Vapor-liquid-solid growth of serrated GaN nanowires: Shape selection driven by kinetic frustration
Zheng Ma, Dillon McDowell, Eugen Panaitescu, Albert V. Davidov, Moneesh Upmanyu, Latika Menon
VVapor-liquid-solid growth of serrated GaN nanowires:Shape selection driven by kinetic frustration
Zheng Ma , Dillon McDowell , Eugen Panaitescu , Albert V. Davidov ,Moneesh Upmanyu , , and Latika Menon Department of Physics, Northeastern University, Boston, MA 02115 Material Measurement Laboratory, National Institute of Standards and Technology,Gaithersburg, Maryland 20899, USA Group for Simulation and Theory of Atomic-Scale Material Phenomena ( st AMP),Department of Mechanical and Industrial Engineering,Northeastern University, Boston, MA 02115 Department of Bioengineering, Northeastern University, Boston, MA 02115
Abstract: Compound semiconducting nanowires are promising building blocks forseveral nanoelectronic devices yet the inability to reliably control their growth mor-phology is a major challenge. Here, we report the Au-catalyzed vapor-liquid-solid(VLS) growth of GaN nanowires with controlled growth direction, surface polarityand surface roughness. We develop a theoretical model that relates the growth formto the kinetic frustration induced by variations in the V(N)/III(Ga) ratio across thegrowing nanowire front. The model predictions are validated by the trends in the as-grown morphologies induced by systematic variations in the catalyst particle size andprocessing conditions. The principles of shape selection highlighted by our study pavethe way for morphological control of technologically relevant compound semiconductornanowires. a r X i v : . [ c ond - m a t . m e s - h a ll ] M a y he vapor-liquid-solid (VLS) route for high-yield nanowire synthesis allows control over the growthform and composition via a capping catalyst particle that serves both as a catalyst and conduitfor material transfer onto the growing wire [1–5]. The size of the particle is the primary length-scale that controls the nanowire diameter while the time-scale is usually set by a combinationof slow surface catalysis and nucleation at the catalyst-nanowire interface [6–8]. In the case ofcompound semiconductors, the growth morphology of thin films is strongly influenced by the relativerates of incorporation of the constituent species [9], and such effects must also modify growth ofnanowires. Indeed, recent studies on semiconducting III-V and II-VI nanowires have shown thatthe incorporation ratio has direct effect on their growth rate and crystal quality [10–12], yet thefundamental mechanisms that affect the growth energetics and kinetics remain unknown. In thisarticle, we systematically explore this interplay during Au-catalyzed growth of GaN nanowires, awide band-gap material of direct relevance in optoelectronics and power nanoelectronics [13–15].The combination of experiments and theoretical frameworks identify a novel mechanism based oninterplay between surface energetics and catalytic kinetics for shape selection in GaN with broadimplications for controlled growth of vertical arrays of compound nanowires.The nanowires are grown by ammoniating solid Ga O over an Au-decorated (cid:104) (cid:105) Si substrate at T = 960 ◦ C and pressure P = 100 Torr (see Methods). The use of hydrogen as a carrier gas buildsGa O vapor pressure under these conditions that is readily abstracted by the flowing NH gas toelemental Ga and N [16–19]. The growth is evident in the low-resolution SEM image (Fig. 1a).Almost all nanowires are capped by a Au particle characteristic of the classical vapor-liquid-solid(VLS) growth mechanism. Uncatalyzed vapor-solid (VS) lateral growth of the nanowires is muchslower and effectively suppressed under these conditions [17, 20–23], a fact further validated bynegligible diameter coarsening upon varying the exposure time (not shown). X-ray diffraction of theas-grown nanowires confirms that they are strain-free hexagonal wurtzite crystals (SupplementaryFigure S1).The as-grown morphology consist of straight nanowires with smooth sidewalls as well as severalinstances of rough yet highly periodic surface morphologies. Higher resolution SEM images of thesmooth nanowires are shown in Fig. 1b. The nanowire radius is approximately that of the catalystparticle during axial growth (inset). In some cases, the droplet etches away and exposes a triangularnanowire cross-section, evident in the figure. Lattice fringes with inter-planar distance d ≈ .
78 ˚Aare visible in HRTEM image normal to the growth axis (Supplementary Figure S2). Secondaryfringes aligned 30 ◦ to the wire axis are also evident as indicated. We rarely see any interruptionsin the fringes indicating that the nanowires are largely defect-free. Taken in toto , the nanowireis composed of non-polar m -planes stacked along the (cid:104) (cid:105) direction. For a nanowire so grown,one of the three lateral facets is the polar { } plane and the other two belong to the (cid:104) (cid:105) family of directions. The non-polar growth is classical in that it has been reported under a varietyof conditions and several synthesis techniques [24], including the VLS route [25, 26].Of interest is the serrated morphology and the conditions that stabilize its growth. Majority ofthese serrated nanowires have larger diameter. The SEM images in Fig. 1c show the detailed viewof the nanowire morphology. The growth of these nanowires is also via the VLS mechanism asthe nanowire is always capped with the Au particle. Figure 2a shows another example with astable Au particle. Although the catalyst particle is faceted at room temperature, the high growthtemperature Au-Ga solution forms a melt for Ga concentrations above a critical value. This followsfrom the phase diagram which predicts a stable liquid Au-Ga solution for Ga concentrations above5 at% [27, 28]. The critical composition is size dependent yet the growth form is unaffected as thecorrections simply scale the critical Ga composition.2igure 1: Morphology of as-synthesized GaN nanowires : (a) SEM characterization of Au-catalyzed GaN nanowires grown via chemical vapor deposition at temperature T = 960 ◦ C andpressure P = 100 Torr. The Ga partial pressure corresponds to the initial mass m = 1 .
