Reaction Kinetics of Germanium Nanowire Growth on Inductively

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Reaction Kinetics of Germanium Nanowire Growth on Inductively Heated Copper Surfaces Benjamin T. Richards,† Samuel R. Schraer,‡ Eric J. McShane,‡ Jacob Quintana,§ Barnaby D. A. Levin,∥ David A. Muller,∥,⊥ and Tobias Hanrath‡ †

Department of Materials Science and Engineering and ‡Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States § Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, United States ∥ School of Applied Engineering and Physics and ⊥Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: This article describes the chemical kinetics of germanium nanowire growth on inductively heated copper surfaces using diphenylgermane as a precursor. Inductive heating of metal surfaces presents a simple, rapid, and contact-free method to activate the direct growth of nanowires on metal surfaces. We show the main effects of synthesis temperature, duration, precursor concentration on the morphology, and loading of the nanowire film. We describe the complex interplay of precursor degradation, nucleation, and growth in context of a multistep reaction mechanism. We studied the temporal evolution of nanowire loading and morphology to develop a kinetic model, which predicts critical thresholds that define the onset of sequential axial and radial nanowire growth modes. These results may be used to commercially scale a nanowire growth process.

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INTRODUCTION Nanowire (NW) growth from catalytic surfaces involves an interesting interplay between thermodynamics, reaction kinetics, and transport phenomena.1 Building on the shoulders of earlier studies of whisker growth via chemical vapor deposition (CVD),2 the surge of interest in nanostructured materials has significantly advanced our understanding of fundamental kinetic and thermodynamic aspects of NW nucleation and growth.3−5 These scientific insights have enabled impressive advances in the fabrication of NWs with precise control over structure, growth direction, and composition.6−13 From a technological perspective, NWs play a promising role as building blocks of emerging nanotechnologies. By virtue of their aspect ratio, NWs provide the necessary electrical and physical contact between nanoscale components and the external macroscopic environment. The immense technological potential of semiconductor NWs has been underscored in a broad range of applications spanning optoelectronic,14,15 energy,16−19 and sensor20,21 technologies. A thorough review of technological applications of NWs is impractical here; excellent reviews and books have been published.7,22−24 To meet the expectations generated by the acclaimed potential of NW technologies, current impediments toward low-cost fabrication of NWs and their devices at industrially relevant scales must be resolved. Unfortunately, the CVD-based growth methods that have enabled many of the seminal © 2017 American Chemical Society

scientific advances will be difficult to scale up to meet emerging technological demands; this is particularly pronounced in highvolume applications such as high-capacity lithium ion batteries.25−27 As an alternative to the conventional vapor−liquid−solid (VLS) NW growth, recent reports of NWs formed on bulk metal surfaces have created new opportunities for scalable NW processing and reaction engineering. Ge NW growth in absence of metal seed particles was recently reported by Hobbs et al.28 Ryan and co-workers have demonstrated that Ge NWs can be grown directly on Cu films.29,30 Yuan et al.31 and Richards et al.32 have shown that single crystalline Si NWs can be synthesized on the surface of various bulk metals and thin films including Ag, Al, Cr, Cu, Fe, Ni, Pb, and Ti. These advances have revealed knowledge gaps concerning the fundamental mechanism of NW growth from bulk metal films, including the mechanism by which seeds nucleate and grow from a continuous metal film, the rate-limiting step of NW growth, and the basic relationships between growth conditions and wire morphology. For example, whereas in conventional VLS synthesis, the relationship between seed particle and wire diameter is well understood, fundamental understanding of the factors governing the diameter of NWs Received: February 12, 2017 Revised: May 20, 2017 Published: May 22, 2017 4792

