Monitoring Seed Formation Dynamics of Bulk-nucleated Vapor-Solid

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Monitoring Seed Formation Dynamics of Bulk-nucleated VaporSolid-Solid Germanium Nanowires via Resistance Measurements Benjamin T. Richards, Eric J. McShane, Samuel R. Schraer, Kevin Whitham, and Tobias Hanrath Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04144 • Publication Date (Web): 15 Jan 2019 Downloaded from http://pubs.acs.org on January 21, 2019

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Chemistry of Materials

Monitoring Seed Formation Dynamics of Bulk-nucleated VaporSolid-Solid Germanium Nanowires via Resistance Measurements Benjamin T. Richards1, Eric J. McShane2†, Samuel R. Schraer2†, Kevin Whitham1†, Tobias Hanrath2* AUTHOR ADDRESS 1Department of Materials Science and Engineering, 2Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853. ABSTRACT: Nanowire growth from metal surfaces presents several scientifically interesting and technologically important research challenges. Scientifically, many knowledge gaps remain about the fundamental mechanism by which nanowires nucleate from bulk surfaces. Technologically, this approach presents a promising pathway towards large-scale continuous nanowire fabrication. We present a novel method to probe nanowire nucleation and growth by in-situ monitoring of the resistance of the thin film from which nanowires form. We show that probing the resistance of the inductively heated thin film provides real-time diagnostic information about the reaction, including temperature, surface composition, and coarsening rate. We relate distinct features in the transient resistance to growth processes using ex-situ characterization via X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and optical microscopy. The in-situ resistance characterization method introduced in this paper provides new physical insight into the nanowire growth mechanism and relationship between grain coarsening and nanowire nucleation.

INTRODUCTION Semiconductor nanowires (NWs) have emerged as attractive building blocks for a broad range of burgeoning nanotechnologies including optoelectronic,1-2 energy,3-5 and sensor6-7 technologies. Future advances towards the anticipated technological impact of NW technologies hinges in large part on the development of scalable nanofabrication capabilities. This challenge is most evident in applications requiring high volumes of NW materials, most prominently in NW-based anodes for next-generation high-capacity Li ion batteries.8-9 Early advances in NW synthesis were built on vacuum-based processes adapted from microelectronics processing schemes.10-11 Practical limitations associated with the cost and scalability of high-temperature vacuum-based processes have inspired the development of solution-based strategies to fabricate NWs. Semiconductor NWs have been fabricated in various liquid12-14, and supercritical fluid15 environments. Notably, these methods can be operated as continuous processes that can be scaled up to realize high throughput, cost effective processing. Recent reports of the direct growth on metal films16-18 have opened doors to new NW fabrication schemes that provide highthroughput (e.g., by roll-to-roll processing) and facilitate device integration (i.e., by forming the NW directly on a current collector). From a mechanistic perspective, NW growth from a metal surface differs significantly from earlier NW growth studies on metal seed particles. The mechanistic differences are most pronounced in the initial nucleation of NW growth. Whereas in the classical vapor-liquid-solid model NW nucleation and subsequent growth from metal particles is well-understood,19-21 the understanding of and control over NW nucleation from bulk metal films is relatively scant. In the case of Ge NWs grown from Cu surfaces, the prevailing hypothesis is that NWs grow from Cu3Ge nuclei. Yet, the mechanism underlying the

