Metal Seed Loss Throughout the Nanowire Growth: Bulk Trapping and

Article pubs.acs.org/JPCC

Metal Seed Loss Throughout the Nanowire Growth: Bulk Trapping and Surface Mass Transport Dany Chagnon,† Eckhard Pippel,‡ Stephan Senz,‡ and Oussama Moutanabbir*,† Département de Génie Physique, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, Québec H3C 3A7, Canada ‡ Max Planck Institute of Microstructure Physics, Weinberg 2, Halle 06120 Germany †

S Supporting Information *

ABSTRACT: The physical and chemical properties of metal-catalyzed semiconductor nanowires are very sensitive to their composition and morphology, which are very sensitive to the behavior of the catalyst nanodroplet during growth. Herein, we identify and investigate the main atomic pathways and processes governing the metal mass transport and the associated variation in the nanodroplet size throughout the growth of metal-catalyzed silicon nanowires. This includes surface diffusion and catalyst trapping in addition to the shift in phase boundaries of the eutectic nanodroplet to count for surface effects, capillarity, and related nanoscale stresses. On the basis of thermodynamic and kinetic considerations, a theoretical framework is presented to elucidate these catalyst nanodroplet instabilities. Moreover, we also address the influence of these phenomena on the shape and impurity concentration in silicon nanowires. Modeling results along with experimental data demonstrate that the combined effects of the kinetically driven catalyst trapping and surface diffusion play the key role in tailoring the nanowire morphology and composition. The proposed model can be extended straightforwardly to describe the evolution of the morphology during the growth of any other system of metal-catalyzed semiconductor nanowires.

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INTRODUCTION

The classical metal-catalyzed growth of nanowires from the vapor phase (the vapor−liquid−solid growth) takes place when a low melting eutectic nanodroplet becomes supersaturated following the absorption of semiconductor atoms resulting from the breakdown of the precursor molecules on its surface. Beyond a critical composition, the supersaturated nanodroplet expels the excess semiconductor atoms to the interface with the substrate thus triggering the one-dimensional growth.21 The elucidation of the complexity of the basic mechanisms and the atomic processes involved in the growth has been the subject of extensive investigations.22−40 Numerous experimental observations provided overwhelming evidence of important variations during the growth in the nanodroplet energetic, structural, morphological, and compositional characteristics.32−37 These phenomena have significant implications for both nanowire composition and morphology and hence on the nanowire electrical, optical, and mechanical properties. The nanowire morphology in particular can be directly associated with the behavior during the growth of the nanodroplet volume, wetting angle, and composition. The latter can be influenced, at a fixed temperature and pressure, by an intentional addition of other elements33 or by a shift in the phase boundary lines that can occur when the size of a sufficiently small nanodroplet varies.37

Semiconductor nanowires are quasi-one-dimensional nanostructures with the premise to impact a broad range of nanoscale technologies.1−20 For instance, these nanostructured semiconductors have been a rich playground to develop innovative, cost-effective, and high-performance devices for applications in nanoelectronics,4−7 biosensing,4,8,9 quantum computing,10,11 and environmentally friendly energy conversion devices such as thermoelectrics12−15 and solar cells.16−20 These emerging or potential technologies capitalize on size-related effects and the flexibility in fabrication offered by the use of nanowires in addition to the tremendous progress in probing nanoscale properties and phenomena. Among nanowire fabrication processes, bottom-up synthesis through metalcatalyzed vapor-phase epitaxy is particularly attractive because of the degree of freedom it provides in design and functionalization of nanoscale devices that extend beyond what is achievable with the planar geometry.5,9,16−20 A scalable and viable integration of metal-catalyzed nanowires requires, however, the mastery of their growth with tailor-made physical and chemical properties including a meticulous manipulation of their composition and morphology. A deep understanding of the underlying physics of metal-assisted growth is thus of paramount importance to precisely control the synthesis of nanowires and identify the important parameters impacting their basic properties. © XXXX American Chemical Society

