Radial Growth of Self-Catalyzed GaAs Nanowires and the Evolution of

Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

pubs.acs.org/NanoLett

Radial Growth of Self-Catalyzed GaAs Nanowires and the Evolution of the Liquid Ga-Droplet Studied by Time-Resolved in Situ X‑ray Diffraction Philipp Schroth,*,†,‡,§ Julian Jakob,‡ Ludwig Feigl,§ Seyed Mohammad Mostafavi Kashani,† Jonas Vogel,∥,† Jörg Strempfer,∥ Thomas F. Keller,∥,⊥ Ullrich Pietsch,† and Tilo Baumbach§,‡ †

Solid State Physics, Department of Physics, University of Siegen, Walter-Flex Straße 3, D-57068 Siegen, Germany Laboratory for Applications of Synchrotron Radiation, Karlsruhe Institute of Technology, Kaiserstraße 12, D-76131 Karlsruhe, Germany § Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany ∥ Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg, Germany ⊥ Fachbereich Physik, Universität Hamburg, Jungiusstraße 9, D-20355 Hamburg, Germany ‡

S Supporting Information *

ABSTRACT: We report on a growth study of self-catalyzed GaAs nanowires based on time-resolved in situ X-ray structure characterization during molecular-beam-epitaxy in combination with ex situ scanning-electron-microscopy. We reveal the evolution of nanowire radius and polytypism and distinguish radial growth processes responsible for tapering and side-wall growth. We interpret our results using a model for diameter self-stabilization processes during growth of self-catalyzed GaAs nanowires including the shape of the liquid Ga-droplet and its evolution during growth.

KEYWORDS: Nanowires, self-catalyzed, growth, tapering, molecular beam epitaxy, polytypism, in situ X-ray diffraction

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variation of the NW diameter along its length, so-called tapering. On the one hand, tapering was first regarded as unintended side-effect3 due to, for example, an inflation of the droplet during growth, as a consequence of unbalanced material fluxes,11 and its minimization was desired.24 On the other hand, by harnessing radial growth processes, tapered NWs geometries could be exploited, for example, for axial NW heterostructures,25 and for advanced device applications.26−28 Hence, current efforts aim at the control5,7,29−31 and understanding8,9,32−41 of radial growth processes responsible for tapering. Of particular interest here are self-stabilizing growth processes that are closely linked to the liquid Gadroplet.42,43 In addition to the radial growth processes involving the droplet (VLS), growth at the NW side-walls via the vapor−solid (VS) mode further influences the final shape of the NW9,24,35,36,40 and impedes the direct observation of the aforementioned self-stabilization processes.

aAs Nanowires (NW) can be grown by the self-catalyzed method1 via the vapor−liquid−solid (VLS) mode.2 In this process their morphology is strongly influenced by the liquid Ga-droplet at the NW tip.3,4 This droplet acts as a catalyst for the uniaxial NW growth and at the same time as material reservoir. The size of the droplet correlates with the actual NW diameter.5−10 Composition11,12 and shape5,13,14 of the droplet, and therefore its wetting conditions at the liquid− solid interface and the facets involved, determine the microstructure of the growing NW.14−18 Regarding the wetting conditions, two different regimes can be identified. The zincblende (ZB) phase is favored for large wetting angles β ≈ 130°, whereas the wurtzite (WZ) phase is typically favored for wetting angles β ≈ 90°.14,17−21 Usually, the transition of β between these two regimes is causing highly faulted segments.21 Altough good control over the crystal structure has been achieved for Au-catalyzed GaAs NWs,22 controlling the droplet shape and crystal structure in self-catalyzed VLS grown NWs is more challenging but could ultimately be performed at CMOS compatible temperatures.23 However, not only the crystalline phase is affected by the droplet. For large wetting angles, radial growth can be strongly enhanced15 resulting in a © XXXX American Chemical Society

Received: August 15, 2017 Revised: November 28, 2017

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DOI: 10.1021/acs.nanolett.7b03486 Nano Lett. XXXX, XXX, XXX−XXX

