinc-blende NWs, signaling a transfer of material from the substrate to the NW, and a pyramid progressively formed at the bottom of wurtzite NWs, as the signature of a transfer from the NW to the substrate.

We have noted that the effect of the additional Te flux and of the growth temperature (Table I) suggests that it is the diffusion of Zn which limits the growth rate -even if a role of Te diffusion is not totally ruled out. The growth of ZnTe NWs thus strongly differs from the growth of self-assembled GaAs NWs, which is characterized by a strong diffusion of Ga towards the tip, and a growth rate determined by the As 4 flux to the Ga droplet 32 , either directly from the effusion cell, or by desorption 33 . In our case, we observe the opposite behavior, that adding a Te flux decreases the axial growth rate by decreasing λ N W .

An important result of the present study is the evidence of an incubation time between the onset of the molecular beam and the start of the NW growth. Different systems have been shown previously to exhibit significant incubation times. One reason may be the formation of the proper catalyst/semiconductor interface. When GaAs NWs are grown by gold-catalyzed MBE on a silicon substrate under vapor-liquid-solid conditions, 34 an initial step is observed where "traces" creep on the Si surface until they meet a GaAs nucleus. This is interpreted as due to a large difference in the interface energy on the Si substrate and on the GaAs nucleus. We do observe such traces (yellow arrows in Fig. 1 and5), but in our case the gold nanoparticles are formed on a ZnTe buffer layer. For other preparation and growth conditions, the incubation is attributed to the formation of a pinhole in the Si oxide, and the formation of the Ga droplet 35,36 . Another contribution may be brought by the existence of a threshold in the composition of the catalyst droplet. In the case of Si NWs on Si substrates, depending on the growth conditions, this threshold has been discussed in terms of supersaturation of the gold droplet, 37 or in terms of diffusion within the solid catalyst to achieve its fusion (transition from vapor-solid-solid, VSS, to vaporliquid-solid, VLS conditions). 38 Such a transition from VLS to non-VLS conditions was observed to depend on the As/Ga ratio for GaAs NWs on Si. 36 In all cases the incubation time is expected to increase with the catalyst size, which is indeed a trend which is suggested by the catalyst size dependence on final NW length (data in Fig. 5, and the heuristic dependence used in the overall fits). A dispersion in the value of the diffusion length on the substrate may enhance the dispersion in the incubation times. A specific study is needed to disentangle and evaluate the possible contributions, in order to obtain a reasonably narrow length distribution.

Finally, we may come back to the NW of Fig. 2b. From quantitative profiles (not shown), the gold nanoparticle diameter is 35 nm, the NW diameter below the gold nanoparticle is 26 nm (total) and 20-22 nm (not counting the oxide shell), the NW diameter at the base is 55 nm (with the oxide) and 40 nm (without the oxide). 8 CdTe insertions are detected along the length of 550 nm, regularly spaced with a period 67±1 nm. The size of the gold nanoparticle is clearly larger than average, and such that we expect it to remain as a 3D object, or to give rise to an inclined NW (see an example with the black arrow in the inset of Fig. 1). In this case a larger contact area and a stronger lateral flux due to the inclined configuration tend to increase the tapering. Note also that the lateral growth of ZnTe on the side of the CdTe insertion is not symmetrical, as evidenced by the off-axis position of the CdTe insertions at the bottom of the NW.

To conclude, we have demonstrated two approaches to unravel the characteristics of the MBE growth of NWs at low temperature, with the help of analytical results from an adapted diffusion-based model. Applied to the growth of ZnTe NWs, the main results are:

• the existence of an incubation time before the actual start of the NW, which remains to be understood, and if possible suppressed;

• except for very short NWs, the central role of lateral flux in determining the axial growth rate (hence the length and composition of an embedded quantum dot); note that the incubation time does not affect this phase of the growth;

• the formation of a narrow contact area, which determines the diameter of the quantum dot [START_REF] Rueda-Fonseca | [END_REF] but also contributes to determine the axial growth rate;

• the possibility of lateral growth without changing the growth temperature, allowing us to fabricate core-shell structures with good interfaces or tapered NWs; at the basis of the NW, the lateral growth is governed by the diffusion of substrate adatoms; higher along the NW, the role of the lateral flux progressively increases.

Appendix A: Calculation

Or goal here is not to derive a general theory of NW growth, but to obtain a simple model, adapted to the present case, with analytical results, likely to serve as a guide for future studies.

We consider a low density of NWs, perpendicular to the substrate. A diffusion-based NW growth model is built from the general solution of the diffusion equations of adatoms on the NW sidewalls in 1D, and on the substrate surface in 2D with a circular symmetry. The flux J s impinging onto the substrate (actually, the ZnTe buffer layer) far from the NW induces the presence of adatoms with a density n 0 s = J s τ s , where τ s is the residence time of an adatom which diffuses on the surface over a length λ s = √ Dτ s before incorporation (or desorption). We define similarly a uniform-limit adatom density on the NW sidewalls, n 0 N W = J N W τ N W , with τ N W the residence time and λ N W = √ Dτ N W the diffusion length. For the sake of simplicity, we keep the same diffusion constant D. The ratio of adatom densities is thus (with α incidence angle, i.e., the angle between the cell axis and the substrate normal)

n 0 N W n 0 s = J N W J s λ N W λ s 2 = tan α π λ N W λ s 2 (A1)
The local densities of adatoms (number of adatoms by surface unit), n s (r) on the substrate, and n N W (z) on the NW sidewalls, are solutions to the diffusion equations and can be written as follows:

n N W (z) = n 0 N W + c + N W exp( z λ N W ) + c - N W exp(- z λ N W ) n s (r) = n 0 s + c + s I 0 ( r λ s ) + c - s K 0 (- r λ s ) (A2)
where r is the radial coordinate centered on the NW axis and increasing when moving away from the NW, and z is the coordinate along the NW axis, perpendicular to the substrate and increasing towards the tip of the NW. I 0 and K 0 are modified Bessel functions.

The four coefficients c + N W , c - N W , c + s , c - s , are to be determined by boundary conditions. We take the simplest ones:

• For a weak density of NWs, n s (∞) = n 0 s hence c + s = 0. • The hopping probabilities of adatoms, from the NW to substrate and from the substrate to the NW, are assumed to be symmetric: n N W (z = 0) = n s (r = R), where R is the nanowire radius at the base.