Received: July 30, 2015 Revised: January 4, 2016

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DOI: 10.1021/acs.jpcc.5b07361 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. (a) SEM image of an array of Si nanowires grown using Al as a catalyst. The scale bar denotes 200 nm. (b) HRSTEM image of Al-catalyzed Si nanowire sidewall. The inset shows the catalyst−nanowire interface (scale bar: 10 nm). (c) STEM image of Al-catalyzed nanowires. EDX measured Al local concentrations in the selected regions (circles) are also shown. The uncertainty on these measurements is ∼ ±0.5 at. %. The scale bar denotes 100 nm. (d) Schematic illustration of different atomic processes that can lead to shrinkage in the catalyst nanodroplet during the nanowire growth. (e) Measured evolution of the nanowire radius as a function of the length (circles). The vertical dotted line indicates the catalyst− nanowire interface. Red solid line corresponds to the evolution of the nanowire radius considering Si sidewall deposition (VS growth) at a growth rate of 3.7 × 10−4 nm/s obtained experimentally.48,49 Red dashed line indicates the best fit of the experimental data assuming that the changes in the nanowire radius originate exclusively from VS growth on the sidewall at a rate of 3.85 × 10−2 nm/s. Purple solid line corresponds to radius changes assuming that catalyst is exclusively shrinking through the incorporation into the growing nanowire (xsM = 4.5 at. %). Gray solid line corresponds to radius changes when surface diffusion is governing the catalyst loss (Ω = 1.6 nm). Green solid line shows the evolution of the nanowire radius during growth as calculated using the current model (xsM = 4.5 at. % and Ω = 0.8 nm).

Several studies have singled out the surface transport of catalyst atoms as a critical factor that shapes the nanodroplet size and morophology.34−36,38−40 In this phenomenon, the fluctuation in the nanodroplet volume, which determines the nanowire diameter, is defined by the balance between metal atom in- and out-fluxes to and from the catalyst, respectively. Interestingly, in addition to surface diffusion, recent investigations have demonstrated that a non-negligible amount of catalyst atoms is also lost by trapping in the nanowire during the growth.41−43 This phenomenon presents an additional atomic pathway for material loss from the nanodroplet. A precise understanding of the interplay between the two aforementioned phenomena of surface transport and catalyst trapping is, however, still conspicuously missing in the literature despite its importance to comprehend the nanodroplet morphological instabilities and their impact on the nanowire growth. With this perspective, in this research, we address these phenomena and elucidate the role of the metal seed instability in shaping the nanowire morphology and composition. To explain the experimental observations, we present a theoretical framework that considers important thermodynamic and kinetic factors governing mass transport during the nanowire

growth. This model is justified through comparison with our data as well as with experimental results reported in the literature.

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EXPERIMENTAL OBSERVATIONS AND THEORETICAL CONSIDERATIONS Atomic Processes That Impact the Nanowire Morphology. We begin the investigation by examining the properties of silicon (Si) nanowires grown using aluminum (Al) and silane as catalyst and precursor, respectively. The growth was performed in an ultrahigh vacuum chemical vapor deposition reactor at temperatures below 500 °C. P- and Bdoped Si(111) wafers were used as substrates in these experiments. The substrate’s surface was conditioned by a standard wet chemical cleaning procedure followed by a dip into 2% hydrofluoric acid to hydrogen passivate the surface. The wafers were immediately transferred into the ultrahigh vacuum chemical vapor deposition reactor. A 1 nm thick Al film was then deposited in situ on the substrate from a thermal evaporation source. Immediately after Al deposition, the substrate was annealed for 30 min at 600 °C. The growth of Al-catalyzed Si nanowires was accomplished by using B


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systematic studies of the VS growth on Si substrates have concluded that the deposition rates at temperatures and pressures comparable to those used in this research remain below ∼5 × 10−4 nm/s for both silane and disilane.49,50 From those studies, the extrapolation of the measured rates to the nanowire growth conditions gives vVS = 3.7 × 10−4 nm/s, which is 2 orders of magnitude smaller than the rate obtained by fitting the experimental data. Expectedly, such a low sidewall deposition rate cannot describe the observed nanowire morphology (solid red line in Figure 1(e)). Moreover, EDX profiles (not shown) indicate a uniform distribution of Al within the entire nanowires. Similar observations were also made based on atom probe analyses.41 This also rules out the VS growth on sidewalls. Indeed, if the VS growth would have taken place, the grown Si homoepitaxial layer on the nanowire sidewalls would have been Al-free. Also, Al overcoating of nanowires is ruled out based on the measured Al concentration profiles. From this, it is reasonable to assume that the nanowire morphology is mainly a result of the interplay between metal surface transport and trapping in nanowires. In a more general case, the VS growth can be easily accounted for by estimating the change in the radius using Δz Δr = v × v VS, where vVS is sensitive to the nature and pressure of the precursors as well as to the growth temperature. In the following, we outline the model to track and evaluate the behavior of the nanodroplet and its influence on the morphology of a growing nanowire.