DOI: 10.1021/acs.chemmater.7b00598 Chem. Mater. 2017, 29, 4792−4800

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Chemistry of Materials grown from bulk (i.e., continuous) metal films has not yet been established. Similarly, the transition from axial to radial growth modes has not been quantitatively modeled for NWs grown from metal surfaces, but has been observed.33 Answering these mechanistic questions hinges on deeper understanding of the NW growth kinetics, which can be experimentally studied in growth reactors that enable rapid initiation of and precise control over conditions and duration of NW growth. To address this challenge, we turned to an inductively heated reactor configuration that enables rapid dynamic control over the surface temperature as an experimental platform to study the NW growth kinetics and fundamental reaction mechanism. As implemented previously in CVD systems,34 this approach offers insights into the coupled reaction and transport subprocesses. In particular, we identify and discuss the relationship between processing conditions and the multistep mechanism involving precursor degradation, incubation (i.e., formation of the Cu3Ge seed), growth of NWs from the metal surface, and ultimately broadening of the NW diameter via radial growth. We investigate the complex interplay between these steps and analyze the reaction kinetics to identify the stages of NW growth, incubation, axial growth, and radial growth. These results enable deeper understanding of the basic reaction mechanism and thereby extend the control over NW growth from bulk metal films. From an applied perspective, the ability to engineer rapid, spatially and temporally programmable heating profiles without physical contact to the heater is advantageous for high-throughput processing methods like rollto-roll manufacturing, as observed for graphene.35 A recent paper by Ellingsen et al.36 highlighted the need to consider energy efficiency of technologically promising nanomaterials; in that context, we note that NW growth on inductively heated surfaces presents a high-throughput synthesis route with a lower thermal budget compared to conventional methods.

Figure 1. (a) Simplified rendering of the reaction apparatus. The experimental apparatus contains three nested glass vessels (vessel 1: L = 87 mm, O.D. = 43 mm; vessel 2: L = 57 mm, O.D.= 27.5 mm; vessel 3: L = 45 mm, O.D. = 15 mm), centered in a rectangular inductive heating coil containing a piece of magnetic stainless steel (L = 35 mm, W = 7 mm, 430 grade) with a copper thin film (Cu = 100 nm) and a 3 mL precursor solution (see Supporting Information S1 for more details). This coil is powered by a 1.4 kW inductive heating unit. The actual (b) graphical representation of the temperature profile near the stainless steel surface. (c) Multistep bulk-nucleated VSS reaction mechanism. NWs grow by a series of coupled processes including precursor degradation (r1), transport and deposition of Ge at the surface, and diffusion into the surface causing germanide formation, and new interfaces produced during nucleation allow for supersaturated Ge to trigger NW growth (r2) and continued diffusion of Ge drives growth. After the overall concentration of Ge in the vapor reaches a threshold, Ge nucleates and crystallizes on the sidewalls of the NW (r3).

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importance of the kinetic variables of precursor concentration and temperature. In the discussion below, we will focus mostly on NW growth in the vapor regime; NW growth in the liquid regime and the underlying vapor−liquid equilibrium for the binary (solvent and precursor) system are detailed in the Supporting Information (S5−6). The inductively heated metal film was contained within an assembly of nested glass vessels containing the precursor solution, and this assembly was positioned inside an inductive heating coil (see Figure S1). During synthesis, an alternating current was passed through the inductive heating coil at frequencies near 180 kHz to produce an alternating magnetic field that flips the magnetic poles in the ferritic stainless steel. The work done by switching the magnetic poles creates localized heating of the metal surface, while the surrounding fluid and reactor walls remain cooler (Figure 1b). We first sought to understand the effects of precursor concentration, temperature, and reaction duration on the NW growth on Cu films. Below, we will first summarize qualitatively fundamental processing-structure relationships and then discuss the basic NW growth mechanism in context of a multistep kinetic model shown in Figure 1c. We surveyed NW morphology (e.g., wire diameter, coverage, and structure) using scanning electron microscopy (SEM) to relate NW growth conditions (i.e., temperature, concentration, growth time) and structure of the NW film. The main effects of NW growth on Cu surfaces are summarized in Figure 2. The concentration of the germanium precursor (diphenylgermane) and the vapor−liquid equilibrium between precursor and the

