Letter pubs.acs.org/NanoLett
Spontaneous, Defect-Free Kinking via Capillary Instability during Vapor−Liquid−Solid Nanowire Growth Yanying Li,† Yanming Wang,*,‡ Seunghwa Ryu,§ Ann F. Marshall,∥ Wei Cai,⊥ and Paul C. McIntyre‡ †
Department of Applied Physics, Stanford University, Stanford, California 94305, United States Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States § Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, South Korea ∥ Stanford Nano Shared Facilities, Stanford University, Stanford, California 94305, United States ⊥ Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States ‡
S Supporting Information *
ABSTRACT: Kinking, a common anomaly in nanowire (NW) vapor−liquid−solid (VLS) growth, represents a sudden change of the wire’s axial growth orientation. This study focuses on defect-free kinking during germanium NW VLS growth, after nucleation on a Ge (111) single crystal substrate, using Au−Ge catalyst liquid droplets of defined size. Statistical analysis of the fraction of kinked NWs reveals the dependence of kinking probability on the wire diameter and the growth temperature. The morphologies of kinked Ge NWs studied by electron microscopy show two distinct, defect-free, kinking modes, whose underlying mechanisms are explained with the help of 3D multiphase field simulations. Type I kinking, in which the growth axis changes from vertical [111] to ⟨110⟩, was observed in Ge NWs with a nominal diameter of ∼20 nm. This size coincides with a critical diameter at which a spontaneous transition from ⟨111⟩ to ⟨110⟩ growth occurs in the phase field simulations. Larger diameter NWs only exhibit Type II kinking, in which the growth axis changes from vertical [111] directly to an inclined ⟨111⟩ axis during the initial stages of wire growth. This is caused by an error in sidewall facet development, which produces a shrinkage in the area of the (111) growth facet with increasing NW length, causing an instability of the Au−Ge liquid droplet at the tip of the NW. KEYWORDS: Germanium nanowire, vapor−liquid−solid growth, nanowire kinking, phase field modeling
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twins.22,23 The mechanisms of spontaneous kinking, without crystal defects, during unperturbed growth of single crystal NWs under normal CVD conditions are largely unexplored. In this context, Au-mediated VLS growth of Ge NWs provides an interesting model system because it has a large process window for stable VLS growth while avoiding complex changes in nanowire sidewall facet structure and surface energy that can occur in the Au−Si VLS system due to the tendency of Au to decorate the sidewalls of Si NWs.19 In this study, the morphologies of kinked Ge NWs of different nominal diameters, synthesized at several different growth temperatures, were examined by scanning electron microscopy (SEM). Statistical analysis of the fraction of kinked NWs reveals correlations among the wire diameter and the growth temperature with kinking probability for Ge NWs. By employing high-resolution transmission electron microscopy (HRTEM) to confirm the crystallographic orientation of the
n important subfield of nanotechnology research focuses on semiconductor nanowires (NWs) for their potential applications in nanoelectronics1−3 and photonics.4−6 In particular Ge NWs are considered to be promising components for high-performance field-effect transistors (FET)7,8 and photodetectors9−12 due to their desirable electronic and optical properties. These properties are highly dependent on the morphology of the Ge NWs, such as their diameter and crystallographic orientation.13 Most Ge NWs are synthesized using the technique of chemical vapor deposition (CVD) by the vapor−liquid−solid (VLS) growth mechanism.14−18 Despite decades of study of VLS growth of nanowires and single crystal whiskers, many of its aspects are not yet well understood, including kinking and the sudden change in the wire growth axis. Reports on kinking of Si NWs indicate that it can be induced by changing the substrate temperature or precursor gas pressures19 or by varying the total pressure during VLS growth.20 Tian et al. demonstrated that kinking can also be induced in Si and Ge NW growth by purging and restarting the precursor gas flow.21 Other studies show that kinking in Si and Ge NWs involves crystal defects such as stacking faults and © XXXX American Chemical Society
Received: November 13, 2015 Revised: January 18, 2016
