Nucleation, Growth, and Bundling of GaN Nanowires in Molecular

Letter pubs.acs.org/NanoLett

Nucleation, Growth, and Bundling of GaN Nanowires in Molecular Beam Epitaxy: Disentangling the Origin of Nanowire Coalescence Vladimir M. Kaganer,* Sergio Fernández-Garrido, Pinar Dogan, Karl K. Sabelfeld, and Oliver Brandt Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5−7, 10117 Berlin, Germany S Supporting Information *

ABSTRACT: We investigate the nucleation, growth, and coalescence of spontaneously formed GaN nanowires in molecular beam epitaxy combining the statistical analysis of scanning electron micrographs with Monte Carlo growth models. We find that (i) the nanowire density is limited by the shadowing of the substrate from the impinging fluxes by already existing nanowires, (ii) shortly after the nucleation stage, nanowire radial growth becomes negligible, and (iii) coalescence is caused by bundling of nanowires. The latter phenomenon is driven by the gain of surface energy at the expense of the elastic energy of bending and becomes energetically favorable once the nanowires exceed a certain critical length. KEYWORDS: Nanowires, GaN, nucleation, coalescence

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other.18 However, in dense arrays, the shadowing of the impinging fluxes by long nanowires hinders radial growth at the bottom part of the nanowire sidewalls. This effect would cause tapering that, however, is not observed. In contrast to these previous reports, the experiments published in ref 16, where the Ga flux was intentionally varied during the growth of nanowire ensembles, indicate that the nanowire radius is self-regulated by the stoichiometry established at the top facet. Hence, if the Ga/ N ratio is not varied during the entire growth process, the nanowire diameter should remain constant after it reaches its self-equilibrated value. The assessment of the temporal evolution of the nanowire diameter is, however, not a straightforward task because GaN nanowires form dense ensembles (with densities up to 5 × 1010 cm−2) and coalesce during growth.14 For well-developed nanowire ensembles, the final areal density is believed to be determined by the mean diffusion length of Ga adatoms on the substrate,8 although this hypothesis is in contrast to the very comparable densities observed on structurally and chemically dissimilar substrates such as crystalline C, Si, AlN, and amorphous SixOy as well as AlxOy.1,2,20−22 Nanowire coalescence and its impact on the optical properties were already recognized in the very first studies on GaN nanowires grown by PA-MBE.23 The relative misorientation of GaN nanowires grown on Si(111) is typically about 3°, both in-plane (twist) and out-of-plane (tilt). 24−27 Consequently, as the nanowires merge together, dislocations are generated at the coalesced joints, which give rise to smallangle boundaries and inhomogeneous strain.21,25,28,29 Coalescence has been tentatively attributed to the radial growth of

n plasma-assisted molecular beam epitaxy (PA-MBE), GaN nanowires form spontaneously on various substrates under suitable conditions (i.e., N excess and elevated temperatures).1,2 In contrast to the vapor−liquid−solid (VLS) growth approach used for the synthesis of the majority of semiconductor nanowires,3−7 the spontaneous formation of GaN nanowires in PA-MBE occurs without any metal particle on their top.8 The main benefits of the spontaneous formation are thus the absence of contamination caused by foreign metal particles and the possibility to fabricate well-defined axial heterostructures by simply alternating the supply of the different elements. The mechanisms underlying the spontaneous formation of single crystalline wurtzite GaN nanowires on bare Si(111) substrates have been intensively studied (see ref 9 for a review). The growth starts after a typically non-negligible incubation time that strongly depends on the growth parameters.10−12 Initially, three-dimensional GaN islands with a spherical cap shape are formed on the substrate.13 Subsequently, the islands grow in size until they reach a critical diameter of about 10 nm.13 At that point, the islands experience a shape transformation toward their final hexagonal geometry, with clearly defined C- and M-plane top and sidewall facets, respectively.14 Upon the shape transformation, the islands grow in diameter and elongate along the [0001̅] axis,2 which results in the formation of vertically aligned nanowires. The nanowire axial growth is fed by both the Ga atoms directly impinging on the top facet and those that reach the nanowire tip via surface diffusion.15,16 The temporal evolution of the nanowire diameter has been controversially discussed in the literature. Several studies10,17−19 report a continuous increase in nanowire diameter during the entire growth process. In a sparse nanowire ensemble, radial growth can be ascribed to layer-by-layer growth along the side facets, with the atomic steps running from one end to the © XXXX American Chemical Society