• The adatom current at the vicinity of the NWsubstrate interface are in equilibrium (conservation of the adatom currents): (dn N W /dz) z=0 = -(dn s /dr) r=R

• Complete trapping at the tip of the NW (catalyst droplet acting as perfect sink): n N W (z = L) = 0, where L is the height of the nanowire. This last condition is valid for a purely diffusion-driven model . 29 In the more complex case of kineticdriven growth 28 (not treated here), where the thermodynamical mechanisms in the catalyst droplet limiting the axial growth need to be taken into account, this condition is modified to a condition on (dn N W /dz) z=L .

These boundary conditions allow us to determine the constants in equations A2 and to obtain the following expression for the NW adatom density:

n N W (z) = n 0 s ω s (z) + n 0 N W ω N W (z) (A3) with ω s (z) = sinh( L-z λ N W ) sinh( L+ λs λ N W ) and ω N W (z) = 1 - sinh( z λ N W ) sinh( L λ N W ) - sinh( L λ N W )+ λs λ N W sinh( L+ λs λ N W ) sinh( L-z λ N W ) sinh( L λ N W )
Here we have defined an effective diffusion length λs = -λ s K 0 ( R λs )/K ′ 0 ( R λs ), and we have assumed that λs << λ N W . Note that if the diffusion equation in the substrate was in 1D instead of in 2D, λs would simply be λ s . In 2D, λs depends on R, hence its value changes as growth proceeds. Indeed, when we calculate the values of λs for R from 10 to 35 nm (the range of NW base radius values found for our ZnTe NWs, see Fig. 1), we find λs = 0.3λ s to 0.5λ s , and for typical values of λ s (see below), λs remains of the order of a few 10 nm. In addition, λs influences mainly the NW growth when they are short (i. e. when the effect of lateral growth is still negligible). When the NWs are longer, it is λs + L that dominates the growth, hence the variations of λs are masked by the larger values of L. In the following, we take λs constant and small with respect to λ N W .

The two contributions to Eq. A3, ω s from the flux arriving to the substrate, and ω N W from the flux arriving laterally, are plotted in Fig. A1 for typical values λ s = 60 nm, λs = 20 nm and λ N W = 100 nm. Note that all curves converge at z = -λs as shown by the dotted lines, which identifies λs as an effective diffusion length on the substrate, as seen from the NW.

The growth rates for the NW length L (axial growth), for the NW radius at the base R (lateral growth) and for the 2D pseudo-substrate with height h are given by:

dL dt = -α L 2DΩ 0 R 0 dn N W dz (z = L) dR dt = α N W n N W (z = 0) τ N W Ω 0 dh dt = α s n 0 s τ s Ω 0 = V s (A4)
In these equations, Ω 0 is the volume occupied by an atom in the crystal; α s , α N W and α L are the incorporation rate at the substrate, at the NW facets and at the tip of the NW (at the interface with the Au catalyst particle); V s is the growth speed on the substrate (at the end of the growth, the final thickness of this re-grown layer is h = V s t).

From Eq. A4 and Fig. A1a, we conclude that the contribution to the growth from adatoms diffusing from the substrate is: i) important for short NWs, L ≪ λ N W , with a linear decrease of n N W with z, and ii) weak for long NWs, L ≫ λ N W , with a exponential decrease of n N W with z. Figure A1b shows that the contribution to the growth from the lateral flux is proportional to L for short NWs. For long NWs, the adatoms arriving at the middle part of the NW are incorporated locally (with the formation of a plateau) and the contribution to the NW axial growth is proportional to λ N W .

Using Eq. A3 and A4, the NW axial growth rate is: With the simplifying assumption that λs is constant, Eq. A5 can be integrated, giving the nanowire length L as a function of the thickness h of the re-grown layer: For the long NWs L ≫ λ N W , the contribution to the NW axial growth from the adatoms arriving to the sub-strate and diffusing up the NW walls up to the catalyst droplets is negligible. The dominant contribution to the axial growth is that from the lateral flux, with a constant growth rate L h ∼ 2 JNW Js λNW R0 = 2 tan α π λNW R0 (dashed black line). A change of the values of λs to 10 nm and to 50 nm (extreme values observed in our samples) makes only minor changes of L(h) (red dotted lines), which validates the hypothesis of a constant λs value.

dL dt = α L α s
h R 0 = J s J N W
Hence, the contribution from the substrate influences the axial growth rate of the NWs only at the early stages of growth. For short NWs (L < λ N W ), it determines how fast the NW starts to grow: the growth speed at λ s = 40 nm is lower than the final slope while at λ s = 80 nm it is larger.

The lateral growth rate at the NW base (z = 0), in the case where λs << λ N W , is given by:

dR dt = α N W α s λ s λ N W 2 V s ω R (z = 0) (A7)
where ω R (z = 0) = sinh( L λNW ) + JNW Js λNW λs (λs) 2 cosh( L λNW ) -1 sinh( L+ λs λNW )

In Fig. A2b we plot the value of ω R , for different contributions from the substrate (different values of λ s ). We observe that for short NWs, the lateral growth is slow and that the lateral flux does not influence the growth (the four lines are merged together). For long NWs, the contribution from the lateral flux remains relatively weak, and the lateral growth rate is constant with R/h ∼ (λ s /λ N W ) 2 , as a result of n N W (z = 0) ∼ n 0 s . Thus, the lateral growth at the NW base is a good measure of the NW growth time, which can be interesting in samples where the NWs start to grow at different times.

Finally, the variation of the NW radius at the base, R, with the NW length can also be determined: Here we made a simplified distinction between the contact radius R 0 during the main part of the growth, and its initial value R(0) at the beginning of the NW growth.

dR dL = α N W 2α L R 0 λ N W

  methods and growth conditionsOur MBE system comprises a Riber 32P II-VI chamber connected under UHV to a Meca2000 III-V chamber equipped with As and Au effusion cells. The sample temperatures are measured by a thermocouple in direct contact with the molybdenum sample-holder. Beam equivalent pressures (BEP) were converted into flux ratios as described in Ref.16 and checked using reflection high-energy electron diffraction (RHEED) oscillations. An important parameter for the growth of NWs, is the angle α of each effusion cell with respect to the normal to the substrate: this angle determines the ratio of average flux J N W impinging onto the facets of a normal NW to the flux J s impinging onto the substrate: J N W /J s = tan α/π. In our system, the values are tan α = 0.21 for CdTe and Mn, tan α = 0.48 for ZnTe and Mg, tan α = 0.65 for Te and tan α = 0.85 for Cd and Zn.Unless otherwise mentioned, a typical growth sequence consisted in the deoxidation of the (111)B GaAs substrate at 650 • C under As flux (1 × 10 -5 torr), the growth of a 250-500 nm-thick ZnTe buffer layer at 260 • C under stoichiometric ZnTe flux, annealing at 420 • C under Te flux, the deposition of a submonolayer gold layer at room temperature in the III-V chamber. Gold seeds were formed by dewetting at 350 • C during 5 min in the II-VI chamber. Then the sample rotation was started and the NW growth initiated immediately at the same temperature. Monitoring each step by RHEED allows us to check the characteristic features of a good quality growth: 2 × 2 and √ 19 × √ 19 reconstruction of the GaAs surface, 17 c(8x4) and 2 √ 3×2 √ 3 R30

FIG. 1 .