RESULTS The inductively heated reactor used in the NW experiments is illustrated in Figure 1a. The reactor embodiment shown in Figure 1a can be used to study NW growth on inductively heated metal surfaces in contact with precursor gas and liquid at the same time; this reactor configuration has some similarities to inductively heated “cold-wall” chemical vapor deposition systems. Experimental details about the reactor and induction coil are provided in the Supporting Information (S1). We monitored the temporal evolution of the metal surface temperature using Tempilaq paste as detailed in the Supporting Information (S2−3). To establish a rigorous quantitative relationship between NW morphology and growth rate, we combined electron microscopy analysis of the NW morphology with measurements of the loading (i.e., mg of NWs/cm2 of metal surface) for various reaction conditions and durations. Details on how the loading measurements are taken are provided in the Supporting Information (S4). Inductive heating of the metal strip partially immersed in the precursor solution enables study of NW growth in vapor and liquid regimes. Comparing the NW growth in vapor (∼mM) and liquid (∼0.1 M) phases enables the study of NW growth with precursor concentrations that span multiple orders of magnitude. In addition, the temperatures achievable in the vapor are much higher, while in the liquid the surface temperature is maintained by the boiling point temperature of the precursor solution. Although the two-phase system does add complexities in dynamics, the investigation of these two regimes underscore the 4793


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Figure 2. SEM analysis shows processing-morphology relationships of germanium NWs. Experiments separated by the red dotted line identify NWs that have undergone radial growth. (a) Effects of increasing concentration on NWs diameter. NWs were formed at 650 °C and 180 s. At high concentrations radial growth is observed. (b) Effects of increased temperature from the surface. NWs were formed in 600 mM DPG for 180 s. Higher temperature at the surface further encourages radial growth from the sides of NWs. (c) Evolution of the surface with time. At 60 s, near the onset of axial growth, the NWs are short and films are low density. At 240 s, radial growth is observed. This indicates that onset of radial growth is dependent on a kinetic condition rather than a critical temperature or precursor composition. NWs were formed at 600 mM, 650 °C. Refer to the center image for a film heated for 180 s. All scale bars represent 1 μm.

analysis on these NWs and compare them to our previous study32 in the Supporting Information (S10). At higher synthesis temperatures (736 °C) NWs with significantly larger diameters are formed. The transition from small to large diameter NWs with increasing temperature parallels the trend with increasing precursor concentration discussed above. The correlation between NW diameter and growth parameters raises questions about the NW growth mechanism. Does the trend in NW diameter result from differences in the size of the copper germanide seeds or does the NW diameter change during the NW growth? To answer this question, we imaged a cross section of NW film. The cross-sectional SEM image Figure 3a shows a pronounced difference in NW diameter near the top, Figure 3b, and bottom of the film, Figure 3c. Statistical SEM image analysis in Figure 3d reveals that the NW diameters near the copper surface have a similar diameter, 71.5 nm, to the NWs observed at low concentrations (e.g., 72.5 nm at 200 mM). However, NWs at the top of the film, adjacent to the gas phase precursor solution, have substantially larger diameter, Figure 3e. We analyzed the tapered NWs by highangle annular dark field scanning transmission electron microscopy (HAADF-STEM). Convergent beam electron diffraction (CBED) and electron energy loss spectroscopy (EELS) analysis confirmed that the radial NW growth material is crystalline Ge (Supporting Information S11). We note that tapered NWs resulting from the combination of axial and radial growth have been previously observed in VSS37 and VLS experiments;38 this has been previously shown in InP nanowire systems where an In seed is used, as unmatched In incorporation into the nanowire will cause the seed to grow and broaden the NW.39 We interpret the effect of temperature and concentration on NW diameter as a transition of