Received: March 10, 2016 Revised: April 22, 2016

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DOI: 10.1021/acs.nanolett.6b01044 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters GaN nanowires8,14,16,21,30 and to their relative tilt, which brings them together during axial growth.9,21,31 However, the actual origin of coalescence has not been clarified yet. Since the detrimental effects of coalescence may prevent these nanostructures from realizing their full potential for electronic and optoelectronic applications, the origin of coalescence must be identified and eliminated. In the present work, we quantitatively study the process of coalescence by combining the experimental analysis of the temporal evolution of nanowire ensembles with Monte Carlo growth models. We show that radial growth and nanowire tilt cannot explain the coalescence of nanowires and the concomitant overall transformation of the nanowire ensemble. Rather, we find that bundling of nanowires, which allows them to reduce their total surface energy at the expense of the elastic energy of bending, is the main process that drives the coalescence of closely spaced nanowires. When the bundling of GaN nanowires is taken into account, our Monte Carlo simulations demonstrate that radial growth is negligible once the nanowire diameter reaches its self-equilibrated value. These simulations also produce an unexpected and surprising result, namely that the final nanowire number density is not determined by the mean diffusion length of Ga adatoms on the substrate but by shadowing effects. To investigate and analyze the temporal evolution of GaN nanowire ensembles, we prepared two series of samples (referred as A and B) in different PA-MBE systems (for details, see the Methods section.) At the high substrate temperatures used in the present study, even small temperature deviations give rise to large variations in the incubation time that precedes the formation of GaN nanowires.12 As a result, we observe large fluctuations in the nanowire growth rates derived from the total growth time. We overcome this uncertainty by studying the dependence of all parameters on the average nanowire length rather than on the growth time. Figure 1 presents top- (left column) and side-view (right column) scanning electron micrographs of some selected samples from series A. The scale is the same for micrographs a−l. The average nanowire lengths h, determined from the sideview images, are indicated in the corresponding micrographs. For the sample grown for the longest time (h = 2430 nm), only the bottom part of the side-view image is shown in the same scale as the other images (Figure 1l). An entire cross-sectional view of this sample is shown in Figure 1, panel m. The top-view micrographs presented in Figure 1 reveal that nanowire nucleation proceeds at least until the average nanowire length reaches 250 nm. With further growth, the nanowire density decreases because of coalescence. We refer hereafter to the density of compact objects, either single nanowires or their aggregates. These two types of objects can hardly be distinguished at the late stages of the growth. Figure 1, panel f shows the coexistence of irregular cross-sectional shapes, believed to be the result of coalescence,14 with shapes close to regular hexagons that, at first sight, could be attributed to uncoalesced nanowires. Note that, at this late stage of the growth, the different objects are surrounded by large empty spaces that were previously occupied by nanowires, as obvious from Figure 1, panels b and c. Consequently, the decrease in the number density of objects cannot be simply explained by assuming that all or the majority of nanowires coalesce because of radial growth. We trace the development of the nanowires that initially occupied these empty spaces by a closer inspection of side-view

Figure 1. (a−f) Top- and (g−l) side-view scanning electron micrographs of some selected samples from series A. The scale is common for all micrographs. The average nanowire lengths h are indicated in the side-view micrographs. (m) Side-view micrograph of the sample shown in panel l with lower magnification.

micrographs. Figure 2, panels a−d highlight the bottom part of the longest nanowires of series A (cf. Figure 1l,m). These micrographs reveal that the thick nanowires and nanowire aggregates seen in top view (cf. Figure 1f) actually emerge from B


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torsion at the coalescence joint. The ratio γ/E entering into eq 1 has a dimension of length. With the Young modulus of GaN E = 3.55 × 1011 J/m3 and a surface energy of γ = 118 meV/Å2 = 1.9 J/m2 for the M-plane facets that constitute the nanowire sidewalls,46 we get γ/E = 0.53 × 10−2 nm. For an estimation, consider two nanowires of diameter 2R = 20 nm at a distance l = 60 nm so that the spacing between their centers is l + 2R = 80 nm. According to eq 1, the bundling of these two nanowires becomes energetically favorable for a nanowire length Hc = 340 nm. This estimate agrees very well with the experimental example shown in Figure 2, panel d. This analysis allows us to conclude that, for nanowire lengths above 1 μm, the majority of nanowires gain energy by bundling. The previous analysis was based on a qualitative inspection of scanning electron micrographs. Next, we perform a quantitative statistical analysis of the main quantities describing the evolution of nanowire ensembles: density, coverage, average diameter, and nearest neighbor distribution. For this purpose, we analyze top-view scanning electron micrographs (as those shown Figure 1) with the help of the open-source software ImageJ.47 In the Supporting Information, we provide details and illustrations of this analysis. For each sample, at least 10 top-view micrographs from different regions of the surface were analyzed to obtain sufficient statistics. Figure 3, panels a and b present the areal density of compact objects (both nanowires and their aggregates, which are not distinguished a priori) and the fraction of the substrate surface that is covered by these objects (coverage θ). Both quantities are directly obtained from the statistical analysis of top-view micrographs without making any assumptions. In contrast, the average nanowire diameters, shown in Figure 3, panel c, are obtained by excluding from the analysis of the top-view scanning micrographs those objects with an irregular crosssectional shape, which is attributed to coalesced aggregates.14 We discriminate between regular and irregular cross-sectional shapes by analyzing their circularity, as proposed in ref 14, and as detailed in the Supporting Information. The error bars in Figure 3, panel c represent the widths of the diameter distributions. Plots similar to Figure 3, panels a and c, namely, which show the development of the nanowire density and average diameter, were presented in a number of studies.10,13,18,30,48,49 The evolution of the coverage (Figure 3b), however, provides a new perspective on the development of the nanowire ensemble. Figure 3, panels a and b demonstrate that, for both series of samples, the density rises steeply with the average nanowire length until the length reaches approximately 250 nm and decreases for longer nanowires. The coverage also increases steeply up to a length of about 250 nm and then changes very little with further nanowire elongation. In the discussion below, we distinguish these two stages of nanowire growth. We refer to them as the first, or early, stage when the average nanowire length is less than approximately 250 nm and the density increases, and the second, or late, stage when the average length is larger than 250 nm and the density decreases. The initial increase in both the density and the coverage evidence that the nucleation of new nanowires proceeds at least until the end of the first stage. The longest nanowires, having nucleated first, have a length of over 300 nm at that time. Note that an increase of the coverage without an increase of density could be explained by radial growth of already existing nanowires. The simultaneous increase of both quantities unambiguously shows that nucleation proceeds continuously