sequence of Cu3Ge nucleation and subsequent NW formation remains unknown. To resolve outstanding questions about the nucleation mechanism, we sought to develop a new diagnostic tool that allows us to probe NW nucleation from metal films by monitoring how the resistivity of a thin film evolves during the course of NW growth. This method exploits the difference in resistivity between Cu and Cu3Ge to detect the solid-state phase transition that produces germanide seeds. Using the resistance measurement as a reaction coordinate, we investigated the processes that occur during these transitions, as illustrated in Figure 1. We fit the resistance data to classical models of nucleation, growth, and coarsening to track the processes that occur in the film during the NW synthesis. The understanding attained by these results enable further optimization of growth conditions to tailor NW growth from bulk metal films. METHODS Nanowire Synthesis Inductive heating experiments were performed in a custommade reactor setup, similar to our previous work22, in which the reactor vial was nested in a secondary container as detailed below. Each vessel was fitted with a septum top with high temperature, insulated, braided wire for resistance measurements (20 Ga nickel-plated copper wire). The insulated wire was terminated by Cu alligator clips which were attached to thin film copper resistor devices that sandwiched a 14 mm ⨯ 17 mm piece (0.15 mm thickness) of 430 grade stainless steel from Trinity Brand Industries, Inc. The apparatus was assembled inside the inert environment of a nitrogen filled glovebox. The cap assembly was inserted into a 20 mL VWR TraceCleanTM glass vial with a 4 mL precursor solution of 600 mM diphenylgermane (DPG) in squalene. The test device was positioned in the vapor space above the precursor solution. The 20 mL vial was sealed and inserted into a jar, which, in turn, was sealed. The assembled setup was removed from the

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glovebox and placed in the inductive heating coil. The device is heated in the inductive heater at varying currents, while resistance measurements were measured with a Keithley 2400 acquired every 250 ms via a Labview program. 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 alternating current was supplied at 60 A, 70A, or 80 A and 160-180 kHz through the inductive coil. After the reaction time elapsed, the setup was allowed to cool before being disassembled and the NW samples removed. The NW films were rinsed in hexane before characterization. Additional experimental details about the reactor and induction coil are provided in section S1 of the supporting information. Temperature profiles measured during control experiments are provided in section S2 of the supporting information.

Figure 1. Resistance of Cu thin film device was measured during the growth of Ge NW on inductively heated devices. a schematic of device inside a glass vial that is partially submerged in a precursor solution. The device tested is in the vapor space above the liquid precursor solution. The inset in image is a picture of the device, where the width of the copper path is 80 µm. b The state of the film can be monitored by the resistance data in c. This diagnostic tool allows for seed formation kinetics to be studied. Thin-film Resistor Fabrication The electrode and resistance patterns were fabricated by photolithography. 100 mm silicon wafers of 500 µm thickness

with 300 nm thermally grown silicon oxide were cleaned by rinsing with acetone and 2-propanol and spun dry. Lift-off resist (Micro-Chem LOR5A) was deposited by spin coating at 3,000 RPM for 45 seconds followed by soft-baking at 180 °C for 4 minutes. Photoresist was deposited by spin-coating Shipley 1805 at 4,000 RPM for 60 s followed by soft-baking at 115 °C for 90 seconds. The pattern was transferred by contact photolithography using a Suss MA6 followed by developing with metal-ion free developer. The metal layer was deposited by thermal evaporation of 5 nm Cr and 100 nm Cu. The remaining photoresist was removed in a bath of n-methyl-2pyrrolidone. The device wafers were then rinsed in deionized water and devices were separated using a dicing saw. In-situ resistance measurements To monitor the resistance during growth, we patterned a copper resistor on top of a dielectric silicon oxide layer on a silicon wafer. The devices were heated by placing them in direct contact with an inductively heated piece of 430 grade stainless steel. This assembly was held together by alligator clips and partially submerged in a precursor solution with the measured device located in the vapor above the precursor solution. The alligator clips provide electrical contact with the device and are connected to leads that pass-through septa tops to exit the reaction vessels.

RESULTS The experimental setup used to grow NWs on inductively heated metal films while monitoring changes in metal film resistivity is shown in Figure 1. Figure 2a shows the resistance profile for a NW synthesis reaction performed at 80 A in a 600 mM DPG solution for 300 s. We identified four distinct regimes in all reactions that produce NWs. Results from replicate experiments (see supporting information section S3) demonstrate reproducibility and temporal margin of error. To understand the processes that occur during these distinct regimes, we performed syntheses that are strategically terminated between temporal regimes. To identify the structural and morphological changes in each regime, we characterized the device via X-ray diffraction (XRD), scanning electron microscopy (SEM), and bright field optical microscopy. The times marked with roman numerals in Figure 2a denote times when experiments were terminated. To decouple changes in resistivity of the metal film due to temperature from changes in the composition (i.e., germanide formation), we performed a control experiment by heating the device in the solvent without DPG precursor (red trace in Figure 2a). The resistance with and without precursor is similar until (ii), at which point the increase in resistance is much more pronounced for the experiment with DPG precursor. The resistance of the control returned to its initial value after cooling. We thus conclude that the increase in resistance (before (ii)) is due to an increase in temperature.