 1 FIG.1. SEM data on the diameter at the base, vs. the length, for the NWs of a sample grown at 350 • C with stoichiometric Zn + Te flux. Green squares mark cone-shaped (tapered) zinc-blende NWs, blue hexagons cylinder-shaped wurzite NWs (corresponding arrows in the 60 deg. SEM image in the inset, which also feature an inclined NW -black arrow -and a creeping object -yellow arrow); the solid line is calculated as described in section III B. The length plotted here is the length visible above the 2D layer, of thickness h ≃200 nm in this sample.

FIG. 2 .

 2 FIG. 2. (a) Schematic of the intended NW structure with 10 identical sequences ZnTe:CdTe, and a twice shorter ZnTe cap, grown at 350 • C under stoichiometric fluxes. The 2D layer is transparently superimposed on the NW showing the part of the NW that is buried. (b) EDX image of a NW deposited on a holey carbon grid (composite of 5 higher resolution images). Colored areas are those where the Cd (red), Zn (yellow), Au (cyan) or O (black) signal exceeds an arbitrary threshold. (c) HAADF image of a complete NW (NW1) with the ZB structure, with the substrate at the bottom (white area). The inset shows the shape of the catalyst particle.(d) BF and (e) HAADF image of the bottom part of the same NW. The inset in (e) shows a zoom of the image revealing lattice planes: the NW is observed along the [110] direction and two 111 planes are marked by dotted lines. (f) GPA analysis of image (d) showing four small regions with a height of around 4 nm with larger lattice spacing (in red). (g) HAADF STEM image and (h) GPA analysis of a second NW on the same sample (NW2; this is the same NW as in Fig. 4b) that also has the ZB structure but is much shorter. The GPA analysis shows only one region with larger lattice spacing. (i) Color coding of the lattice spacing in the GPA analysis. All scale bars are 10 nm for (c)-(h), 100 nm for (b).

FIG. 3 .

 3 FIG. 3. (a) Effect of the flux incidence angle: length of individual components of structured NWs (from Fig. 2 and Ref. 20), divided by the 2D thickness, as a function of the angle factor tan α, where α is the angle between the molecular beam and the NW axis. (b) Steps of the growth of a NW with a CdTe insertion. (c) Plot of the visible length of NW1 and NW2 of Fig. 2, as a function of the 2D layer thickness;we plot (squares) Ln vs. hn (as defined in (b), and marked here by the red arrows) at the time of insertion of CdTe, and L at the end of the growth, vs. h. NW3 is the longest NW observed by SEM on the same sample. The hatched triangle represents the masking by the 2D layer (i.e., the thickness (h -hn) remaining to grow after the formation of the CdTe insertion). The solid lines are the fit with Eq. A6, with the same values of the diffusion length λs = 18 nm on the substrate and λNW = 78 nm on the sidewall facets, and different incubation times. We assumed that the gold nanoparticle was close to a full sphere from the beginning of the growth, with the contact diameter 7.7 nm (NW1) and 7.9 nm (NW2), as measured on the HAADF image, and assuming 7.3 nm for NW3. An additional constraint (not shown) is that the diameter of the crystalline core at the base of the NW agrees with Eq. A9. With these values of the parameters, we deduce an incubation time for NW1 and NW2, and an immediate start for NW3.

FIG. 4 .

 4 FIG. 4. HAADF STEM images of gold nanoparticles at the tip of NWs (a) closer to half-sphere at the tip of a wurzite NW. The image was made along the [2 11 0] direction of observation and the planes are indexed. The inset shows the wurtzite structure of the NW that can be observed closer to the base of the NW. (b) The gold catalyst particle is almost a full sphere at the tip of a zinc-blende NW. The direction of observation is [011] and both the 111 planes are indexed. All scalebars are 10 nm. The vertical lines most visible in the bright gold catalyst particle are due to scan errors.

  and also Fig. 5 of Ref. 16); such a value fairly matches the diameter of CdTe dots imaged by EDX in Ref. 20.

FIG. 5 .

 5 FIG. 5. (a) 60 deg. SEM image of a sample grown at 375 • C under Te-excess (yellow arrows mark 3D objects, green arrows zinc-blende NWs and blue arrows wurtzite NWs); (b) size of the gold nanoparticle, and (c) plot of the base diameter, vs. NW length (with identification of the cylinder-shaped wurtzite NWs, open hexagons, and of the cone-shaped zinc-blende NWs with a half-sphere or full-sphere gold particle at the tip, as indicated by the half-filled or full circles, respectively); the grey lines are guides for the eye; (d) Base diameter to nanoparticle size ratio, and (e) base diameter, vs NW length; crosses in the lower part of (e) display the nanoparticle diameter for the NWs at the edge of the distribution in (d), i.e., the 5 NWs on the solid line at the left top side of the distribution, and the longest one; lines in (d) and (e) are calculated as described in section III.

  FIG. A1. (a) Contribution to the NW density of adatoms diffusing from the substrate (Eq. A3): ωs(z) is plotted for different values of the NW length as specified with λs = 60 nm, λs = 20 nm and λNW = 100 nm. (b) Contribution to the NW density of adatoms from the lateral flux (Eq. A3), ωNW (z). All curve would coincide at z = -λs.

  λs λNW ) -1 sinh( L+ λs λNW ) (A5)

  This dependence of L on h is plotted in Fig.A2afor different contributions from the substrate (different values of λ s ).

  FIG. A2. (a)Nanowire length L as a function of the thickness of the re-grown layer h divided by the radius of the catalyst particle R0 (Eq. A6). The continuous curves are plotted for: JNW /Js = 0.15, λNW = 100 nm, λs = 20 nm and three different values of λs = as indicated. The dotted red curves have the same parameter except for λs changed to 10 nm and 50 nm. Finally, the black line is the asymptotic line due to lateral flux. (b) ωR as a function of L (Eq. A7). This value is proportional to the lateral growth rate at the NW base (z = 0). The curves are plotted for: JNW /Js = 0.15, λNW = 200 nm, λs = 20 nm and three different values of λs = 40, 60, 80 nm (in red, blue and green). The curve for the case where there is no contribution from the lateral flux (J 0 NW = 0) is plotted in black.

  which can be integrated to obtain R(L). If λs ≪ λ N W , a good approximation is to ignore the second term in the numerator, so that R -

TABLE I .

