Letter pubs.acs.org/NanoLett
Catalytic Role of Gold Nanoparticle in GaAs Nanowire Growth: A Density Functional Theory Study Peter Kratzer,* Sung Sakong,* and Volker Pankoke Fakultät für Physik and Center for Nanointegration (CENIDE), Universität Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg, Germany ABSTRACT: The energetics of Ga, As, and GaAs species on the Au(111) surface (employed as a model for Au nanoparticles) is investigated by means of density functional calculations. Apart from formation of the compound Au7Ga2, Ga is found to form a surface alloy with gold with comparable ΔH ∼ −0.5 eV for both processes. Dissociative adsorption of As2 is found to be exothermic by more than 2 eV on both clean Au(111) and AuGa surface alloys. The As−Ga species formed by reaction of As with the surface alloy is sufficiently stable to cover the surface of an Au particle in vacuo in contact with a GaAs substrate. The results of the calculations are interpreted in the context of Au-catalyzed growth of GaAs nanowires. We argue that arsenic is supplied to the growth zone of the nanowire mainly by impingement of molecules on the gold particle and identify a regime of temperatures and As2 partial pressures suitable for Au-catalyzed nanowire growth in molecular beam epitaxy. KEYWORDS: Nanowire growth, gold catalyst, molecular beam epitaxy, first-principles method
E
Recent theoretical treatment of the nanowire growth has focused on the description of nucleation and material transport, its dependence on the wire radius and the degree of supersaturation reached in the Au particle7−11 at an empirical level, achieving agreement with experimental findings. However, the atomistic processes and even the thermodynamics of the particle surface and interface region are not precisely known. First, it is unclear how the Au particle promotes the supply of the material to the growth zone. This mass transport could proceed by surface diffusion or bulk diffusion. While the catalyst particle is in the liquid state under the conditions of many growth experiments, it has been shown experimentally that, at least in some cases, solid catalyst particles (realized experimentally just by lowering the growth temperature) work as well.12,13 Thus, facile material transport between the interior and the surface of the particle does not seem to be a prerequisite of its catalytic function. In addition, we argue that diffusion on the surface is usually associated with lower effective activation energy, and hence is faster, than diffusion in a dense liquid. Using the Stokes−Einstein relation with a typical viscosity of η = 5 × 102 Poise of metal alloys close to their melting point,14 we arrive at an estimate for the diffusivity in the liquid of D = 5 × 10−6 cm2/s. Because of the low diffusion barriers at surfaces, Ga and As atoms are found to have surface diffusion coefficients of the order of 10−3 cm2/s (see below). Therefore, knowledge about the surface chemistry of the gold catalyst particle is essential for understanding its catalytic function. The second major lack of understanding concerns the
arly theories of whisker growth rationalized this anisotropic growth as being driven by segregation of material at the phase boundary between the whisker and a liquid droplet consisting of a supersaturated alloy. According to this concept, termed vapor−liquid−solid (VLS) mechanism,1 the coexistence of three phases constitutes a necessary condition for the directional growth to occur. For the growth of GaAs nanowires assisted by a gold particle, early work assumed the VLS mechanism and considered the approach of the gold alloy toward its eutectic as primary source of material.2 However, for steady-state growth, continuous supply of gallium and arsenic from the vapor phase via impingement on the Au particle, on the substrate and on the wire side walls needs to be considered, too.3−5 In this extended view, the gold particle may serve one or more of the following functions: (i) It could act as a collector for Ga being deposited on both the substrate surface and the side walls, furthering growth by maintaining a constant chemical potential of Ga at the growth zone; (ii) it could act as a catalyst for the adsorption and dissociation of arsenic molecules, and for the formation of intermediates (e.g., GaAs molecules) on its surface; and (iii) the Au−GaAs interface could act as a promoter for nucleation, that is, it helps to reduce the energy barrier for nucleation.6 In this Letter, density functional theory (DFT) calculations are used to study the thermodynamic stability of possible intermediate species from an atomistic perspective, that is, we try to elucidate aspects (i) and (ii). Issue (iii), nucleation at the nanowire-particle interface, will be assumed, but its detailed atomic realization may be very complex; therefore its investigation must be postponed to a future study. To keep the theoretical analysis simple, we stick to the case of molecular beam epitaxy, using atomic Ga and As2 molecules as supply. © 2012 American Chemical Society
Received: November 14, 2011 Revised: January 17, 2012 Published: January 23, 2012 943