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DOI: 10.1021/acs.nanolett.5b04633 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters kinked structures, two different characteristic kinking morphologies were identified. Computer simulations based on a phase field model were performed to explain and characterize the observed modes of nanowire kinking. The Ge NWs examined in this paper were synthesized by VLS growth using presized colloidal gold particles (with diameters of 20, 40, and 80 nm) as catalysts in a cold-wall CVD chamber. In the following, we will refer to the diameter of the gold catalysts as the nominal diameter of the NWs. Germanium (111) wafer substrates were subjected to standard RCA cleaning24 to remove the native oxide and surface contaminants. The substrates were then dipped into an aqueous HF (2%) solution for 30 s, followed by a water rinse to control the final areal density of the gold colloid particles on the surface.14,16,17 This process was repeated five times before coating the Ge substrates with a 10:1 mixture of gold colloids and aqueous HF (2%) solution for 10 min at room temperature to deposit the catalysts.24 Epitaxial NW growth was carried out in a cold-wall, lamp-heated CVD chamber with a GeH4 precursor flow of 10 standard cubic centimeters per minute (s.c.c.m.), H2 carrier gas flow of 490 s.c.c.m., and a total pressure of 30 Torr. The substrates were heated for 2 min (the typical nucleation duration in the two-step growth method for Ge NWs14,25) at growth temperatures of 360, 390, and 420 °C, respectively. Under these conditions,14 uncatalyzed decomposition of the GeH4 precursor along the nanowire sidewalls occurs at a non-negligible rate, producing a tapered shape of the wires that is visible in scanning and transmission electron microscopy images. The NWs, including those that ultimately kink, begin their growth along the [111] direction, normal to the (111) substrate surface. As shown in Figure 1, some Ge NWs kink away from the vertical [111] crystallographic direction, with the probability of kinking depending on the growth temperature and the wire diameter. Statistics for the fraction of kinked NWs as a function of diameter and growth temperature are shown in Figure 2. A clear trend is indicated for wires grown at 390 °C: the kinked fraction decreases as the NW diameter increases, and it is much higher for 20 nm samples than for the other two nominal NW diameters studied. Figure 2 also shows that 40 nm nominal diameter wires samples have strongly temperature-dependent kinking behavior, where the fraction of kinked NWs increases by about 6 times as the growth temperature increases from 390 to 420 °C. On the other hand, 20 nm NWs have a generally high kinking fraction for all temperatures and, therefore, do not show as strong a temperature-dependent trend as do the 40 nm NWs. This difference is consistent with the coexistence of two different diameter-dependent kinking modes (see below), as also suggested by the kink morphology differences noted for the images in Figures 1 and 3. Ge NWs were examined by HRTEM in order to observe the details of the kink morphologies, orientations, and the crystalline structure near the kinks. Two distinct types of kinked structures are observed, as shown in Figure 3. In Type I kinking, Ge NWs can kink from the vertical [111] to a ⟨110⟩ axis. In some cases, the same wire will kink again onto an inclined ⟨111⟩ axis, so that it contains a transient ⟨110⟩oriented segment, as in Figure 3a. Type I kinking is only observed in the studied Ge NWs having a nominal diameter of 20 nm. The location along the wire axis at which Type I kinks form appears to be somewhat random.
Figure 1. SEM images of Ge nanowires grown with (a) 40 nm diameter colloidal Au catalysts at 390 °C; (b) 40 nm catalysts at 420 °C; (c) 20 nm catalysts at 360 °C; and (d) 20 nm catalysts at 390 °C for 2 min. Dashed circles show Ge NWs that the kink from the vertical [111] axis onto an inclined ⟨110⟩ axis, while solid circles show kinking from the vertical [111] axis onto an inclined ⟨111⟩ axis. Details of these two kink morphologies are shown in Figure 3. All scale bars are 200 nm in length.
Figure 2. Statistics for the fractions of kinked NWs for samples of different nominal diameters at different growth temperatures. Each kinking fraction is calculated based on a sample containing more than 200 NWs.