monosilane, SiH4 (diluted to 5% in argon), as a precursor in the temperature range ∼400−470 °C. The partial pressure of the monosilane was held below 0.15 mbar during growth. Although the growth was carried out at temperatures below the Al−Si bulk eutectic temperature (577 °C), it is practically impossible to know the exact phase of the catalyst during the growth. In fact, it is expected that the small size should affect the droplet thermodynamic properties and hence its phase diagram. Early observations have shown that the undercooling of Al−Si droplets becomes already significant at a diameter on the order of a few micrometers.44 Indeed, a significant undercooling was reported by Wacaser et al. who demonstrated that the catalyst remains liquid at temperatures about 100 °C below the macroscopic eutectic temperature.45 Figure 1(a) exhibits a scanning electron microscopy (SEM) image of an array of Al-catalyzed Si nanowires grown at 470 °C. We note that the nanowires are tapered as is clearly seen in Figure 1(b) displaying a high-resolution cross-sectional scanning transmission electron microscopy (HRSTEM) image of a single Al-catalyzed Si nanowire sidewall. Recently, it was demonstrated that there is a significant incorporation of the catalyst atoms during the nanowire growth.41 The amount of trapped metal atoms depends on the growth temperature, and their distribution is uniform as shown in Figure 1(c). This figure displays an STEM image of Al-catalyzed nanowires and the measured Al local concentrations in the selected regions (circles) within a single nanowire grown at 470 °C. The Al concentration was obtained using high-resolution dispersive Xray spectrometry (EDX) in an aberration-corrected (Cs probe corrector) FEI TITAN 80-300 microscope. The average Al content was found to be (4.5 ± 0.8) at.% in nanowires grown at 470 °C. This injection of catalyst atoms was also evidenced from the electrical properties of Al-catalyzed Si nanowires which were found to be p-type doped.45−48 Notwithstanding the colossal amount of metal atoms trapped in the nanowire, the associated continuous reduction in the nanodroplet volume as the nanowire grows cannot alone explain the observed change in the nanowire diameter. This is discussed below. In order to describe the apparent change in the nanowire diameter during the growth, Figure 1(d) exhibits a schematic illustration of different processes that may take place during the growth and can induce a change in the nanowire morphology. This concerns the aforementioned catalyst surface transport and trapping in the growing nanowire in addition to vapor− solid (VS) growth on the sidewalls. Although it was proposed in some instances to explain the tapering of nanowires,45 the influence of the VS growth on the nanowire morphology may be rather insignificant. Figure 1(e) displays the evolution of the nanowire radius over a ∼160 nm long segment up to the interface with the catalyst (open circles). The nanowire radius was evaluated from HRSTEM analyses. If one assumes that the VS growth is the sole source of tapering, the change in the radius when the nanowire length varies by Δz can be expressed Δz as Δr = v × v VS, where v is the nanowire growth velocity and vVS is the rate of the VS growth on the sidewalls. From this, the best fit of the experimental data was obtained at vVS = 3.85 × 10−2 nm/s (red dashed line in Figure 1(e)). It is noteworthy that the VS growth leads to a linear change in the nanowire radius as a function of the length, whereas HRSTEM data indicate that the nanowire sidewalls are slightly curved. More importantly, the obtained value of vVS is significantly larger than the measured growth rates on Si surfaces.49,50 Indeed, early