dx.doi.org/10.1021/nl204004p | Nano Lett. 2012, 12, 943−948
Nano Letters
Letter
embed a Ga atom into a 5 × 5 × 5 bulk Au matrix. Then, the substitution of a Ga
role of the arsenic species for the overall growth kinetics. It has been shown that the MBE growth of GaAs nanowires without gold particle is limited by the uptake of arsenic.15 This points to a possible role of the metal particle as catalyst in the adsorption and dissociation of the arsenic molecules impinging from the gas phase. While Ga readily forms alloys with Au, the solubility of As in Au is small16 with the consequence that the interior of the Au particle is unlikely to act as a collector for arsenic. Therefore we have investigated the surface chemistry of As2 molecules on pure and Ga-alloyed gold surfaces. The DFT calculations have been performed using the VASP software package,17 employing the projector-augmented-wave method.18 Both in Au and Ga, the 5d and 3d electrons, respectively, were treated as valence electrons to ensure an accurate description of the Au−Ga bonding. The wave functions are described by a plane-wave basis set up to the energy cutoff of 300 eV. Previous studies of GaAs had indicated substantial differences between the local density approximation (LDA) and the generalized gradient approximation (GGA), both in the binding energy of arsenic and gallium at surface sites with varying coordination number,19 as well as in Ga diffusion barriers at the surface.20 To be able to assess possible errors due to the choice of the density functional, we decided to perform calculations with both the LDA21 and the PerdewBurke-Ernzerhof (PBE)22 functionals. In the bulk calculations of Au (fcc), GaAs (zincblende) and Au7Ga2 (hexagonal), care has been taken to use sufficiently fine Monkhorst−Pack k-point meshes for the numerical integration over the Brillouin zone. From the calculations we obtain LDA lattice constants of aAu = 4.06 Å, aGaAs = 5.61 Å and aAu7Ga2 = 7.62 Å with cAu7Ga2/aAu7Ga2 = 1.15 and PBE lattice constants of aAu = 4.17 Å, aGaAs = 5.75 Å and aAu7Ga2 = 7.84 Å with cAu7Ga2/aAu7Ga2 = 1.15 Å. Overall the LDA lattice constants are 1% smaller than the experimental lattice constants and the PBE lattice constants are 2% larger than the experimental lattice constants, respectively. The Au nanoparticle surface is modeled by a Au(111) slab consists of 9 atom layers separated by a 15 Å vacuum layer. In the directions parallel to the surface, a 3 × 3 supercell has been chosen to simulate Ga and As adsorbates at low coverage, as well as films with the Au7Ga2 stoichiometry. For the slab calculations, we use a 5 × 5 k-points mesh for integration of the surface Brillouin zone. The five topmost layers are fully relaxed, while the atoms in the four bottom layers are fixed at their bulk positions. The phase diagram of binary Au−Ga alloys23,24 shows that small amounts of Ga in bulk Au form a solid solution whose melting temperature strongly decreases (starting from the melting temperature of bulk Au, 1337 K). At a composition of 20 atom %, an ordered intermetallic compound Au7Ga2 starts to form. It has a hexagonal crystal structure with 21 Au and 6 Ga atoms per unit cell and belongs to space group P6̅2m.25 Here, we employ the Au7Ga2 compound as a model for the Au−Ga alloy, which is in line with experimental findings.5 Since nanoparticles have a considerable number of surface sites compared to bulk sites, it is not a priori clear if the thermodynamics of bulk alloying carries over to small Au particles. Therefore, we have performed DFT calculations to study the energetics of Ga atoms in bulk gold and near the surface of thin gold slabs. For small Ga concentrations, we find that substitution of a Au atom by Ga is energetically more favorable than interstitial Ga. The latter may only be obtained from the elements by an endothermic process. To simulate a dilute Ga alloy in Au, we
Ga bulk + 124Au bulk ⇌ (Au124 Ga)bulk is found to be exothermic by 0.43 eV per Ga atom in LDA (0.45 eV in PBE) with respect to thermodynamic reservoirs of bulk Ga (orthorhombic) and bulk Au. Next, we calculate the heat of formation of the Au7Ga2 compound (β-phase of Au−Ga alloy). After optimizing both the unit cell size and all atomic positions in the unit cell, we obtain a heat of formation from the bulk elements of 0.52 eV in LDA (0.45 eV in PBE) per Ga atom. These values are at zero temperature and without external pressure, neglecting any entropic contribution to the free energy at nonzero temperatures. We find that the formation of the ordered compound is energetically only slightly more favorable than a substitutional alloy at low Ga concentration. Therefore we expect that coexistence of a Ga− Au solution and an ordered phase of Au7Ga2 (or another compound at higher Ga concentration) in the catalyst particle is likely. In the following, the behavior of single Ga atoms at or near the Au particle surface is studied, corresponding to growth conditions with low Ga concentration. Single Ga atoms are supplied from the substrate by diffusive transport along the side-walls of the