02 g of thesolid precursor Ga O . (b) High-resolution image of a straight nanowire with the exposed growthfront that reveals a triangular cross-section. (inset) Low-resolution image showing the smoothlateral facets and the capping catalyst particle. (c) Low- (inset, scale bar 200 nm) and high-resolution image of a serrated GaN nanowire capped by an Au-catalyst particle. The parametersassociated with the nanowire morphology are as indicated: 2 R i = 125 nm 2 R o = 200 nm, λ =120 nm, and α ≈ ◦ . (d) Size dependence of the wavelength λ (top) and amplitude 2 R o − R i (bottom) associated with the serrations. 3igure 2: Characterization of serrated nanowires : (a) Low-resolution TEM image of a serratednanowire. (b) The magnified view of the particle-nanowire interface near the contact line. Theimage is tilted slightly with respect to (a) for clarity. (c-d) Magnified views of the intersectionof the two facets as indicated by the arrows. The scale bar is 5 nm. The fringes in (c) and (d)correspond to planes normal to the growth direction. The average inter-planar spacing of d = 2 .
63 ˚Ais consistent with growth along the polar [0001] direction. (e) The hexagonal wurtzite GaN unitcell. The non-polar m -plane (shaded green) and the semi-polar { } plane (shaded yellow) areshown as reference. The insets show the unreconstructed semi-polar surface structure observedalong two orthogonal directions indicated by arrows.The size of the catalyst particle is approximately the average nanowire size defined as R i . Thelow-resolution image in the inset shows that the nanowire maintains its hexagonal cross-section.The lateral facets, visible in the the magnified image are consistent with the six-fold symmetryand give an appearance of truncated hexagonal bipyramids stacked along the growth direction.The serrations are remarkably periodic; for a given nanowire radius R i the wavelength λ andthe amplitude 2 A = ( R o − R i ) are both preserved along the length of the nanowire. The facetreorientation angle 2 α is also preserved but it is independent of the nanowire size, i.e. 2 α ≈ ◦ averaged several nanowire segments.HRTEM characterization of the serrations shown in Fig. 2 do not indicate the presence of anyobvious defects/grain boundaries. Rather, the lattice fringes are unbroken and continue across theserrations indicating that the nanowire is a high quality single crystal. This crystalline nature is alsopreserved at points where the sidewall facets reorient (Fig. 2c and Fig. 2d). Viewed approximatelynormal to the growth axis we see lattice fringes with clear variations in grayscale contrast. Thefringe spacing d ≈ .
63 ˚A is consistent with growth of polar bilayers along the (cid:104) (cid:105) direction4igure 3:
Variations and transitions in GaN nanowire growth morphology : (a) SEM imagesshowing serrated-to-smooth shape transitions. The scale bar is 200 nm. (left and middle) Circledregions indicating distinct reduction in the nanowire diameter accompanying the transition. (topand bottom, right) Early stages of the transition to a non-polar growth direction with smoothsidewall morphology. The encircled region (bottom) shows the discrete kinks consisting of truncatedbipyramids. (b) Local and reversible morphology changes seen in low-resolution TEM image (left)and high resolution SEM images (top right).( c -axis). Unlike classical polar growth, though, the enveloping sidewall facets are inclined at anangle α ≈ ◦ for each facet which we then identify to be the { } or { } family of planes.Selective area electron backscatter diffraction (EBSD) analysis of serrated segments confirms thegrowth direction and identifies the orientation of the semi-polar planes that form the sidewall facetsof the truncated hexagonal bipyramid segments to be the { } family of planes; the analysis isdetailed in Supplementary Figure 3. The wurtzite unit cell drawn schematically in Fig. 2e showsthe details of the crystallographic relationship for one of the six semi-polar planes. The atomicconfigurations of the (unreconstructed) N-polar surface structure viewed along two orthogonaldirections are also shown in the insets.The serrated morphology depends on the nanowire size and the variation is plotted in Fig. 2d.Although there is scatter, both λ and 2 A increase with the nanowire size R i . A linear fit toour data yields λ ≈ . R i . The amplitude of the serrations varies as 2 A ≈ R i and yields thewavelength/amplitude ratio, λ/A ≈ .