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RESULTS AND DISCUSSION Modeling the Evolution of the Nanowire Morphology. In general, the variation in the volume of the metal in the nanodroplet can be expressed as ΔVND = ΔVNW + ΔVDiff, where ΔVNW is the effective volume of metal atoms trapped in the nanowire and ΔVDiff represents the variation of catalyst volume caused by sidewall diffusion. Herein, ΔVDiff can be either positive (out-diffusion) or negative (in-diffusion). For simplicity, the nanodroplet aspect ratio α = h/r (h and r are the height and radius, respectively) is assumed to be constant during the growth. The fluctuations in the nanodroplet size should also influence its basic thermodynamic properties. Indeed, the nanodroplet composition and phase can be very sensitive to surface effects, capillarity, and related nanoscale stresses which become more important as the size shrinks.37 Schwalbach and Voorhees have investigated theoretically the influence of these thermodynamic effects on the nanodroplet phase diagram.37 On the basis of their analysis, the influence of the size on the metal equilibrium concentration in the Aβ 1/3

nanodroplet, x̂lM, can be expressed as xM ̂ l = x0̂ l + r1 , where x̂0l is the bulk equilibrium concentration; r is the nanodroplet radius; and β1 = (α(2 − α))3/2. The parameter A depends on the second derivative with respect to composition of the molar Gibbs free energy of the liquid, the solid−vapor surface energy, and the liquid−vapor surface energy.37 The change in the nanodroplet volume can then be written as ⎡⎛ Aβ11/3 ⎞ 3 ⎟r0 − ΔVND = β1β2π ⎢⎜⎜x0̂ l + ⎢⎣⎝ r0 ⎟⎠

⎛ Aβ11/3 ⎞ 3⎤ ⎜⎜x0̂ l + ⎟⎟r ⎥ r ⎝ ⎠ ⎥⎦ (1)

where r0 is the initial radius of the nanodroplet−nanowire

(

1

)

interface and β2 = α 2 − 3 α 3 . C


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Figure 2. Simulations of the nanowire growth based on the model described by eqs 3 and 4. (a) The evolution of the nanowire shape as a function of the level of the catalyst trapping in the growing nanowire in the absence of metal surface transport (Ω = 0). (b) The influence of the catalyst surface diffusion on the nanowire morphology in the absence of the catalyst trapping (xsM = 0). In both (a) and (b) size-induced shift in boundaries of the nanodroplet phase diagram is neglected (A = 0). (c) The effect of A on the nanowire morphology with the presence of both incorporation and sidewall diffusion (xsM = 0.045 and Ω = 0.5 nm).

the radius is larger as a result of the nanodroplet contact angle with the substrate. Note that it is very straightforward to include in the model above the possible effect of the VS overgrowth. The latter does not depend on the change in the volume of the catalyst nanodroplet and only influences the nanowire radius but not the nanowire−catalyst interface. As mentioned above, the change in the radius due to VS growth is Δz given by Δr = v × v VS. Thus, to account for this phenom-

The effective volume of the catalyst trapped in the nanowire after the growth of Δz = z − z0 is given by ΔVNW = xsMπ∫ zz0r2dz, where xsM is the catalyst concentration in the nanowire. The radial and axial concentrations of the injected metal atoms are assumed to be identical and do not change within a nanowire even when the radius varies. This is reasonable in light of the EDX data (Figure 1(c)) and consistent with recent analyses.41 The catalyst volume change associated with sidewall diffusion can be written as ΔVDiff = 2πΩ∫ zz0rdz, where Ω = Φ/v corresponds to the thickness of an effective metal layer that would form on the nanowire sidewalls when all atoms that diffused from the catalyst remain on the nanowire surface. Φ is a volumetric flux of metal atoms per unit of length along the circumference of the nanodroplet−nanowire interface, and v is the nanowire growth velocity. Thus, the variations in the nanodroplet volume, ΔVND, can be written as s ΔVND = xM π

∫z

z0

r 2dz + 2π Ω

∫z

z0

r dz

Δz

enon, the quantity v × v VS should be added to (r0 − r) given by eq 3. In a system where catalyst trapping does not occur (i.e., xsM = 0), eq 3 becomes Δz =

⎪

⎪

⎪

⎪

(4)

Note that when assuming that the nanodroplet shrinks exclusively by losing material via surface diffusion (i.e., xsM = 0), eq 4 describes very well the evolution of the nanowire morphology at Ω = 1.6 nm as shown in Figure 1(e) (gray solid line). Nevertheless, this case is not relevant due to the importance of the observed catalyst trapping in nanowires investigated in this work (xsM ≈ 4.5 at.%). Indeed, the effective volume of metal atoms trapped in the nanowire is ∼4 times larger than the volume of the nanodroplet at the end of the growth. Importantly, as mentioned above, the use of the measured composition (xsM ≈ 4.5 at.%) at Ω = 0 (i.e., no surface diffusion) in eq 3 does not reproduce the observed nanowire morphology as demonstrated in Figure 1(e) (purple solid line). Indeed, this assumption overestimates the nanowire radius. Consequently, one has to consider both surface diffusion and