high-boiling solvent (squalene) have a profound effect on the NW morphology and yield (Figure 2a). We explored concentration effects in a series of NW syntheses performed at 650 °C for reaction times of 180 s. We observed NW growth at all tested concentrations. Notably, the diameter of NWs grown in the vapor increases from a mean of 72 nm at 200 mM to 1200 nm at 800 mM. These concentrations are of the liquid precursor solution. During the reaction, the concentration of DPG in the gas is in equilibrium with the liquid and is primarily dependent on the temperature of the metal surface submerged in the precursor solution. The diameter of NWs grown in the liquid regime remains in the range of 40−60 nm for the same concentration range. Histograms containing statistics of NW diameters for each concentration are included in the Supporting Information S7. Systematic analysis of the effect of synthesis temperature, while keeping precursor concentration (600 mM) and reaction time (180 s) constant, reveals three distinct growth regimes (Figure 2b). First, at synthesis temperature of 500 °C (∼100 °C below the lowest liquid eutectic point in the Cu−Ge phase diagram) we observe malformed wires. The formation of these noodle-like wires indicates that wire growth, albeit of lower quality, is possible from solid CuxGe seeds (see the Supporting Information S8 for XRD data). Ryan and co-workers found that NWs grow with 5 min reactions at lower temperatures and concentrations.29 At longer reaction times (250 s), we observe a mixture of malformed and straight NWs (see Supporting Information S9). Raising the synthesis temperature to 650 °C, which is just above the Cu−Ge eutectic point, yields a film of high-density small diameter NWs. At 650 °C, the reactions occur above the eutectic temperature. As this would be a different regime than our previous study, we perform a TEM 4794


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Figure 3. Tapering of Ge NWs grown from Cu film. (a) Cross-sectional SEM image of a NWs film grown in 700 mM DPG for 200 s at 650 °C. Notably, NWs have larger diameter near the top of the film than near the substrate. The inset is an ADF-STEM micrograph of a germanium nanowire at the onset of radial growth, which features crystalline Ge nucleates that are on the sidewall of the nanowire (see the Supporting Information S11 for additional information). The scale bar in the inset represents 100 nm. (b,c) Higher magnification images of the bottom and top of the films, respectively. (d,e) Statistical analysis of NW diameters via image analysis of the bottom (N = 100) and top (N = 61) of the film. The diameter of the NWs at the bottom are similar to NWs grown at lower concentrations.

longer wires and denser films. Figure 2c shows that NWs grown at 120 and 180 s show increasingly fuller NW films. Importantly, the NW diameter appears to increase dramatically between reaction durations of 180 and 240 s; this trend is consistent with the transition from axial to radial growth discussed above. The temporal evolution of NW morphology and diameter revealed in Figure 2c provides important insight into the dynamics of the initial incubation period and the subsequent transition from axial to radial NW growth. Below, we discuss the basic trends in context of the multistep reaction mechanism illustrated in Figure 1c.

predominantly axial NW growth (at moderate temperatures and concentration) to radial NW growth (at high temperatures and high concentration). To better understand the factors governing the transition from axial to radial NW growth modes, we studied the temporal evolution of the NW film by performing a series of syntheses at varying growth times while keeping precursor concentration (600 mM) and synthesis temperature (650 °C) constant (Figure 2c). We first probed the NW growth shortly after nucleation. The reaction products formed with short heating (60 s) are characterized by short NWs that form at an area density of about 1.5 NWs/μm2. The NW density for short growth times (right after nucleation) is about an order of magnitude lower than NW density for fully developed films (see Supporting Information S12), which suggests that NW nucleation does not occur as a burst but rather continues into later stages of the growth process. These nucleation dynamics are similar to those recently observed in the case of carbon nanotubes by Hart and co-workers.40 These short heating experiments reveal the onset of axial NW growth, whereas NW films formed with longer reaction times lead to significantly