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Figure 2. Temporal evolution of the structure, properties, and morphology during growth. a Resistance profile for a reaction occurring at 80 A, 600 mM DPG, for 300 s. Resistance of a control in the absence of precursor is also shown. b X-ray diffraction data for the times indicated in (a). c SEM images show sample morphology. All images are taken at the same magnification. d graphical summary of the structural and morphological evolution of the film.

The resistance of the device terminated at (ii) deviates from the control device indicating that this change in resistance is part of the NW nucleation and growth process. To identify the phenomena driving the resistance change, we characterized the device using XRD to investigate changes in the crystal structure and detect the presence of NWs. Figure 2b summarizes XRD scans for all devices terminated at different points in the reaction. Comparison to the device at (ii) shows a noticeable presence of the ε1 - Cu3Ge (111) and ε1 Cu3Ge (020). The ε1 - Cu3Ge (111) shares a peak angle with the Ge (220); however, the absence of a Ge (111) peak suggests that crystalline Ge has not yet formed. The ε1- Cu3Ge (020) appears at the shoulder of the Cu (111) peak. The relative signals of Cu3Ge to Cu indicates a partial conversion of the device to copper germanide. To resolve whether the partial conversion is due to a surface or depth nonuniformity, we probed the morphology of the surface using SEM. Figure 2c shows non-uniform roughening of the surface at stage (ii), which leads us to conclude that this increase in resistance is due to a partial conversion of the surface, and possibly sub-surface. The conclusion for substrates (ii) - (iv) is further corroborated by optical microscopy and energy dispersive X-ray spectroscopy analysis provided in the supporting information S.4 – S.5. Figure 2d provides a simple graphical illustration of the four regimes denoting the Cu-toCu3Ge transformation of the film and the subsequent NW growth.

The most dramatic resistance change occurs between stage (ii) and (iii). The corresponding XRD patterns of experiments terminated at stage (iii) reveal ε1 - Cu3Ge (020) reflections with greater intensity than the Cu (111) and ε1 - Cu3Ge (111), which we take as an indication of the Cu-to-Cu3Ge transformation of the film. The larger ε1 - Cu3Ge (020) peak compared to ε1Cu3Ge (111) indicates a preferred orientation of the germanide relative to the substrate (see supporting information section S6 about texturing). No Ge NWs could be identified with XRD or SEM at stage (iii). Instead, SEM images (Figure 2c), reveal that the germanide film is uniform across the metal surface. Following the rapid increase from stage (ii) to (iii), the resistance of the film decreases slightly until stage (iv). As discussed in detail below, this resistance decreases as NWs first grow from the film. At (iv), the presence of Ge NW growth is indicated by the appearance of the Ge (111) XRD reflection (Figure 2b) and short NWs visible in SEM images (Figure 2c). The onset of Ge NW growth coincides with the disappearance of the Cu reflections, which suggests that the Cu in the thin film is completely converted to Cu3Ge before Ge NW nucleation and growth can begin. Optical microscopy images (supporting information section S5) show a uniform darker film compared to previous devices. During the extended growth stage (iv to v), NWs lengthen and new NWs form, as seen in the SEM image in Figure 2c. The corresponding XRD in stage (v) shows a much more