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10 nm (measured from edge to edge, compare inset in Figure 1b), and a tip diameter below the droplet de(4 μm) = 157 nm ± 8 nm, resulting in a tapering angle δ ≈ 0.5° ± 0.1°. The SEM image in the top left panel of Figure 1a illustrates the homogeneity of the grown NW ensemble. The inverse tapering of the NWs becomes evident in the panel at the bottom left. On the high-resolution image at the right panel of Figure 1a, (110)-type side-facets48 and the pronounced Ga-droplet are visible. The contact angle between droplet and NW top-facet is βSEM ≈ 135° ± 2°. In Figure 1b, the mean radius after growth rNW(z, tf) is shown as a function of height z above the substrate. Further, rNW(z, tf) is well characterized by a third order polynomial fit given by the red solid line. Hence, describing tapering by a constant tapering angle δ along the NW length is insufficient. For the remainder of the manuscript we will refer to the distance between opposite side-facets when using the terms “diameter” or “radius”. In this case, the distance measured in the SEM image (see the inset of Figure 1b) has to be multiplied by a factor of √3/2. For in situ structure characterization of the growing ensemble of self-catalyzed GaAs NW, we monitor the evolution of the phase-selective Bragg reflections (311) of GaAs zinc-blende (ZB), (220) of GaAs twinned zinc-blende (TZB) and (10.3) of GaAs wurtzite (WZ).49,50 Figure 2a illustrates the scanning geometry (for further details see Supporting Information (SI)). For this set of reflections, scattering from ZB, TZB, and WZ is well separated in reciprocal space, in contrast to the symmetric (111) reflection where the signals of WZ and ZB can overlap.50,52 In the right panel of Figure 2b, the time-evolution of the integrated intensities 0p(t ) of 2D-cuts through the centers of those three phase-selective Bragg reflections (illustrated in the reciprocal space map (RSM) in the left panel) are shown after renormalization to correct their structure-factor differences and subtraction of the contribution from parasitic GaAs islands to the scattering signal.44,53 We take the integrated scattered intensity of a phase-selective Bragg reflection as a measure for the volume of the respective phase in the crystal. During the nucleation, we observe that the (10.3) WZ reflection emerges first, providing evidence that the NW base consists mainly of WZ GaAs. Until t = 30 min (dotted vertical line in Figure 2b), WZ GaAs is almost exclusively formed until the nucleation probabilities14,44 start to change in favor of the formation of GaAs ZB and TZB phases. This may be caused by a transition of the wetting angle14,17,21 to values favoring ZB over WZ. In our case, this transition could be related to the abrupt change in the slope of the integrated intensity of the GaAs (10.3) WZ reflection, and the concomitant emergence of the GaAs ZB and TZB reflections. Subsequently, the majority of growing GaAs is of ZB or TZB type. In fact, postgrowth transmission-electron microscopy (TEM) did not reveal any extended WZ segments in the NWs at heights corresponding to growth times t > 30 min (see also additional TEM and XRD data given in the SI). Consequently, the remaining intensity increase observed in the WZ reflection after the distinct change is an indication for radial VS side-wall growth, increasing the radius of already existing WZ segments at the NW base. In the kinematical approximation, and in absence of nonhomogenous strain the distribution of scattered X-ray intensity around a Bragg peak reflects the square modulus of the Fourier-transform of the NW shape.54 From suitable key interference features of the (10.3) WZ and (220) TZB

In the following we show for self-catalyzed GaAs NW, that tapering and subsequent side-wall growth can be distinguished by a combination of time-resolved in situ X-ray diffraction (XRD) during growth and postgrowth ex situ characterization by scanning electron microscopy (SEM). Our results allow for a refinement of recently presented growth-models42,43 and give insight into the evolution of the shape of the liquid Ga-droplet during growth. We use molecular-beam-epitaxy (MBE) for the growth of self-catalyzed GaAs NWs on Si(111) substrates covered by native oxide. In order to monitor the growth process nondestructively, we apply time-resolved in situ XRD which has recently gained appeal in the field of NW structure characterization,16,20,44,45 and from which we infer information on the evolution of crystal structure and the shape of the NWs during growth. The XRD experiments for this study have been performed at the beamline P0946 at the synchrotron facility PETRA III, using a specially designed portable MBE chamber.47 SEM images of the NWs grown for this study are shown in Figure 1. After a final growth time of tf = 255 min at a substrate temperature of Tsub = 600 °C and a V/III ratio of FV/III ≈ 2.6 ± 0.1, the GaAs NWs are inversely tapered with a length of approximately l(tf) ≈ 4 μm, a base diameter de(0) = 79 nm ±