7. The ratio is remarkably small indicating a fully facetedyet extremely rough morphology which can be tuned simply by changing the nanowire size.A careful examination of the as-grown samples also reveals transitions between the two growthmorphologies. Several instances of serrated-to-smooth transitions are highlighted in Fig. 3a (en-circled, left and middle panels). We have also carried out EBSD analysis transition zones and theresults are shown in Supplementary Figure 3. The change in growth morphology is preceded by agradually tapering cross-section, i.e. the dynamic transitions are strongly correlated with decreasein the nanowire size. The tapering is most likely due to a decrease in the catalyst particle sizeduring growth as the Au atoms diffuse down the nanowire sidewalls. [29] In each case, the effectivenanowire growth direction changes (top right). Closer examination shows that the transition pointconsists of a series of visibly discrete kinks consisting of increasingly truncated bipyramids suchthat the effective growth direction is along intermediate, low-energy orientations (right, bottom).Although the crystallographic orientation of each of the kinks is still polar, the effective orien-tation of these transition zones is semi-polar. In essence, the kinking reflects local variations inprocessing conditions and/or geometry that modify the growth direction as well as the nanowire5orphology.We see similar kinks within confined regions in an otherwise serrated nanowire (Fig. 3b). Evidently,the change in the growth direction is not dynamically stable as the nanowire reverts back toits original growth direction. There is negligible change in the nanowire size (left and top rightpanels) and detailed characterization of the transition zone shows modified serrations due to theintermediate semi-polar growth orientation/s (bottom right panel). We note that majority of thetransition are observed at relatively large Ga partial pressures (higher mass of solid Ga O ), andwe do not observe smooth-to-serrated transitions.The interplay between the growth direction and the V:III ratio is consistent with several paststudies on GaN thin films and nanowires [17, 30, 31]. The non-polar growth direction is favoredfor ratios close to unity. This indicates that the combination of growth parameters that result ingrowth of the (cid:104) (cid:105) non-polar nanowires is such that that the V:III ratio at the growth front isclose to unity. Reducing the amount of Ga in the gas phase increases the V:III ratio at the growthfront and the growth direction switches to the polar direction.The serrated morphology of the polar nanowires is unlike past reports of the rough morphologiesobserved during VS growth. The surface roughness there is controlled by the Ga diffusion lengththat is directly influenced by the V:III ratio; low ratios result in smooth morphologies while largeratios lead to surface roughening as the Ga diffusion length at the crystal-vapor interface is dra-matically reduced by N-rich conditions [17]. This is in direct contrast to the our observations as theserrations occur under N-deficient conditions. Evidently, the droplet and the solid-liquid interfaceplays a central role in the combined interplay between the size, interface energetics and kineticsduring the morphological evolution of the nanowire.Development of a detailed theoretical model is handicapped by the lack of quantitative under-standing of these aspects in GaN in particular and multicomponent systems in general, and wepresent a simplified analysis of the competing effects. Current understanding of the interplay be-tween size and energetics during general VLS growth revolves around the interfacial balance atthe vapor-particle-nanowire trijunction [6, 32–39]. The serrations are reminiscent of similar growthform observed during VLS growth of Si(111) nanowires marked by absence of low-energy facetsnormal to the growth direction. Then, surface energy considerations alone force the nanowire sizeto shrink or widen to accommodate the low-energy inclined facets as illustrated schematically inFig. 4a. The size cannot change monotonically since it is constrained by the wetting angle be-tween the droplet and the nanowire along the contact line. As the nanowire widens or narrows,the droplet is stretched and compressed respectively. Beyond a critical size, the pressure exertedby droplet forces the sidewalls to reorient at regular intervals. Ross et al. have recently analyzedthis interplay between geometry and energetics for 2D near-equilibrium nanowire growth based ona balance between i) changes in the surface and (nanowire-particle) interphase area, and ii) thework done against the surface tension γ d of an almost hemispherical particle [40]. The angle θ f between the facets and the growth axis is fixed as the shrinking and growing facets belong to thesame family of planes. Then, the wavelength of the serrations varies as [40] λ ∼ Γ c γ d θ f sin α R i , (1)where Γ c is a critical barrier associated with facet reorientation at the apex and troughs in theserrations. The size dependence of the serration wavelength and amplitude plotted is roughlyconsistent with this theoretical model. The small λ/A ratio indicates that the serrations are largein extent and sensitive to the size suggesting a large barrier Γ c .6here is considerable scatter in the size dependence, though, and that is likely due to severaloversimplying assumptions. One, the model assumes that the nanowire-particle interface is flat.Recent studies have shown that that is not the case, rather the interface is enveloped by truncatingfacets as it meets the contact line [41–44]. The fully faceted morphology is shown schematically inFig. 