Figure 2. (a−d) Side-view scanning electron micrographs of the bottom parts of nanowires from the sample shown in Figure 1, panels l and m. (e) Schematic showing the geometry of two nanowires that merge together at a certain length h. H is the height of the shorter nanowire, Ri indicates the nanowire radii, and l = l1 + l2 shows the distance between the closest side facets of the two nanowires.

several thin pillars. These pillars, which represent the initially uncoalesced nanowires after nucleation, bent toward each other and bundle to form the thick aggregates seen in the top part of the sample. Their deviations from the vertical direction much exceed those of the short nanowires observed at the beginning of the growth as seen, for example, in Figure 1, panels g and h. This observation suggests that GaN nanowires attract each other after they reach a certain critical length. The phenomenon of bundling or clumping is known for diverse kinds of nanowire-like (quasi-one-dimensional) objects. It occurs when the gain in surface energy exceeds the elastic energy of bending. Nanowire bundling has been observed and investigated on several semiconductor materials: Si,32,33 GaAs,34−36 and ZnO,37,38 and also on C nanotubes,39 but so far not for GaN. Interestingly, the foot-hairs of geckos, which allow them to move on vertical surfaces, have an antiselfclumping structure that has been studied using different biomimetic models.40−44 In another context, bundling also constrains microcontact printing by stamp deformation.45 In the Supporting Information, we analyze the energetics of nanowire bundling in detail and generalize the results of previous works to the case of two nanowires with different diameters. As shown in Figure 2, panel e, we consider two nanowires of radii R1 and R2 separated by a distance l between their side surfaces. We find that bundling becomes energetically favorable when the length of the shorter nanowire exceeds the critical value: ⎛ E I1I2 2⎞1/4 l ⎟ Hc = 4⎜ ⎝ 9γw I1 + I2 ⎠

(1)

Here, E is the Young modulus, γ the surface energy, w the width of the contact area (for the calculations, we take w to be equal to the radius of the thinner nanowire), and Ii indicates the geometrical moments of inertia of the cross-section of the corresponding nanowire (i = 1,2). For a cylinder, I = πR4/4. The present calculation does not take into account that the crystallographic planes of the two nanowires may not be initially parallel to each other, which would cause an additional C


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the average diameter, are equally accurately derived from the same top-view micrographs. However, the interpretation of the coverage is direct and reliable, while the treatment of all objects with circularity exceeding some threshold value as single nanowires, rather than aggregates, is a question of interpretation and is not unambigious. Hence, by resolving this conflict in favor of the coverage as the quantity obtained directly, it seems that the objects with circular or hexagonal cross-sectional shapes do not necessarily correspond to single nanowires but rather to aggregates, which were able to restore a regular shape after coalescence. This process would evidently require at least some radial growth to transform the irregular shape of the coalesced aggregate into a more regular shape with circularity CA > 0.762 (see Supporting Information), which again seems to contradict the fact that the coverage of the nanowire ensemble stays constant. In this context, it is important to note that the axial growth rate of the nanowires is substantially enhanced by Ga impinging on the sidewall facets and diffusing toward the top facet.15,16,50 The amount of this contribution is limited by shadowing from neighboring nanowires. Upon a bundling event, the nanowires constituting the bundle recede from all others and thus instantaneously receive a larger Ga flux onto their sidewalls. The increased contribution from sidewall diffusion results in a sudden change of the stoichiometry on the top facet, which potentially leads to intermittent radial growth directly following the bundling event until stoichiometric conditions are reestablished.16 In this way, the nanowire bundle may restore a regular shape even in the absence of continuous radial growth. The experimental data in Figure 3, panel c show the diameters of such nanowire bundles. To gain further insight into the temporal evolution of the nanowire ensemble, we study the statistical distribution of distances between nearest neighbor (NN) objects. Figure 4 shows the probability density distributions of the NN distance at different stages of the growth for series A. For low coverages (θ = 0.01), the NN distances x are well described by the Poisson probability density distribution p(x) = 2πρx exp(−πρx2), where ρ is the areal density of the objects. Therefore, nanowires initially nucleate on the substrate homogeneously and independently. However, as growth proceeds and the coverage increases, close nanowires merge together due to coalescence, and the NN distance distribution changes and shifts toward larger distances, as shown in Figure 4, panels b and c. Note that, for θ = 0.19, the probability of finding a nanowire (or aggregate) closer than 0.25 of the mean distance between nanowires is actually negligible. In an attempt to provide a comprehensive description of the temporal evolution of the nanowire ensemble, we compare the experimental results presented in Figures 3 and 4 with two Monte Carlo simulations that model the growth and coalescence of GaN nanowires in PA-MBE under different assumptions. In our simulations, nanowires nucleate randomly as disks, which can grow radially and elongate as cylinders. The detailed algorithms can be found in the Supporting Information. The first model (Model 1) is based upon the assumption that the radial growth of GaN nanowires is the origin of coalescence, as proposed previously by several groups.8,16,21,30 Since an unrestricted nucleation of nanowires would result in the formation of a compact layer, the model needs to comprise a mechanism that stops the nucleation process. We assume that, as suggested in ref 8, nanowire nucleation is limited by the

