Mass Transport in Nanowire Synthesis: An Overview of Scalable Nanomanufacturing

Accepted Manuscript Mass Transport in Nanowire Synthesis: an Overview of Scalable Nanomanufacturing Matthew J. Crane, Peter J. Pauzauskie

PII:

S1005-0302(15)00064-X

DOI:

10.1016/j.jmst.2015.01.009

Reference:

JMST 490

To appear in:

Journal of Materials Science & Technology

Received Date: 17 December 2014 Revised Date:

7 January 2015

Accepted Date: 23 January 2015

Please cite this article as: M.J. Crane, P.J. Pauzauskie, Mass Transport in Nanowire Synthesis: an Overview of Scalable Nanomanufacturing, Journal of Materials Science & Technology (2015), doi: 10.1016/j.jmst.2015.01.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Mass Transport in Nanowire Synthesis: Scalable Nanomanufacturing

an Overview of

Matthew J. Crane1, Peter J. Pauzauskie2,3 * 1

Department of Chemical Engineering, University of Washington, Seattle, WA 98195-1750, USA Department of Materials Science & Engineering, Seattle, WA 98195-2120, USA 3 Fundamental Computational Science Directorate, Pacific Northwest National Laboratory, Richland, WA, USA

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[Manuscript received 17 December 2014; received in revised form 7 January 2015, accepted 23 January 2015]

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* Corresponding author. E-mail address: [email protected] (Peter J. Pauzauskie).

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The ability to rationally engineer the growth and nanomanufacturing of one-dimensional nanowires in high volumes has the potential to enable applications of nanoscale materials in a diverse range of fields including energy conversion and storage, catalysis, sensing, medicine, and information technology. This review provides a roadmap for the development of largescale nanowire processing. While myriad techniques exist for bench-scale nanowire synthesis, these growth strategies typically fall within two major categories: 1) anisotropically-catalyzed growth and 2) confined, template-based growth. However, comparisons between growth methods with different mass transport pathways have led to confusion in interpreting observations, in particular Gibbs-Thomson effects. We review mass transport in nanowire synthesis techniques to unify growth models and to allow for direct comparison of observations across different methods. In addition, we discuss the applicability of nanoscale, Gibbs-Thomson effects on mass transport and provide guidelines for the development of new growth models. We explore the scalability of these complex processes with dimensionless numbers and consider the effects of pressure, temperature, and precursor material on nanowire growth.

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1. Introduction

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Key words: Nanowire; Mass transport; Modeling; Scalable growth

Research over the past century has led to a renaissance of unique effects and potentially disruptive technologies observed in and designed from materials with nanoscale dimensions, where quantum effects dominate. Confinement of electrons along one, two, or three dimensions at this scale alters the density of states of nanomaterials and yields discrete energy levels that differ from their bulk counterparts. Further, nanostructured materials have enormous surface area to volume ratios that enable highly-efficient processes[1,2] allowing surface states to play a major role. As such, quantumconfined materials, including quantum dots, nanowires (NWs), and graphene exhibit unique and fascinating electrical, thermal, mechanical, optical, and magnetic properties. Of these materials, NWs

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maintain the advantage of exhibiting quantum phenomena along one radially confined dimension and macroscale lengths along another, thereby bridging these enticing phenomena with bulk applications. These bridging effects offer scientists and engineers an unparalleled range of variables to rationally design new materials for applications in thermoelectrics[3], photodetectors[4,5], photovoltaics[6–8],

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batteries[1,9], transistors[10], sensor[11,12], catalysis[2,13], and medicine[14]. For instance, single crystal NWs can be processed into bulk fabric-like materials that exhibit quantized properties and can be manipulated at the macroscale for new battery technologies, as shown in Fig. 1.

Growth of 1D nanostructures stems from two distinct strategies: suppressing growth in axial directions relative to the propagation direction, typically by lowering an energy barrier to growth in a

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certain direction, or physically confining growth with a template or structured technique[15,16]. The first of these two techniques encompasses a broad swath of CVD- and solution-based synthesis methods

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that have largely dominated NW growth literature including vapor-liquid-solid (VLS)[17], solutionliquid-solid (SLS)[18], liquid-solid (LS)[19], supercritical fluid-liquid solid (SFLS)[20], molecular beam epitaxy (MBE)[21], screw dislocation[22], laser ablation[23], plasma-enhanced CVD (PECVD)[24], metaloxide assisted (OAG) growth[25], and oriented attachment (OA)[26]. These methods proceed through similar mechanisms, in which precursor materials arrive at the NW tip, where they preferentially incorporate to form a one-dimensional structure, as shown in Fig. 2. In the latter category of templated

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synthesis, concentration gradients drive transport through porous patterns until precursor materials reach the growing NW, where they are incorporated, as shown in Fig. 3. While the experimental determination of critical reaction parameters such as pathways, rates, diffusion constants, and thermodynamic limitations for myriad materials systems is challenging to observe, parameters are

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slowly being collated in literature, and growth trends provide significant insights into our knowledge of nanoscale size effects[27–29], informing future and current synthesis techniques.