4a. Note that the equilibrium Wulff plot associated with the inclination dependent solid-liquidinterface energy determines the relative areas of the two classes of facets. Following Ref. [35], thechange in energy of the nanowire per unit length of growth becomes dEdz = R ∆ µ + γ sv cos θ f + ( γ d cos θ d + γ tsl ) sin α + γ msl sin( α + θ f ) (2)where θ f + α is the angle that the truncating facet makes with the main facet. The first termis the energy gain due to the driving force of the excess chemical potential, the second term isthe work done against the liquid surface tension, and the last two terms are the costs associatedwith increasing the areas of the truncating and main facets with energies γ tsl and γ msl , respectively.For small α such that the truncating facet is approximately normal to the sidewalls, the energyminimizing morphology is one with low γ sv and γ msl . The droplet surface tension plays a minorrole and this highlights another factor that stabilizes the truncating facet and also determines itsorientation. It has not escaped our attention that the small α assumptions require that solid-liquidinterface must adopt a concave morphology, i.e. the truncating facets switch their orientation aboutthe horizontal. This can certainly take place during the reorientation of the sidewall facets. Theconcavity has implications for the supersaturation of the droplet and this is addressed below.The second assumption relates to the the chemical potential difference ∆ µ between the solidnanowire and supersaturated droplet that drives the nanowire growth. The is a key issue as Nhas negligible solubility within the Au particle [28] and its catalysis is limited to the contact line,approximated as an annular ring of width δR . Ga incorporation, on the other hand, occurs throughthe particle as Au not only catalyzes the decomposition of the Ga precursor but also forms a stableAu-Ga solution [27]. The scenario is shown schematically in Fig. 4b. Then, the size of the Au-particle impacts the V:III ratio at the growth front in that the atomic incorporation rates I Ga and I N scale differently with the catalyst particle size, R . Ignoring differences in the atomic volume ofGa and N across the phases, the steady-state supersaturation at the growth front evolves as (seeSupplementary Notes, Eqs. S1-S8) dX Gal dz = d ( X Gal − X Gal ( eq ) ) dz ∼ vR (cid:0) k Gavl − v (cid:1) (3) dX Nc dz ≈ dX Nc dz ∼ k Nc v − RδR , (4)where v is the overall nanowire growth velocity and k Gavl and k Nc are the catalysis rate constantsfor Ga and N at the particle (liquid-vapor) surface and contact line, respectively. The first term ineach relation is the build up due to catalysis and the second term is the decrease due to nanowiregrowth. In the limit that the growth velocity is size-independent [6, 45, 46], the excess N along thecontact line decreases linearly with nanowire size. The decrease is quite dramatic since we expectthe width of the contact line to be order of the interatomic width .The scaling relations (3 and 4) capture the main effect of size on the asymmetry in the build upof excess Ga and N and therefore the V:III ratio at the growth front. This has a direct effect on The droplet can control this width by receding away from the nanowire edge. We ignore this effect, althoughsuch a regulatory mechanism has been reported for epitaxially grown GaN nanowires [47].
Growth model : (a) Schematic showing the evolution of the droplet-nanowire systemas the size oscillates. The interplay between size dependent droplet supersaturation and the fullyfaceted morphology of the droplet-nanowire interface is shown. (a) Schematic showing the mainelements of the theoretical model that relates the size and the V:III ratio to the growth morphologyof the serrated nanowire. The nitrogen incorporation is assumed to occur over an exposed annularring (thickness δR ) enveloping the contact line (shaded blue), which also serves as the preferred sitefor GaN nucleation as illustrated. (c-d) The energetics at the contact line during (c) the widening(d) and narrowing phases of the growth. The colored regions near the contact line represent thevolume swept out by the truncating facets during each oscillatory growth cycle. The dark solid anddotted lines represent the initial and final states of the droplet and the sidewall facets, respectively.The lightly shaded dotted line in (d) is an alternate concave morphology of the solid-liquid interfacethat is also possible as the sidewalls narrow inwards. See text for details.8he driving force as both the Ga and N chemical potentials are related to their supersaturation.Consider the extreme case where the N-supply sets the overall nanowire growth velocity. Then,the excess N-coverage along the contact line is negligible such that dX Nc /dz ≈ v ∼ δRR k Nc . (5)Then, the periodic modulations in the nanowire size during serrated growth are coupled to oscilla-tions in Ga supersaturation in the droplet and therefore the overall V:III ratio at the growth front(Supplementary Eq. 16). Specifically, d (∆ µ Ga ) dz ∼ ¨ G ( X Gal ( eq ) ) vR (cid:18) k Gavl − δRR k Nc (cid:19) + d (cid:80) i κ γi dz ,d ∆ µ N dz ∼ γ d cos θ d dθ d dz . (6)The second term in ∆ µ Ga is the contribution from the weighted mean curvatures of the two classesof facets that make up the nanowire-particle interface [48, 49]. It is directly related to the relativelengths (areas) of the facets. In essence, its effect is such that chemical potential in the dropletvaries inversely with the extent of truncation [42]. Observe that µ Nc is regulated by the dropletcontact angle. The combined effect results in a non-trivial interplay between the net driving force∆ µ = X GaGaN ∆ µ Gal + X NGaN ∆ µ Nc and the energy minimizing sidewall facet given by minimization ofEq. 2.The analysis is consistent with recent experiments that have shown direct correlation between theV:III ratio and changes in nanowire size [50]. The size change is believed to be entirely due tochange in droplet size, i.e. there the kinetics results in an interplay between the V:III ratio and thedroplet size Unlike these studies, though, the highly periodic modulations we observe here indicate aself-regulating mechanism which follows directly from size controlled chemical