 I Diffusion length values used in the fits for different growth conditions.

	350 • C-stoichio 78	18	2, 3
	350 • C-stoichio 78	23	1
	350 • C-Te	57	18	Ref. 19
	375 • C-Te	126	38	5

ACKNOWLEDGMENTS

This work was performed in the joint CNRS-CEA group "Nanophysique & semiconducteurs", and in the frame of the French National Agency project "Magwires" (ANR-11-BS10-013). We thank all the members of the Magwires project for many discussions. We also acknowledge a grant from the Laboratoire d'excellence LANEF in Grenoble (ANR-10-LABX-51-01).


Daria V Beznasyuk

Eric Robin

Martien Den Hertog

Julien Claudon

Moïra Hocevar

Dislocation-free axial InAs-on-GaAs nanowires on silicon

We report on the growth of axial InAs-on-GaAs nanowire heterostructures on silicon by molecular beam epitaxy using 20 nm diameter Au catalysts. First, the growth parameters of the GaAs nanowire segment were optimized to achieve a pure wurtzite crystal structure. Then, we developed a two-step growth procedure to enhance the yield of vertical InAs-on-GaAs nanowires. We achieved 90% of straight InAs-on-GaAs nanowires by further optimizing the growth parameters. We investigated the composition change at the interface by energy dispersive X-ray spectroscopy and the nanowire crystal structure by transmission electron microscopy. The nominal composition of the InAs segment is found to be In x Ga 1-x As with x=0.85 and corresponds to 6% of lattice mismatch with GaAs. Strain mapping performed by the geometrical phase analysis of high-resolution images revealed a dislocation-free GaAs/In 0.85 Ga 0.15 As interface. In conclusion, we successfully fabricated highly mismatched heterostructures, confirming the prediction that axial GaAs/In 0.85 Ga 0.15 As interfaces are pseudomorphic in nanowires below 40 nm diameter.

Introduction

Integrating direct bandgap III-V compound semiconductors on silicon is seen as an appealing strategy to realize optical emitters on a chip. Considerable challenges faced by thin film epitaxy of III-V semiconductors on Si due to strain and materials chemistry motivated research towards new fabrication strategies, including wafer bonding [START_REF] Tanabe | III-V/Si hybrid photonic devices by direct fusion bonding[END_REF], selective area growth [START_REF] Li | Dense arrays of ordered GaAs nanostructures by selective area growth on substrates patterned by block copolymer lithography[END_REF] or nanowire growth [START_REF] Plissard | Gold-free growth of GaAs nanowires on silicon: arrays and polytypism[END_REF]. Nanowires have a nanometer-scale cross section which enables the release of strain via lateral elastic relaxation, not only across the nanowire/substrate interface [START_REF] Cirlin | Critical diameters and temperature domains for MBE growth of III-V nanowires on lattice mismatched substrates[END_REF] but also across material interfaces in the nanowire axis [START_REF] Ercolani | InAs/InSb nanowire heterostructures grown by chemical beam epitaxy[END_REF][START_REF] Kaganer | Strain and x-ray diffraction from axial nanowire heterostructures[END_REF]. Elastic relaxation prevents the formation of dislocations and, in theory, enables combinations of infinitely long semiconductor segments with up to 7 % lattice mismatch (InAs and GaAs for example) in nanowires below 40 nm in diameter [START_REF] Glas | Critical dimensions for the plastic relaxation of strained axial heterostructures in freestanding nanowires[END_REF]. In comparison with two dimensional systems, the critical thickness below which no dislocation appears is only few monolayers for InAs-on-GaAs layers [START_REF] Grandjean | Epitaxial growth of highly strained InxGa1-xAs on"GaAs (001): the role of surface diffusion length[END_REF]. Yet, experimental data for InAs-on-GaAs nanowires are missing to confirm the prediction of dislocation-free interfaces below critical diameter because the growth is still challenging.

Most axial nanowire heterostructures grow by the vapor-liquid-solid (VLS) mechanism with a gold nanoparticle used as a catalyst [START_REF] Lauhon | Semiconductor nanowire heterostructures[END_REF]. In VLS, the switch from one material to the other is delicate, in particular, when interchanging the group III element (Ga and In) for III-V semiconductor combinations. Those heterostructures are affected by interface grading and kinking [START_REF] Dick | Controlling the abruptness of axial heterojunctions in III-V nanowires: beyond the reservoir effect[END_REF][START_REF] Paladugu | Novel growth phenomena observed in axial InAs/GaAs nanowire heterostructures[END_REF][START_REF] Paladugu | Nature of heterointerfaces in GaAs/InAs and InAs/GaAs axial nanowire heterostructures[END_REF]. Interface grading is a consequence of both group III elements being soluble in the liquid Au droplet. If the first element is not properly purged from the droplet, it will continue to incorporate in the new segment and form a graded interface, which is detrimental for the control of optical properties. Moreover, kinking of the upper segment happens when the gold nanoparticle is destabilized during the group III element switch. One way to prevent kinking is to use buffer layers of InGaAs between GaAs and InAs [START_REF] Xin | Growth and characterization of straight InAs/GaAs nanowire heterostructures on Si substrate[END_REF][START_REF] Huang | Control of the crystal structure of InAs nanowires by tuning contributions of adatom diffusion[END_REF] but this solution is very similar to having a graded interface as it circumvents from controlling optical confinement for example. Another solution to avoid both interface grading and kinking is to grow Au-free-catalyzed nanowires [START_REF] Scarpellini | InAs/GaAs sharply defined axial heterostructures in self-assisted nanowires[END_REF]. However, it still remains unclear whether the formation of thin diameters (and therefore dislocation-free interfaces) is possible by this technique. In a nanowire system using Au catalysts, InAs-on-GaAs and GaAs-on-InAs interface grading can be minimized using growth interrupts, small diameter catalysts and high V/III ratios [START_REF] Dick | Controlling the abruptness of axial heterojunctions in III-V nanowires: beyond the reservoir effect[END_REF][START_REF] Priante | Abrupt GaP/GaAs interfaces in selfcatalyzed nanowires[END_REF]. Additionally, InAson-GaAs interfaces are usually much sharper than GaAs-on-InAs interfaces [START_REF] Krogstrup | Junctions in axial III-V heterostructure nanowires obtained via an interchange of group III elements[END_REF][START_REF] Venkatesan | Direct observation of interface and nanoscale compositional modulation in ternary III-As heterostructure nanowires[END_REF]. This discrepancy was explained by the higher affinity of In with Au [START_REF] Paladugu | Nature of heterointerfaces in GaAs/InAs and InAs/GaAs axial nanowire heterostructures[END_REF], making it more difficult to expel from the droplet.

