K.w. Kolasinski/ Current Opinion in Solid State and Materials Science 10(2006)182-191 leads us to contemplate what is the nature of the on the growth parameters(pressure and temperature)but is. Originally, Wagner and Ellis figured that the also the diameter of the catalyst particle. It is often found s was of an ordinary variety. The metal particle cat- that, the growth rate should decrease with decreasing dia alyzed the decomposition of the molecule that supplied the meter [67, 76]. However, this conclusion depends on the growth material. But we see that this does not have to be growth conditions [46]since the extent of supersaturation the case for catalytic nanowire growth to proceed. The acti- within the catalyst depends on the temperature and gas- vation energy of growth can be associated with activated phase composition. A transition from smaller diameters adsorption or with surface or bulk diffusion. However, having lower growth rates to smaller diameter having the essential role of the catalyst appears to be in lowering higher growth rates can occur as temperature and gas- the activation energy of nucleation at the axial growth inter- phase composition are changed face. There is a substantial barrier associated with the for Gosele and co-workers [66, 77, "78] have examined mation of the critical nucleation cluster at a random whether there is a thermodynamically determined mini- position on the substrate or nanowire according to classical mum size and the parameters that affect not only the nano- nucleation theory. If the catalyst can lower the nucleation wire size but also the size of the catalytic particle. During barrier at the particle/nanowire interface, then growth only SiNw growth in the presence of a Au catalyst, the catalyst occurs there. Any of a number of processes may be the rate minimum size is determined by the vapor pressures of si determining step depending on the exact conditions, but and the metal. The SiNW minimum determined by the most important role of the catalyst particle is to ensure the catalyst composition and its size. They arrive at the that material is preferentially incorporated at the growth conclusion that there is no thermodynamically determined interface minimum size. rather that the minimum size is determined Virtually all of the theoretical work on catalytic growth by kinetic limitations. In the case of SiNWs, Tan et al. [77] has treated the VLS mechanism explicitly. Therefore, there predict that the catalyst should be larger than the nano- is little information on why root growth and multiprong wire, but this is clearly not universally true for all materials. growth occur under some circumstances. We do not know Chandrasekaran et al. [32] have attacked the problem why a system such as the growth of B nanowires studied by of trying to explain the nucleation of uniformly sized nano- Yun et al. [35]changes from multipronged root growth at wires in multipronged root growth. They specifically trea low temperatures to single-pronged float growth at high ted the case of GeNw growth from Ga particles and temperatures. Root growth is also observed by Chen developed an expression for the nanowire diameter et al. [36] for CsN nanotubes grown from an Fe-Co cata- lyst but in this case the growth is single-pronged. Zno do can exhibit root growth as shown by Xu et al. [53] for a Zn-B-I thin film catalyst though it is more conventionally where dc is the diameter of the resulting nanowire, Vm is the grown in a float growth mode with, for instance, a Sn cat- molar volume, o is the interfacial energy, and XGe/XG is alyst [59]. Zhang et al. [27]report that both SiOx nanowires the ratio of solute concentration at the point of instability and SnO2 nanobelts form via multiprong root growth from to the corresponding equilibrium solubility at a given tem- an Sn/Si/o alloy catalyst whereas Al, Ni, Cu, Pd, Ag and perature, T. The agreement with experiment is reasonable Au can all be used for float growth of SnO2 nanowires as and predicts that the nanowire diameter should depend shown by Nguyen, Ng and Meyyappan[52]. on the temperature and the metal used for catalysis Theoretical approaches to nanowire growth can be sep important conclusion of th arated into at least three different categories: molecular studies of Ding et al. [24, 72, 73] is that a thermal gradient dynamics, thermodynamics and kinetics. Molecular is not required for the growth of single-walled carbon dynamics has been used, for instance, by Rosen and co- nanotubes. Their study shows that a concentration gradi workers [24, 72, 73] to examine the growth of CNTs Kinet- ent is more important than a thermal gradient for the ics(mass-transport) based models have been considered by growth of Sw-CNTs on small metal particles. Further Verheijen et al. [40]. Dubrovskii et al. [15]. Tersoff and co- more, SW-CNTs growth can occur in the presence of an workers [14, 16], Persson et al. [44]and Johansson et al. opposing thermal gradient, ie, the SW-CNTs grow from [41, 46]. Thermodynamic approaches trace back to Blak- the hot region of the catalyst particle ely and Jackson [74] as well as Givargizov [67] and more Experimental studies of growth kinetics are not numer- recently have been treated by Kwon and Park [75]. Wang ous. Verheijen et al. [40] have studied the growth of GaP et al. [12]. Chandrasekaran et al. [ 32] Chen and Cao and GaAs in heterostructured GaP-GaAs nanowires [76]. Mohammad [60], and Tan, Li and Gosele [66,77, 781. GaAsNWs exhibit diffusion-limited growth wherein the The Gibbs-Thomson effect expresses how a curved rate is determined by the partial pressure of both reagents interface affects the chemical potential of a body. This (trimethyl gallium or AsH3)but has little dependence on causes the vapor pressure and solubilities to become depen- the temperature. In what might be called classical VLS dent on the size of a catalyst particle. Thermodynamic behaviour, they show that activated PH3 dissociation on treatments are then able to show how the Gibbs-Thomson the Au catalyst following Langmuir-Hinshelwood kinetics effect leads to nanowire growth rates that depend not only is the rate determining step for GaP growth. SidewallThis leads us to contemplate what is the