Figure 1. Representative scanning electron images of the grown NW ensemble (a). The large field of view at the upper left gives an impression on the homogeneity of the NW ensemble. At the lower left, the inverse tapering of the wires is visible. In both images, the view-direction is parallel to the normals of one pair of (110) sidefacets which allows us to calculate the facet distance. The highmagnification image at the right51 shows a single NW from a tilted view. The (110)-type side-facets and a pronounced Ga droplet at its tip are visible. In the bottom panel (b), the height-resolved mean NW radius is depicted, as well as a fit using a third order polynomial (red). B


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Figure 2. (a) The drawing of the experimental setup gives a schematic view of the scattering geometry inside the MBE growth chamber, which is mounted on the beamline diffractometer. The X-rays enter and leave the chamber via circular Be-windows. After impinging upon the specimen (red), the diffracted X-rays leave the chamber and are recorded at the detector as a two-dimensional intensity distribution. By rotation of the sample about its surface normal, Bragg reflections for ZB, TZB, and WZ GaAs and Si can be excited without changing the incidence angle.49,50 (b) Time-evolution of the integrated intensity of phase-selective Bragg reflections of GaAs as a measure of the growing material in the NW ensemble. Initially GaAs nucleates in WZ phase. After 30 min, a transition toward ZB and TZB takes place. For better visibility, the intensity of WZ I(10.3) is multiplied by a factor of 10.

corresponding WZ segments are present only at the NW base (t < 30 min) and tapering is negligible. The first-order side-maxima are not detectable (compare Figure 3b), and the (10.3) Bragg reflection is weak but yet sufficiently strong in order to estimate the mean radius of WZ segments rW ̅ Z(t) from the fwhm of the reflection, as we discussed earlier. In this way, direct information on the side-wall growth is accessible. In the following discussion, we correlate the in situ results for rW ̅ Z(t) with the NW radius rNW(z, tf) along the NW growth axis z obtained by SEM after the growth. We model the evolution of NW length and radius, where we allow radial growth processes containing contributions of tapering and side-wall growth. We associate rW ̅ Z(t) with the time-evolution of the NW base radius rNW(0, t). Supposing the initial NW radius is r(0, 0) at growth time t = 0 min and l = 0 nm, we express the height- and timedependent NW radius rNW(z, t) as

reflections we can therefore infer information on the evolution of the mean radius of segments of WZ and TZB GaAs in the growing NW ensemble. Because the scattering vector Q z is defined to be parallel to the [111] growth direction, the intensity distribution I(q⃗,t) with scattering vector q⃗ in the Q x/ Q y-plane around these reflections, contains direct information on the cross-sectional shape ΩNW of the [111]-oriented NW and therefore its radius (see Figure 3a, in absence of tapering). The full width half-maximum (fwhm) of the Bragg reflection qfwhm(t) and the distance of the first-order size-oscillation qmax(t) are inversely proportional to the radius of the NW. In the absence of tapering the radius can be directly determined by a sinc-squared function via r(t) ≈ 2.78/qfwhm(t), and r(t) ≈ 4.49/qmax(t). If tapering is present, an additional weightfunction has to be applied in order to consider the effect of height dependent radius variation, providing a weighted mean radius rw̅ (t), averaged over the NW length (see SI). The intensity distribution around the (220) TZB Bragg reflection in the Q x/Q y-plane crossing the Q z-axis at Q z = 2.542 Å−1 at the final growth time tf is shown in Figure 3b. We observe a characteristic scattering feature with 6-fold symmetry, originating from the (110) side-facets of TZB segments with hexagonal cross-section. From the intensity profiles I(q, t), essentially along a so-called facet truncation rod, as indicated by the dotted line in Figure 3b, we estimate qfwhm(t) and the position of the first-order side maximum qmax(t). The measured intensity profiles I(q, t) are shown in Figure 3b for several different times during growth. In our case, qfwhm(t) and qmax(t) of the intensity profiles from the (220) reflection decrease for increasing growth time t, which is indicative for radial growth as result of both inverse tapering (as newly grown TZB-type layers at the NW top have larger radii than the segments below), as well as subsequent side-wall growth. As a consequence of this superposition, the interpretation of the results from the (220) TZB reflection needs further modeling. Before we discuss a model that is capable of describing both aspects of radial growth, we now focus on the WZ reflection. The (10.3) WZ Bragg reflection is an ideal starting point for our evaluation, since the