GaAs nanowire. In molecular beam epitaxy, Ga atoms may adsorb on the Au(111) surface directly from the gas phase. The most favorable site for a Ga atom is the fcc hollow site of Au(111), where the binding energy, relative to the binding in bulk Ga, is 0.32 eV in LDA (0.31 eV in PBE). Relative to a free Ga atom, this corresponds to an adsorption energy of 3.80 eV in LDA (3.00 eV in PBE). The adsorption in the hcp hollow site of Au(111) is only slightly (by about 0.04 eV) weaker than at the fcc hollow site. From the binding energy of the Ga adatom at the bridge site, which is 0.09 eV higher than on the fcc site, one can obtain the energy barrier for surface diffusion. Using a pre-exponential factor of 1013 s−1, one arrives at an estimate of the diffusion coefficient of Ga adatoms of 1.8 × 10−3 cm2/s at T = 700 K. Ga readily substitutes for Au in the Au(111) surface layer, forming a surface alloy. In the following, this Ga species is denoted by Ga@Au. The energy gain of 0.56 eV in LDA (0.46 eV in PBE) is even slightly larger than the heat of formation of Au7Ga2. The tendency of forming a surface alloy can be understood from the fact that the Au surface is under considerable tensile stress26−28 and thus substituting an Au atom by a smaller Ga atom partly reliefs this stress. Substituting a Au atom in the second or third Au layer of a relaxed Au(111) slab by a Ga atom is still exothermic, but less so than substituting Au by Ga in Au bulk. Our results for Ga atoms at or near the Au(111) surface are summarized in Figure 1. With increasing the Ga concentration, the nanoparticle locally approaches the stoichiometry of the Au7Ga2 compound. Calculations for two Ga atoms in adjacent sites on the Au nanoparticle show that the interaction between these Ga atoms is slightly repulsive, by 0.05 eV in LDA and 0.08 eV in PBE. The same tendency is observed for the substitutional Ga pairs created with replacing Au atoms in adjacent sites in the Au(111) substrate. We simulate the growth of an alloy film on Au(111) by successively replacing two neighboring Au atoms by two Ga atoms in each layer of the (3 × 3) supercell to obtain the stoichiometry of Au7Ga2 in the topmost layers. Figure 2 shows the formation energy as function of the number of Au− 944
dx.doi.org/10.1021/nl204004p | Nano Lett. 2012, 12, 943−948
Nano Letters
Letter
concentrations, we expect the catalyst particle to consist of some domains of Au7Ga2 and a dilute surface alloy where Ga atoms substitute Au atoms of the topmost layer. Since Ga substitution in the subsurface layers is less favorable, transport of Ga between the surface layer and the interior of the particle is associated with some effective diffusion barrier (in addition to the energy barrier for hopping between sites). In summary, a Ga atom impinging from the gas phase interacts attractively with the surface of the gold particle, and the Ga atom has a high probability of sticking to the surface, becoming an adatom. An even more stable situation can be reached if this adatom is incorporated into the Au surface, and a surface alloy is formed. We expect this to take place preferentially at steps or kinks on the particle’s surface. In consequence, as shown in the TEM experiments using aerosol Au−Ga nanoparticles,30 material transport of Ga will mostly be carried by the abundant Ga surface alloy species. Ga atoms dissolved in the interior of the Au particle can be exploited as a further reservoir of Ga, but this reservoir will be used for GaAs growth only after the Ga surface species have been consumed, since the additional diffusion barriers in the few outermost layers amount to about 0.25 eV, as seen from Figure 1, and hence the diffusivity at 700 K is about a factor 50 reduced in these subsurface layers compared to the interior of the Au particle. In MBE of (001)-oriented GaAs films, the adsorption and incorporation of the molecular arsenic species is an important, often rate-limiting step, giving rise to reaction-limited nucleation of islands.31 Hence it is interesting to investigate if the Au particle is able to catalyze the uptake of arsenic from the gas phase. Our DFT calculations show that As2 molecules indeed bind strongly to the Au(111) surface. We consider two typical reaction geometries, one where the As2 molecule is oriented perpendicular to the surface and binds vertically on a fcc hollow site, and another geometry where the As2 molecule binds with its bond axis parallel to the surface. The two As atoms point toward adjacent hollow sites in this geometry. The adsorption energies of As2 are summarized in Table 1. We find
Figure 1. Formation energy for a substitutional Ga atom for various layers below the Au(111) surface, and for a Ga adatom in the Au(111) hollow site. Energies are calculated in LDA and PBE and given relative to the formation energy per Ga atom of the intermetallic compound Au7Ga2 from bulk gold. Relative to bulk Ga in the orthorhombic structure, this formation energy is −0.52 eV in LDA (−0.45 eV in PBE). The formation energy of an isolated substitutional Ga impurity in bulk Au is −0.43 eV in LDA (−0.45 eV in PBE).