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pronounced signature of crystalline Ge. Optical microscopy (Figure S5) shows material deposits on and near the resistive metal test strip, as the surface color has changed from an offgold color to a brown color, similar in color to a thick film of Ge NWs18. DISSCUSION The diagnostic technique presented here provides new insights into the solid-state transformations that occur in the metal film during NW nucleation and growth. The XRD results presented in the previous section demonstrates that the large change in resistance between stage (ii) - (iii) demarks the Cu-to-Cu3Ge transformation of the film followed by NW growth between stages (iii) - (v). To bring the full potential of this diagnostic method to fruition, we sought to go beyond merely monitoring the stages of NW formation and investigate how different NW growth conditions can inform the basic mechanism underlying NW nucleation and growth from a thin metal film. To gain deeper mechanistic insights, we performed reactions at different time-temperature profiles controlled by varying the applied induction current. Figure 3 summarizes the results of NW formed at induction currents of 60 A, 70 A, and 80 A. SEM micrographs of the surface after heating reveal that NWs are grown in 70 A and 80 A, but absent for low induction currents 60 A (Figure 3a.) Figure 3b shows the time-temperature profile corresponding to the three induction currents. The corresponding resistance profiles in Figure 3b reveal noticeable differences. 70 A and 80 A have a greater resistance gradient with time between (ii) - (iii). Moreover, the high current (high temperature) experiments show a slight decrease in resistance after stage (iii), which is absent in the low current (60 A) experiment in which NWs did not form. We will now discuss how the resistance changes in stages (ii) through (iv) can be related to the nucleation, growth and coarsening of the Cu-to-Cu3Ge transformation preceding NW growth. We first investigate the large increase in resistance between (ii) - (iii), which corresponds to Cu-to-Cu3Ge transformation. To determine if this follows classical nucleation and growth kinetics, we used the resistance as a reaction coordinate to fit the data to an Avrami equation, where the fractional conversion is calculated by 𝑓 = (𝑅(𝑡) ― 𝑅𝑜)/(𝑅𝑚𝑎𝑥 ― 𝑅𝑜) (see the supporting information S.7). This fitting is shown in Figure 3d. In all three cases the trends appear to be approximately linear. The Avrami exponent (n) in each case is a different value that typically provides information about the mechanism of crystallization. Traditional statistical models of nucleation and growth would produce integer values; in the case of diffusion controlled nucleation and growth of Cu3Ge from supersaturated Cu, non-integer values of n where n > 2.5 represent increasing nucleation rate during the transformation, while 1.5 < n < 2.5 indicate decreasing nucleation rate.23 Accordingly, in the case of the high induction current (70 A and 80 A) experiments, we expect more rapid and extensive nucleation whereas fewer nuclei lead to the formation of larger grains in the 60 A experiment. We provide additional data on the Cu3Ge grain size under different growth conditions based on Scherrer analysis of XRD patterns in Section S8 of the supporting information.

Figure 3. NW growth at different heating rates. a SEM images of devices heated at different inductive heating currents. At 80 A and 70 A NWs are observed to grow, but 60 A shows an absence of NW growth (scale bar = 200 nm) b Resistance profiles measured during growth. The dotted red lines indicate when heating was terminated. Note that the 60A experiment does not exhibit the resistance drop associated with NW growth after stage (iii) The 60 A reaction is missing the characteristic dip in resistance following the large increase in resistance. c Temperature profiles corresponding to the


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experiments above. d Fitting the nucleation and growth regime to the Avrami equation using the resistance profile as a reaction coordinate for nucleation and growth. The decrease in exponent value represents a change in mechanism of nucleation and growth.

supersaturation and NW nucleation we need turn our attention to the thermodynamic phase diagram of the Cu-Ge system in Figure 5a. This shows the equilibrium phases that are pertinent to the formation of Ge NWs on Cu thin films.

Next, we turn our attention to explain the cause of the resistance drop after stage (iii) and its relation to NW growth. We are particularly interested in understanding the process by which a 1D NW nucleates from a continuous Cu3Ge film. The resistance of the thin film can be analyzed in context of Matthiessen's rule: 𝑅𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 𝑅𝑙𝑎𝑡𝑡𝑖𝑐𝑒(𝑇) + 𝑅𝐺𝐵