potential variationswithin the liquid droplet. More concretely, the growth of large diameter nanowires is nitrogendeficient which initially leads to diameter reduction along the energy minimizing facet orientationof the sidewalls, i.e. the sidewall shape selection is no longer governed completely by interfaceenergetics. It is now modified by kinetics since it must also increase the V:III ratio while maintaininggrowth along the c -axis. Note that if ignore the much smaller changes in the droplet size, the dropletangle θ d increases as the droplet is squeezed in and this enhances the µ Nc . At a critical point, theV:III ratio increases to close to unity. The nanowire can change its growth direction to non-polargrowth, and we see successful as well as failed attempts at these transitions in Fig. 3. Clearly, thereis an energy barrier that needs to be overcome to effect the growth direction change. The barrierfor changing the growth direction is expectedly smaller than that for reorientation of the sidewallfacets, and the nanowire starts to widen by reorienting the sidewall facets which also alleviates thecompression in the droplet. At this point, the Ga supersaturation in the droplet is at a minimum asthe difference in the effect the effective catalysis rates k Gavl − ( δR/R ) k Nc decreases with size. Then,the nanowire-particle interface is significantly truncated as shown in Fig. 4a. The widening of thesidewalls again minimizes the interface energies and occurs along the direction that rectifies the Gadeficiency. The droplet becomes increasingly stretched and at a critical point the capillary forcesfavor narrowing of the sidewall facets. The nanowire again reorients. The droplet is significantlyGa-rich and that minimizes the lengths (areas) of the truncating facets. As mentioned earlier,the reorientation into the narrowing sidewalls can lead to a faceted yet concave morphology, asshown in Fig. 4d (lightly shaded). This not at odds with the Gibbs-Thomson effect associated with9igure 5: Interplay between particle size and III/V ratio and growth morphology : (a)-(b)Effect of Au catalyst size at fixed Ga O partial pressure, m = 0 . .
02 g. (a) The serrated morphology isnoticeably absent for small sizes ( R ≈
80 nm) and dominates much of the as-synthesized network at largersizes (
R >
100 nm). (c-f) Effect of increasing partial pressure of Ga O ; the input mass for the four casesare m = 0 .
61 g, m = 0 .
75 g, m = 1 .
03 g and m = 1 .
91 g, respectively. undercooled withrespect to the solid nanowire [49]. Although we do not have direct evidence during growth, 2b doessuggest a concave interfacial morphology near the contact line.The kinetic anisotropy of the growth rates can also dictate the shape selection of the sidewallfacets. This follows from the fact that non-polar planes normal to the to c -axis d o exist, and wegenerally expect these to be lower in energy compared to the semi-polar surfaces. This is by nomeans conclusive as it is well-known that relative energies are sensitive to the reactor conditionsincluding the V:III ratio and the partial pressures in the gas phase. Nevertheless, selected areagrowth (SAG) experiments on c + axis GaN crystals show that under N-deficient conditions, thegrowth is dominated by the very same semi-polar sidewalls [51]. Current understanding of theshape selection during vapor-solid (VS) crystal growth is based on the kinetic Wulff-plots that cancompletely dominate the growth form for large kinetic undercoolings that scale as ∆ µ = v/M ,with M the mobility of the growth front [52]. The serrated growth occurs through a Ga-richdroplet under N-deficient conditions, and therefore we expect c + (Ga) growth for which the (cid:104) (cid:105) planes have been observed to the slowest growing and therefore the dominate the sidewalls duringgrowth of the convex and faceted solid-liquid interface. Interestingly, SAG experiments on annularrings reveal that the concave growth is dominated by (cid:104) (cid:105) semi polar facets since they are thefastest growing facets [51]. Although there is overwhelming evidence that the sidewall facets inthe serrated nanowires here are enveloped by the (cid:104) (cid:105) planes, we cannot completely rule outthe presence of (cid:104) (cid:105) planes as they have approximately the similar inclination to the c-axis (28 ◦ versus 32 ◦ ). Then, the inclination dependent kinetic anisotropy in the growth rates solid-liquidinterface would become important. The sidewall orientation selection occurs during crystallizationfrom the droplet, and more specifically during each oscillatory cycle of growth consisting of increaseand decrease in the extent of the truncating facets which eventually leads to the nucleation of a newlayer on the main facet [41, 42]. The truncating facets maintain their orientation as they changetheir size and the contact line moves up and down the sidewalls during growth cycle. This is shownschematically in Fig. 4c and Fig. 4d. As reference, the path traced by the contact line for straightand narrowing/widening sidewalls are also shown. Then, for convex growth, the kinetic anisotropywill pick the (cid:104) (cid:105) provided it is the slowest moving solid-liquid interface inclination for the rangeof all possible orientations that preserve c + polar growth.Although it is clear that kinetic frustration modifies the principles of shape selection in the serratednanowires, a quantitative understanding of the anisotropic energetics and kinetics of solid-liquidand solid-vapor interfaces is essential to develop a more concrete understanding of GaN nanowiregrowth. To test several elements of our model, we have repeated our growth experiments withi) varying average Au seed particle sizes, and ii) varying V:III ratio. In each case, we report theyield of serrated nanowires over the entire growth region. Figure 5 shows SEM images of thenanowires under varying growth conditions. A two-fold increase in the Au particle size results inan almost three-fold increase in the yield of serrated nanowires, showing a clear correlation betweenthe growing particle size and the nanowire morphology. Similarly, decreasing the V:III ratio byincreasing the mass of the precursor oxide results in significant increase in the yield of the serratednanowires indicating the N-deficiency promotes the formation of the serrations. At very low ratios(5e), the growth is sporadic and marks an upper limit for VLS growth. More importantly, bothtrends are consistent with the main elements of the growth model, and we expect the interplaybetween size, component ratio and growth morphology to be a general aspect of VLS growth ofmulticomponent nanowires. 