nature of the catalysis. Originally, Wagner and Ellis figured that the catalysis was of an ordinary variety. The metal particle cat￾alyzed the decomposition of the molecule that supplied the growth material. But we see that this does not have to be the case for catalytic nanowire growth to proceed. The acti￾vation energy of growth can be associated with activated adsorption or with surface or bulk diffusion. However, the essential role of the catalyst appears to be in lowering the activation energy of nucleation at the axial growth inter￾face. There is a substantial barrier associated with the for￾mation of the critical nucleation cluster at a random position on the substrate or nanowire according to classical nucleation theory. If the catalyst can lower the nucleation barrier at the particle/nanowire interface, then growth only occurs there. Any of a number of processes may be the rate determining step depending on the exact conditions, but the most important role of the catalyst particle is to ensure that material is preferentially incorporated at the growth interface. Virtually all of the theoretical work on catalytic growth has treated the VLS mechanism explicitly. Therefore, there is little information on why root growth and multiprong growth occur under some circumstances. We do not know why a system such as the growth of B nanowires studied by Yun et al. [*35] changes from multipronged root growth at low temperatures to single-pronged float growth at high temperatures. Root growth is also observed by Chen et al. [36] for C5N nanotubes grown from an Fe–Co cata￾lyst but in this case the growth is single-pronged. ZnO can exhibit root growth as shown by Xu et al. [53] for a Zn-B-I thin film catalyst though it is more conventionally grown in a float growth mode with, for instance, a Sn cat￾alyst [59]. Zhang et al. [27] report that both SiOx nanowires and SnO2 nanobelts form via multiprong root growth from an Sn/Si/O alloy catalyst whereas Al, Ni, Cu, Pd, Ag and Au can all be used for float growth of SnO2 nanowires as shown by Nguyen, Ng and Meyyappan [*52]. Theoretical approaches to nanowire growth can be sep￾arated into at least three different categories: molecular dynamics, thermodynamics and kinetics. Molecular dynamics has been used, for instance, by Rose´n and co￾workers [24,72,73] to examine the growth of CNTs. Kinet￾ics (mass-transport) based models have been considered by Verheijen et al. [40], Dubrovskii et al. [*15], Tersoff and co￾workers [14,16], Persson et al. [44] and Johansson et al. [*41,*46]. Thermodynamic approaches trace back to Blak￾ely and Jackson [74] as well as Givargizov [67] and more recently have been treated by Kwon and Park [75], Wang et al. [12], Chandrasekaran et al. [*32], Chen and Cao [76], Mohammad [60], and Tan, Li and Go¨sele [66,77,*78]. The Gibbs–Thomson effect expresses how a curved interface affects the chemical potential of a body. This causes the vapor pressure and solubilities to become depen￾dent on the size of a catalyst particle. Thermodynamic treatments are then able to show how the Gibbs–Thomson effect leads to nanowire growth rates that depend not only on the growth parameters (pressure and temperature) but also the diameter of the catalyst particle. It is often found that, the growth rate should decrease with decreasing dia￾meter [67,76]. However, this conclusion depends on the growth conditions [*46] since the extent of supersaturation within the catalyst depends on the temperature and gas￾phase composition. A transition from smaller diameters having lower growth rates to smaller diameter having higher growth rates can occur as temperature and gas￾phase composition are changed. Go¨sele and co-workers [66,77,*78] have examined whether there is a thermodynamically determined mini￾mum size and the parameters that affect not only the nano￾wire size but also the size of the catalytic particle. During SiNW growth in the presence of a Au catalyst, the catalyst minimum size is determined by the vapor pressures of Si and the metal. The SiNW minimum size is determined by the catalyst composition and its size. They arrive at the conclusion that there is no thermodynamically determined minimum size, rather, that the minimum size is determined by kinetic limitations. In the case of SiNWs, Tan et al. [77] predict that the catalyst should be larger than the nano￾wire, but this is clearly not universally true for all materials. Chandrasekaran et al. [*32] have attacked the problem of trying to explain the nucleation of uniformly sized nano￾wires in multipronged root growth. They specifically trea￾ted the case of GeNW growth from Ga particles and developed an expression for the nanowire diameter dc ¼ 4V mr RT lnðX Ge=Xl GeÞ where dc is the diameter of the resulting nanowire, Vm is the molar volume, r is the interfacial energy, and X Ge=Xl Ge is the ratio of solute concentration at the point of instability to the corresponding equilibrium solubility at a given tem￾perature, T. The agreement with experiment is reasonable and predicts that the nanowire diameter should depend on the temperature and the metal used for catalysis. An important conclusion of the molecular dynamics studies of Ding et al. [24,72,73] is that a thermal gradient is not required for the growth of single-walled carbon nanotubes. Their study shows that a concentration gradi￾ent is more important than a thermal gradient for the growth of SW-CNTs on small metal particles. Further￾more, SW-CNTs growth can occur in the presence of an opposing thermal gradient, ie, the SW-CNTs grow from the hot region of the catalyst particle. Experimental studies of growth kinetics are not numer￾ous. Verheijen et al. [40] have studied the growth of GaP and GaAs in heterostructured GaP–GaAs nanowires. GaAsNWs exhibit diffusion-limited growth wherein the rate is determined by the partial pressure of both reagents (trimethyl gallium or AsH3) but has little dependence on the temperature. In what might be called classical VLS behaviour, they show that activated PH3 dissociation on the Au catalyst following Langmuir–Hinshelwood kinetics is the rate determining step for GaP growth. Sidewall 188 K.W. Kolasinski / Current Opinion in Solid State and Materials Science 10 (2006) 182–191