(2)

From eqs 1 and 2, the length of a growing nanowire as a function of the radius can be described by the following equation ⎧ l ⎛ 2Aβ 1/3 ⎪ 3x ̂ 6x ̂ l Ω ⎞ 1 ⎟ Δz = −β1β2⎨ sM (r − r0) + ⎜⎜ − M s s 2⎟ ⎪ x (x M ) ⎠ ⎝ xM ⎩ M ⎛ x s r + 2Ω ⎞⎫ ⎪ log⎜ sM ⎟⎬ ⎪ ⎝ xMr0 + 2Ω ⎠⎭

⎫ −β1β2 ⎧ 3xM ̂l 2 ⎨ (r − r02) + 2Aβ11/3(r − r0)⎬ 2Ω ⎩ 2 ⎭

(3)

It is important to keep in mind that the above equation gives the evolution of the length far from the nanowire base where D


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Figure 3. Measured (dots) and calculated (solid line) morphology of a selected set of nanowires grown at 470 °C using Al as a catalyst. At this temperature, xsM = 0.045 and x̂lM = 0.765.

Figure 4. Evolution of the radius at different length (dots) in nanowires grown at 520 °C.45 Solid lines correspond to the simulated nanowire shapes. (a) Comparison of the measured nanowire shape with the result of the calculations assuming that catalyst material loss occurs exclusively through surface diffusion (xsM = 0). (b) Result of the fit in the absence of surface diffusion (Ω = 0). (c) Result of the fit of the nanowire morphology using xsM = 0.08 and Ω = 12 nm.

observed experimentally only after the growth interruption followed by an extended annealing.34−36 As mentioned above, the variation in the nanodroplet size can possibly induce a change in its equilibrium composition.37 This effect is reduced in the model to the parameter A, which describes the shift in the equilibrium composition of the nanodroplet as a function of its radius. Figure 2(c) displays the effect of this phenomenon on the nanowire morphology (see the Supporting Information for details). Our calculations show that the shape of the nanowires becomes more sensitive to the shift in the nanodroplet equilibrium composition for a radius below 5 nm, thus the size effect cannot be significant for the nanowires investigated here. Comparison between Experiments and Theoretical Calculations. In the following, we employ the model presented in the previous section to describe the morphology of Si nanowires grown using Al as a catalyst. Since the incorporation of Al atoms into Si nanowires grown at 470 °C is already quantified (Figure 1(c)), the sidewall diffusion parameter (Ω) remains the only free parameter in eq 3. At this temperature, xsM = 0.045 and x̂lM = 0.765. The latter was obtained from the phase diagram by extrapolating the liquidus to the growth temperature. Figure 3 displays the result of the fit of the morphology of a representative set of nanowires grown at 470 °C. Note that the shape of the analyzed nanowires was determined using HRTEM imaging (dots) and that only the part of the nanowire far from the interface with the substrate is considered in this analysis (i.e., the larger nanowire base is not considered). The figure shows that the model reproduces perfectly the experimental data for an average parameter Ω of ∼0.8 nm. The result of this fit is also displayed in Figure 1(e) (green line). It is noteworthy that Ω increases slightly as the radius of the nanowire−nanodroplet interface increases. Indeed, the analysis of several nanowires demonstrated that