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All of these methods can be described by developing basic transport, kinetic, and thermodynamic models, which frequently overlap.

For example, steady state VLS NW growth

involves 4 distinct processes: 1) precursor-containing molecule transport to the catalyst, 2) precursor decomposition and adsorption at the catalyst surface, 3) diffusion into and through the catalyst, and, 4) incorporation at the metal-NW interface, as shown in the Fig. 2. An intimate understanding of these processes, their dependence on reaction conditions, and their rate-limiting steps are essential to rationally engineering scalable NW syntheses. An important distinction between mass transport, thermodynamics, and kinetics in NW growth methods is that the growth method largely dictates key aspects of mass transport whereas the material systems and choice of catalyst defines overall thermodynamic and kinetic pathways. For instance,

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VLS, SLS, SFLS, MBE, MOCVD, and laser ablation have used Au catalysts to promote Si NW growth and typically exhibit identical kinetics and thermodynamics. However, mass transport varies widely for these different techniques: from continuum to molecular fluid physics, from laminar to convective flows, and from physical to chemical to atomic deposition. Thus, a fundamental understanding of mass

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transport, arguably the simplest variable to control, enables research on kinetics and thermodynamics. Comparing NW growth observations without regard to differences in transport dynamics and ratelimiting growth assumptions has led to confusion, viz. reports of diameter-dependent[27,28,30–37] and diameter-independent[29,38,39] growth.

The most general Fickian diffusion model for precursor transport is the convection-diffusion

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equation,

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 =  ∙   −  ∙  + 


(1)

where  is the concentration of a species ,  is the mass diffusion coefficient for species  in the

fluid,  is the velocity vector of the fluid, and  constitutes species source or sink terms. For constant diffusion coefficients and incompressible flow, Eq. (1) is commonly simplified to,

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 =  ∇  −  ∙ ∇ + 


(2)

As shown in Table 1, dimensionless numbers provide a versatile metric to simplify complex

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processes and to understand the scalability of synthesis techniques. Reynold’s number, the ratio of inertial to viscous forces, determines whether flow is laminar (Re < 2100) or turbulent (Re > 4000). Pe, the ratio of advective to diffusive transport, provides a guideline for simplifying Eq. (2): when Pe

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>> 1, the diffusive term may be ignored; when Pe << 1, the convective term may be ignored. Similarly, Kn, the ratio of mean free path to chamber length, and chamber pressure are invaluable in determining whether a fluid should be described with continuum or molecular flow. When Kn << 1, continuum mechanics dominate, and Pe, Re, and Sc will guide mass transport to the growth region,  in Eqs. (1) and (2). When Kn is above 10, molecular flow models mass transport to the growth region, . DaI and DaII describe the ratio of reaction velocity to convective and diffusive mass transport velocities, respectively. For this review, it is assumed that 1) DaI and DaII are much greater than unity and mass transport is rate-limiting, 2) in the case of two materials (alloyed wire), equations are written for the rate-limiting material, 3) NWs are sufficiently far apart that wire-wire interactions are

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negligible, and 4) the combined processes of adsorption and cracking at the catalyst tip can be described with the same rate. 2. Catalytic Action at the Tip: CVD and VLS

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In VLS growth, organometallic precursors containing NW materials diffuse (Kn << 1) or randomly walk (Kn > 10) to a heated catalyst, where they either first adsorb and then dissociate or first dissociate and then adsorb onto the surface—the distinction is not well known. Catalysts are prepared on the surface by sputtering and annealing to produce islands for NW growth or spin coating from

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colloidal solutions. Precursor atoms form a low-temperature eutectic alloy with the catalyst. At steady state, adsorbing precursor vapors continuously supersaturate the liquid catalyst to drive nucleation and

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growth of a solid NW. When the catalyst remains solid, the growth is referred to as vapor-solid-solid (VSS). Wagner and Ellis first reported this now-ubiquitous process for Si NW growth with a Au catalyst and SiCl4 precursor gas[17]. Since then, NW growth, in particular Si, has experienced a rebirth of research and a range of different precursor materials, most commonly SiH4 and Si2H6, and catalysts, including Al, Ag, Zn, Cd, and Ti, to name a few. Schmidt et al. have assembled a wonderful review on Si NW growth detailing a range of catalyst materials[40]. In addition, continuous VLS growth using this process[41].

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aerosol Au particles as catalysts was recently accomplished, demonstrating the potential scalability of

The first case we will consider is for steady state NW growth under high vacuum conditions (Re << 1; Kn > 10). In this instance, we assume precursor material is incorporated by impingement at the

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surface of the catalyst without diffusion along NW or substrate and without convection of the bulk carrier gas. A schematic of this process is shown in Fig. 2 where only Pathway A is active. This basic model describes CVD growth methods like VLS and VSS when gas-catalyst incorporation is

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significantly faster than surface diffusion-catalyst incorporation, such as, when the growth velocity is significantly faster than surface diffusion or when precursor material adsorbs preferentially at the catalyst surface.