For all of the Ge NWs examined, the kinked NWs are single crystals, free of dislocations or other 1D or 2D crystallographic defects in the vicinity of the kinks. A representative atomic resolution HRTEM image and its fast Fourier transform (FFT) are shown in Figure 4, where a 20 nm Ge NW coherently kinks from the vertical [111] direction onto an inclined ⟨111⟩ axis via a short ⟨110⟩-oriented segment. A similar kink morphology has been reported for Si NWs previously.19 The FFT and the observed invariance of lattice fringes across the kinked region indicate that this is coherent (defect-free) kinking. Type II kinking, as can be observed in Figure 3b, occurs as an abrupt transition from vertical [111] growth to an inclined B
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Figure 3. (a) A Type I kinked NW kinking from the vertical [111] to a transient ⟨110⟩-oriented segment, followed by second kinking event onto an inclined ⟨111⟩ axis; (b) a type II kinked NW abruptly kinking from vertical [111] to inclined ⟨111⟩ via a characteristic faceted structure.
Table 1. Comparison of Surface Energy of Ge NWs along ⟨111⟩ and ⟨110⟩ Directionsa orientation
σs (J/m2)
σls (J/m2)
trend
⟨111⟩ ⟨110⟩
1.149 1.100
0.542 0.626
preferred at larger NW diameter preferred at smaller NW diameter
σs stands for NW sidewall (solid) surface energy, σls stands for NW growth (liquid-solid) surface energy.31 The data are computed from multi-phase field simulations (see Supplementary Information). a
sidewall surface energy is dominant, making ⟨110⟩ the more stable growth orientation. While the interface energy analysis provides a qualitative picture of diameter dependence of the preferred NW growth orientation, it does not provide a quantitative prediction of the critical diameter at which the preferred orientation transitions from ⟨111⟩ to ⟨110⟩. At the same time, recall that Type I Ge NW kinking is most pronounced at the nominal diameter of 20 nm, and both inclined ⟨111⟩ and ⟨110⟩ orientations are observed at this diameter. This leads us to a hypothesis that Type I kinking in Ge NWs occurs most frequently at the nominal diameter of 20 nm because this is precisely the diameter at which ⟨111⟩ and ⟨110⟩ growth are equally preferred, energetically. To test this hypothesis, we performed VLS growth simulations for Ge NWs using the 3D multiphase field model.33 NW growth simulations with different catalyst droplet sizes were performed to study the NW growth orientation dependence on diameter. The results are shown in Figure 5. Starting from the (111) surface of the substrate, all NWs initially grow along the vertical [111] direction. However, NWs with smaller diameter show spontaneous kinking from [111] to an inclined ⟨110⟩ direction. At the nominal diameter of D = 15 nm, the kinking occurs close to the base. At D = 20 nm, the
Figure 4. HRTEM image of a kinked region of a Ge NW of 20 nm nominal diameter that kinks from the vertical [111] to an inclined ⟨111⟩ direction via a small ⟨110⟩-oriented “elbow” segment. Inset is an FFT of the image, indicating it is a single crystal wire and its crystallographic orientation.