Figure 2. Formation energy for Au−Ga alloy layer with increasing thickness at the Au(111) surface. Energies are calculated in LDA and PBE in the same way as in Figure 1.
Ga alloy layers on the surface. Again, there is an energy increase as the pair of Ga atoms is placed in deeper layers, that is, as it is buried by more Au layers. However, in the case of the Ga pair the increase is less pronounced as compared to isolated Ga atoms. As possible explanation, we argue that the gradual transformation of the fcc Au structure into the hexagonal structure of Au7Ga2 and the energy thereby released counteracts the trend observed for the single Ga atoms. Finally, we studied the possibility of Ga atoms forming a pseudomorphic (fcc) layer on Au(111) after prolonged deposition. As the surface energy of Ga is considerably lower than the surface energy of Au, bulk Ga is able to form a pseudomorphic wetting layer on Au. For a single monolayer, the energy gain is 0.31 eV per Ga atom in LDA (0.25 eV in PBE) and less for thicker layers. This energy gain is smaller than for single Ga adatoms. Thus, there is no thermodynamic driving force for Ga adatoms to form adatom islands on Au(111). Moreover, according to our calculations formation of a surface alloy of the Au7Ga2 compound is clearly more favorable than forming an ad-layer of Ga. We conclude from these calculated values that only for very large Ga concentrations, about ∼25 atom %, will the catalyst particle display a complete Ga layer at its surface. (Note that for InAs growth, values in the range of 30 to 35 atom % In have been reported, depending on growth conditions.29) For lower
Table 1. Adsorption Energy of As2 on the Pure Au(111) Surface and at Sites with One and with Two Substitutional Ga Atoms in the First Au Layer config vertical vertical parallel parallel
LDA PBE LDA PBE
Au(111)
Ga@Au(111)
2Ga@Au(111)
1.46 0.74 3.15 2.06
1.31 0.62 3.26 2.16
1.29 0.60 3.43 2.29
that As2 binds to the surface in both geometries, but binding in the parallel geometry is considerably stronger (e.g., by about 1.3 eV in PBE) than binding vertically. Quantitatively, the results of the two exchange-correlation functionals differ considerably, the LDA yielding by more than 1.1 eV stronger As2 binding than the PBE functional. This is related to the known fact that the electronic levels of small molecules are too shallow in the local and semilocal variants of DFT and in particular the LDA, and hence the LDA overestimates the binding energy of small molecules at surfaces.32 The As atoms resulting from dissociation adsorb at the hollow sites of the Au(111) surface. From the energy difference between bridge and hollow site, which is 0.17 eV, we again estimate the surface diffusivity in a similar way as for the Ga adatoms. At 700 K, a surface diffusion 945
dx.doi.org/10.1021/nl204004p | Nano Lett. 2012, 12, 943−948
Nano Letters
Letter
coefficient for As atoms of 0.5 × 10−3 cm2/s is obtained. We also investigated the effect on the As2 adsorption energy of preadsorbed Ga in its most stable form as surface alloy. It is observed that the adsorption energy is increased for both functionals and most geometries with the exception of the vertical geometry calculated in PBE, where preadsorbed Ga atoms tend to weaken the binding of As2 to the surface. Thus, As2 molecules impinging from the gas phase have an energetic preference to adsorb in parallel geometry at the Ga surface alloy sites. However, this preference is rather modest. For the most relevant parallel geometry, one additional Ga atom at the adsorption site of the As2 