(𝑥𝐺𝑒)…,

( )+𝑅 1

𝑑

( )+𝑅

1 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑓𝑖𝑙𝑚

𝑖𝑚𝑝𝑢𝑟𝑖𝑡𝑦

(1)

where 𝑅𝑙𝑎𝑡𝑡𝑖𝑐𝑒 is the phonon scattering contribution which depends on temperature and atomic structure, 𝑅𝐺𝐵 is the resistance due to electron scattering on grain boundaries and depends on the grain size (d), 𝑅𝑠𝑢𝑟𝑓𝑎𝑐𝑒 is the resistance due to surface scattering of the thin film and depends on the thickness 𝑡𝑓𝑖𝑙𝑚, and 𝑅𝑖𝑚𝑝𝑢𝑟𝑖𝑡𝑦 is the contribution from electrons scattering off of impurity atoms in the lattice and, in this case, depends on excess germanium content. Interpreting the decrease in resistivity during stage (iii) to (iv) in context of the contributing factors to the resistance indicated by Matthiessen’s rule (eqn 1) provides an important insight into the evolution of the Cu3Ge grain size. Since resistance due to lattice scattering and impurity scattering all increase during this stage, the observed decrease in resistivity is most likely dominated by reduced grain boundary scattering (i.e., grain coarsening). We can therefore correlate the resistivity transients to the temporal evolution of the Cu3Ge grain size and, in turn, relate the evolution of the grain size to the nucleation of NW seeds from the film. To test this interpretation, we probed the grain size using XRD. XRD can be used to track crystallite sizes in films if the grains are less than ~150 nm. The average crystallite size can be easily estimated by performing a Scherrer analysis on the peaks (see the supporting information section S7). We analyzed the crystallite sizes at different points along the transformation (Figure 4a) and plotted them in relation to time for reactions performed at 80 A in Figure 4b. This analysis reveals a rapid increase in grain size between (ii) - (iii). Afterwards, the grain size increases relatively slowly with time. To determine if grain growth could explain the decrease in resistance, we fit a linear function to 𝑅𝐺𝐵(1/𝑑) (see the supporting information section S10). By combining insights into the evolution of the temperature and grain size (from XRD), we can infer the grain size in the fully converted film from the resistance profile plotted in Figure 4b (see the supporting information for additional details). Since this provides a good estimate for the average grain size, coarsening of grains provides a reasonable explanation for the decrease in resistance. Importantly, the concurrent coarsening of Cu3Ge grains and observation of NWs provides an important clue to the NW nucleation mechanism. The mechanism by which NWs nucleate from continuous metal films has been a longstanding question. The analysis described in the previous section provides critical clues since Cu3Ge grains coarsen at the same time as NWs nucleate. To understand the fundamental relationship between Cu3Ge grain size,

Figure 4. a Selected temporal regime of the resistance profile of 80 A reaction to match the location with crystallite size in b. During the large increase in resistance there is a drastic change in crystallite, which is expected during nucleation and growth. Following nucleation and growth there is a slower increase in resistance associated with a slower increase in crystallite size typically associated with coarsening.

To graphically illustrate the underlying thermodynamic driving forces behind NW nucleation, Figure 5b provides a simplified qualitative free energy landscape derived from the equilibrium phase diagram24. Given the nanoscale dimension of the Cu3Ge grains, their chemical potential must be considered in context of the Gibbs-Thomson relation (i.e., increasing chemical potential with decreasing grain size). The mechanism behind Ge NW formation on thin Cu films can be described as a sequence of sub-processes. The thermolytic degradation of the Ge precursor near the surface of the heated metal surface provides a chemical potential gradient to drive Ge into the Cu film. The progressively increasing concentration of Ge in the film can be visualized as a transition from left to right in the phase diagram at sub-eutectic reaction temperatures (Figure 5a,b). As the system pushes beyond the solubility of Ge in Cu, Cu3Ge seeds start to form.