rNW(z , t ) = r(0, 0) + Δrradial(z , t )

(1)

= r(0, 0) + ΔrT(z , t ) + ΔrF(z , t )

(2)

assuming that the radius of the NW can be described by two independent quantities constituted by tapering ΔrT(z, t), and subsequent side-wall growth at the NW facets ΔrF(z, t), both depend on z and growth time t in general.55 ΔrT(z ,t) describes the radial VLS growth of the top-facet due to tapering42,43 at z = l(t) and can thus be expressed by ΔrT(l(t)) = ΔrT(t). The term ΔrF(z, t) accounts for subsequent VS side-wall growth along the NW. Although ΔrF(z, t) can in general be a function of NW length and growth time, we here first assume that the side-wall growth rate mfacet = drF/dt is constant and homogeneous along the NW growth axis (drF/dz = const.), and ΔrF(l, t) = 0 at the tip of the NW. Moreover, we assume that the NW grows with a constant axial growth rate va, resulting in the NW length l(t) = va·t at time t. At our growth conditions the axial growth rate is va = 15.68 nm/min ± 0.19 nm/min, and side-wall growth at height z = l(t0) ≤ l(t) in the interval δt = t − t0, and t ≥ t0 can be expressed as C


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rW ̅ Z(t) at t = 0. The values rSEM(z) measured by SEM can then be expressed by rSEM(z) = rNW(z , t f ) = r(0, 0) + ΔrT(l(t )) + ΔrF(l(t ), tf )

(5)

where we have to keep in mind that z at the left-hand of the equation is the height above the substrate after growth, and l(t) on the right-hand is the corresponding NW length during growth. The initial radius r(0, 0), as well as the facet growth rate mfacet have been extracted from the X-ray experiment. With eq 4 and rSEM(z) and assuming homogeneous facet growth, this allows us to conclude the NW shape during growth. More precisely, we obtain ΔrT(l(t)) empirically by ΔrT(l(t )) = rNW(l(t ), tf ) − ΔrF(l(t ), tf ) − r(0, 0)

Knowing ΔrT(l(t)), the NW shape rNW(z, t) at any time during growth can be determined according to eq 2, based on the in situ XRD and ex situ SEM results. No further model for ΔrT is required for calculation of the NW shape evolution during growth. The results are summarized in Figure 4a. The broken black curve, rNW(z, tf) is a fit to rSEM (z) given by the black circles. The red circles show the evolution of the topfacet radius rtop(t) = ΔrT(t) + r(0, 0) as calculated from rSEM and ΔrF. The linear fit rNW(0, t) to rW ̅ Z(t) is given by the green broken line. We now briefly check the values so obtained at the beginning and the end of growth for consistency. The initial radii r(0, 0) and rtop(0) (using eq 6) are consistent within the errors as shown in Figure 4a. Moreover, the value of the WZ base radius at the end of growth is consistent with the measured value by SEM at the NW base. In order to verify our assumptions, we use the results from Figure 4a to simulate the temporal evolution of the diffraction pattern and compare these simulations with the experimental results from the (220) TZB reflection. In other words, we simulate the X-ray scattering from a NW during growth, based on the NW shape evolution shown in Figure 4a. Therefore, we calculate the two-dimensional scattered intensity distribution I(q⃗,t) for a single NW with nonuniform radius rNW(z, t) as given by eq 2, at a certain time t. We build the incoherent sum over the squared absolute values of the two-dimensional Fourier transforms