Preventing kinking requires to maintain a stable position of the droplet on a flat nanowire top facet during group III element switch. During growth, wurtzite nanowires only nucleate when all edges below the gold droplet are sharp, whereas truncated facets at the liquid solid interface produce zinc-blende nanowires [START_REF] Jacobsson | Interface dynamics and crystal phase switching in GaAs nanowires[END_REF].

Therefore, constraining GaAs and InAs segments to the wurtzite crystal phase is one solution to stabilize the droplet on flat facets and increase the vertical yield of InAs-on-GaAs nanowires [START_REF] Messing | Growth of straight InAs-on-GaAs nanowire heterostructures[END_REF]. The wurtzite crystal structure of arsenide compounds forms for high levels of supersaturation in the droplet [START_REF] Jacobsson | Interface dynamics and crystal phase switching in GaAs nanowires[END_REF][START_REF] Glas | Why does wurtzite form in nanowires of III-V zinc blende semiconductors?[END_REF]. Moreover, high supersaturations produce layer-by-layer growth of the new segment in nanowire heterostructures [START_REF] Hocevar | Growth and optical properties of axial hybrid III-V/Si nanowires[END_REF] and minimize the length of truncated edge facets [START_REF] Jacobsson | Interface dynamics and crystal phase switching in GaAs nanowires[END_REF], which are suspected to be responsible for the formation of kinks in nanowire heterostructures based on group V elements. Promoting these effects contributes to the droplet mechanical stability and to the growth of straight heterostructures. It was recently proposed that increasing the group III concentration in the catalyst also induces a higher stability in nanowire heterostructures based on group III element [START_REF] Zannier | Catalyst composition tuning: the key for the growth of straight axial nanowire heterostructures with group III interchange[END_REF]. The authors pre-deposited In before the growth of their GaAs nanowires, which led to an increase of the Ga solubility in the Au droplet from 33% to 45% and to an increase of the vertical yield of InAs-on-GaAs nanowires.

Here, we report on the growth of axial InAs-on-GaAs nanowire heterostructures below critical diameter using both the growth temperature and In flux as optimization parameters. We show that by maintaining both a high supersaturation and a high group III concentration in the gold droplet during the whole growth sequence, the yield of straight InAs-on-GaAs nanowires reaches 90%. We measured the composition of the InAs segment, which happens to be In x Ga 1-x As with x ≈ 0.85, corresponding to a lattice mismatch of 6% with GaAs. We demonstrate that the interface between GaAs and In 0.85 Ga 0.15 As depends on the In flux and the V/III beam equivalent pressure (BEP) ratio and can be as sharp as 5 nm. Finally, strain mapping of the InAs-on-GaAs nanowire revealed a dislocation-free interface.

Experimental details

Growth of wurtzite GaAs nanowires on Si (111) substrates

We carried out the growth of GaAs nanowires in a molecular beam epitaxy (MBE) reactor. The nanowires were grown via the Au-assisted vapor-liquid-solid (VLS) mechanism on n-type (111)-oriented silicon substrates (figure 1). We chemically treated the substrates prior to their introduction into the MBE reactor.

First, a combination of HF and NH 4 F was used to remove the native oxide and to create atomically flat terraces on the silicon surface [START_REF] Higashi | Comparison of Si (111) surfaces prepared using aqueous solutions of NH4F versus HF[END_REF]. Then, the substrates were covered with a gold colloid solution and finally rinsed in deionized water. We loaded the samples into the introduction module immediately after their chemical preparation to prevent re-oxidation of the silicon surface. Before reaching the growth chamber, the substrates were degassed at 200 °C in a transfer module until the pressure dropped below 2.0×10 -8 Torr. We grew the GaAs nanowires as follows. The sample was heated to the desired growth temperature with a ramp of 40 °C/min. After one minute of stabilization, we opened the arsenic cracker-cell shutter and, ten seconds later, the gallium shutter. After 30 minutes, we closed the gallium shutter and we finally cooled down the sample under an arsenic flux. To promote the formation of the wurtzite crystalline phase, the gold colloids diameter and the growth temperature were intentionally set to 20 nm and 610°C, respectively [START_REF] Tchernycheva | Temperature conditions for GaAs nanowire formation by Au-assisted molecular beam epitaxy[END_REF][START_REF] Glas | Why does wurtzite form in nanowires of III-V zinc blende semiconductors?[END_REF]. We strategically choose a diameter of 20 nm, since it is below the theoretical critical diameter to prevent the formation of dislocations at the interface between GaAs and InAs and to achieve high group III concentration in the droplet. In our MBE system, the GaAs deoxidation temperature equals 630 °C. We studied the nanowire morphology and crystal structure for two different V/III BEP ratios at a fixed Ga flux of 2.0×10 -7 Torr corresponding to a growth rate of 0.34 monolayers per second (ML/s) on GaAs. The nanowires were grown at a V/III BEP ratio of 15 and 30 under an As flux of 3.0×10 -6 Torr and 6.0×10 -6 Torr, respectively.

Growth of straight InAs-on-GaAs nanowires on Si (111) substrates

Once we obtained the desired wurtzite GaAs nanowires, we switched to the growth of InAs-on-GaAs nanowires. The growth temperature of InAs nanowires by MBE is significantly lower than that of GaAs nanowires, usually around 410 °C [START_REF] Tchernycheva | Au-assisted molecular beam epitaxy of InAs nanowires: Growth and theoretical analysis[END_REF]. We introduced a two-step temperature procedure (figure 2), where the GaAs segment grows at high temperature (610°C) and InAs at lower temperatures. The growth time for GaAs was 30 min, including the cooling down process of 5 min.

As growth interruptions are known to improve the abruptness of nanowire heterointerfaces [START_REF] Dick | Controlling the abruptness of axial heterojunctions in III-V nanowires: beyond the reservoir effect[END_REF][START_REF] Dubrovskii | Factors Influencing the Interfacial Abruptness in Axial III-V Nanowire Heterostructures[END_REF],

we studied two growth interruption strategies: (a) we interrupted the growth of GaAs during the whole cooling procedure (figure 2a) and (b) we interrupted the growth of GaAs after the cooling procedure (figure 2b) during 2 minutes. In both cases, we interrupted GaAs growth by closing the gallium shutter while maintaining the arsenic flux.