Figure 3. Evolution of (a) the density of nanowires and their aggregates, (b) the coverage, and (c) the average diameter of nanowires and aggregates with a circularity exceeding a threshold value of CA ≈ 0.762. The experimental data are represented by circles (series A) and squares (series B). The error bars in panel c indicate the widths of the diameter distributions. The lines show the results derived from two different Monte Carlo growth models. Model 1 (blue lines) is based on the assumptions of a continuous radial growth of all nanowires and the preferential diffusion of Ga adatoms on the substrate toward already existing nanowires so that new nanowires do not nucleate at distances from the existing nanowires shorter than the Ga diffusion length on the substrate (taken to be 30 nm). Model 2 (red lines) simulates the coalescence by bundling. In this second model, radial growth is absent, and nanowire nucleation ceases because of the shadowing of the substrate from the impinging fluxes by already existing nanowires.

so that new nanowires still nucleate when the initial ones are 300 nm long. With further growth, as the average nanowire length increases by one order of magnitude from 250 to 2500 nm, the coverage saturates, as evident from the experimental data in Figure 3, panel b. Hence, both nucleation and radial growth cease since any of these processes would result in an increase of the coverage. Our conclusion on the absence of radial growth at the late stage of the growth is in good agreement with the model presented in ref 16. Unlike other reports,10,17−19 this model establishes that radial growth ceases when the nanowire radius reaches a self-equilibrated value that depends on the Gato-N ratio at the nanowire tip. Interestingly and surprisingly, Figure 3, panel c shows that the average diameter of circular objects increases linearly during growth. Obviously, this result and the almost constant coverage θ at the late stage of the growth (see Figure 3b) are in an apparent contradiction; since the average diameter increases linearly, their coverage should increase quadratically (the average diameter of the coalesced aggregates was found to increase in a similar fashion). Both quantities, the coverage and D


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Figure 5. Top-view snapshots of the Monte Carlo simulations of models 1 and 2 at coverages θ = 0.1 (left) and θ = 0.25 (right). Single nanowires are shown in white and coalesced aggreagates in green.

our experimental observations, namely, a rapid decrease in the number density of objects immediately after reaching a maximum value. The model fails again to describe the saturation of the coverage (it predicts a superlinear increase) but describes well the linear increase of the nanowire diameter (see Figure 3b and c, respectively). Nevertheless, as discussed earlier, the apparent contradiction between Figure 3, panels b and c has to be resolved in favor of the coverage because it is this quantity that is determined unambigiously. In the framework of Model 1, the diffusion of Ga adatoms on the substrate toward already existing nanowires induces an effective repulsion between adjacent nanowires. Diffusional repulsion among clusters or islands on a surface was established in several systems by analyzing their NN distance distributions.51−54 The distributions presented in Figure 4 can thus be used to investigate the repulsion among nanowires as a result of Ga diffusion. According to Model 1, as the nanowire density increases, the NN distance distribution should never contain small distances since nucleation at distances smaller than the diffusion length L from already existing nanowires is inhibited. This effective repulsion is evident from Figure 5, panels a and b, and quantitatively described by the blue hatched histograms shown in Figure 4, panels b and c. Obviously, as can be observed in the latter figures, the NN distance probability density distributions derived from Model 1 are in clear disagreement with our experimental data. It follows from the failure of Model 1 that the diffusion length of Ga adatoms on Si(111) cannot be derived from the density of GaN nanowires. In other words, the final nanowire number density is not determined by the mean Ga adatom diffusion length L on the substrate. In fact, selective area growth experiments55 reveal that the diffusion length of Ga adatoms on Si(111) is about 400 nm, that is, a much larger value than the final average distance between adjacent nanowires. Hence, for such a large diffusion