Figure 3. (a) Top panel: Schematic illustration of NW cross-sectional geometry and resulting scattering signal in reciprocal space. Bottom panel: The corresponding cross sections indicated by the gray lines. (b) Measured intensity distribution around the (220) TZB reflection after growth. Upper left panel: Qy/Qz-RSM of the (220) TZB reflection. Tilted structures (mainly crystallites) scatter along a Debye−Scherrer ring causing the oblique feature passing through the reflection. The NW side facets cause the scattering streaks perpendicular to Qz. Upper right panel: Qx/Qy-RSM at the Qz-level depicted by the dotted line left. The line on the right corresponds to the direction along which the intensity profiles I(q,t) of the facetstreaks were evaluated during growth. The bottom left panel shows the facet-streaks extracted from the TZB reflection, the bottom right panel shows the corresponding profiles of the (10.3) WZ reflection. In both cases, the fwhm decreases with time.

drF (t − t0) dt m = facet (vat − z) va

ΔrF(z , t ) =

(6)

z = l(t )

I (q ⃗ , t ) =

∑ z=0

|Ω̃(z , t )|2 (7)

of the hexagonal cross sections Ω(z, t) of the NW with radius rNW(z, t) from the base at z = 0 to the NW tip at z = l(t) with a step-size of Δz = 1 nm. In this approximation, we neglect interference related to the vertical stacking in the NW. From the simulated two-dimensional intensity distribution I(q⃗,t), we extract the line-profiles INW(q,t) along a NW facet streak in analogy to the procedure shown in Figure 3a. The inset in the top of Figure 4b shows those line-profiles INW(q,t) normalized to the maximum intensity at each time t (or equivalent NW length l(t)). With increasing growth time t, NW both qNW fwhm(t) and qmax (t) decrease. The values of these key features (red solid line) are compared to the experimental results given in Figure 4b. Although we can not fully exclude contributions of parasitic GaAs islands to the fwhm of the (220) TZB Bragg reflection, the agreement of simulation and experiment is remarkable. Further, this agreement confirms that the shape-evolution based on the results from the WZ

(3) (4)

Because of VS side-wall growth, the mean radius rW ̅ Z(t) increases with time as shown in Figure 4a. The side-wall growth rate mfacet = 0.094 nm/min ± 0.009 nm/min follows from the slope of rW ̅ Z(t) and defines the time-evolution of the NW base radius rNW(0, t). In addition we estimate the initial radius r(0, 0) = 11.1 nm ± 1. 0 nm from linear extrapolation of D


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Figure 4. (a) Top: Illustration of the NW shape at several exemplary growth times t shown for our growth parameters. The contribution of VS facet growth ΔrF is depicted by the red area. The inner yellow shape corresponds to rtop(t) (VLS growth). Bottom: Mean NW radius obtained by SEM and fit (black), mean radius of WZ segments rW ̅ Z (t > 50 ̅ Z(t) (green circles), interpreted as mean radius of the NW base rNW(0, t) (linear fit for rW min), green broken line). The resulting top-radius rtop(t) below the Ga-droplet from eq 6 is given by the red circles and the broken red line shows the corresponding fit. (b) Comparison of key features extracted from experiment (symbols) and simulation (red solid lines). The calculated values are obtained from the simulated intensity profiles shown in the inset. Each profile INW(q,l(t)) corresponds to scattering along a facet streak from a NW with length l(t) and shape defined by rNW(z, t) at growth time t. For completeness, also the fwhm corresponding only to the NW base is compared to the fwhm of the WZ reflection.