In this instance, the growth velocity becomes,  =

d = 2Ω d

(3)

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where  is the growth velocity,  the NW length, Ω the molar volume of the atomic precursor in the

droplet, and  the atomic precursor rate in mol/s[32,35]. This case exhibits no radius dependence of

growth rate[38], as frequently observed in VLS nanowire growth, Fig. 4(e). Data frequently show that the Gibbs-Thomson effects at the nanoscale can impact NW growth dynamics significantly. The high curvature of NW growth surfaces affects the chemical potential of

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incorporation to the catalyst droplet and crystallization at the NW surface via  = 2Ω, where

 is the chemical potential of the solid NW,  is the surface tension of the NW material, and  is the NW radius. The driving force of incorporation at the NW surface is  ! =  −  . Givargizov

applied this concept to crystallization-limited NW growth: as the radius of the NW and catalyst

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increase,  grows, enhancing the supersaturation of the catalyst droplet and increasing the growth velocity[27,30]. However, radius-dependent growth rates have also been observed in mass transport

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limited regimes, as discussed earlier and shown in Fig. 4. Schmidt et al. reconciled some of these observations by noting that Gibb’s Thomson effects influence the chemical potential of crystallization and of precursor adsorption. By including these effects and taking the Taylor series expansion around steady state supersaturation, they developed a radius-dependent growth velocity,

(4)

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$% &% 2Ω  = " + # ' $% − &% 

where the &% is the pressure- and chemical potential-dependent precursor incorporation velocity and $% is the chemical potential-dependent crystallization velocity. This insight importantly allows for a

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radius-dependent increase in growth velocity when &% < 0 or decrease in growth velocity when $% > 0

and &% > 0. Nanoscale size effects may also be included in growth models via Gibbs-Thomson

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boundary conditions[31,42,43]. The limit of Eq. (4) as $% and &% tend to infinity give the diffusion-

limited and crystallization-limited radius-dependent growth equations for this model, respectively. This analysis also highlights the limited ranges of the frequently-misused Givargizov[27,30] growth equation for crystallization-limited growth.

 = " +

%$2Ω 

(5)

We note that different diameter-dependences are observed contingent on the rate-limiting step. When Da << 1 (crystallization-limited), growth rate has a reaction rate power dependence on

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diameter[44]. When Da >> 1 (mass transport-limited), the diameter-dependence of growth rate changes with diffusion pathways, as discussed below. Furthermore, it is critically important to note that GibbsThomson effects can be ignored when the concentration of reactants in the vapor or liquid is significantly higher than precursor concentration in the catalyst tip[32]. Nanoscale size effects also produce a thermodynamic minimum diameter, below which VLS growth will not occur, ( =

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2Ω∆ , where ∆" is the chemical potential difference to a catalyst or nanowire surface with "

infinite radius—that is addition to a flat surface. Avoiding nanoscale size effects by controlling mass transport and precursor concentration allows growth to extend below this thermodynamic limit for VLS

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growth[28]. These observations can consolidate much of the confusion regarding nanoscale size effects in NW synthesis literature, and illustrate that an intimate knowledge of transport-dependent processes is essential to compare results from different growth techniques.

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In addition, the catalyst diameter can change during Au-catalyzed Si NW growth due to diffusion onto the sidewalls, further convoluting diameter-dependent growth[45]. Thus, some materials systems will require a time-dependent radius term. Shin and Filler[46] demonstrated that Au catalyst diffusion on NW sidewalls depends on surface passivation. Under certain growth conditions, hydrogen from Si precursors passivates <112> sidewalls, preventing Au migration as NWs grow. Controlling mass transport of hydrogen deposition on the walls provides the ability to engineer Si kinking between

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<111> and <112> growth direction[46,47]. Hydrogen adsorption and desorption can be developed using strategies to model Pathway B, as explained below. Fig. 4(c) illustrates control of Ge NW kinking by introduction of methyl Ge precursors. Lieber and coworkers[48] developed a similar pressure-dependent

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strategy to rationally induce NW kinking. Si NW growth was initiated with Au and silane precursors. Cyclically purging and reintroducing reactants to the chamber caused the catalyst to continually saturate and supersaturate, which induced kinking of the nanowires, shown in Fig. 4(d) and Fig. Separately, mass transport in the catalyst droplet has been leveraged to produce

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4(e)[48].

compositionally abrupt axial heterojunctions[49]. An alloyed Au–Al catalyst droplet limits Si and Ge solubility, allowing for monolayer control of Si/Ge heterojunctions when changing precursor material. Thus, advances in mass transport enable the design of complex nanowire superstructures[29,50].