11 iscussion and Conclusions Our study highlights the potential of VLS route for concurrent control over the growth directionand morphology of multicomponent nanowires. The interplay between catalyst particle size andthe V:III ratio can be further tuned by the controlling the growth temperature, and although thisremains to be explored systematically, we expect a considerably rich set of growth morphologies.Control over the surface roughness has important ramifications for their properties. For example,nanowires of these wide band-gap materials hold promise as active materials in solar cells, lightemitting diodes, and high-fidelity sensors. For most of these applications, a common desirablefeature is the enhancement of the effective surface area. This can result in enhanced solar energyabsorption (in solar cells) and enhanced p − n junction interfaces for electron-hole pair generation (inboth solar cells and LEDs). While the one-dimensional nanowire morphology naturally presents en-hanced effective surface areas spanning the entire cylindrical surface, this may be further enhancedby modulating the diameter along the length of the wire. Diameter modulation demonstrated herecan also lead to additional benefits such as reduced reflections from the surface thus enhancing theabsorption [53], and to reduced thermal conductivity for thermoelectric applications [54].In addition to roughness, control over the surface structure and polarity can enable novel applica-tions. For example, Chin et al. [55] have observed crystal orientation dependent photoluminescence(PL) effects in GaN nanowires. Surface states are known to act as traps of photoexcited carriers.By controlling the morphology of the nanowires and their growth direction, we have tighter controlof such PL phenomena that can lead to better performance of lasers or LEDs based on GaN andrelated compound semiconductor nanowires.The transitions in the growth direction can lead to nanowires with engineered interfaces which canthen be used as single nanowire devices. We observe transitions from the polar growth direction(serrated nanowires) to non-polar (straight nanowires) (see also Supplementary Figures S3 and S4).The transitions are associated with semi-polar segments, and the polarity-dependent anisotropictransport response can be engineered for a range of nanoelectronic and optical devices based onindividual nanowires. Further investigations of external and local growth parameters favoring thistransitional growth can even lead to control over the semi-polar growth mode that remains to berealized.In summary, this study shows a simple route based on for VLS growth of GaN nanowires withcontrolled growth direction, surface polarity and surface roughness. Specifically, a unique serratedmorphology all through the length of the wire has been obtained for specific growth conditions.The growth morphology is attractive for a host of applications as it i) provides enhanced activesurface with controlled surface polarity for specific applications, and ii) it has been achieved bycontrolling two growth parameters, namely the initial catalyst size and the initial V:III ratio. Atheoretical model shows that the newly discovered growth mode arises due to kinetic frustrationin turn induced by energetic and geometric constraints. The model predictions are validated bythe trends in the as-grown morphologies induced by systematic variations in the catalyst particlegeometry and processing conditions, and the principles of shape selection are relevance for catalyzedgrowth of general multicomponent nanowires. 12 ethods The GaN nanowires were synthesized using a chemical vapor deposition (CVD) method. A 5 −
11 nmthick Au catalyst films were deposited by thermal or e-beam evaporation onto Si(111) substrates.The samples were subsequently placed in the center of a 35 mm ID quartz tube, in a hot-wall CVDsystem, about 2 cm downstream from the gallium source (Ga O powder, 99.999% purity, AlfaAesar). The VLS growth of GaN nanowires was carried out for 1 hour at fixed temperature (960 ◦ C)and pressure (100 Torr) conditions, while flowing a mixture of NH (30 sccm, the nitrogen source)and H (50 sccm, carrying gas) through the system. The heating and cooling were performed inan inert atmosphere with a flow rate of Ar of 70 sccm. The ammonia and hydrogen lines werekept open only during nanowire growth, after thermal equilibrium was reached at 960 ◦ C, andcorrespondingly the argon line was open only during heating and cooling. Separate study of theAu catalyst particle formation as a result of thin film dewetting during annealing was carried outunder the same temperature and pressure conditions, but only in argon atmosphere, without thegallium and nitrogen sources, and without flowing hydrogen.
Acknowledgements
The experimental component of this work was performed under the auspices of the National ScienceFoundation(NSF)-ECCS Program
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Nano Lett. , 626–631(2007). 16 upplementary Information for Vapor-Liquid-Solid Growth of Serrated GaN Nanowires: Shape Se-lection via Kinetic Frustration
Figure S1: X-ray diffraction scan of an as-grown sample consisting of serrated and straight GaNnanowires indexed to the wurtzite phase with the experimental lattice parameters of a = 3 .
194 ˚Aand c = 5 .