molecule is found to increase the adsorption energy by 0.1 eV, while two Ga atoms in the surface layer increase the adsorption energy further by 0.2 eV. The relative changes in the adsorption energy are of similar size in LDA and PBE. To see the consequences of these results for the Au-assisted growth of GaAs nanowires, it is important to realize that, both on clean Au(111) and on Ga@Au(111), the adsorption energy of As2 is higher than on clean GaAs(001) (cf. ref 33). While binding of As2 with an energy larger than 2 eV on GaAs(001) is possible only if preadsorbed Ga atoms are present, this binding energy is reached already for all sites on the (111) facets of the Au particle. For more open Au surface areas, and for the Ga− Au surface alloy, the binding energy is expected to be even larger. Thus, the Au particle is very efficient in capturing gasphase arsenic and making it accessible for GaAs growth. In this sense, the Au particle acts as a chemical catalyst. Next, we discuss the formation energy (relative to gas-phase As2) of all intermediate As-containing surface species on common grounds, assuming that the concentration of Ga atoms (if present in the structure) is in equilibrium with both reservoirs of bulk Au7Ga2 and of bulk Au. Figure 3 shows the
surface, three energy levels are indicated, corresponding to As2 molecules in vertical and parallel adsorption geometry, and to two isolated As atom infinitely separated, sitting in fcc hollow sites of Au(111). The latter corresponds to the lowest energy level. This implies that dissociation of As2 is thermodynamically possible already on the clean Au(111) surface, although there exists an energy barrier for dissociation. We note that adsorption of As atoms on the hcp sites of Au(111) (not shown in the Figure) is also possible, but with an adsorption energy that is smaller by 0.13 eV/As compared to the fcc site. For the synthesis of GaAs, it is important to know if there is a thermodynamic driving force to form mixed Ga−As species that could become incorporated at the growth zone in a later stage. From Figures 3 and 4, it can be seen that both the
Figure 4. Formation energy of various As-derived surface species on Au(111) calculated in PBE. For further details, see caption of Figure 3.
parallel As2 species and the dissociated form of arsenic are slightly more stable at sites with one or two Ga atoms substituting Au surface atoms. The dotted lines in the figures, connecting similar surface species, provide a guide to the eye. Thus, there is indeed a tendency to form intermediate GaAs species already at the surface of the Au particle. The most stable intermediate (clearly seen in the PBE calculations) is a species in which a single As atom binds to a surface Ga atom substituting for Au in the first layer of Au(111). This intermediate, termed As−Ga@, is even slightly more stable than bulk GaAs in the presence of gold. This conclusion is obtained by considering the reaction enthalpies of the two reactions
1 1 As2 + Au7Ga 2bulk 2 2 7 ⇌ GaAs bulk + Au bulk + ΔHalloy 2
Figure 3. Formation energy of various As-derived surface species on Au(111). The levels (thick lines) show the formation energy calculated coh coh coh in LDA, using −1/2(EAu − 7EAu ), and −EAu as reservoirs for 7Ga2 excess As, Ga or Au atoms. The small figures next to the levels sketch the atomic configurations (small and large grey balls are Ga and As atoms, respectively.) The dashed horizontal line indicates the chemical potential of As atoms for the case of solid GaAs in equilibrium with an As2 vapor at 700 K and 10−4 Pa.