3. Surface Diffusion in Growth: MBE and MOCVD

Models must consider surface diffusion effects (Pathways B and C) when the precursor adsorption rate on NW sidewall and substrate surface is similar to the catalyst tip adsorption rate

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(Pathway A). MBE growth is initiated by heating high vapor pressure elemental precursors in Knudsen cells. For some materials systems, this process occurs via a VSS mechanism[51]. Because Kn > 10, precursor material randomly hops to the surface where it adsorbs. These adatoms then diffuse according to Eq. (1). Each surface of the system can be described with a Fickian diffusion equation,

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connected with boundary conditions, and solved simultaneously. Boundary conditions specifying the catalyst as a “sink” provide a method to solve for NW growth rate. Similarly, MOCVD vapor phase precursor materials diffuse and adsorb to heated substrate, sidewalls, and catalyst. Adsorbed species react to form a precursor adatom, which diffuses to the growing NW, and byproducts, which desorb and are removed from the chamber. In MOCVD, a gas is bubbled through metalorganic liquids and

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acts as a carrier for the molecular precursor. The flow of low Re number carrier gas continuously supplies the surface with precursor materials. When the reactions happen along a limited length of the

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chamber, the rate of adsorption does not vary significantly, and the change in precursor concentration and the effects of convection and diffusion are combined into a single impingement rate on the substrate, sidewalls, and catalyst tip. Eq. (1) is reduced to,


! ! = ! ∇ ! − + !
 *!

(6)

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where ! is the surface adatom concentration of the rate-limiting species, ! is the surface diffusion

coefficient, *! is the effective adatom lifetime before incorporation for NW growth or at another surface for continued diffusion, and ! is the rate of adatom deposition on a surface. The characteristic

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time to adsorb a new adatom serves as an upper limit to *! =

+!  , where +! is the density of !

unoccupied surface sites. By solving for , and taking the derivative at the catalyst, it is possible to

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solve for the flux into the catalyst and to determine the growth velocity. This methodology can be extended to account for any number of additional surfaces, including diffusion through bulk fluid to the growing nanowire, specifying ! . Johansson et al. developed and expand this model for adsorption on the substrate (Pathway C) and NW sidewalls (Pathway B) and diffusion to the wire tip, where adatoms are incorporated[32]. Significantly, this analysis yields a diameter-dependent growth velocity while ignoring Gibbs-Thomson effects. This underscores important differences in growth methods. In physical and chemical vapor deposition methods that have similar sticking probabilities, surface adsorption incorporation (Pathways B and C) dominates over catalyst incorporation (Pathway A). When mass transport to the catalyst is limiting in physical and

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chemical vapor deposition, smaller wires grow faster than larger wires[33,36,37] due to higher surface area for adsorption rather than supersaturation effects. In methods where catalyst incorporation dominates, such as VLS, diameter-dependent growth is due to supersaturation effects. Because Gibbs-Thomson effects produce a lower limit to NW diameter growth, enhancing Pathways B and C incorporation

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provides a potential method to surpass the Pathway A’s inherent thermodynamic limits. Further studies on incorporation via surface diffusion and the differences between VLS and VSS growth are essential to enable the rational growth of small diameter NWs.

However, a range of boundary conditions can be included to add nanoscale size effects in a

28Ω 

(7)

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- . ln12 2,456 7 = ∆" +

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catalyst by modifying the conventional Gibbs Thomson equation for adatom diffusion,

where 2 is the area of the NW, 2,456 is the concentration of material at the catalyst interface, - is the Boltzmann constant, . is the growth temperature, and 8 is the surface tension of the catalyst droplet.

The addition of desorption, nanoscale size effects, and many other conditions are easily incorporated into Eq. (6) with lengthy but simple algebra[31,32,37,42,43,52]. For instance, at high N2 overpressure and high temperature, spontaneous, uncatalyzed growth of NWs will occur, a process that is presumed to be

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driven by selectively high sticking and low desorption probabilities at NW growth sites[53]. It is important to note that MBE and MOCVD occur in different pressure regimes: UHV and near atmospheric, respectively. As such, changes to pressure produce different and complicated effects

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on NW growth engineering for these seemingly-similar processes. In MOCVD, increases in growth pressure result in tapering of that NWs due to sidewall deposition, and additional sink terms must be incorporated for sidewall deposition[54]. Similar sidewall deposition terms can be developed for doping

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in other growth methods[55–57]. Increases in pressure can also enhance the role of bulk diffusion. This methodology can describe diffusion of gas to a surface in the absence of convection-driven mass transport—that is, when Pe is low. As the Pe number increases, convection-driven transport occurs alongside diffusion-driven transport, and advective transport effects must be included. Finally, temperature effects[58] can be included by allowing for a temperature-dependence of adsorption and diffusion coefficient. Thus, temperature can leverage the importance of Pathways A, B, and C, guide model development, and engineer NW growth.