Figure 4. Probability density distributions of the nearest neighbor distances between nanowires or aggregates at different stages of the growth. The histograms present the experimental data of some selected samples from series A (green) and the results derived from the Monte Carlo growth models 1 (hatched blue) and 2 (hatched red). The black line in panel a is the Poisson probability density distribution of NN distances.

diffusion of Ga adatoms on the substrate surface toward already existing nanowires. Consequently, within the frame of this model, each nucleus is surrounded by a circular zone with a radius L equal to the mean Ga diffusion length on the substrate, in which Ga is collected for the growth of the nucleus. Within these zones, nucleation is inhibited because Ga adatoms preferentially move to already exiting nanowires. Figure 5, panels a and b show snapshots of the Monte Carlo simulation of the nanowire growth for two coverages corresponding to different growth times. These snapshots are taken from a video, presented in the Supporting Information, that shows the complete development of the nanowire ensemble. In the snapshots, single nanowires are white, while aggregates with an increasing number of nanowires are shown in different colors. The blue lines in Figure 3 present the evolution of the density of objects, the coverage, and the nanowire diameter as derived from Model 1. A mean Ga adatom diffusion length on the substrate surface of L = 30 nm is chosen to reproduce the maximum number density of objects observed in the experiment. The interval of almost constant density in Figure 3, panel a corresponds to a time interval where nucleation is accomplished but coalescence does not yet take place because the radii of the existing nanowires are too small to provide contact among them. This behavior is, however, in conflict with E


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from Model 2 are shown in Figures 3 and 4, panels b and c using red lines and red hatched histograms, respectively. As can be observed in Figure 3, panels a and b, Model 2 properly describes the evolution of the density of objects as well as the surface coverage during the two growth stages. Within the first stage, the nanowire density and the surface coverage increase rapidly due to nucleation. At the later stage, the density decreases due to coalescence. Note that coalescence is entirely caused by the bundling of nanowires, as radial growth is absent in this model. As shown in Figure 3, panel c, the diameter of uncoalesced nanowires was set to 18 nm. The slow increase in the coverage during the second stage is the result of continuous nucleation, albeit with an exponentially decreasing rate due to shadowing effects. The bundling of nanowires also modifies their NN distance probability density distributions, as shown in Figure 4, panels b and c. Closely spaced nanowires bundle when their lengths exceed the critical value given by eq 1. As a result of bundling, the number of objects separated by short distances continuously decreases during growth, and the peak in the probability density distribution of the NN distances shifts toward larger distances. As can be seen in in Figure 4, panels b and c, the results derived from Model 2 are in good agreement with the experimental data. These results demonstrate that the coalescence of spontaneously formed GaN nanowires in PA-MBE is primarily caused by bundling. However, unoptimized growth conditions, namely low substrate temperatures or an insufficient N flux (see growth diagram in ref 1), may very well result in coalescence due to an insufficient surface adatom mobility or cause large self-regulated radii associated with low N-to-Ga ratios.16 In these cases, radial growth may be the dominant mechanism but will result eventually in the formation of a compact layer.61 Nanowires bundle because they can thus reduce their total energy, as shown by the simple energy balance considerations we have discussed earlier. In fact, nanowire bundling has been observed for various materials systems.32−45 What remains to be clarified is the driving force for bundling to occur, that is, the nature of the attractive interaction between adjacent nanowires that should be strong enough to bring them close to each other. In the Supporting Information, we estimate the orders of magnitude of the forces arising from two fundamental interaction mechanisms, the van der Waals and the Coulomb interactions. We show that the van der Waals force, suggested in refs 32 and 39 as the source of nanowire attraction, is too weak to induce the required deflection of the nanowire tips. In contrast, an electric charge on the order of 10−18 C, that is, ten elementary charges, is found to be sufficient to cause a sizable deflection of adjacent nanowires by the Coulomb interaction. Note that a mutual attraction between different objects does not necessarily require opposite charges.62 First of all, while the repulsion between two like charged nanowires would deflect them from each other, in a dense ensemble, this process will also bring the nanowires closer to their other immediate neighbors. Second, if one nanowire gets charged, the charges can polarize the surrounding nanowires. The result of such an interaction would not be a repulsive but an attractive force. The possible sources of charging considered for nanowires prepared using the VLS growth approach33,34,63 do not apply in the present context since spontaneously formed GaN nanowires do not carry a metal particle at their tip. However, there are other possible reasons for the presence of uncompensated charges during the growth of GaN nanowires in PA-MBE. First,