1 As2 + Ga bulk ⇌ GaAs bulk + ΔHGa 2 In LDA, we find ΔHGa = 1.99 eV/As and ΔHalloy = 1.46 eV/As at zero temperature and pressure. For PBE, these enthalpies are 1.57 and 1.12 eV, respectively. If the chemical potential of arsenic in the gas phase, μAs, is lower than −ΔH for one of these reactions, the backward reaction will occur spontaneously, leading to decomposition of GaAs. The interval formed by the
formation energy at zero temperature and pressure, that is, neglecting any contribution to the free energy coming from configurational or vibrational entropy. For the clean Au(111) 946
dx.doi.org/10.1021/nl204004p | Nano Lett. 2012, 12, 943−948
Nano Letters
Letter
bulk material itself. Therefore, it is not fully consumed in the growth zone, even after its gas-phase supply is turned off and growth has been switched to a compound with another groupV element. Recently, a thorough analysis of the growth kinetics of InP1−xAsx nanowires36 has shown that the layer nucleation events are temporarily anticorrelated.37 As the most likely reason, the authors suggested that the time interval between subsequent nucleation events is determined by the time to restore the local concentration of group-V species that has been depleted by the previous nucleation event. They proposed that a time-averaged steady-state concentration of group-V of about 2 atom % in or at the gold particle would quantitatively fit their observation. Here we point out that, for the case of GaAs, the As−Ga@ surface species found in our calculations could act as such a consumable buffer of group-V-atoms. If it is assumed that about half of all surface sites (on a hemispherical catalyst particle) are occupied by this species prior to the nucleation event, the growth of a new monolayer will almost fully deplete the As−Ga@ buffer. Refilling of the buffer is only possible by arsenic molecules from the gas phase and is thus limited by the rate of impingement. Under the experimental conditions of ref 36 using an As4 partial pressure of 10−3 Pa and T = 700 K, this rate equals 23 nm−2 s−1 As atoms and thus corresponds to 1.7 As atoms per seconds per Au(111) surface site, which is comparable to the measured growth speed (about 1−3 nm/s or 3−9 ML/s, see Figure 4b of ref 36). Thus, we conclude that As molecules impinging directly on the Au particle account for a sizable part of the arsenic uptake at the growth zone, while for the group-III species diffusion of Ga atoms or GaAs groups along the nanowire side walls contributes appreciably to the overall supply (see Figure 5). We note that such a growth
two enthalpies is indicated as shaded region in Figures 3 and 4. For the steady-state growth of nanowires, the chemical potential ought to be chosen (by selecting gas temperature and pressure) in such a way that neither the surface alloy nor the Au7Ga2 are consumed, but the arsenic atmosphere is sufficiently reactive to produce GaAs and to prevent segregation of Ga droplets. This condition is met for values of μAs inside the shaded area. The relative stability of the As−Ga@ surface species explains the experimental observation that Au particles are able to dissociate solid GaAs if a GaAs surface with Au particles is heated in vacuo.34 In this case, first the Au surface will get covered with As−Ga@ species formed from the GaAs substrate. Second, two such As−Ga@ surface species will react to release gas-phase As2 and Ga atoms that are being dissolved in the bulk AuGa alloy, thus recreating vacant surface sites. In this way, new As−Ga@ species can be formed and the consumption of the GaAs substrate will continue due to the Au particle acting as a dissociation catalyst. Under growth conditions, however, the background pressure of As2 gives rise to a steady state in which a certain concentration of As− Ga@ species is retained. The dashed horizontal line in Figures 3 and 4 indicates the chemical potential of As atoms in an As2 vapor at T = 700 K and pAs2 = 10−4 Pa. Those surface species which have their energy levels lower than μAs will be fully populated in equilibrium. We conclude that, according to the LDA calculations, an As2 partial pressure of 10−4 Pa is sufficient to maintain a considerable concentration of intermediate species in parallel adsorption geometry, while vertically adsorbed As2 species will only exist as short-lived transient state. According to the PBE calculations, all energy levels in Figure 3 lie above μAs, and thus the surface intermediates are predicted to be populated only by a small concentration under the specified equilibrium conditions. We believe that the LDA and PBE approximations mark opposite limits of the true surface chemistry on gold. While LDA is known to overestimate adsorption energies at surfaces, PBE in this case tends to underestimate these energies. Consequently, the PBE calculations predict a higher As2 pressure (or lower temperature) required to stabilize the surface intermediates. The uncertainty of the approximate exchange-correlation functional thus limits our ability to quantitatively predict the optimal growth conditions. It should be noted, however, that the relative position of the energy levels and the overall picture of the intermediate species involved in Au-catalyzed growth is very similar in both LDA and PBE. By the involvement of As−Ga@ species it is implied that the catalyst particle is capable of buffering a small amount of groupV atoms at its surface. In experiments where the group-V species is changed during growth (e.g., alternating growth of InAs and InP segments), intermixing in group-V-sublattice between segments could indicate the ability of the system to store the group-V-species. Typically, the switching is atomically sharp; it occurs within one or two monolayers. However, it was found experimentally after growth interruption that the few topmost layers below the nanowire−particle interface contain a contamination of the group-V species used in previously grown, already completed segments.35 It is conceivable that this contamination stems from group-V surface species on the Au particle that have “survived” the switching of the group-V source. In view of our calculations, this appears plausible since the intermediate V−III-compound surface species identified by us is even more stable in the presence of gold than the III−V
Figure 5. Schematic representation of the molecular processes in Aucatalyzed growth of a GaAs nanowire. The growth zone at the triplephase boundary (GaAs−Au−vacuum) is the sink for the flows of material. Transport of impinging species takes place by surface diffusion of atomic Ga, atomic As, or molecular GaAs species on the Au particle surface.