catalyst incorporation to describe the nanowire growth (Figure 1(e), green solid line). The equations above demonstrate that the relation radiuslength can only be defined through the interplay between the phenomena associated with the parameters xsM, Ω, and A. Figure S1 (Supporting Information) summarizes the calculated nanowire morphology when the significance of each phenomenon is varied over a broad range. Interestingly, regardless of its extent, metal surface diffusion is always associated with slightly curved nanowire sidewalls. However, in the absence of surface diffusion, the nanowire radius decreases linearly when the growth involves trapping of metal atoms (i.e., xsM ≠ 0). Obviously, the decrease in the nanowire radius becomes more important as xsM increases. This effect is demonstrated in Figure 2(a) exhibiting three nanowires simulated when the growth takes place in the absence of catalyst surface loss and at a fraction of trapped metal atoms of 0, 0.04, and 0.10. Here, when trapping is considered, the simulated nanowire grows from an initial radius of 52 nm, and the growth continues while the catalyst shrinks until the radius reaches 40 nm. At xsM = 0.04, the nanowire grows about 480 nm for the radius to reach 40 nm (Figure 2(a)). However, this length drops drastically to ≈200 nm when the level of catalyst trapping jumps to xsM = 0.10. The parameter Ω = Φ/v represents sidewall diffusion of catalyst atoms to (Ω < 0) and from (Ω > 0) the nanodroplet. The effect of Ω on the nanowire morphology is shown in Figure 2(b) at xsM = 0.045 and x̂lM = 0.765, which are characteristic of Al-catalyzed Si nanowires grown at 470 °C (Figure 1(a)). For Ω > 0, nanowires were simulated using two arbitrary values of Ω (0.5 and 1.0 nm). It is noteworthy that the nanowire tapering becomes more pronounced as Ω increases. In the case of Ω < 0 (not shown here), the transport of metal atoms to the nanodroplet was found to lead to an increase in nanowire diameter. Note, however, that this behavior was E


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Figure 5. Modeling results of the morphology of Al-catalyzed Si nanowires grown at different temperatures.45 (a)−(c) Display the sets of (xsM; Ω) pairs that reproduce the measured nanowire shapes. (d), (e), and (f) Show results of the fit of the measured nanowire shapes (dots) using the model described in the text at a fixed catalyst concentration in the nanowire of 0.08, 0.03, and 0.01 at 520, 490, and 460 °C, respectively.

Ω follows a linear trend (slope ∼1.8 × 10−2) as a function of the interface radius. As Ω is inversely proportional to v, the observed behavior of Ω suggests that the nanowire growth velocity experiences a slight increase of ∼10−20% when the nanowire−nanodroplet interface radius decreases by ∼8 nm in average (Figure 3). Next, we extend the above model to address different sets of Al-catalyzed Si nanowires reported in ref 45. In that work, the growth conditions differ from those used in the current study. Namely, higher temperatures were utilized to grow Si nanowires. Interestingly, the growth at 520 °C has led to strongly tapered nanowires.45 The evolution of the radius at different length in these nanowires is exhibited in Figure 4 (dots). The simulated nanowire shapes are also shown in this figure (solid lines). Although the growth temperature is higher than the experiment shown in Figure 1, the VS growth on the sidewall is omitted here based on the measured growth rates for both silane and disilane.49,50 Therefore, we only consider surface diffusion and catalyst trapping as possible processes for the nanowire tapering. The case where the overgrowth on the sidewalls can be significant will be addressed later on. Figure 4(a) compares the measured nanowire shape with the result of the calculations assuming that catalyst material loss occurs exclusively through surface diffusion (i.e., xsM = 0). The figure indicates that, under this assumption, the model does not reproduce the nanowire shape particularly near the interface with the nanodroplet where the model underestimates the radius. Figure 4(b) displays the result in the absence of surface diffusion (Ω = 0) when the catalyst nanodroplet loses atoms only through trapping in the growing nanowire. Here, the model reproduces perfectly the experimental data. However, the fit requires an excessively high level of trapping (xsM = 0.47). Figure 4(c) shows that an excellent fit of the nanowire morphology can also be obtained at a lower trapping level of xsM = 0.08 for Ω = 12 nm. The fact that the composition of these nanowires is unknown imposes a set of (xsM; Ω) pairs that can reproduce the nanowire morphology. Figure 5(a−c) shows the obtained (xsM; Ω) pairs for nanowires grown at different