⟨111⟩ growth direction with no transition segment. These nanowires have faceted sidewalls, and a kink position that is always very close to the substrate surface, indicating that Type II kinking usually occurs at a very early stage of NW growth. Type II kinking is most frequently observed in the studied Ge NWs of nominal diameter ≥40 nm. It has been shown empirically that both Si and Ge NWs exhibit a preference for growth along ⟨110⟩ axes when the diameter is ≤20 nm and along ⟨111⟩ axes when the diameter is larger.26−29 Theoretical analysis of this orientation preference for Si NWs grown by the VLS mechanism has been described, based on consideration of surface energies of nanowire sidewalls and the catalyst/wire growth facet interface.30,31 A similar diameter dependence has also been observed for Ge NW growth.32 This dependence is caused by the higher sidewall energies of ⟨111⟩ oriented compared to ⟨110⟩ oriented NWs. Using the recently developed multiphase field model for VLS growth of Ge NWs,33 we computed the average interfacial energies of ⟨111⟩ oriented and ⟨110⟩ oriented NWs. The input parameters of the model include interfacial energies of Ge from the literature.17,34,35 The interfacial energy anisotropy of the Ge crystal is assumed to be the same as that of Si36 in the absence of further experimental data. The results are given in Table 1. The total surface energy is the sum of the catalyst/nanowire interfacial energy and the sidewall surface energies. When the NW diameter is large, the total surface energy is dominated by the catalyst/wire (growth facet) interfacial energy, which scales as the square of the diameter. Therefore, growing along ⟨111⟩ is preferred energetically for large diameter NWs. The situation is reversed for sufficiently small diameter NWs, where the
Figure 5. Phase field simulation results show the effect of (nominal) diameter on the preferred NW growth orientation (see Supporting Information). C
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Figure 6. (a) SEM image of a Type II kinked NW with triangular top cross surface, and large (111) sidewall facets; (b) TEM image of a Type II kinking structure showing top and sidewall (111) facets and taper angle α. Part c is a side view of the NW pedestal created by the phase field model based on the experimental image. Parts d, e, and f show 3D views of the base structures at different NW height. Part g plots the free energy curves as a function of the droplet lateral displacement from center. Experimental images: 40 nm Au catalyst diameter and 420 °C NW growth.
the low energy {111} sidewalls are clearly available for the droplet to wet for this kink structure. Under these combined conditions, when the faceted structure forms with a shrinking growth surface, the liquid droplet is easy to unpin, moving onto a sidewall {111} facet, and thus to continue to grow, forming a Type II kink. We performed phase field simulations to test this hypothesis. The NW base structure is created to be consistent with the experimentally observed Type II kink morphology. Figure 6c shows a side view of the constructed NW pedestal with a droplet on its top, where the red and yellow lines highlight the {111} facets in agreement with the TEM and SEM images. The NW is truncated at different heights to form three representative configurations (Config 1, 2, 3) for different NW growth facet features. This can be seen more clearly from a 3D view with removing the top droplet. As shown in Figure 6d, e, and f, Config 1 has a typical hexagonal growth facet; on the contrary, the top surface of Config 2 presents a more triangular shape; while Config 3 keeps a triangular growth facet but with a smaller area due to further growth of the inclined {111} sidewall facets adjacent to the NW tip. The center-of-mass of the liquid droplet is constrained at different locations along the [112̅] direction, while all the remaining degrees of freedom of the droplet are allowed to relax in order to minimize the free energy. Figure 6g plots the total free energy as a function of the droplet displacement from the NW center axis. For Config 1 with hexagonal growth facet, it is found that extra energy is required to move the droplet center-of-mass away from the growth facet center. In Config 2, the energy-minimizing centerof-mass position of the droplet is actually displaced from the center of the top facet. In Config 3, the droplet is unstable on the top of NW, because the free energy decreases monotonically as the droplet center-of-mass is moved toward the edge of the growth facet. The above analysis confirms that the