model, where As uptake is controlled by the impingement of molecules at the catalytical particle only, is also applicable to gold-free growth: the As-limited growth speed of Au-free GaAs nanowires observed in the MBE experiment of ref 15 is reported to be 5.26 × 103 nm/s × pAs4/Pa. For the values of the As4 partial pressures used (3.5 × 10−5 to 2.3 × 10−4 Pa) and at the growth temperature of 900 K, the rate of impact of the As molecules at the surface of the Ga particle on top of the GaAs wire is sufficient to account for the observed growth speed. Note that the growth rate in this experiment is lower than in the Au-catalyzed growth of ref 36, despite the higher 947
dx.doi.org/10.1021/nl204004p | Nano Lett. 2012, 12, 943−948
Nano Letters
Letter
(10) Plante, M. C.; LaPierre, R. R. J. Appl. Phys. 2009, 105, 114304. (11) Jong, E. D.; LaPierre, R. R.; Wen, J. Z. Nanotechnology 2010, 21, 045602. (12) Persson, A. I.; Larsson, M. W.; Stenström, S.; Ohlsson, B. J.; Samuelson, L.; Wallenberg, L. R. Nat. Mater. 2004, 3, 677. (13) Dick, K. A.; Deppert, K.; Mårtensson, T.; Mandl, B.; Samuelson, L.; Seifert, W. Nano Lett. 2005, 5, 761−764. (14) Shimoji, M.; Itami, T. Atomic Transport in Liquid Metals; Trans Tech Publications Inc.: Zurich, 1986. (15) Colombo, C.; Spirkoska, D.; Frimmer, M.; Abstreiter, G.; Fontcuberta i Morral, A. Phys. Rev. B 2008, 77, 155326. (16) Schmid-Fetzer, R. In Ternary Alloys − A comprehensive compendium of evaluated constitutional data and phase diagrams; Petzow, G., Effenberg, G., Aldinger, F., Eds.; VCH: Weinheim, Germany, 1994; Vol. 9; p 162. (17) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169. (18) Blöchl, P. Phys. Rev. B 1994, 50, 17953−17979. (19) Kratzer, P.; Morgan, C. G.; Scheffler, M. Prog. Surf. Sci. 1998, 59, 135−147. (20) Rosini, M.; Kratzer, P.; Magri, R. J. Phys.: Condens. Matter 2009, 21, 355007. (21) Perdew, J. P.; Zunger, A. Phys. Rev. B 1981, 23, 5048−5079. (22) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (23) Elliott, R. P.; Shunk, F. A. J. Phase Equilib. 1981, 2, 356. (24) Okamoto, H.; Massalski, T. B. In Binary Alloy Phase Diagrams; Massalski, T. B., Ed.; American Soceity for Metals: Metals Park, OH, 1986; Vol. 1. (25) Frank, K. J. Less-Common Metals 1970, 23, 83−87. (26) Needs, R.; Godfrey, M.; Mansfield, M. Surf. Sci. 1991, 242, 215− 221. (27) Narasimhan, S.; Vanderbilt, D. Phys. Rev. Lett. 1992, 69, 1564− 1567. (28) Feibelman, P. J. Phys. Rev. B 1997, 56, 2175−2182. (29) Fröberg, L. E.; Wacaser, B. A.; Wagner, J. B.; Jeppesen, S.; Ohlsson, B. J.; Deppert, K.; Samuelson, L. Nano Lett. 2008, 8, 3815. (30) Karlsson, M. N. A.; Deppert, K.; Magnusson, M. H.; Karlsson, L. S.; Malm, J.-O. Aerosol Sci. Technol. 2004, 38, 948−954. (31) Kratzer, P.; Scheffler, M. Phys. Rev. Lett. 2002, 88, 036102. (32) Schimka, L.; Harl, J.; Stroppa, A.; Grüneis, A.; Marsman, M.; Mittendorfer, F.; Kresse, G. Nat. Mater. 2010, 9, 741. (33) Morgan, C. G.; Kratzer, P.; Scheffler, M. Phys. Rev. Lett. 1999, 82, 4886−4889. (34) Hilner, E.; Mikkelsen, A. 2009, private communication. (35) Tizei, L. H. G.; Chiaramonte, T.; Ugarte, D.; Cotta, M. A. Nanotechnology 2009, 20, 275604. (36) Harmand, J. C.; Glas, F.; Patriarche, G. Phys. Rev. B 2010, 81, 235436. (37) Glas, F.; Harmand, J.-C.; Patriarche, G. Phys. Rev. Lett. 2010, 104, 135501. (38) Ruban, A.; Hammer, B.; Stoltze, P.; Skriver, H. L.; Nørskov, J. K. J. Mol. Catal. A 1997, 115, 421−429.