We then grew the InAs nanowire segment by opening the In shutter during 25 minutes. We cooled down the sample after switching off the In shutter while maintaining an As flux down to 400°C. We studied how the nanowire morphology is influenced by the InAs growth temperature and the In flux. First, we grew the InAs segment at a fixed In flux of 3.0×10 -7 Torr (0.48 ML/s) and a V/III BEP ratio of 20 from 420 °C up to 540 °C. Then, we grew another set of samples at an In flux of 1.2×10 -7 Torr (0.2 ML/s) and a V/III BEP ratio of 50 from 510 °C up to 610 °C.

Characterization of the nanowires

We characterized the GaAs and InAs nanowire segments length and shape by scanning-electron microscopy (SEM). The yield of straight InAs-on-GaAs segments was also analyzed by SEM. We observed 60-80 nanowires per sample. A CM300 transmission electron-microscope (TEM) equipped with a LaB6 thermionic emitter operated at 300 kV was used for detailed crystalline structure investigations in TEM mode. The chemical composition and the morphology of the nanowires were investigated by energy-dispersive X-ray spectroscopy (EDX) and high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) on a probe corrected FEI Titan Themis working at 200 kV, equipped with four silicon drift detectors for EDX. Quantification of In L-lines, Ga K-lines, As K-lines and Au L-lines was performed using the Cliff-Lorimer method assuming no X-ray absorption in the investigated samples which is justified considering the relatively high energy of the measured X-ray lines (> 3.3 keV) and the small diameter of the nanowires [START_REF] Cliff | The quantitative analysis of thin specimens[END_REF]. The Cliff-Lorimer factors were calibrated on the same equipment, at the same operating conditions, using reference samples of known composition and thickness. Finally, we applied the geometrical phase analysis (GPA) method [START_REF] Hÿtch | Quantitative measurement of displacement and strain fields from HREM micrographs[END_REF][START_REF] Rouviere | Theoretical discussions on the geometrical phase analysis[END_REF] to our high-resolution STEM images to evaluate the lattice deformation in the nanowire heterostructures.

Results and discussion

Wurtzite GaAs nanowires on a Si substrate

We first discuss the morphology of GaAs nanowires for different V/III ratios. At a V/III ratio of 15, the nanowires are tapered with a large diameter along the growth axis (figure 1b). The diameters at the basis and at the top are 99±13 nm and 35±3 nm, respectively. We measured an average length of 863±85 nm.

When increasing the V/III ratio to 30 (figure 1c), the nanowires show a slight tapering at the basis and a thin and homogeneous diameter along the whole length. All nanowires have an average length and diameter of 1.2±0.1 µm and 25±3 nm, respectively. During growth, the evolution of the nanowire morphology is governed by the competition between adatom surface diffusion and direct impingement on the droplet (figure 1a) [START_REF] Dubrovskii | General form of the dependences of nanowire growth rate on the nanowire radius[END_REF]. Generally, low V/III ratios (low As coverage) increase Ga diffusion along the nanowire facets [START_REF] Nomura | Surface diffusion length of Ga adatoms on (111) B surfaces during molecular beam epitaxy[END_REF], which leads to a combination of lateral and axial growth. Moreover, the catalyst diameter is larger at low V/III ratios for nanowires grown in MBE systems [START_REF] Paek | MBE-VLS growth of GaAs nanowires on (111) Si substrate[END_REF], which is in agreement with our observations. In contrast, high V/III ratios (high As coverage) reduce the Ga diffusion along the nanowire facets and thus the catalyst droplet diameter: axial growth due to direct impingement is fostered at the expense of radial growth. In conclusion we succeeded to control the GaAs nanowire morphology by controlling the respective contributions of direct impingement and surface diffusion to the axial growth rate. Additional data in supplementary information (SI) (see figure S1) clearly show the transition between tapered and straight nanowires.

We then study the GaAs nanowires crystal structure by TEM. At a V/III ratio of 15 a major part of the nanowires have the wurtzite crystal structure but exhibit many stacking faults (see figure S2). At a higher V/III ratio of 30, the nanowires grow with a pure wurtzite crystal phase, as observed on the selected area diffraction pattern (figure 1e). Such nanowires have less than four stacking faults per micrometer (see figure S3). To the best of our knowledge, this is the first demonstration of pure wurtzite GaAs nanowires grown on silicon using gold as a catalyst.

Influence of the growth parameters on the morphology of InAs-on-GaAs nanowires

As described earlier, we use a two-step temperature procedure, where the GaAs nanowire stems grow at 610°C and the following InAs segments at a lower temperature. First, we discuss the two different strategies applied to the growth of InAs-on-GaAs nanowires, where the cooling procedure between GaAs and InAs growths takes place under an As flux only (Figure 2a) or during GaAs growth (Figure 2b). After cooling under As only, most InAs segments grow kinked with respect to the GaAs nanowire stem (Figure 2c). Moreover, we notice that the InAs segment has a significantly larger diameter than the GaAs stem (Figure 2e). In contrast, the InAs segments grow straight on top of the GaAs stems when GaAs continues growing during the cooling procedure (Figure 2d). We observe that the InAs-on-GaAs nanowire diameter evolves along the growth axis (Figure 2f): the GaAs nanowire segments have a bottle-shaped morphology, where the base of each nanowire has a larger diameter than the tip. It is an indication of GaAs and/or InAs radial overgrowth. The InAs segment is clearly visible above GaAs with a homogeneous diameter of 37±3 nm along the whole growth axis.

Our observations suggest that the excess of Ga present in the droplet determines whether the InAs segment will kink or not, which is in agreement with the work reported in [START_REF] Zannier | Catalyst composition tuning: the key for the growth of straight axial nanowire heterostructures with group III interchange[END_REF], where the concentration of group III element in the droplet is correlated to its stability. During the cooling step under As, the Ga is purged from the droplet by forming a GaAs nanowire section. In this situation, the droplet size and the contact angle formed with the nanowire top facet (see Figure 1a) decrease, favoring the formation of a GaAs zinc blende section which diameter shrinks below 20 nm [START_REF] Glas | Critical dimensions for the plastic relaxation of strained axial heterostructures in freestanding nanowires[END_REF][START_REF] Persson | Solidphase diffusion mechanism for GaAs nanowire growth[END_REF] (see the cooling neck on figure 1d, as well as the contact angle <90°). At the In shutter opening, a large amount of In dissolves into the depleted droplet both from direct impingement and from adatom surface diffusion. We think that such abrupt volume expansion destabilizes the droplet, which falls on the side, leading to the growth of kinked InAs segments (see figure S4). On the contrary, during the cooling step under Ga and As, the droplet is constantly fed with Ga.