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DISCUSSION To understand the complex rate laws governing NW growth from metal surfaces we need to consider the elementary processes of formation of seeds, supersaturation of seeds, and growth schematically illustrated in Figure 1c. The first step is the thermolytic degradation of the organogermane precursor to yield active species Ge*, which can then either deposit as a Ge thin film or diffuse into the copper film. In case of the latter 4795


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Chemistry of Materials pathway, the Ge content in the metal copper germanide film will gradually increase; this process can be visualized as a progression through various CuxGe phases in the Cu−Ge binary phase diagram prior to the formation of a liquid CuxGe above the bulk equilibrium eutectic (644 °C) (see the Supporting Information S14). We note that the presence of multiple intermediate CuxGe phases complicates the binary equilibrium phase behavior relative to the Au−Ge system commonly used in VLS synthesis. A recently study by O’Regan et al. elegantly showed that the Ge NW nucleation kinetics can be controlled through the supersaturation of the binary Au/Ge system.41 In our earlier work, we identified the composition of the seed of Ge NWs grown from copper films to be Cu3Ge.32 Nucleation of NWs from a bulk metal surface involves two sequential nucleation events. First, Cu3Ge nuclei form at the surface of the metal film followed by the subsequent nucleation of Ge at the surface of the seed. By contrast, NW growth via the conventional VLS method involves only the second nucleation event since the seed particle from which the wires grow is already defined (either by the shape of the colloidal seed particle or by lithographic patterning). In the case of NWs grown from Cu metal surfaces, the wire diameter is defined by the size of the Cu3Ge nucleus formed at the metal surface. We developed a kinetic model of the multistep NW reaction process illustrated in Figure 1. We model the generation rate of Ge* and growth rate of Ge NW as r1 and r2, respectively. Informed by the equilibrium phase diagram for the binary Cu− Ge system, this model implies the existence of a threshold concentration [Ge*]inc that must be overcome to saturate the seed and to initiate NW growth. At sufficiently high supersaturation of Ge*, we expect a second threshold to enable the pathway of direct deposition of Ge onto the sidewall of the formed wires. We interpret the observation of tapered NW (Figure 3) as an indication of the direct deposition responsible for the radial growth. We model the deposition of Ge on the NW sidewall as a “radial” growth process at a rate r3. Taken together, the nucleation, NW growth, and side-wall deposition process can be described as three consecutive subprocesses defined by the temporal evolution of [Ge*] near the metal surface. Figure 4a schematically illustrates the (i) incubation, (ii) axial growth, and (iii) radial growth stage. Based on the experimentally observed temporal evolution of Ge NW loading (Figure 4b), we expect the concentration of Ge* during the sequential growth stages to evolve as illustrated in Figure 4c. In context of the chemical potential of the active Ge species, μGe*, the reaction kinetics in the three stages can be delineated as Stage 1, incubation, (μGe * < μCu Ge ): r1 = x

Figure 4. (a) Evolution of loading observed for reactions run at T = 736 °C and 600 mM. This canonical example shows the three periods of growth, incubation (no loading accumulates), growth (loading accumulates linearly), and radial (loading accumulates at a faster rate). (b) Illustrative profile of [Ge*] corresponding to the three regimes of growth. A quantitative example is provided in the Supporting Information S13.