temperatures of 460, 490, and 520 °C. The striking observation is the linear evolution of Ω vs xsM with a slope that increases with the growth temperature and the associated extent of nanowire tapering. This linear behavior is also observed for the set of nanowires shown in Figure 3 (see Figure S2 in Supporting Information). Figure 5 also exhibits the experimental and modeling results for selected nanowires at fixed xsM in the 1.0−8.0 at. % range depending on the growth temperature (Figure 5(d−f)). From data displayed in Figures 3−5, one can conclude that both catalyst incorporation and sidewall diffusion must be considered to discuss the change in the nanodroplet volume and its impact on the morphology of the growing nanowire. Finally, it is important to note that the analysis presented in Figure 5 rules out the possible Al coating of the nanowires. Although our experimental data suggest that Al does not accumulate on the nanowire sidewalls, there might be other experimental conditions under which the catalyst accumulation on the sidewalls can be significant. In that case, the growth on the sidewalls can be greatly affected, and thus it would be critical to include this effect in modeling the nanowire tapering. Indeed, the presence of the catalyst on the nanowire surface can enhance the dissociation of the precursor, leading to a faster deposition on the sidewalls. For Al-catalyzed Si nanowires, an upper limit of the growth rate of this process can be estimated by assuming that the incorporation (xsM = 0.045) and surface diffusion (Ω = 0.8 nm) do not change when the growth temperature is increased from 470 to 520 °C. This yields a sidewall growth rate of 3 nm/min (the nanowire growth rate is 13 nm/min). The result of our simulations is displayed in Figure S3. Obviously, any increase in the incorporation or surface diffusion should lead to a decrease in the rate of VS growth on the nanowire sidewalls. Insights into the Kinetics of Catalyst Loss. It is important to note that catalyst surface diffusion is sensitive to metal atom fluxes from and to the nanodroplet as well as to the growth velocity given the fact that the parameter Ω depends on these quantities (Ω = Φ/v). Therefore, controlling these F


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complete bilayer); and VBL is the volume of the grown bilayer. The chemical potential in the nanodroplet can be expressed, to the lowest order, as μCAT = μ0 + (1 − x̂lS)g″(xlS − x̂lS), where μ0 is the equilibrium chemical potential; g″ is the second derivative with respect to the composition of Gibbs free energy of the nanodroplet; and xlS and x̂lS are the contents of semiconductor in the nanodroplet and at the equilibrium, respectively. By examining the behavior of the thermodynamic properties of the nanodroplet during the mass transport (see Supporting Information for details), the amount of metal atoms trapped in the nanowire can be expressed as

parameters should enable a better control of metal atom surface transport and thus the nanowire morphology. At a fixed pressure,51 it is reasonable to assume that the flux of catalyst atoms increases with temperature as expected for thermally activated processes (metal atoms attachment and detachment from the nanodroplet). As for the growth rate, it is expected, to a certain extent, to increase either when temperature or pressure increases. This means that controlling the effect of surface diffusion on nanowire morphology should be more straightforward through the control of the precursor gas pressure rather than temperature. This is consistent with the shape of Si nanowires grown using Al catalyst at different precursor gas pressures.45 Indeed, it was demonstrated that higher precursor gas pressure leads to faster growth and lower tapering. This description of sidewall diffusion can also be extended to explain gold clusters observed by Baron and coworkers.39 According to that study, gold clusters were found to form on the nanowire sidewalls but only at a certain distance from the nanodroplet. They attributed this to a faster decrease in the precursor gas pressure as compared to the sample temperature. During growth, the high growth velocity makes Ω very small, corresponding to a very small amount of gold on the sidewalls. However, when growth gradually slows down to eventually stop, Ω becomes increasingly important before it starts decreasing during the cooling. This leads to a layer of AuSi on the sidewall that, when temperature decreases, breaks down and agglomerates to form the observed gold-rich clusters. Note, however, that similar clusters can also be observed on the nanowire sidewalls when a very rapid quenching is used.40 In a different study,34 catalyst nanodroplets coarsening was observed after an intermediate annealing step during growth interruption. In that case, catalyst atoms can diffuse away from the nanodroplet leading to tapered nanowires with slightly curved sidewalls. The discussion above suggests that surface diffusion is strongly related to the growth kinetic parameters. A better understanding of the underlying physics of metal seed instability and its impact on the nanowire growth and morphology would also require a detailed discussion of the key parameters in catalyst trapping. Although the exact atomic processes of the injection of metal atoms are not completely known,41 energetic considerations suggest that trapping is likely to occur at the step edge during the successive addition of bilayers through the step-flow growth because atoms at the step edges have few nearest neighbors, which provides them with more steric freedom for the exchange. In this process, as the step swipes across the nanowire diameter, metal atoms can jump back and forth between the catalyst and the nanowire.41 This exchange process can lead to trapping when metal atoms become buried after the growth of the next row of atoms. After the complete growth of the bilayer over the entire nanowire diameter, interfacial jumps of metal atoms may cease during the incubation time to resume with the next nucleation. At the end of the incubation, the volume of the nanodroplet, VICAT, is given by VICAT = V0CAT + τI(ΦS − ΦM), where V0CAT is the nanodroplet initial volume; τI is the incubation time (i.e., time between the end of a bilayer growth and the next nucleation): ΦS is the flux of semiconductor atoms absorbed by the nanodroplet after the breakdown of precursor molecules; and ΦM is the flux of diffusing metal atoms. After a bilayer growth, the volume of the 0 nanodroplet becomes VBL CAT = VCAT + τ(ΦS − ΦM) − VBL, where τ = τI + τBL; τBL is the time needed for a step to swipe across the entire nanowire diameter (i.e., the growth of a