Therefore, its size and the contact angle formed with the nanowire top facet remain constant (or decrease to a lesser degree due to the Ga diffusivity drop). Moreover, in Au droplets, the Ga concentration increases exponentially with the decrease of the diameter. Ga solubility reaches 40% for 20 nm diameter droplets [START_REF] Zhou | Quality control of GaAs nanowire structures by limiting as flux in molecular beam epitaxy[END_REF][START_REF] Han | Manipulated growth of GaAs nanowires: controllable crystal quality and growth orientations via a supersaturation-controlled engineering process[END_REF], which contributes to maintaining a high group III concentration (and supersaturation) in the catalyst. Thus, the GaAs nanowires keep growing in the wurtzite crystal structure, forming sharp edge facets at the liquid-solid interface. We believe that InAs nucleates from a mechanically stable Au droplet on a flat top facet, favoring straight growth. Earlier works on axial heterostructures of energetically non-favorable semiconductor combinations (InAs-on-GaAs [START_REF] Zannier | Catalyst composition tuning: the key for the growth of straight axial nanowire heterostructures with group III interchange[END_REF], Si-on-GaP [START_REF] Hocevar | Growth and optical properties of axial hybrid III-V/Si nanowires[END_REF], InP-on-InAs [START_REF] Svensson | Control and understanding of kink formation in InAs-InP heterostructure nanowires[END_REF]) suggested that a high supersaturation and/or a high group III concentration in the droplet during the upper segment formation favors vertical growth. We will show later that a high group III concentration in the droplet is required not only during the upper segment formation but along the entire interchange sequence to prevent droplet depletion and favor straight growth of InAs-on-GaAs nanowires.

Before optimizing the morphology of the nanowires, we investigate the influence of the growth temperature on the yield of vertical InAs segment (see figure S5). We find a maximum yield of 90% of straight InAs segments at temperatures ranging between 510°C and 570°C for various In fluxes. Below 510 °C, InAs hardly contributes to the axial growth on top of GaAs and mostly forms a thick and irregular shell around the GaAs nanowire (see figure S5a and figure S6 for the EDX measurements). On the contrary, above 570°C, InAs segments grow on top of GaAs. However, the segments kink (see figure S5c and figure S7). At such high temperatures, the In desorption rate increases (yet remains slower than As) resulting in a lower In fraction in the catalyst and correspondingly lower supersaturation. As discussed earlier, low supersaturation favors long truncated edges at the solid/liquid interface resulting in a decrease of droplets stability and a higher probability of kinks. Based on our observations, we set the optimum growth temperature to 540°C for the InAs segment.

We now study whether we can control the nanowire morphology using different In fluxes (Figure 3).

As already observed by SEM on figure 2b, an In flux of 3.0×10 -7 Torr leads to a bottle-shape morphology. A 300 nm-long InAs segment grows on top of GaAs (Figure 3a), indicating an InAs axial growth rate of 12 nm/min. Yet, a 40 nm thick InAs shell surrounds the bottom of the GaAs segment (inset of Figure 3a). This shell forms at a lateral rate of 1.6 nm/min. By decreasing the In flux down to 1.2×10 -7 Torr under a constant As flux (thus increasing the V/III ratio from 20 to 50), we observe that the nanowire morphology is more uniform. A 60 nm-long InAs segment grows on top of GaAs (Figure 3b) with an axial growth rate of 2.5 nm/min. The parasitic shell around the GaAs segment seems suppressed (inset Figure 3b). Yet, we measure a shell of 4 nm, which corresponds to a radial growth rate of 0.16 nm/min. The ratio between axial and radial growth rates is twice as large at low In flux compared to high In flux. For InAs segments of similar length obtained at low and high In fluxes, the parasitic shells would be half as thin using a low In flux. Finally, we observe that the InAs segment grown at a high In flux features more stacking faults and crystal phase switches (approximately 15 per 50 nm) along the entire growth axis than the one grown at low In flux (approximately 10 per 50 nm).

In conclusion, using an In flux of 1.2×10 -7 Torr improves the InAs-on-GaAs nanowire morphology and crystalline quality. We can see the similarity with the wurtzite GaAs nanowires: a high As coverage (high V/III ratios) reduces the In surface diffusion and leads to the reduction both of tapering and of crystalline defects.

Still, we need further work to fully suppress the crystal phase switching in the InAs segment by fine tuning the In flux and V/III ratio.

InAs-on-GaAs nanowire interface sharpness and crystalline quality

Now that we created straight InAs-on-GaAs nanowires, we first study the interface quality in terms of sharpness. The most direct way is to measure the chemical composition by EDX along the nanowire axis (see paragraph 2.3). Figure 4a shows a HAADF STEM image of our nanowire. The upper segment has a larger diameter and features dark and bright areas which correspond to a change either in material composition or in crystal structure. We studied the average chemical composition along and across the nanowire axis as indicated in Figure 4a. On the axial EDX line profile we clearly see three zones (Figure 4b): the long bottom segment is pure GaAs, the upper segment with a larger diameter is InAs and the droplet is Au. The nominal composition of the InAs segment is a ternary In x Ga 1-x As alloy (x varying from 0.9 at the GaAs interface to 0.8 near the top). A pure 5 nm InAs segment is visible below the Au catalyst. The droplet contains 70% of Au and 30% of In. We measure a GaAs/In 0.85 Ga 0.15 As interface sharpness length which ranges between 15 and 30 nm (measured on several nanowires). The EDX line profiles taken perpendicular to the growth axis of the same InAs-on-GaAs nanowire are presented in Figure 4 c,d. We find that a few nm-thick In 0.5 Ga 0.95 As shell surrounds the GaAs segment (Figure 4c). Finally, we observed that the samples grown with an In flux of 3×10 -7 Torr (Figure 3a) feature sharper GaAs/In 0.85 Ga 0.15 As interfaces down to 5 nm (see figure S8).

The interface length is significantly reduced when using higher In flux, approaching the values obtained for self-catalysed InAs-on-GaAs nanowires [START_REF] Scarpellini | InAs/GaAs sharply defined axial heterostructures in self-assisted nanowires[END_REF]. By introducing In in the gold droplet, the Ga solubility decreases. The faster In enters the Au (higher In flux), the faster Ga is depleted and the sharper is the interface. However, the question remains why the expected InAs segment is in fact a ternary alloy and not pure InAs, as seen in the EDX line profile in Figure 4b (and S8b)? The In 0.85 Ga 0.15 As segment has a constant composition in the radial direction, confirming that Ga adatoms are incorporated in the volume (Figure 4c).