196 ˚A. The a and c values indicate stress-free GaN crystal lattice [23]. The gold peaksare due to the capping catalyst particle. 17 haracterization of straight nanowires Figure S2:
HRTEM image of a straight GaN nanowire viewed normal to the basal (0001) plane. The fringespacing along the growth direction indicates non-polar growth along the [10¯10] direction. haracterization of serrated nanowires Electron Backscatter Diffraction Analysis
Figure S3: EBSD characterization of serrated nanowire that transitioned into straight nanowire. (a) SEMplan-view image of the whole nanowire capped by the Au catalyst particle (encircled with dashed line, bottomleft). (b) EBSD pattern of the serrated segment with the simulated crystallographic orientation of the GaNunit cell (top left inset). Indexing of the EBSD pattern shows that the serrated nanowire grow along the[0001]-axis. (c) EBSD pattern of the straight nanowire segment with the simulated GaN unit cell (bottomleft inset). The straight nanowire has a noticeably smaller size and the growth is along the non-polar [10¯10]direction. igure S4: SEM (a)-(c) and EBSD (d) characterization of a serrated nanowire with small “zigzagged tran-sition zone (shown in the middle inset in (b)) that reverts back to serrated growth (lower inset in (b)).SEM 70 ◦ -tilt image of the nanowire that was harvested from the as-grown sample; SEM plane-view imageof the same nanowire with magnified top, middle and bottom segments in the insets (scale bar in each insetis 100 nm) EBSD characterization along the [1010] direction identifies the growth along the polar axis en-veloped by semi-polar (1011) sidewall facets. (c) High-magnification SEM of the nanowire tip with labeled { } sidewall facets and [0001] growth axis as identified from the EBSD analysis (explained below in (d));eye-guiding dashed lines indicate six out of twelve { } facets in the truncated hexagonal bipyramid topsegment. (d) Typical EBSD pattern from the nanowire with the simulated crystallographic orientation ofthe GaN unit cell. Conservation of the EBSD pattern collected from various points along the nanowire,including the serrated top, “zigzagged transition zone, and serrated bottom segments, indicates that thenanowire preserves the [0001] growth axis and (10¯10) in-plane surface orientation along its whole length.The (10¯10) surface orientation unambiguously defines the side facets of truncated bipyramid segments to be { } family (as labeled in (c)). upplementary Notes Theoretical Model
We employ a near-equilibrium theoretical framework to relate the energetics of the nanowire-particlesystem to the V:III ratio at the growing nanowire front. The central aspect of Au-catalyzed GaNgrowth is the inherent bias in that N incorporation is limited to the contact line while Ga forms aliquid solution with Au diffuses through the particle. The relatively high growth temperature resultsin a liquid Au-Ga solution for sufficiently rich Ga in the gas phase. Then, the catalyst particleserves as a reservoir for Ga that changes its volume in accordance with the III:V ratio.We begin with geometry-based scalings for the incorporation rates (atoms/time). The Ga incorpo-ration rate scales with the exposed particle surface area, I Ga = k Galv A lv / Ω Gal ∼ k Galv R / Ω Gal , (S1)where k Galv ≡ k Galv ( p Ga , T ) is the Ga catalysis rate at the droplet surface that depends on the reactortemperature and precursor gas partial pressure, A d is the droplet surface area and Ω Gal is the Gaatomic volume within the liquid particle. The nitrogen incorporation is assumed to occur alongan annular ring of width δR around the contact line. The width is of the order of the truncatingfacet that is stabilized at the point where the polar [0001] facet meets the nanowire sidewalls.Then, I N = k Nc A c / Ω Ns ∼ k Nc [ R − ( R − δR ) ] / Ω Ns ≈ k Nc R δR/ Ω Ns , (S2)where k Nc ≡ k Nc ( p NH , T ) is the catalysis rate associated with NH abstraction at the contact lineand Ω Ns is the nitrogen atomic volume.The build-up of the excess Ga and N available for nucleation and growth at the particle-nanowireinterface is controlled by their respective chemical potentials. Since Ga diffuses through the liquidparticle, its excess is proportional to the difference in chemical potential between the liquid particleand the solid nanowire nanowire. In the limit of small supersaturations, the chemical potentialscan be simplified as µ Gas − µ Gas ( eq ) ∼ Ω Gas (cid:34)(cid:88) i κ γi + γ lv κ (cid:35) (S3) µ Gal − µ Gal ( eq ) ∼ ¨ G ( X Gal ( eq ) ) (cid:104) X Gal − X Gal ( eq ) (cid:105) + Ω Gal γ lv κ. (S4)Here, the reference potentials correspond to those