length of Ga-atoms at (110)-facets is given by λGa. FV/III is the V/III ratio, and ηeq is the equilibrium droplet shape factor, which relates the height of a spherical droplet to the radius of the NW top-facet. The discussions in ref 43 focus on a constant value for the Ga-droplet shape ηeq independent of its volume and the topfacet radius rtop(t) during growth. This requires a mechanism for easy tapering, for example, when the side-walls are not oriented along stable surface facets.43,57 Then the NW radius below the droplet can be readily adjusted in order to maintain ηeq. In our case of self-catalyzed GaAs NWs, however, the sidefacets are composed of (110)-type surfaces. Therefore, the actual droplet shape factor η(t) may differ from its equilibrium value and may also change during growth in order to approximate the equilibrium value ηeq.43,56 Because the exact functional behavior of η(t) during growth is unknown, a Fermifunction has been chosen in order to empirically describe the behavior of η(t) with growth time t. In this way we can express η(t) as a function of initial ηi and equilibrium value ηeq, whereas the transition between both limits is described by the width f w of the Fermi-function and the transition time t0

reflection and SEM shown in Figure 4a is consistent with our X-ray data extracted from the (220) TZB Bragg reflection. In the bottom panel of Figure 4b the corresponding values qWZ fwhm(t) obtained from the (10.3) WZ reflection are compared to the calculated fwhm values obtained from rNW(0, t), showing reasonable agreement as well. Until now, we distinguished tapering and side-wall growth and gained insight into the evolution of the top-facet radius rtop(t). This is of particular interest since rtop(t) is in contact with the liquid Ga-droplet which acts as the catalyst for axial NW growth. The growth model suggested in ref 43 links the radial growth of the top-facet radius rtop(t) to the shape η of the Ga-droplet. Here, we employ eq 11 in ref 43 in order to model the evolution of the NW radius due to tapering, expressing rtop(t) using 2ΩGa ÑÉÑ ÅÄÅ yz i ÑÑ ÅÅ drtop(t ) λGa ΩGaAs z Ñ Å −1 jjj z Å zz − 1ÑÑÑ ÅFV/IIIjj1 + = 2 Å 2 z j ÑÑ Å j dt ηeq (3 + ηeq ) ÅÅ (1 + ηeq )rtop(t ) z ÑÑÖ ÅÇ { k (8)

where ΩGa is the volume of Ga in liquid, ΩGaAs is the volume of a GaAs pair in the solid, and ΩGa/ΩGaAs = 0.42.43 The diffusion E


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Figure 5. (a) Evolution of the NW radius measured after growth rSEM(z), and measured mean weighted radius during growth rZ̅ B(t) from XRD in comparison with the calculations of rNW(z, tf) according to eq 5 and the calculated mean NW radius rw̅ (t). The calculated curves correspond to the set of the best parameters for η(tf) = 2.41+0.13 −0.11 which is compatible with SEM. In addition, rtop(t) and the contribution of facet growth to the NW bottom rNW(0, t) in comparison with the mean radius of WZ segments rW ̅ Z(t) is given. (b) Evolution of the droplet wetting angle. Starting below β(0) ≈ 155° the wetting angle decreases over time, approaching the final value β(tf) ≈ 135°.