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Figure 5. Thermodynamics of NW formation. a Shows a simplified binary phase diagram that includes only the ε-Cu3Ge solid phase. b Qualitative plot of the molar free energy of copper and copper germanide in relation to crystalline germanium. The inset highlights the sizedependent molar energy of Cu3Ge grains due to the Gibbs-Thomson effect. The marked arrows illustrate the increase in molar free energy with decreasing grain size. NWs nucleate preferentially from smaller grains with higher supersaturation. c Graphical summary of the proposed model correlation grain coarsening and NW nucleation. As an example, consider two coarsening grains, one slightly larger than the other, is displayed. 1. both grains will take on additional Ge to reach the solubility limit of the average grain; (+) the larger grain can take on additional Ge and is thereby stable. (-) The smaller grain is forced to enter the two-phase region and exceeding the solubility limit, thus increasing the probability of supersaturation. d Relationship between Cu3Ge calculated grain size distribution (black) and NW diameter distribution (red) illustrates that NW preferentially nucleate from the smaller Cu3Ge grains (see supporting information for details).

The free energy of the resulting Cu3Ge depends on their grain size as described by the Gibbs-Thomson relation. This indicates that the smallest grains will be the least stable. Accordingly, the size-dependent free energy of the grain evolves as is illustrated in the inset of Figure 5b. The lower chemical potential of Ge in the smallest Cu3Ge grains increases the probability for nucleation of crystalline Ge in the form of a NW emerging from the nucleating grain, as shown in Figure 5c. The mechanism outlined in Figure 5 provides new physical insights into the relationship between grain size and NW nucleation; beyond CuGe, this principle can be extended to other material systems provided that the transformations are not limited by slow diffusion. Cu and Cr are fast diffusing atoms with Ge and have been identified previously to be the best metal surfaces for growing NWs from metal surfaces.18 To better understand how Gibbs-Thomson effect spurs on NW nucleation from small grains in the film, we analyzed the temporal evolution of Cu3Ge grain size distribution in more detail. We calculated the distribution using the Avrami data from Figure 3D and the volume-weighted average grain size as described in the supporting information S12. Figure 5d shows the Cu3Ge grain size distribution derived from this semiempirical model and good agreement with the experimentally

determined NW diameters at the smaller end of the distribution range. The probability of NW nucleation from a given Cu3Ge grain depends the supersaturation which is related to the sizedependent chemical potential. Details of this probability function and the predicted NW diameter distribution shown in Figure 5d are discussed in the supporting information. Interestingly, beyond the NW diameter distribution, this approach can also be used to predict the area NW coverage on the surface (see supporting information S12) CONCLUSION We present a simple yet powerful diagnostic technique that enables precise tracking of the stages of NW growth from thin Cu films. We used the in-situ resistance measurement to relate the arrival of NWs to coarsening of the Cu3Ge film and show that the transient resistance results can also be used to predict Cu3Ge grain size and NW diameter distribution. We provide a thermodynamic argument that demonstrates how coarsening contributes to seed formation, and show how diffusion-limited conditions can affect the mechanism of coarsening, thereby leading to seed formation and NW nucleation and growth preferentially from the smaller Cu3Ge seeds in the distribution.


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ASSOCIATED CONTENT Supporting Information. Contains sections on the inductive heating coil and reaction assembly, heating transients, compositional analysis via energy-disperse x-ray spectroscopy, optical microscopy, individual resistance profiles , nucleation and growth model, Scherrer analysis, analysis of 60 A reactions, and calculations predicting grain size. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Tobias Hanrath, [email protected]

Present Addresses †Eric J. McShane-Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720. Samuel R. Schraer-Georgetown University Law Center, Washington D.C., 20001.

Author Contributions All authors have given approval to the final version of the manuscript.

Funding Sources This work made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC program (DMR- 1719875). B.T.R. and T.H. gratefully acknowledge support from NSF-CBET 1510024.

ACKNOWLEDGMENT This work made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC program (DMR- 1719875). B.T.R. and T.H. gratefully acknowledge support from NSF-CBET 1510024. The authors would like to acknowledge Michael O. Thompson for his intellectual conversations on solid-state thermodynamics and kinetics.

ABBREVIATIONS NW, nanowire; SEM, Scanning Electron Microscope; XRD, X-ray diffraction.

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Table of Contents Figure


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Monitoring Seed Formation Dynamics of Bulk-nucleated Vapor-Solid

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