One explanation can be found in our two-step growth procedure where GaAs continues to grow during the temperature decrease down to 540 °C. Ga adatoms do not desorb from the surface during the group III interchange at 540°C [START_REF] Ohachi | Arsenic pressure dependence of Ga desorption from MBE high index GaAs substrates[END_REF], creating a reservoir of available Ga adatoms. Therefore, residual Ga diffuses to the Au droplet and contributes to the formation of the In x Ga 1-x As segment by the VLS mechanism. We interpret the observation of a decrease in In composition along the In x Ga 1-x As by the presence of a competing mechanism between In and Ga adatom diffusion from the surface. We suggest that another source of Ga in the In x Ga 1-x As segment could be the diffusion of Ga from the bottom GaAs segment across the GaAs/In x Ga 1- x As interface, as observed in Stransky-Krastanov InAs quantum dots grown on GaAs [START_REF] Joyce | Composition of InAs quantum dots on GaAs (001): Direct evidence for (In, Ga) As alloying[END_REF]. Growing InAs segments during different times, at different In fluxes and using different cooling down rates would provide useful data to conclude on the diffusivity competition between In and Ga and its dependence on temperature, as well as on the diffusivity of Ga across GaAs/InAs interfaces. The formation of a thin shell around the bottom segment is usual in axial nanowire heterostructures and can be suppressed via fine tuning of the growth parameters. After optimization, the shell is still In 0.5 Ga 0.95 As, which further confirms the presence of mobile Ga adatoms and competing mechanisms between In and Ga. Finally, the presence of the pure InAs cooling neck is probably related to In segregation [START_REF] Muraki | Surface segregation of In atoms during molecular beam epitaxy and its influence on the energy levels in InGaAs/GaAs quantum wells[END_REF] or rapid crystallization from the AuIn alloy.

We are now interested in the crystal structure of the nanowires, especially in the structural quality of the GaAs/In 0.85 Ga 0.15 As interface. Figure 5a shows a bright field high-resolution TEM image of a structure.

The major part of the nanowire has the wurtzite crystalline structure (see figure S9 for the diffraction patterns). The GaAs segment is defect free, as already seen in Figure 1d, yet the In 0.85 Ga 0.15 As segment features randomly distributed zinc-blende inclusions. Interestingly, we clearly see an expansion of the In 0.85 Ga 0.15 As diameter in Figures 5 a andb. The GaAs and In 0.85 Ga 0.15 As segments measure 32.6 nm and 38 nm in diameter, respectively. This diameter expansion was explained earlier by the variation of the catalyst composition and thus of the contact angle [START_REF] Borg | Synthesis and properties of antimonide nanowires[END_REF][START_REF] Jeppsson | GaAs/GaSb nanowire heterostructures grown by MOVPE[END_REF][START_REF] Caroff | High-Quality InAs/InSb Nanowire Heterostructures Grown by Metal-Organic Vapor-Phase Epitaxy[END_REF]. Here, In 0.85 Ga 0.15 As has a lattice parameter ̴ 6% larger than GaAs: a large strain builds across the GaAs/In 0.85 Ga 0.15 As interface and has to be released to minimize the energy of the system. We calculate that for a certain number of planes in a GaAs segment of 33 nm in diameter (a = 0.39845 nm in wurtzite GaAs), the diameter expansion is 2.36 nm for a fully relaxed InAs segment containing the same number of planes (a = 0.4269 nm). We therefore believe that strain relaxation at the interface is partly responsible for the diameter variation.

The careful visual inspection of high-resolution STEM images (Figure 5c, see figure S9c for the whole interfacial region) did not reveal any misfit dislocations in the crystal at the interface between the GaAs and In 0.85 Ga 0.15 As segments, though the crystal phase switches from WZ to ZB in the transition region. We found this effect for all investigated nanowire heterostructures both for low and high In fluxes. We speculate it could be an additional source to release strain for the system. Finally, we applied the GPA method to the high resolution HAADF image in Figure 5b using the (0002) reflection, to map the local interplanar spacing at the GaAs/In 0.85 Ga 0.15 As interface (Figure 5d). The orange top segment is In 0.85 Ga 0.15 As and the green bottom segment is GaAs. The interface does not present any sign of abrupt color variation, which indicates the absence of misfit dislocations [START_REF] Frigeri | Structure, interface abruptness and strain relaxation in self-assisted grown InAs/GaAs nanowires[END_REF][START_REF] De La Mata | Atomic scale strain relaxation in axial semiconductor III-V nanowire heterostructures[END_REF].

Conclusion

In conclusion, we have successfully fabricated dislocations free axial InAs-on-GaAs nanowire heterostructures on silicon with a yield up to 90%. By a careful optimization of the growth parameters, we obtained for the first time pure GaAs wurtzite nanowires with Au as a catalyst on Si by MBE. We then proposed a two-step growth procedure to stabilize the Au catalyst during the group III element interchange by constantly maintaining a high supersaturation. By decreasing the In flux and increasing the V/III ratio, we reduced the formation of a radial shell around the GaAs stem as well as the density of crystal defects. We performed EDX, HRTEM and GPA and demonstrated that our GaAs/In 0.85 Ga 0.15 As interfaces are free of dislocations despite a ̴ 6% lattice mismatch. Such interface control of high lattice mismatched materials is crucial for the design of future optical emitters on Si substrates.

Figure 1 .

 1 Figure 1. Au-GaAs wurtzite nanowires on Si substrates. a) Schematic model of VLS GaAs nanowire growth

Figure 2 .

 2 Figure 2. Comparison of two different cooling strategies applied to the growth of InAs-on-GaAs nanowires.

Figure 3 .

 3 Figure 3. Morphology of InAs-on-GaAs nanowires grown at 540 °C for two different In fluxes. a) Bright-field

Figure 4 .

 4 Figure 4. Investigation of the nanowire chemical composition. a) HAADF-STEM image (scale bar 30 nm) of an InAs-on-GaAs nanowire grown at 540 °C with In = 1.2×10 -7 Torr and V/III ratio of 50. b) EDX line profile of

Figure 5 .

 5 Figure 5. Investigation of the nanowire crystal structure. a) Bright-field TEM image in the <2-1-10> viewing direction (scale bar 40 nm) of an InAs-on-GaAs nanowire grown at 540 °C with In = 1.2×10 -7 Torr and V/III

Acknowledgments

This work was supported by LANEF PhD Program and by the University of Grenoble-Alpes through the AGIR program. The authors are grateful to Yann Genuist and Didier Boilot for their MBE technical support.


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