length, the diffusion of Ga adatoms toward already existing nanowires reduces the Ga adatom density uniformly, which leaves an almost equal probability of nanowire nucleation at every position on the substrate. The results shown above demonstrate that Model 1 does not properly describe the development of the nanowire ensemble. In the Supporting Information, we show that further modifications of this model, particularly, the introduction of the random tilt of GaN nanowires as another source of coalescence, also fail to describe the entire set of experimental data. Hence, the fundamental assumptions of Model 1 do not hold. Consequently, radial growth does not explain coalescence, and the final nanowire density is not determined by the diffusion length of Ga adatoms on the substrate surface. In our second model (Model 2), we consider nanowire bundling as the source of coalescence as observed in Figure 2. In this model, nonoverlapped nanowires nucleate at random positions on the substrate at random times. They grow in length with a constant rate. Radial growth is, however, assumed to be completely absent. The bundling condition eq 1 is checked at each time step for every pair of nanowires. When the critical length Hc for a pair of nanowires is exceeded, their bundling is modeled by replacing the two cylinders that represent the nanowires by a single one with the cross-sectional area and the volume equal to the sums of the respective values of the constituents. Nanowire nucleation is assumed to be stopped by the shadowing of the substrate from the impinging fluxes by already existing nanowires.56,57 Since both Ga and N atoms impinge on the substrate under a certain angle, they cannot directly reach the substrate surface when the nanowires form a dense ensemble. Ga atoms still have a chance to reach the substrate as result of diffusion or scattering among the sidewall facets of adjacent nanowires.57 However, N atoms have a small diffusion length on the sidewall facets of GaN nanowires16,58−60 and desorb as inert N2 molecules. Therefore, the amount of reactive N atoms reaching the substrate is negligible, which in turn prevents further nucleation once shadowing sets in. This argument also restricts the model of axial and radial growth proposed by Dubrovskii et al.18 to low nanowire densities, where shadowing effects are insignificant. Note that radial growth as a result of the propagation of atomic steps along the entire nanowire length18 is only possible as long as both Ga and N atoms can reach the bottom part of the nanowire sidewalls. Shadowing effects are included in Model 2 as follows. Let us consider first a sparse nanowire ensemble so that the shadows of separate nanowires do not overlap. A nanowire of diameter d and length h shadows an area dh tan ϑ, where ϑ is the angle between the impinging beam and the substrate normal. For a nanowire density ρ, the shaded area fraction is ρdh tan ϑ. The nanowires nucleate at the remaining area fraction 1 − ρdh tan ϑ. A dense nanowire ensemble can be subdivided into lateral layers, and successive application of this consideration gives rise to an exponential decay of the nucleation rate, f = f 0 exp(−ρdh tan ϑ). Therefore, in Model 2, nanowires nucleate randomly on the substrate with a rate that decreases during growth. In the Monte Carlo model, we use the average lengths and diameters of nanowires as well as their density to calculate the nucleation rate at each step. Figure 5, panels c and d present snapshots of the Monte Carlo simulation of Model 2. A complete video can be found in the Supporting Information. As before, single nanowires are white and coalesced aggregates colored. The results derived F


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repulsion of nanowires does not occur. The nucleation density is thus not restricted by adatom diffusion, which explains why it is experimentally found to be similar for various structurally and chemically dissimilar substrates. Monte Carlo simulations taking into account the energy minimization by bundling as well as shadowing lead us to the following understanding of the development of GaN nanowire ensembles. Nanowires nucleate randomly, independently, and homogeneously. After nucleation, they approach a selfequilibrated diameter, after which they only grow axially but not radially. Nucleation of new nanowires stops once the nanowires attain a length and density sufficient for a shadowing of the substrate from the impinging fluxes. Similarly, once a high density of well-developed nanowires has formed, neighboring nanowires start to bundle together as soon as they exceed a certain critical length, thus reducing the nanowire density. The associated reduction of shadowing may lead to intermittent radial growth. Methods. Synthesis of GaN Nanowire Ensembles. The GaN nanowires under investigation were synthesized in two different molecular beam epitaxy systems equipped with a solidsource effusion cell for Ga and a radio frequency plasma source for generating active N. All samples were grown on Si(111) substrates, which were previously etched in diluted HF (5%). For series A, prior to the growth, the substrates were outgassed above 900 °C for 30 min to remove any residual SixOy from the surface and exposed to the N plasma for 10 min. In the case of series B, the substrates were not outgassed at 900 °C. Instead, 40 monolayers (ML) of Ga were deposited at 500 °C and flashed-off at a temperature of 800 °C to remove residual contaminants from the surface. The samples of series B were exposed to the N plasma for 5 min prior to growth. For both series of samples, the substrate temperature was approximately 800 °C as measured with an optical pyrometer. The Ga and N fluxes were calibrated by determining the thickness of GaN films grown under N- and Ga-rich conditions, respectively.64 The Ga flux and N fluxes for series A were 0.29 and 0.75 ML/s, and for series B 0.26 and 1.15 ML/s. The growth time is the only parameter that was varied among the samples of each series. The growth was monitored in situ by RHEED in the case of the samples of series B but not for those of series A. Scanning Electron Microscopy. The morphology of all samples from series A and B was imaged by field-emission scanning electron microscopy carried out in a HITACHI S4800. Top-view micrographs were recorded using an acceleration voltage of 5 kV and magnifications, for different samples, from 50 000× to 100 000×, which provided several hundreds of nanowires on each image. Typically, ten of such micrographs from each sample were recorded to obtain a sufficient statistics.