vapor phase concentration of diphenylgermane. Aseed and ANW are the area of the catalytic seeding surface and the NW. r2 has a functional form of r2 = k2[DPG]m. Next, we analyze the reaction kinetics in each of the three stages in detail. The rapid heat-up and cool-down dynamics of the inductively heated system enable us to study NW growth for precisely defined heating and reaction times. Figure 5a shows the temporal evolution of NW loading for reaction times up to 4 min. In a typical experiment, inductive heating raises the surface temperature to 650 °C within less than 5 s (see Supporting Information S2 for details of the heat up dynamics). Interestingly, no loading is observed during the first 60 s, which is consistent with “incubation periods” observed in previous Si NW growth studies by Arbiol et al.42 Incubation times have been attributed to a variety of factors including the surface reaction (reaction/adsorption)43 and diffusion of Ge into the seed.44 To understand the relationship between the thermolytic decomposition of the organogermane precursor and the incubation time, we compared the dynamics of NW formation from phenylgermane (PG) and diphenylgermane (DPG). Based on the hypothesis that the thermolytic degradation of the precursor is kinetically limited by detachment of the phenyl ligand, we expect PG to degrade faster (i.e., shorter incubation time) than DPG. The direct comparison of incubation time and NW morphology obtained from PG and DPG confirms that the incubation time of former is approximately 30 s less (see Supporting Information S15). The generation rate of Ge* is given by the decomposition kinetics of the organogermane precursor as described by r1 (eq 1). To maintain generality, we have based the degradation rate on a nth order rate. We note that the good fit of the

d[Ge*] dt

= k1[DPG]n

(1)

Stage 2, axial growth, (μGe * > μCu Ge ): x

d[Ge*] dt

= k1[DPG]n − r2·A seed

Stage 3, radial growth, (μGe * > μGe(s)): = k1[DPG]n − r2·A seed − r3·ANW

(2)

d[Ge*] dt (3)

where μGe*, μCuxGe, and μGe(s) are the chemical potential of the active Ge species, the seed, and solid germanium. [DPG] is the 4796


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is constant for a given growth temperature, we can quantitatively relate incubation time and [DPG]0 as follows: 1 t inc

∝

k1 ·[DPG]0 [Ge*]inc

(4)

Figure 5b shows that 1/tinc is linearly proportional to [DPG]0, which confirms that DPG degradation in the presence of Cu can be modeled as a first order reaction (n = 1). By predicting tinc for the vapor and liquid regime, this model is accurate for [DPG] spanning multiple orders of magnitude. Using this same technique, we can now investigate the effect of temperature on the tinc. We illustrate the relationship between temperature and precursor degradation in the Arrhenius plot of ln(1/tinc) vs 1/T, shown in Figure 5c. This analysis reveals an activation energy of 0.80 eV. More generally, this demonstrates how tinc can be used to study precursor kinetics of reaction limited incubation periods. We now turn to discuss the NW growth rate, r2, in context of the elementary reaction steps and the rate limiting step (RLS). In conventional VLS NW growth, the RLS has been discussed as being either limited by (1) the crystallization of Ge at the seed/NW interface, (2) the surface reaction to decompose the precursor DPG and incorporate Ge into the CuxGe seed,47 or (3) diffusion of Ge through the seeds. Given the relatively fast diffusion and short distances, the growth is generally not considered to be diffusion limited.38,48,49 The RLS governing growth of NWs from bulk metal films and the kinetic competition between crystallization and surface reaction have not yet been established for this system, but studied for a silicon NW system.50 Notably, these two rate-limiting mechanisms are restricted by two distinct kinetic variables; however, both mechanisms have a dependence on temperature. Crystallization is controlled by the activity of germanium in the Cu3Ge seed, whereas the surface reaction is limited by [Ge*] and temperature through the kinetic decomposition reaction and adsorption/desorption reaction. To understand the kinetic competition between surface reaction and crystallization, we analyzed the dependence of r2 on [DPG] and temperature. Figure 6a shows the dependence of r2 on [DPG]0, which reveals that, similar to r1, r2 is proportional to [DPG]. Moreover, as r1 increases, r2 increases proportionally. This trend suggests that r2 has the same rate limiting determining factors r1. In other words, like incubation, axial growth may be governed by a surface reaction of the decomposition of the precursor. The axial growth rate increases with increasing temperature from 30 μg/cm2/s at low temperatures (650 °C) to 38 μg/ cm2/s at high temperatures (772 °C). An Arrhenius analysis of the temperature dependence reveals an activation energy (0.38 eV) (Figure 6b). Since this activation energy is significantly lower than that for the incubation processed discussed, we conclude that the crystallization at the heart of r2 is not the rate limiting step. An additional line of evidence pointing to the surface reaction at the seed fluid interface as the RLS can be inferred from the impact of the concentration of the active species, [Ge*], on the NW growth rate. Figure 5a shows that the growth rate, r2, is constant during the growth process. However, during the growth period, [Ge*] continues to increase on the surface as indicated in Figure 4c; this inference is supported by the fact that the NW growth transitions from an axial mode to radial growth at later stages in the process. This accumulation