4. Advection-dominated Nanowire Growth: Oxide-assisted and Laser Ablation Growth

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In laser ablation synthesis of NWs, a target of compressed, heated precursor material is ablated with a pulsed laser to generate a complex range of clusters that seed NW growth. Carrier gas flowing over the target transports the clusters, some of which nucleate aerosol seeds that deposit downstream in a low-temperature region of the reactor where NW growth occurs, as shown in Fig. 5. Other clusters

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react with these seeds to form NWs[23,25,59]. Thus, with Pe >> 1, advective mass transport dominates over diffusive transport to the substrate surface, and changes in carrier gas and reactor pressure have direct impacts on mass transport and NW diameter, crystal structure, and morphology[60,61]. Catalysts for NW growth can be introduced in the low temperature regime or in the target material. Further, two

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different growth processes in laser ablation can occur. For instance, the Si NW growth mechanism is dependent on temperature when two different catalysts are present. Including oxide materials in the

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target can result in a lower temperature (~900 °C) OAG; including Fe catalysts in the target can result in VLS growth at higher temperatures (~1200 °C)[23,25]. Lee et al. have investigated a range of clusters for OAG and suggest that high energy, unbonded Si atoms at the growth front act as catalysts for NW growth[62–64]. Like SFLS, the non-equilibrium cluster formation and high pressures allow for the growth of small, ~1 nm diameter NWs[65].

Laser ablation growth typically occurs in cylindrical furnaces with Ar carrier gas pressures of ;<

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200–500 torr, flow rates of 50–200 sccm, and temperatures between 800 and 1400 °C. Re for growth is ~ 10  , where D is the diameter of a cylindrical reactor. Flow is laminar, and adsorption rate is proportional to carrier gas velocity in the absence of diffusion (Pe >>1). However, Gr in the

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downstream growth regime is ~ 10= < , and the carrier gas flow is potentially turbulent due to natural convection induced by strong temperature and concentration gradients. As Gr grows, precursor cluster

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concentration and NW growth rate is a function of reactor length, decreasing along the length of the reactor according to local Gr with weak radial variation. This is likely a general feature of convectiondominated NW growth in the low Kn regime for heated substrates and will become exacerbated as reactor volume increases. Further, for laser ablation, more massive clusters that seed for NW growth will deposit on reactor walls closer to the target while less massive growth clusters will adsorb farther from the target and catalysts, and changes in flow dynamics may increase NW yield. Depending on precursor diffusion coefficients and atmosphere temperature, pressure, and fluid choice, diffusive and advective mass transport processes must both be taken into account. Pe, Kn, Re, Sh, and Gr numbers will dictate what effects need to be considered when scaling up growth processes. Solutions for these processes frequently require stagnant film, penetration, or flat-plate boundary layer

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models, streamline transformations, diffusion-convection assumptions, dimensionless number correlations, or numerical modeling[66,67].

5. Solution-phase Growth with Diffusion: Solution-liquid-solid, Supercritical Fluid-liquid-solid,

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Oriented Attachment, and Liquid-solid Growth Solution-liquid-solid and supercritical fluid-liquid-solid methods[18,20,68,69] are the solutionphase analogs to vapor-liquid-solid NW growth.

Precursor materials undergo a combination of

adsorption and desorption at a dispersed catalyst surface, where they alloy to form a eutectic, liquid

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droplet. Upon supersaturation, the colloidal eutectic catalyst nucleates a NW, which is driven by continuous precursor incorporation within the catalyst tip. In SFLS, growth occurs at supercritical

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temperatures and pressures necessary to decompose precursor materials. An identical growth in high boiling point solvents can occur via SLS[70]. Recently, SLS NWs have been grown in a continuous process, as shown in Fig. 6[71]. Similarly, the high precursor concentration in SFLS allowed for the first growth of quantized Si NWs[20]. These demonstrations illustrate the exciting potential of this method for low-cost, sustainable quantized NW production, features which have eluded many CVD methods. Mass transport for SFLS NW growth can dramatically impact growth: subtle changes in

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temperature or concentration can generate different morphologies, amorphous NWs, or uncontrolled growth[72]. Thus, scale-up of SLS or SFLS will require an enhanced understanding of mass transport. Continuous SLS growth of CdSe and ZnSe NWs was modeled by the by extending Eq. (6) with

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nanoscale size effects and surface adsorption as

(8)

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Δ" 4Ω8  2A  = ># − ' #1 + ' - . - .