wurtzite GaN is a polar material, and nanowires elongate along the polar [0001̅] direction.2 During growth in an ultra high vacuum environment, the fixed polarization charges present at the (0001)̅ facet cannot be compensated by surface adsorbates or by free carriers because of the high purity of the material. Second, the impinging active N flux is produced by a radio frequency N2 plasma source. Although the plasma source is designed to mainly provide neutral species, the discharge produces a certain (albeit small) fraction of N+ ions and electrons. Another possible source of electrons in PA-MBE is the electron gun used to monitor the growth by reflection highenergy electron diffraction (RHEED). However, we have used RHEED only during the growth of the samples of series B, and we do not see any significant difference in the evolution of the coalescence degree for series A and B (cf. Figure 3). Hence, the bundling is definitely not caused by the exposure of the nanowires to the electron beam during growth. Clearly, further theoretical and experimental work is necessary to identify the origin of the interaction between GaN nanowires in PA-MBE. Our study shows that the coalescence of spontaneously formed GaN nanowires on common substrates is an inherent consequence of the high density of nucleated nanowires. Lowering the density requires a reduction of the nucleation rate. On Si(111), we have found the nucleation rate to exponentially decrease with increase in growth temperature,12 and we have subsequently attempted to reduce the nanowire density by growth at higher temperatures.65 However, at temperatures approaching 900 °C, the high Ga desorption rate results in a decrease of both the nucleation and the axial growth rate, making it very difficult to obtain well-developed, long nanowires with this approach. To obtain such nanowires, we need instead to identify a substrate on which the nucleation rate of GaN nanowires is low compared with their axial growth rate. An impeded nucleation is expected for materials used as masks in selective area growth. Among them, TiN has been reported to offer very high selectivity.66 In fact, we have recently demonstrated a GaN nanowire ensemble on a metallic TiN film with a density below 109 cm−2.67 In subsequent experiments, we have obtained ensembles of nanowires exceeding 2 μm in length but with densities not higher than 109 cm−2. Because of this much reduced nanowire density on TiN, coalescence by bundling occurs only very rarely despite the nanowires’ considerable length, and the average nanowire diameter is thus as small as 30 nm. A detailed account on the synthesis and properties of these samples will be presented elsewhere. To summarize and conclude, the key processes for an understanding of the development of GaN nanowire ensembles are the evolution of the area fraction covered by nanowires (the coverage) and the NN distances between them. Both of these quantities can be determined from top-view scanning electron micrographs in an unambigious fashion and with high accuracy. The fact that the coverage does not change after the end of the nucleation stage directly demonstrates that the nanowires do not undergo continuous radial growth during their axial elongation. The concurrent decrease in density is due to coalescence of nanowires. The coalescence process was observed to be triggered by bundling of neighboring nanowires. Further important conclusions can be drawn from the evolution of the NN distance distribution. In particular, Ga adatom diffusion on the substrate during the nucleation stage would result in denuded zones around already nucleated nanowires where further nucleation is suppressed. The NN distance distributions directly show that this diffusional

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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.6b01044. Detailed discussion of the following topics: energetics of nanowire bundling, Monte Carlo algorithm, quantitative analysis of scanning electron micrographs, further Monte Carlo models of nanowire growth, forces acting between nanowires; videos of the growth process according to different Monte Carlo models (ZIP) G