for the ternary equilibrium between a solid GaNand a binary (Au-Ga) alloy at the growth temperature conveniently expressed in terms of thecomposition of the droplet, i.e. µ Gas ( eq ) = µ Gal ( eq ) . The change in the solid potential is the Laplacepressure exerted by the abutting liquid particle and the contributions of the truncating and mainfacets. They are compactly expressed as the weighted mean curvatures κ γi = ± Λ i /L i where Λ i isthe length (area) assigned to the facet on the Wulff plot and L i is the actual facet length (area).The sign denotes the convexity of the each facet. The expression changes at the contact line asthere is an additional term due to the capillary force exerted by the liquid surface tension and thesolid-vapor interface energy, γ d cos θ d − γ sv cos α , as shown in Fig. 4c. The liquid chemical potentialincreases linearly with the supersaturation X Gal − X Gal ( eq ) , where X Gal ( eq ) is the liquidus compositionand ¨ G ( X Gal ( eq ) ) is the second derivative of the free energy with respect to composition at equilibrium.21he last term is the classical Gibbs-Thomson term due to the Laplace pressure within the liquid.Then, the change in Ga chemical potential due to abstraction from the vapor is∆ µ Ga ∼ ¨ G (cid:16) X Gal ( eq ) (cid:17) (cid:104) X Gal − X Gal ( eq ) (cid:105) + ∆Ω Ga γ d /R + Ω Gas (cid:88) i κ γi (S5)The nitrogen chemical potential of interest along contact line is set by the concentration (coverage)over the area of the surrounding annular ring that scales as RδR ,∆ µ N ∼ ¨ G (cid:16) X Nc ( eq ) (cid:17) (cid:16) X Nc − X Nc ( eq ) (cid:17) + γ d sin θ d − γ sv cos α (S6)where X Nc ( eq ) is the equilibrium nitrogen coverage at the contact line and the last term is that dueto the capillary force exerted by the liquid surface tension.The concentration X Gal and X N evolve in accordance with the balance between the incoming andoutgoing atomic flux (catalysis and nanowire growth, respectively). For an initially equilibratedparticle-nanowire system, the steady-state values (increase per unit time) scale as d (cid:16) X Gal − X Gal ( eq ) (cid:17) dt = v d (cid:0) ∆ X Gal (cid:1) dz ∼ (cid:18) I N − vR ¯Ω (cid:19) Ω Aul R = Ω Aul R (cid:18) k Gavl Ω Gal − v ¯Ω (cid:19) (S7) d (cid:16) X Nc − X Nc ( eq ) (cid:17) dt = v d (cid:0) ∆ X N (cid:1) dz ∼ (cid:18) k Nc − v Ω Ns ¯Ω RδR (cid:19) , (S8)where we have approximated the concentrations as the atom ratios of the relevant atomic species,i.e. X Gal ≈ n Ga /n Au and X N ≈ n N /n Na where n Na is the available sites along the contact linethat can be occupied by nitrogen. This is reasonable due to the low solubility of Ga ( ∼ d (cid:0) ∆ µ Ga (cid:1) dt ∼ ¨ G ( X Gal ( eq ) )Ω Aul (cid:18) k vl Ω Gal − v ¯Ω (cid:19) − ∆Ω Ga γ d R dRdz + d (cid:80) i κ γi dt (S9) d (cid:0) ∆ µ N (cid:1) dt ∼ ¨ G (cid:16) X Nc ( eq ) (cid:17) (cid:18) k Nss − v Ω Ns ¯Ω RδR (cid:19) + γ d cos θ d dθ d dt . (S10)Equations S7-S10 capture the effect of geometry and processing conditions on the temporal increasein the concentrations and their effect on the chemical potentials of the two species. At microscopictime-scales, the growth is obviously not uniform; a critical supersaturation is required at the growthfront for formation of a stable nucleus (interface-controlled regime). In the limit the catalysis is ex-tremely slow, super-critical nucleus must wait for incorporation, and to a minor extent the diffusion,of Ga and/or N at the growth front catalysis-controlled regime which we analyze below. Catalysis-limited growth
We consider the extreme case when the N incorporation is the rate-limiting event, i.e. the rateat which N becomes available through catalysis equals the rate at which it is absorbed into thegrowing nucleus, In essence, the growth velocity is kinetically limited by N-supply such that the22 excess chemical potential is exactly at equilibrium and therefore constant, i.e. d (∆ µ Nc ) /dt ≈ v = ¯ΩΩ Ns δRR k Nc (S11)Substituting in Eqs. S7-S8, we arrive at the temporal evolution of the concentration and chemicalpotential of Ga, d (cid:0) ∆ X Ga (cid:1) dt ∼ Ω Aul R (cid:18) k Gavl Ω Gal − δRR k Nc Ω Ns (cid:19) (S12) d (∆ µ Ga ) dt ∼ ¨ G ( X Gal ( eq ) )Ω Aul R (cid:18) k Gavl Ω Gal − δRR k Nc Ω Ns (cid:19) (S13)Ignoring the differences in the atomic volume, we recover the relations in the main text (Eqs. 1 and2) that we reproduce for completeness, v ∼ δRR k Nc (S14) d (cid:0) ∆ X Ga (cid:1) dt ∼ R (cid:18) k Gavl − δRR k Nc (cid:19) , d (cid:0) ∆ X N (cid:1) dt ∼ d (∆ µ Ga ) dt ∼ ¨ G ( X Gal ( eq ) ) R (cid:18) k vl − δRR k Nc (cid:19) + d (cid:80) i κ γi dt , d ∆ µ N dt ∼ γ d cos θ d dθ d dt .dt .