η(t ) = ηi −

ηi − ηeq e

−(t − t 0)/ fw

+1

neighboring NWs. In contrast, our values are lower than Gadiffusion length λ > 2 μm on GaAs (110)-facets reported, for example, by Lopez et al.58 Such high values for λ would, in our case, require large η(tf) which are incompatible with our observations. This implies that either the diffusion length on Ga-adatoms at NW (110)-type side-walls is different compared to extended plain GaAs(110)-surfaces, or the growth conditions are not directly comparable to 2D layer growth. This may be caused by As re-evaporation effects in the case of NW growth59,60 or a lower effective Ga-diffusion length, reduced by the number density and mean distance of neighboring NWs.42 The evolution of the wetting angle β(t) during growth (calculated from the droplet shape factor η(t)) for our case is depicted in Figure 5b. Within the model the wetting angle decreases monotonously with growth time and approaches its equilibrium value βeq = 134.34° (ηeq = 2.38). We note that the wetting-angle during WZ growth (t < 30 min) may differ from the values obtained by the model. In order to investigate the nucleation and early growth-stage, further dedicated experiments, for example, taking advantage of grazing-incidence Xray geometry are required, which is out of the scope of this study. In conclusion, we have determined the evolution of crystalstructure and shape of inversely tapered self-catalyzed GaAs NWs by time-resolved in situ XRD. Combined with postgrowth electron-microscopy analysis, we gain insight into the processes of radial growth which are responsible for tapering and side-wall growth. We have refined a theoretical model for diameter self-stabilization processes, enabling its application to growth experiments and allowing the extraction of Ga-diffusion length and evolution of the Ga-droplet shape during growth. The proposed experimental approach opens the way for further fundamental studies aimed at validating and refining existing NW growth models. Furthermore, the approach allows correlation of the wetting properties of the liquid-droplet directly to the evolution of polytypism in VLS-grown semiconductor NWs, which is an essential for crystal phase

(9)

We point out, that we obtain the original model for ηi = ηeq. We further substitute ηeq in eq 8 by η(t) from eq 9, which allows us to model rNW(z, t). Now we determine a set of parameters which yields rNW(z, t), which describes simultaneously both SEM and XRD data. Therefore, sampling of the parameter space given by λ, r(0, 0), FV/III, and ηi, ηeq, t0, and f w is required. From our growth calibrations, we obtained FV/III = 2.6. Also r(0, 0) = 11.1 nm is known from the X-ray experiment. From SEM, we obtain the wetting angle βSEM = 135° ± 2° which allows us to limit a probable range of ηeq ∈{2.1, 5.7} with a certain safety margin to higher values, accounting for a possible shrinkage of the droplet wetting angle after growth.13 In the remaining parameter space bounded by λ ∈{550, 4500}, ηi ∈{4.5, 11.4}, f w ∈{20, 60}, and t0 ∈{0, 32} (for further details see SI). In fact, solutions within this parameter space are found which describe the experiment to a very high degree. We note, however, that the solutions are not unique for η(t) and λ, but can be parametrized via the diffusion length λ (see SI). Thus, by choosing values of η(tf) compatible to the wetting angle βSEM obtained from SEM, a range of possible solutions can be identified. Figure 5a depicts the radii measured by SEM and the calculated values rNW(z, tf), which show good agreement. Also, the radii obtained by in situ XRD rZ̅ B and rW ̅ Z are well reproduced by the calculated values for the weighted mean radius rw̅ (t) (see SI) and the radius at the NW base rNW(0, t). In addition, the final value η(tf) = 2.41, equivalent to a wetting angle β(tf) = 135.0°, is consistent with the measured wetting angle by SEM βSEM ≈ 135° ± 2° as observed after growth. With the limits for βSEM we obtain values for the Gadiffusion length λ = 991+134 −111 nm. Compared to literature, Dubrovskii et al.42 obtained similar values λ = 750 nm obtained from site-selective grown self-catalyzed GaAs NWs. This value is close to ours and differences may be caused by different growth parameters used and the different mean distance of F


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control and an important step toward the synthesis of phase pure self-catalyzed nanowires.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b03486.

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Description of experimental conditions and supplemental experimental data; growth model and numerical simulations (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Philipp Schroth: 0000-0002-5016-9520 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors express their gratitude towards Emmanouil Dimakis, Lutz Geelhaar, Daniel Hauck, and Anton Plech for feedback and interesting, fruitful discussions. We are grateful for the valuable discussions with Martin Köhl and for his criticism and recommendations. Further, we gratefully acknowledge the support of Bärbel Krause, Hans Gräfe, Helmuth Letzguss, and Annette Weißhardt at the UHVlaboratory at ANKA, KIT, and Sonia Francoual and David Reuther at PETRA III beamline P09. Moreover we are grateful for Simone Dehm at INT, KIT for her support at the SEM and the KNMF for access to TEM measurements. This work was supported by the German BMBF project 05K13PS3.

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REFERENCES

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Radial Growth of Self-Catalyzed GaAs Nanowires and the Evolution of

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