s = xM xM ̂l −

+

V0 τ (x M ̂ l ΦS + xŜ l ΦM ) − CAT (xS0 ̂ l − xŜ l) VBL VBL

0 μBL (V CAT + τ(ΦS − ΦM ) − VBL) g″ VBL(1 − xŜ l)

(5)

x̂lM

where is the metal equilibrium concentration in the nanodroplet and x̂lS0 and μBL are, respectively, the semiconductor concentration and the excess in the chemical potential of the droplet after the complete growth of a bilayer (i.e., the chemical potential is μBL + μ0). In the hypothetical case of μBL ≈ 0, i.e., when the nanodroplet gets back to equilibrium at the end of each growth cycle, eq 5 reduces to τ s xM = xM ̂ l − V (x M ̂ l ΦS + xŜ l ΦM ), which suggests that the solid BL

composition approaches the liquid equilibrium composition τ when the term V (xM ̂ l ΦS + xŜ l ΦM ) approaches 0. The expected BL

large incorporation of metal atoms in the solid in this extreme case is similar to the level of solute trapping observed in rapid solidification experiments where the growth velocity is on the order of m/s corresponding to extremely small τ.51 However, it is important to note that bulk solute trapping occurs as a result of atomic jumps over the entire infinite liquid−solid interface until the impurity atoms f reeze following the passage of the next layer. This picture cannot be extended to describe the trapping during nanowire growth, which is characterized by a delay (incubation time) between two successive layers. As a matter of fact, the exchange of metal atoms between the catalyst and the growing layer can only take place during the propagation of the step, thus suggesting that the step lateral velocity may be more critical than the average growth velocity v. This lateral velocity would depend on both thermodynamic and kinetics factors for a given metal−semiconductor system. Finally, it is important to notice that an enhanced metal incorporation can be associated μ with an increase in BL , which corresponds to an increase in μBL g″

or decrease in g″. The latter in particular can be modified by controlling Si solubility by adding, for instance, impurities to the nanodroplets.52

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CONCLUSION In summary, we have investigated the instability of catalyst nanodroplets and its influence on the morphology of a growing nanowire. We have elucidated qualitatively and quantitatively the interplay between the processes inducing significant changes in the nanodroplet radius. This concerns two main atomic pathways consisting of metal atom surface diffusion and trapping in the nanowire. A model was developed to track and evaluate the behavior of the nanodroplet and its role in shaping the nanowire morphology and composition. The application of the model to Al-catalyzed nanowires demonstrated that the G


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nanowire shape is defined by the combined effects of the two phenomena of catalyst surface transport and injection into the nanowire. Finally, it is important to note that the current study focuses on the case of Al-catalyzed nanowires, but the model can be extended easily to address other cases where, for instance, catalyst trapping is limited or VS growth is more significant. Indeed, the analysis presented in this work makes a straightforward coupling of theory and experiment to enable valuable insights into metal-catalyzed growth of semiconductor 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.jpcc.5b07361. Figures S1−S3 and modeling catalyst atom trapping in a growing nanowire (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS OM acknowledges funding from NSERC-Canada (Discovery Grants) and Canada Research Chair, Fondation de l’École Polytechnique de Montréal.

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Metal Seed Loss Throughout the Nanowire Growth: Bulk Trapping and

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