temperature used. We think that this finding can be explained by the larger role of re-evaporation of atoms and molecules from the particle in case of gold-free growth. The easy materials transport on the surfaces, as indicated in Figure 5, facilitates nucleation of a new GaAs layer at the triple-phase boundary between GaAs, Au, and vacuum. To complete growth of a new GaAs layer of the nanowire, materials transport along the interface or through the bulk toward the interior parts of the interface is required in addition to surface transport. The atomistic details of these transport processes are beyond the scope of the present work. In conclusion, our calculations have revealed several aspects of Au-catalyzed growth of GaAs nanowires that had received little attention so far: The Au particle is catalytically active in dissociating As2 molecules impinging from the vapor phase. Furthermore, the ability of Au to form a stable surface alloy with Ga provides additional reactive sites at the surface, an aspect that has been intensively discussed in the general catalysis literature38 and could also play a role in CVD growth where precursor molecules need to get dissociated at the particle’s surface to release the Ga or As species. The alloy formation helps to prevent losses of Ga by evaporation, that are unavoidable if Ga droplets (e.g., in ref 15) rather than Au droplets are used for nanowire growth. Moreover, the As−Ga species formed by reaction of As with the AuGa surface alloy is a relatively stable growth intermediate. This fact allows for the build-up of a local concentration of both As and Ga near the growth zone which is required for nucleation of another GaAs layer. According to our findings, the growth temperature T and the partial pressure p of arsenic should be chosen such that −ΔHGa ≤ μAs(p,T) ≤ −ΔHalloy, that is, formation of elemental Ga droplets can be avoided.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: (P.K.)
[email protected]; (S.S.) sung.
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS Financial support by Deutsche Forschungsgemeinschaft (Grant KR2057/5-1) and the computer time through the bwGRiD project are gratefully acknowledged.
■
REFERENCES
(1) Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89−90. (2) Duan, X.; Lieber, C. M. Adv. Mater. 2000, 12, 198. (3) Jensen, L.; Bjork, M.; Jeppesen, S.; Persson, A.; Ohlsson, B.; Samuelson, L. Nano Lett. 2004, 4, 1961−1964. (4) Cirlin, G. E.; Dubrovskii, V. G.; Sibirev, N. V.; Soshnikov, I. P.; Samsonenko, Y. B.; Tonkikh, A. A.; Ustinov, V. M. Semiconductors 2005, 39, 587−594. (5) Harmand, J. C.; Patriarche, G.; Péré-Laperne, N.; Mérat-Combes, M.-N.; Travers, L.; Glas, F. Appl. Phys. Lett. 2005, 87, 203101. (6) Wacaser, B. A.; Dick, K. A.; Johansson, J.; Borgström, M. T.; Deppert, K.; Samuelson, L. Adv. Mater. 2009, 21, 153−165. (7) Dubrovskii, V. G.; Sibirev, N. V. Phys. Rev. B 2008, 77, 035414. (8) Dubrovskii, V. G.; Sibirev, N. V.; Harmand, J. C.; Glas, F. Phys. Rev. B 2008, 78, 235301. (9) Dubrovskii, V. G.; Sibirev, N. V.; Cirlin, G. E.; Soshnikov, I. P.; Chen, W. H.; Larde, R.; Cadel, E.; Pareige, P.; Xu, T.; Grandidier, B.; Nys, J.-P.; Stievenard, D.; Moewe, M.; Chuang, L. C.; Chang-Hasnain, C. Phys. Rev. B 2009, 79, 205316. 948
dx.doi.org/10.1021/nl204004p | Nano Lett. 2012, 12, 943−948