Here K is the crystallization coefficient, - and the latter term represents direct incorporation on the catalyst tip (Pathway B) and sidewall diffusion to the catalyst (Pathway C)[31,37,71]. This modeling suggests that precursor decomposition occurs homogeneously in the solution prior to surface diffusion along the sidewalls or heterogeneously at all surfaces, rather than exclusively at the catalyst. Reports of SLS or SFLS growth producing wires chemically bonded to a substrate do not yet exist, despite the potential for patterning and array growth for direct, ordered implementation in devices, though Eq. (6) could easily be extended by allowing for substrate adsorption. Assuming injected precursors diffuse quickly throughout the volume and catalyst-catalyst interactions do not occur, this model will describe

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batch SFLS growth of NWs because reactants achieve thermal equilibrium before growth occurs and NWs surfaces are hydrogen passivated upon nucleation[73], allowing for similar surface diffusion. Due to the high yield of SFLS growth, the bulk precursor will be a function of time. Interestingly, the small diameters of Si NWs possible in SFLS growth imply that Gibbs-Thomson effects are not as significant

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as in CVD growth. However, a model with Gibbs-Thomson effects describes SFLS NW growth well. An enhanced understanding of supercritical diffusion coefficients, viscosity, and density and studies investigating diameter- and length-dependence are critical to develop scalable SFLS synthesis techniques.

Oriented attachment (OA) is another scalable pathway to NW growth that proceeds in a two-

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step process by first synthesizing a solution of nanocrystals and then inducing them to align anisotropically to form wires. Thus, nanocrystals define NW width, and the monodispersity of the

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nanocrystals and NWs is a strong indicator of an oriented attachment growth mechanism[26,74–77]. Like VLS growth, oriented attachment succeeds in NW growth by employing a low-energy surface for preferential addition of precursor material. Typically, these low-energy surfaces are created by control of ligand-passivated facets, which allows for the creation of wires, rings, and sheets from discrete nanocrystal precursors[74,78]. For instance, amine-based ligands bind weakly with the <111> facets of Au nanocrystals. By synthesizing a solution of Au nanocrystals and limiting ligand concentration, Au

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NWs spontaneously form along a <111> growth direction by oriented attachment of ligand-free twinned nuclei[76]. These twinned defects are observed in the produced NWs. For other materials, such as PbSe, the driving force for growth is dipole-dipole interactions between these ligand-free surfaces[26]. After alignment of nanocrystals into a pearl string morphology, NWs are formed via

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Ostwald-ripening, surface diffusion growth or via direct fusion of crystals[26,76]. Unlike VLS methods, OA growth occurs by random, Brownian collision of two spherical particles, and discrete changes in

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length are proportional to



3CD 1 <  = # '# ' - . 

(9)

where D is the viscosity of the fluid and  is the nanocrystal concentration of the solution. In the continuous analog of oriented attachment, liquid-solid (LS), solution phase synthesis of NWs uses molecular precursors in place of nanocrystals and employs sidewall-selective ligands and preferential surface reduction to promote anisotropic growth. El-Sayed and coworkers first demonstrated shape control of Pt nanoparticles by reducing metal ions generated from a salt to a zero

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valent state. Tetrahedral and cubic nanocrystals were preferentially generated by varying the amount of ligand, which exposed different nanocrystal facets promoting Kossel-Stranski face-selective growth[79]. These techniques have been extended to Au and Ag nanoparticles[80,81]. In addition, these nanoparticles can act as seeds in the two-step growth of NWs. First, nanoparticles are generated from a precursor

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salt, capping ligand to induce spherical growth, and a strong reducing agent. In a second step, these nanoparticles are mixed with more metal salt, a weak reducing agent, and a ligand that promotes NW morphologies. Because of the low reduction potential, metal ions reduction is only favorable at bare nanocrystal surfaces, and the heterogeneous reaction drives NW growth at the low-energy surface[19]. This versatile mechanism has been extended to grow high and low aspect ratio Au and Ag NWs via a

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simple bench-scale process[82–84].

There is a growing body of literature for LS and OA synthesis showing that oxidative etching of

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nanocrystals has a significant impact on the overall yield and size distribution of metallic nanowires[85– 87]

. In oxidative etching, intentional or accidental introduction of oxygen or chlorine has been shown to

selectively etch twinning defects, yielding single crystal products. Controlling the complex rate of atomic addition by reduction of metal ions in solution and oxidation of zerovalent atoms allows for the one-step synthesis of NC morphologies from a range of metals, including NWs, nanorods, cubes, cuboctahedra, plate, twinned nuclei, and hollow structures[88–90]. These same fundamental processes

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control the nucleation of nanocrystals for OA and the nucleation and subsequent growth of NWs for LS. The study of oxidative etching is critical for the development of scalable OA and LS NW synthesis. For instance, an excellent review on oxidative etching points out low concentrations of dissolved oxygen from the atmosphere and Fe ions from water sources in growth solutions are

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sufficient to affect NC morphology[91]. Because they selectively etch twinned defects necessary for NW growth, oxidative species must be finely controlled for NW growth, particularly due to the long

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growth times necessary for oriented attachment-based growth of NWs. The controlled addition of etching agents may also lead to new developments in solution-phase NW growth.