Letter

Nano Letters

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(17) Foxon, C. T.; Novikov, S. V.; Hall, J. L.; Campion, R. P.; Cherns, D.; Griffiths, I.; Khongphetsak, S. J. Cryst. Growth 2009, 311, 3423−3427. (18) Dubrovskii, V. G.; Consonni, V.; Geelhaar, L.; Trampert, A.; Riechert, H. Appl. Phys. Lett. 2012, 100, 153101. (19) Dubrovskii, V. G.; Consonni, V.; Trampert, A.; Geelhaar, L.; Riechert, H. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 165317. (20) Schuster, F.; Furtmayr, F.; Zamani, R.; Magén, C.; Morante, J. R.; Arbiol, J.; Garrido, J. A.; Stutzmann, M. Nano Lett. 2012, 12, 2199−2204. (21) Fan, S.; Zhao, S.; Liu, X.; Mi, Z. J. Vac. Sci. Technol. B 2014, 32, 02C114. (22) Sobanska, M.; Wierzbicka, A.; Klosek, K.; Borysiuk, J.; Tchutchulashvili, G.; Gieraltowska, S.; Zytkiewicz, Z. J. Cryst. Growth 2014, 401, 657−660. (23) Sanchez-Garcia, M. A.; Calleja, E.; Monroy, E.; Sanchez, F. J.; Calle, F.; Muñoz, E.; Beresford, R. J. Cryst. Growth 1998, 183, 23−30. (24) Geelhaar, L.; et al. IEEE J. Sel. Top. Quantum Electron. 2011, 17, 878−888. (25) Jenichen, B.; Brandt, O.; Pfüller, C.; Dogan, P.; Knelangen, M.; Trampert, A. Nanotechnology 2011, 22, 295714. (26) Wierzbicka, A.; Zytkiewicz, Z. R.; Kret, S.; Borysiuk, J.; Dluzewski, P.; Sobanska, M.; Klosek, K.; Reszka, A.; Tchutchulashvili, G.; Cabaj, A.; Lusakowska, E. Nanotechnology 2013, 24, 035703. (27) Fernández-Garrido, S.; Kaganer, V. M.; Hauswald, C.; Jenichen, B.; Ramsteiner, M.; Consonni, V.; Geelhaar, L.; Brandt, O. Nanotechnology 2014, 25, 455702. (28) Consonni, V.; Knelangen, M.; Jahn, U.; Trampert, A.; Geelhaar, L.; Riechert, H. Appl. Phys. Lett. 2009, 95, 241910. (29) Grossklaus, K. A.; Banerjee, A.; Jahangir, S.; Bhattacharya, P.; Millunchick, J. J. Cryst. Growth 2013, 371, 142−147. (30) Consonni, V.; Knelangen, M.; Trampert, A.; Geelhaar, L.; Riechert, H. Appl. Phys. Lett. 2011, 98, 071913. (31) Brubaker, M. D.; Levin, I.; Davydov, A. V.; Rourke, D. M.; Sanford, N. A.; Bright, V. M.; Bertness, K. A. J. Appl. Phys. 2011, 110, 053506. (32) Khorasaninejad, M.; Abedzadeh, N.; Jawanda, A. S.; O, N.; Anantram, M. P.; Saini, S. S. J. Appl. Phys. 2012, 111, 044328. (33) Sun, Z.; Wang, D.; Xiang, J. ACS Nano 2014, 8, 11261−11267. (34) Dai, X.; Dayeh, S. A.; Veeramuthu, V.; Larrue, A.; Wang, J.; Su, H.; Soci, C. Nano Lett. 2011, 11, 4947−4952. (35) Chen, B.; Gao, Q.; Chang, L.; Wang, Y.; Chen, Z.; Liao, X.; Tan, H. H.; Zou, J.; Ringer, S. P.; Jagadish, C. Acta Mater. 2013, 61, 7166− 7172. (36) Carapezzi, S.; Priante, G.; Grillo, V.; Montès, L.; Rubini, S.; Cavallini, A. ACS Nano 2014, 8, 8932−8941. (37) Han, X.; Wang, G.; Zhou, L.; Hou, J. G. Chem. Commun. 2006, 212−214. (38) Liu, J.; Lee, S.; Lee, K.; Ahn, Y. H.; Park, J.-Y.; Koh, K. H. Nanotechnology 2008, 19, 185607. (39) De Volder, M. F. L.; Vidaud, D. O.; Meshot, E. R.; Tawfick, S.; Hart, A. J. Microelectron. Eng. 2010, 87, 1233−1238. (40) Sitti, M.; Fearing, R. S. J. Adhes. Sci. Technol. 2003, 17, 1055− 1073. (41) Geim, A. K.; Dubonos, S. V.; Grigorieva, I. V.; Novoselov, K. S.; Zhukov, A. A.; Shapoval, S. Yu. Nat. Mater. 2003, 2, 461−463. (42) Glassmaker, N. J.; Jagota, A.; Hui, C.-Y.; Kim, J. J. R. Soc., Interface 2004, 1, 23−33. (43) Gao, H.; Wang, X.; Yao, H.; Gorb, S.; Arzt, E. Mech. Mater. 2005, 37, 275−285. (44) Zhou, M.; Tian, Y.; Zeng, H.; Pesika, N.; Israelachvili, J. Adv. Mater. Interfaces 2015, 2, 1400466. (45) Hui, C. Y.; Jagota, A.; Lin, Y. Y.; Kramer, E. J. Langmuir 2002, 18, 1394−1407. (46) Northrup, J. E.; Neugebauer, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, R10477. (47) Schneider, C. A.; Rasband, W. S.; Eliceiri, K. W. Nat. Methods 2012, 9, 671−675.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Addresses

P.D., Department of Electrical and Electronics Engineering, Faculty of Engineering, Mugla Sitki Kocman University, Kotekli, 48000 Mugla, Turkey. K.K.S., Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences and Novosibirsk State University, Lavrentiev Prosp. 6, 630090 Novosibirsk, Russia. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Carsten Stemmler for the help with preparing the samples and for the dedicated maintenance of the MBE system together with Michael Höricke, Hans-Peter Schönherr, and Claudia Herrmann. We are indebted to Anne-Kathrin Bluhm for providing the scanning electron micrographs presented in this work, Johannes K. Zettler for the preliminary experiments on the effect of the RHEED gun on nanowire bundling and the help to analyze scanning electron micrographs, Viktor Kopp for the preliminary analysis of the effect of nanowire tilt on coalescence, and Lutz Geelhaar for a critical reading of the manuscript. K.K.S. acknowledges the support of the Russian Science Foundation under Grant No. 14-11-00083.

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Nucleation, Growth, and Bundling of GaN Nanowires in Molecular

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