NW is able to enter the steady-state regime (only the top section of the simulated NW is shown in the figure) but eventually kinks onto a ⟨110⟩ growth axis. For NWs with nominal diameters of 25 and 30 nm, we find vertical [111] growth is maintained. Based on the above results, a transition of preferred growth orientation should exist at a critical nominal diameter Dc between 20 and 25 nm. This is consistent with our observation that the kinking fraction is highest at the nominal diameter of 20 nm. We have also found that, by applying an external force on the liquid droplet during the NW growth simulation, Ge NWs of nominal diameter greater than 25 nm can be induced to undergo Type I kinking. The magnitude and duration of the external force necessary to induce kinking increases with increasing NW diameter, consistent with the diameter dependence of kinking probability observed in the experiments. (see Supporting Information) A characteristic faceted structure plays an important role in inducing Type II kinking in Ge NWs. Figure 6a and b show two transient kink structures with faceted sidewalls near the substrate surface. The top cross surface of the NW is triangular instead of the hexagonal growth interface typically seen for ⟨111⟩-oriented Ge NWs after steady state growth.26,31,37 The structure is 3-fold symmetric with three large inclined {111} sidewall surfaces, as seen in Figure 6a. Figure 6b shows a similar structure but without a solidified Au catalyst present; the Au− Ge droplet appears to have fallen off the wire onto the substrate during the kinking event. The top (111) surface and large {111} sidewall can be identified from a different perspective. These Type II kink structures appear to form as a result of an error in sidewall facet development in the initial stages of vertical wire growth from the substrate surface. The triangular top surface in Figure 6a has a smaller area compared to its base cross-section, indicating that the droplet became progressively more unstable prior to this Type II kinking event.38 In addition, D
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Nano Letters triangular shape and the area shrinkage of the growth facet induce droplet instability, which triggers Type II kinking. The probability of Type II kinking is more strongly temperature-dependent than that of Type I, giving rise to the pronounced temperature sensitivity shown in Figure 2. The strong influence of temperature on Type II nanowire kinking indicates a temperature-dependent probability of Au−Ge catalyst droplet unpinning from the Ge (111) growth facet. Considering the case of a random external lateral force of short duration that promotes unpinning of the droplet, a large viscosity of the Au−Ge liquid may limit the ability of the droplet surface to deform sufficiently to unpin from the facet edge in the time frame of such an impulse. The shear viscosity of the Au−Ge liquid is expected39−41 to decrease strongly with increasing temperature above the eutectic (361 °C), consistent with the observed increase in kinking probability. In addition to the liquid droplet viscosity, temperature affects the hydrogen coverage of the Ge NW sidewalls during their growth in a hydride-based CVD reaction.42 At higher VLS temperatures, desorption of atomic hydrogen from the sidewalls will increase the sidewall facet energies relative to the interface energy of the Au/Ge (111) growth facet. This may promote NW kinking by providing a driving force for the droplet to unpin from the growth facet edge so as to wet an adjacent sidewall facet. Spontaneous and crystallographic defect-free kinking in Ge nanowires during VLS growth has been observed and studied. Two diameter-dependent kinking modes were identified and analyzed. Type I kinking occurs because of the similar stability of Ge NWs with diameters of around 20 nm grown along ⟨111⟩ and ⟨110⟩ directions. This diameter-dependent growth orientation is confirmed by both a qualitative surface energy analysis and a 3-D phase field model simulation. Type II kinking occurs when the growth facet surface area of the NW shrinks during the very early stages of [111] NW growth upward from the substrate surface. If the growth facet shrinks excessively, the liquid droplet unpins from wire/vapor/droplet triple boundary at the edge of the growth interface, and migrates onto one of the low energy {111} sidewall surfaces, thus forming a new growth interface. Based on the results of this study, several approaches have promise for reducing the kinking probability of Ge nanowires grown by the vapor−liquid−solid method. For example, to avoid Type I kinking, NWs with either substantially smaller or larger diameter than ∼20 nm are preferred. To eliminate Type II kinking, promising approaches include: (1) careful control of the temperature and precursor partial pressure to reduce the growth temperature so that it remains sufficient for Au−Ge liquid formation and Ge NW nucleation, but not so high as to cause errors in sidewall facet development as the droplet is lifted off the substrate surface during initial growth; (2) using larger diameter catalysts, as the effective energy barrier for kinking increases with NW diameter.
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diameter; (4) estimation of energy cost for Type I kinking (PDF)
AUTHOR INFORMATION
Author Contributions
Y.L. and Y.W. are equally responsible for the results reported. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by National Science Foundation Division of Materials Research programs DMR-1206511 and DMR-0907642. Part of this work was performed at the Stanford Nano Shared Facilities (SNSF). S.R. is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1010091).
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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.5b04633. (1) Parameters of phase field model; (2) calculation of average surface energies from phase field model; (3) relation between the actual NW diameter and nominal E
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