6. Template-based Growth of Nanowires

Templates are used to produce NWs by limiting 2D epitaxial growth and by defining NW diameters. Template patterning and post-processing removal provides the ability to construct complicated 3D networks that can be manipulated with bulk processing techniques and structured for specific applications, such as solar cells[92,93], batteries[9], or transistors[94]. Ordered or random arrays of features are defined in template material, which include silica[93,95], anodic alumina oxide[96,97],

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polymer[98], and colloidal systems[99], among others. Precursor materials are introduced from the bulk solution and diffuse into the pores where they are incorporated at the NW tip, as shown in Fig. 2. CVD-based growth methods include selective area MOVPE in which NW nucleation is defined by a 2D pattern or patterned defects for nucleation and growth proceeds via surface diffusion and incorporation at the high-energy growth front[100]. Similarly, Au has been deposited in templates for

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VLS growth directed by pore structure[96]. Modeling of CVD growth can be extended directly from surface diffusion Eqs. (3)–(5) with modified diffusion coefficients due to pore confinement[96]. Electrodeposition of charged, dissolved precursor materials represents the most well studied template growth method. Electric potential between the solution and precursors drives deposition and continued

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NW growth[95,99,101,102]. Heterostructures can be generated by changing out growth solutions during growth[97]. However, complex heterostructures with junctions at desired lengths require an intimate

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knowledge of growth, which is found to be mass transport limited[103–105]. For electrochemical deposition the amount of mass added to the NW tip is given by

E=

FG HI

(10)

where m, I, M, z, and F are the amount of mass added, current passed through the NW, molar

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mass of the added material, the number of electrons to reduce the precursor material, and Faraday’s constant, respectively. Deriving the steady state current from Fick’s law, Sherong et al. have developed an equation for the growth velocity,

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G  = 1.23 # '  + K

(11)

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where K the density of the NW material and  and + are the diffusion coefficient and concentration of the precursor salt, respectively[103]. We note that other transient current equations can be used to develop a growth velocity[104,106,107] and that Gibbs-Thomson effects have not yet been observed. Metal-assisted chemical etching (MACE) of silicon substrates is a recent bulk-scale method to produce arrays of aligned Si NWs. In this process, noble metal films are deposited on a conductive substrate and subsequently etched by an HF/HNO3 solution in an electroless process based on the formation of a metal-semiconductor Schottky junction[108–110]. Etching of Si happens quickly at metal interfaces and slowly on bulk Si. Thus, templated, porous metal films will define NW growth. Diameters, porosity, and tapering of NWs are a complex function of mass diffusion and substrate

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conductivity[111–113]. While atom-inefficient due to the need to first purify bulk Si, this process avoids the use of expensive vacuum systems, glove boxes, or reactors and remains one of the simplest ways to synthesize NWs on a bench top scale.

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7. Conclusions and Future Milestones

Broadly impactful applications of NWs require the ability to produce materials at large scales with earth-abundant precursors and via environmentally low-impact technologies. Bottom-up growth techniques discussed in this review possess an inherent advantage when compared to top down

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techniques, which require costly, energy intensive bulk purification prior to nanoscale patterning, wasting the majority of refined materials. Compatible synthetic methods will rely on a bridging of

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fundamental nanoscale effects with bulk processing conditions that are dependent on mass transport. For catalyzed methods, the NW synthesis and characterization community must elucidate the complex thermodynamics, mass transport, and kinetics at the catalyst.

Milestones that need to met in order to rationally implement NW nanomanufacturing are: 1) in situ studies to determine the catalyst phase and the application of the Gibbs-Thomson effects to solid and liquid catalysts at various growth conditions[29,16], 2) advanced models for close-packed catalyst-

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catalyst effects on NW synthesis[114], 3) unsteady state mass transport and kinetics within the catalyst that control morphology[48,50] and crystal growth direction[46,47,115], and 4) patterning and nanoscale manipulation observations

of

NWs

[103,120]

into

bulk

devices[116–118]. [121]

, and computational modeling

In

situ

characterization[119],

real-time

are essential techniques to achieve these

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milestones and must be rabidly pursued. These fundamental studies will enable accurate, generalizable models that can be applied to new catalysts and new materials. High purity, UHV techniques inform

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low cost solution-based methods. With an enhanced understanding of basic mass transport and thermodynamic nanoscale effects[47,122], nanomanufacturing can become a macroscale reality.

Acknowledgements

The authors thank E.J. Davis for thoughtful discussions and comments. M.J.C. would like to thank Amy Dixon for figure design and the Department of Defense (DoD) for support from a National Defense Science & Engineering Graduate Research Fellowship. P.J.P. would like to acknowledge support from the ACS Petroleum Research Fund (#52582-DNI10), UW Royalty Research Fund (RRF),

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15

and a Young Investigator Award from the Air Force Office of Scientific Research (Contract #FA95501210400).