Figure 5. (a) Effects of initial concentrations of DPG ([DPG]0) on evolution of loading for 180 s reactions (T = 650 °C). Incubation times decrease with precursor concentration. Axial growth rate (r2) increases with [DPG]0. The gas phase concentrations were calculated by the vapor−liquid equilibrium data in the Supporting Information S6. (b) Investigating the inverse of the incubation time vs [DPG]0 reveals a linear trend. These experiments were performed at 650 °C for 180 s. This indicates that DPG degradation can be modeled via a first order reaction. (c) Arrhenius plot of 1/tinc vs 1/T providing the activation energy for the degradation of DPG.

experimental results to the first order degradation kinetics suggests that the rate limiting step of the thermolytic degradation of the organogermane differs from the presumed bimolecular disproportionation of phenylgermanes previously discussed for Ge NW growth in solution.45 Determining the time required for incubation requires an investigation into when loading begins to accumulate on the surface. This involves temporal analysis of NW growth. Following incubation and nucleation, NW loading increases at a rate of about 30 μg/cm2/s. Figure 5a shows the evolution of NW growth with time for syntheses performed in 200, 400, 600, and 700 mM at 650 °C. The comparison of NW growth experiments at varying precursor concentrations reveals three main trends. First, the NW growth rate, r2, increases with increasing initial concentration of precursor ([DPG]0). Second, the linear correlation between NW loading and reaction time indicates that the growth rate is approximately constant. Third, the duration of the incubation time (tinc) decreases with increasing precursor concentration [DPG]0. The relationship between incubation time and precursor concentration has been discussed in a previous paper by Kalache et al.46 Since the threshold concentration of Ge required to initiate axial growth 4797


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degradation kinetics of a precursor. Using this method, we provided kinetic data for degradation of DPG. We determined the RLS of Ge NW growth for our system and found that axial growth is limited surface reaction at the seed/vapor interface. We determined and modeled the rate of NW loading increase, based on kinetic theories, and studied the threshold for radial growth. From this we were able to relate the amount of depletion due to axial growth to the degradation of the precursor to solve for the constants in the Arrhenius relationship. This allowed us to develop a model that fully predicts incubation time, loading, and the onset of radial growth for any precursor concentration, temperature, and time. In addition, we have used this apparatus and model to study the degradation kinetics of PG. We report that PG is a faster precursor than DPG and calculate the parameters for the Arrhenius relationship. We confirm our model by calculating the threshold for axial growth independently. The precise kinetic data can be extended to other systems by scaling to the system. The kinetic relationships described in this paper provide important mechanistic insight of NW growth.

Figure 6. (a) Axial growth rate (r2) with vapor phase [DPG] for syntheses at 650 °C and 600 mM. This appears to be of similar functional form as r1 with [DPG]. The gas phase concentrations were calculated by the vapor−liquid equilibrium data in the Supporting Information S6. (b) Arrhenius plot of r2 and 1/T. All reactions were performed with the same [DPG] for 180 s. Axial growth appears to have a lower activation energy than r1; this may be due to the difference in adsorption on copper vs CuxGe.