[1]

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Figure and table captions Table 1 Dimensionless numbers, abbreviations, and equations

Fig. 1 Bulk, non-woven felt-like structure made from nanowires can exhibit quantized electronic and optical properties. Single crystal Si nanowires (d) are tangled on multiple length scales (c, b) into a

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flexible, conductive material (a)[123].

Fig. 2 Precursor materials (blue spheres) are transported to the growing nanowire by three different pathways. In Pathway A, precursor materials adsorb directly to the surface of the catalyst. In Pathway

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B, precursor materials adsorb to the nanowire sidewalls, where adatoms diffuse to the catalyst surface. In Pathway C, precursor materials adsorb to the substrate, where adatoms diffuse along the surface to

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the nanowire sidewalls and catalyst. Transport processes are driven by surface concentration gradients. The numbered mechanism shows the vapor-liquid-solid growth method. Step 1 of this process is represented by Pathway A, B, and C. After being transported to the catalyst, precursor molecules adsorb, step 2, and diffuse through the liquid, alloyed catalyst droplet, step 3. Upon reaching the surface, atomic precursors crystallize and are incorporated at the NW tip, step 4.

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Fig. 3 A template-based approach to NW growth. Initially, a porous template defines NW growth (white grid), which is driven by concentration gradients at the nanowire growth front. The template can then be used to create devices or removed to generate a solution of NWs.

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Fig. 4 Field emission-scanning electron microscopy images taken at the same magnification, showing diameter-dependence of the growth velocity induced by the Gibbs-Thomson effect[28]. Ge NWs were

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grown from Au catalysts with a range of different sizes via a VLS mechanism for 15 minutes at 276°C. (a) Comparison of Ge NWs synthesized from randomly-dispersed Au colloids. The angle-corrected scale bar on the left is 1.41 um, and red numbers at the top of each image show NW diameter. (b) Comparison of NWs grown form lithographically-defined Au catalyst. The dashed red line is a guide to illustrate change in NW length with catalyst size, and the scale bar is 3 um. (c) Demonstration of chemical control of nanowire Ge NW superstructures by adding GeH3CH3 (MG) during VLS growth with GeH3 precursor in a H2 atmosphere. The addition of MG causes NWs to kink and grow in a <110> direction[47]. (d) Illustration of pressure control of Si NW superstructures. Si NWs can be engineered to coherently kink by removing and adding precursor materials, briefly decreasing pressure. This process

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as well as the linear dependence on time is shown in (e). The yellow arrow indicates the catalyst location, and the scale bar is 1 µm[48].

Fig. 5 A schematic of a laser ablation growth process. A high energy UV laser pulse (1) is focused (2)

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into the hot zone of an insulated furnace (4) at a target composed of compressed precursor material. Absorption of this high energy radiation results in non-equilibrium ablation, generating a wide range of cluster depending on growth conditions and material. These precursors are carried (6) downstream from left to right where deposition and growth occurs at a lower-temperature region of the chamber or and growth via a conventional VLS mechanism[23].

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a cold finger (5). A substrate with immobilized catalyst can also be included downstream for deposition

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Fig. 6 A continuous process for solution nanowire synthesis. (a) Indication of the different paths for flow in the continuous solution reactor with Rhodamine 6G dye. (b) Description of the process of SLS NW growth. Briefly, electron beam deposition defines a thin Bi film, which is subsequently annealed in a static solvent to form Bi nanoparticles. Then, carrier solvent flows into the chamber with precursor solution, forming NWs through the SLS mechanism. SEM images of the products, CdSe (d) and ZnSe (e) NWs synthesized from 10 and 2 nm nanoparticles, are shown in (d) and (e). Nanoscale size effects

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are shown in contour map, (c), of the length as a function of diameter and residence time[71].

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Table list: Table 1. Dimensionless numbers, abbreviations, and equations Abbreviation

Equationa

Reynolds

Re

K 

Sherwood

Sh

Grashof

Gr

Schmidt

Sc

Peclet

Pe

Damkohler

-L



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MN < Δ. O  K  PQ

M AN U

Knudsen

RI PT

Dimensionless Number

Kn

Da

A  -R 

-L,STURV

 is the diffusion coefficient of the precursor through the bulk fluid,  is the velocity, K is the density,  is the viscosity, is the characteristic diameter of a cylindrical reactor volume, -L is the mass transfer coefficient, M is the standard acceleration due to gravity, Δ. is the change in temperature between the walls of a reactor and bulk solution temperature, O is the kinematic velocity, A is the mean free path of a precursor molecule,  is the characteristic length of the reactor volume, -R is the reaction rate constant, and -L,STURV is the overall mass transport coefficient, defined as the sum of convective and diffusive components.

AC C

EP

TE D

a

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SC

RI PT

Figure list:

Fig. 2

Fig. 3

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TE D

M AN U

Fig. 1

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Fig. 5

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TE D

Fig. 4

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Fig. 6

Graphical abstract

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