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METHODS

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CHARACTERIZATION

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ASSOCIATED CONTENT

Inductive heating experiments were performed in a custom-made reactor setup in which the reactor vial was nested in secondary and tertiary containers as detailed below. A 100 nm of film of Cu (99.9 mol % purity), along with a 5 nm chromium (99.9 mol % purity) adhesion layer, was thermally evaporated onto the surface of a 7 mm × 35 mm piece (0.006 in thickness) of 430 grade stainless steel from Trinity Brand Industries, Inc. The assembly of the apparatus was performed inside of a nitrogen filled glovebox. The stainless steel was inserted into a 4 mL VWR glass vial (short form style with phenolic cap) with a 3 mL precursor solution of various concentrations between 200−800 mM diphenylgermane (DPG) and 600 mM phenylgermane (PG). The 4 mL vial was sealed and inserted into a VWR TraceCleanTM 20 mL vial. The 20 mL vial was sealed and inserted into a jar, which, in turn, was sealed. The assembled ensemble was removed from the glovebox and placed in the inductive heating coil. The inductive heating current and time of the reaction was set in the inductive heating coil of the Ambrell EasyHeat 1.4 kW inductive heating system. The AC current was supplied at ∼160−180 kHz through the inductive coil. After the reaction time elapsed, the ensemble was allowed to cool before the ensemble was opened and the NW samples removed. The NW films were rinsed in hexane before characterization.

of [Ge*] is consistent with by the surface reaction limited growth. Since the growth rate does not appear to increase with time, this would indicate that r2 is independent of [Ge*]. If the surface reaction is not rate limiting, the concentration of Ge would increase in the seed over time, which would increase the crystallization rate. One would expect loading to increase superlinearly with time. In contrast, the observation of a constant growth rate, r2, leads us to conclude that the overall reaction is not limited by crystallization at the Ge/CuxGe interface, but rather by the surface reaction at the vapor/CuxGe interface. Lastly, we studied the onset of radial growth. As shown in Figure 4c, when the concentration of [Ge*] reaches a threshold [Ge*]rad radial growth will begin. As radial growth is often considered as undesirable, radial growth will be avoided when the rate of Ge* produced by the precursor degradation is equal to the rate of Ge* consumed by axial growth. Written mathematically, k1·[DPG] ≈ r2·Aseed. The simplest way to balance precursor degradation rate with axial growth rate is to adjust the substrate seeding area (Aseed). Since there is a large difference in activation energy of k1 and r2, temperature is the most effective parameter to avoid radial growth. Lower temperatures will prolong the transition to radial growth, but will result in extended incubation periods. The best solution would be to incubate NWs at a higher temperature, but grow at a lower temperature.

SEM characterization was performed on a LEO 1550 field effect SEM (FESEM) and Tescan Mira3 FESEM. High-resolution STEM imaging, CBED, and EELS was performed on an FEI Tecnai F20 TEM/STEM, operated at 200 kV. S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b00598. Description of inductive heating coil, model of gas phase temperature transients, model of liquid phase temperature transients, procedure of loading measurements, characterization of liquid regime product morphologies, vapor−liquid equilibrium data for precursor solution, statistical analysis of diameter for various precursor concentrations for the vapor and liquid regimes, X-ray diffraction data, NW grown at 500 °C for 250 s, structural and compositional characterization in the TEM, characterization of nucleation sites on the

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CONCLUSION We have demonstrated NW growth on inductively heated metal surfaces as a simple, rapid, and precise method to grow Ge NWs and study the kinetics of the multistep reaction process. We observed three distinct NW growth phases: incubation, axial growth, and radial growth. We have shown that an investigation of the incubation period can model the 4798


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sidewalls of the nanowires, defining nanowire area density, solving for kinetic parameters and validation of kinetic model, Cu−Ge binary phase diagram, and comparison of nanowires growth from diphenylgermane vs phenylgermane (PDF)

AUTHOR INFORMATION

ORCID

Tobias Hanrath: 0000-0001-5782-4666 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC program (DMR-1120296). B.T.R. and T.H. gratefully acknowledge support from NSF-CBET 1510024.

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Reaction Kinetics of Germanium Nanowire Growth on Inductively

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